Some erection deflaters I've been thinking about:
Simple to progressively more difficult mathematics Conjugations of a foreign language Modus ponens problems Push-ups with intervals of plank positions
Can anyone think of some more besides the cold shower routine?

zz* + 2z = 12 + 6i
Find the possible values of z.

What's the complex conjugate of z = re^θi in exponential form? Can someone possibly help me tackle this?

I am a fourth-year PhD student (international student) at a well-known university in Boston. I work on mathematical optimization. I want to graduate as soon as possible (my advisor won’t let me). I am getting very frustrated with my PhD, during my PhD I have not received any single technical advice/knowledge from him. I've worked on and published several papers with him, I am the first author in our most works. He doesn’t understand or criticize these papers, because I have never seen him say anything technically useful whatsoever. Most of the time he suggests some buzzwords (most of the time these are inappropriate), he suggests some formatting/grammatical adjustments. Most of the time he doesn’t even read the whole paper. I find a paper idea, I do the theoretical analysis, I do the numerical experiments, then give him the paper. Throughout this process, I don’t receive any advice from him. However, I have to explain to him the whole paper top to bottom before submission. I have to prepare/submit my own review/rebuttal without any help from him. During my PhD/paper revision, he asked me the following questions (these are simple questions for people who study optimization and machine learning):
What is a convex function? What is gradient descent, Steepest Descent? Difference between the interior point method and the Simplex? What is Heavy ball momentum/ Nesterov momentum? Why positive definite matrix has positive eigenvalues only? What is linear convergence? What is the conjugate gradient method? etc.
I hate my advisor because he doesn’t have any ethics, he doesn’t know the basics of optimization (he is an imposter). He calls himself Large-Scale Optimization, Artificial Intelligence, Machine Learning, and Causal Inference specialist!!!! He did his post-doc from MIT (his post-doc work is still unpublished, after 6 years !!!!).
During my PhD, I wrote/submitted four research proposals for funding. I wrote two of them completely top to bottom (research idea, objective, tasks, implementation). He is the PI of these proposals, yet he doesn’t have the slightest idea of what we are proposing? When I ask him any technical questions, he suggests me to work hard (he believes I will find the solution). He is not opened to collaborate with other people who know this stuff (I managed two researchers from UCLA and Boston College to collaborate with us, he is not interested in doing this). I sometimes do reviews for him and he submits my reviews almost verbatim. He doesn’t give funding always (no funding in summer 2, and you are not allowed to do internship without his authorization). I have to buy my own laptop to do large-scale computing work (the laptop is basically for experiments; he doesn’t have money for this). He is very unprofessional, he calls 11 pm at night to do something for him at that time, during my 4 years I haven’t receive a single break (not for one week).
Now, he is asking me to do something which I have no idea, he doesn’t know the subject as well. I can’t take it anymore.
Why did I put up with him for 4 years? I already did masters from a US university (mathematics major), I want to finish my PhD and move on, I didn’t want to switch after one year. Also, as an international student, you don’t have many options either. He is from my home country/same undergraduate university, there are other students in our lab with a similar background.
FYI: During my PhD I have submitted a total of 12 papers (7 of them are related to my research work, I am the first author in 9 of them). Here is the list of journals:
Published: Measurement, Computers & Operations Research, Journal of Global Optimization.
Minor revision submitted: Mathematical Programming, INFORMS Journal on Computing
Under review: SIAM Journal on Optimization, Journal of Machine Learning Research, INFORMS Journal on Computing.
I am currently working on another 5 papers without his knowledge. I am planning to submit them by myself. Is it a good idea? Will I be in trouble? I bought my own Laptop for this work. I worked on my own personal time without any help from him. In the meantime, I wrote proposals, papers with him.
Sorry for the rant and long post. What should I do? Do I have any rights as a graduate student? What are the implications if I complain to the university? Can someone please advise me if you have any experience?

So I was reading Leonard Susskind and Art Friedman’s book, “Quantum Mechanics: The Theoretical Minimum, What You Need to Know to Start Doing Physics” and in chapter 4.5 named “The Hamiltonian” the writer of this section derived, basically, that the “Quantum Hamiltonian” is Hermitian from the principle of Unitarity.
Let me set this up in the same way they did to make this make more sense:
(Note on notation: the authors use a dagger in the superscript of a linear operator to symbolize the Hermitian Conjugate of that operator. Idk how I would do that on here so I’m just gonna write the Hermitian conjugate of some linear operator H as H*’)
Part 1: SETUP
So first they derive that the time evolution of an operator U(t) is unitary, meaning UU*’=I Where I is the identity matrix
They then go on to say that they would like to describe U in terms of some infinitesimally small time unit ε, and then they pull this out of thin air (they say that the reader should just take it for granted right now): U(ε)=I-iεH Where H is the supposed “Quantum Hamiltonian” and i=sqrt(-1) They then deduce that U’(ε)=I+iεH’ They then plug these into the definition of unitarity, so (I+iεH*’)(I-iεH)=I
Part 2: THE PROBLEM
After plugging the equations into the definition of unitarity, the authors state this:
“Expanding to first order in ε, we find H’-H=0 ... H’=H”
What in god’s name is “expanding to first order in ε” supposed to mean??? I cannot for the life of me find how they got this answer or how those words would be a good definition of any mathematical action.
If someone could please give a step by step connecting-the-dots from this point that would be very amazing.

In the back corner of the Yuusei Library, three students were continuing a tradition that had existed long before the Lawgiver united California - cramming for tomorrow’s exam.
“Why do we have to know so many Gurus?” the Calotion man bemoaned. He was wearing the dark black robes of a Seraphine monk and, well away from his brothers, looked somewhat out of place.
“Because this isn't a monastery where Guru Jesus is always the right answer, Bao. If you put the same Guru for every question they’re gonna think you don’t know anyone else” the man across from him explained. His clothing was a sharp contrast to the monk’s robes of his companion - bright embroidery decorated his collar and his wide belt was adorned with silver medallions as was the Anjalusi fashion.
“Ali is right, you know,” the young bayfolk woman across from him added. “I tried the whole ‘just know one Guru really well’ technique last time. Why do you think I’m retaking it?” Though her red robes indicated she was already a bureaucrat, the duck feather pattern on her collar explained why she would want to retake the exam.
“I know Maria, but I just need to pass. I don’t need to do well. The monastery just needs one person who is authorised to fill out the tax ledgers. I’m not gonna be a bureaucrat like you two.” The bureaucracy was a hungry beast and Nazarene monasteries were its latest prey. Now, religious institutions were required to have their ledgers written by an imperial servant. Many had chosen to get a brother to pass the exam rather than hire some outsider to keep their books. Bao had been working with his monastery’s steward for years now so he was the obvious choice, much to his chagrin.
“I think we could all use a break. I am just as tired of reviewing Valleyan conjugations as Bao is reviewing Gurus, I bet. Let's leave the books for a minute and get something to eat,” Ali offered, rising to his feet. No one else stood though.
“The exam is tomorrow morning Ali, we can’t put off studying any longer,” Maria said, pouring over her notes for something she might have missed.
“We haven’t put off studying though. We’ve been doing it non stop for the past week. Now, let's go get some food. Have you guys been to that new Calotian taqueria on Peltason? I’ve only heard good things,” Ali continued, hoping to entice them away from their books.
“I ate at the monastery before I left. And I suppose Maria is right--we are running out of time to study...Brother Adrian did mention that taqueria though. He said it was the best meal he had had in months…” Bao paused for a second before continuing. “We eat the same thing most days though, maybe not the best source of recommendations,” Bao said, his resolve wavering with the promise of food.
Maria was still firm in her convictions though. “Now is not the time to be discussing food. Unless we are discussing the mathematics of the rice dole.”
“Fine. A family of four requests a week of rations on the public dole. How much should they receive?” Ali asked in appeasement.
“Well do any of them work in labor intensive industries? Are there any infants? You did not give me near enough information to answer the question Ali,” Maria responded instantly.
“The standard is eight ounces of rice per person per day. That's two pounds for the family each day. Fourteen pounds total by the end of the week. Plus a jar of fruit preserves per person per week. So four of those.” Bao added.
“See, you guys know this stuff. Stressing out over it won’t help. So let’s get some food and a full night’s worth of sleep. What do you say?” Ali said, looking between his two companions. Bao looked to Maria, silently asking permission.
“Fine we can go get tacos,” Maria conceded and the others sighed with relief. “BUT I’m bringing my notes so we can study while we’re eating.”
“We should probably all bring our notes, I don’t know if we will be coming back here after. It is getting late and I will probably have to leave for the monastery before Compline,” Bao said, collecting the scattered pages of notes he had sprawled out across the study room table. Ali’s notes were already packed and it did not take long for Maria to collect her neat stack of papers.
“A good night's sleep is very important. Remember the words of Guru Washington ‘Early to bed, early to rise, makes a man healthy, wealthy, and wise’” Ali said with far too much confidence.
“Guru Franklin said that. Guru Washington was the Americanist general” Bao offered in correction.
“Really?” Ali glanced over to Maria who nodded in agreement. “Damn, I need to study more.”

A previous version got removed for spoilery titles, so hopefully this is a sufficiently non-spoilery title. Over the last couple of years various explanations have been advanced for the powers and motives of the Ring Builders and the Others, as I’ll call them here. I’m going to collate everything here, (mostly written by me) and unify it, and put my cards on the table in preparation for any revelations that remain in Season 5.
Tl,DR:

The Ring builders are made out of unobservable matter that exists in our universe. Brane theory and a version of quantum theory that links consciousness to quantum effects are both correct in-universe. This may or may not be the classic roger penrose objective reduction theory.
The ring builders can open wormholes through and into the bulk (higher dimensions) and construct an artificial brane-world (the ringspace). They can also influence consciousness by modifying the quantum vacuum.
The Others are beings native to the bulk (higher dimensions) and can force aside the ‘AdS (anti de sitter) layer shielding our braneworld at will to exert effects anywhere in space acausally.
They don’t understand that we are alive, let alone conscious, and attack us because ring builder technology such as the inertialess drive, USM projector, solar system destroying beam and ring gates emit their (vastly greater than observed) waste heat directly into the Others’ native dimension.
‘Fucking Duarte and his fucking tests’ did the same thing (but with a much smaller energy release), and now the Others are trying to stem the cause of the pollution.

Higher Dimensions

Original, and thanks to kabbooooom for extra info.
My guess is that the Goths are something like the 'bulk beings' that were humanity's distant descendants in Interstellar, that the gate space was another braneworld and that the ring gates are wormholes that lead into a small separate braneworld that is the ring space.
My physics degree didn't cover anything like this stuff, but there's some informed speculation about travel to other brane worlds in Kip Thorne's excellent The Science of Interstellar
The ring builders are much more like us than the Goths, but found a way to create an unusual kind of wormhole, one that leads into the bulk, rather than just connecting two parts of our spacetime.
That would make the PM builders capable of more than mere FTL travel, but I could well imagine that the Goths are the native inhabitants of the bulk and get angry at intruders. It would explain their ability to reach into our 4D space-time at any point and induce effects that look acausal - they're not actually acausal, just short-cutting the distance in our 3+1 dimensional spacetime. There is a problem - the 'bulk beings' explanation by itself doesn't make sense of the weird way the Goths affect human consciousness.
One thing that really stood out is that the light orb we see in PR that appeared on the Magnetar-class behaved like an optical illusion or hallucination - people who looked at it didn't have their vision of anything inside blocked, and saw both the orb and anything passing through it with equal clarity. That effect would make the most sense if it somehow hotwired the retinas or brains of whoever was watching it, like a Blindsight Scrambler. The effect is apparently inspired by chimerical colours. The fact that the light orb emits no radiation except visible light also implies its some kind of induced hallucination rather than a real object. It would fit with the abilities of the protomolecule to manipulate consciousness, which is vastly outclassed by the goths.
But, the really weird thing is that the light orb's effects transfer over to images of it - even though its just a photo of a blank white orb Captain Singh gets a headache when he looks at a picture of it. That suggests weird conceptual stuff going on, or else there's some kind of subtle memetic kill pattern in the apparently uniform orb, one that transfers even to photographs. Again, it reminds me of the Scramblers.
These effects all point to the Goths being relentlessly hostile and kind of evil, but that could easily just be a misinterpretation on our part. But they also point towards an ability to manipulate fundamental physics also working to manipulate consciousness, which is a very controversial idea right now.

The role of Consciousness

The missing piece that explains how the higher dimensional beings can directly affect consciousness has already been provided, and funnily enough it showed up in the show before it showed up in the books. This is an analysis I wrote of the 'technobabble' in S3E9, when proto-miller tries to explain how he works to Holden. At the time I hadn't read PR or TW, so had no idea the consciousness connection was going to be relevant:

I wanna know exactly what you know.
Oh, so you wanna talk about the non-local quantum hologram, the phase-conjugate adaptive waves resonating in micro-tubules in the brain, which of course requires some closed-timeline curves and Lorentzian manifold, and you catch up, I'll wait.
Those words aren't technobabble, they actually make sense as a vague description of how the protomolecule goop is affecting Holden's brain to produce hallucinations.
If Holden knew enough physics to understand what some of them meant it would scare the wits out of him. I can't even conceive of a technology this advanced; no human being can. Miller's off-the-cuff line was final proof that the Protomolecule builders are geological eras more advanced than humanity.
For starters, a closed timelike curve is a particle that loops backwards into its own past! If Time Travel, at least on tiny scales, is allowable (since FTL is equivalent to time travel and the ring is FTL, this shouldn't be surprising) all conservation laws are immediately broken.
A 'non-local quantum hologram' probably refers to using quantum non-locality to transmit information - faster than light, faster than anything, infinitely fast. This is theoretically impossible - despite what you might have heard, the 'nonlocal' way that some quantum systems seem to behave can't be used to transmit anything faster than light. Clearly whoever built the protomolecule doesn't care what humans think is impossible.
The remark about a Lorentzian Manifold refers to the general mathematical description of how space behaves in general relativity. 'A Lorentzian Manifold' could be any kind of space with any number of dimensions, as long as it follows the laws of general relativity. So bring it all together, a closed timeline curve is produced by some quantum gravitational process to acausally affect the microtubules in the neurons in Holden's brain.
Finally, the reference to 'adaptive waves resonating in micro-tubules' refers to an unproven hypothesis by Roger Penrose that links human consciousness to quantum effects - possibly something to do with how Miller's consciousness merged with the protomolecule goop, and with Holden? For all we know, the Protomolecule builders have advanced in this direction too.

What's the relevance of this to the Goths? Elvie's hypothesis from TW that human brains are a support mechanism for a quantum-based consciousness field is confirmed true by proto-miller (at least in the Show). I think it is very revealing that the extra 'technobabble' was included in the show (which has the authors as producers) but wasn't in the original Abbadon's gate. The protomolecule are more advanced in their ability to manipulate the quantum fields underlying consciousness, and the Goths are more advanced still than the protomolecule builders.
The Okoye-Proto-MillePenrose theory of consciousness as exotic quantum gravitational effects has another bonus point in its favour - it explains away some of the implausible aspects of the setting - the lack of general artificial intelligence built by humans.
If the Expanse is a universe where mental functionalism is false - where Roger Penrose is right and intelligent behaviour (not just consciousness, but human-level intelligence) requires more than computation, then we know why there is no AGI.
That would explain why, despite the fact that Mars' AI labs have been trying to advance the state of the art for 200 years, there has been no detectable progress since about 2050. In other settings, like the Xeeleeverse or Revelation space or even Star Trek/40k, there are similar explanations as to how binding laws prevented AGI arising.
If Penrose/Elvi/Proto-miller is right in the Expanse, it would explain a lot - the weird interface between the Goth Tech and consciousness, the fact that the protomolecule has acausal connections among itself, and the fact that the only AIs known in the setting are based on alien technology that is definitely doing more than computation and could be incorporating whatever weird physics Penrose thinks is necessary.
I've dug a little deeper into what Elvi actually said in the conference, and it does sound very similar to what the Investigator told Holden. I did a bit of Philosophy of Mind in uni as well - it's good to be able to put it to use for once.

“It’s about the nature of consciousness.” “That may be a wider context than I was looking for, Major.”
“Bear with me,” Elvi said. “Unless we’re reaching for religious explanations, which I’m not the person to comment on, consciousness is a property of matter. That’s trivial. We’re made out of matter, we’re conscious. Minds are a thing that brains do. And there’s an energetic component. We know that neurons firing is a sign that a particular kind of conscious experience is happening. So, for instance, if I’m looking at your brain while you imagine something, I can guess reliably whether you’re imagining a song or a picture by seeing if your visual or auditory cortex is lighting up.”
“All right,” Trejo said.
“There’s no reason to believe that a brain is the only structure capable of having that combination of structure and energy. And in fact, there’s a fair amount of evidence that the gate builders had a conscious structure—a brain-like thing—where the material component wasn’t at all the same kind of thing we use. Anecdotally, we’ve found at least one brain-like structure that was a diamond the size of Jupiter.”

What Elvi is getting at here is what philosophers of mind call Multiple-realizability. This is the claim (accepted by most philosophers and basically all neuroscientists) that there's nothing special about neurons per se, that experience and subjective, first-person consciousness can be supported by lots of different physical systems as long as they all are doing the same kind of thing. What that kind of thing is, we have no idea.
There is a stronger claim (popular among neuroscientists, and accepted by some philosophers like Dennett), which is mental Functionalism, that the kind of thing you need to be doing to support consciousness is just information processing of the right sort, and the particular kind of matter or energy you're doing it with doesn't matter. So an electronic computer, or a giant committee of people pushing papers around, could be conscious if it was running the right algorithms. Elvi is saying here that multiple-realizability is true but that Functionalism is false - consciousness doesn't exclusively require neurons but it isn't just computation either, it's something more. This is probably the majority view right now among philosophers, anyway. Generally neuroscientists are more willing to say the mind is pure computation.

“I don’t know what that means,” Trejo said.
“Like we don’t have a steel chamber in fusion reactors. We have magnetic bottles. Magnetic fields that perform the same basic function as matter. The older civilization appears to have developed its consciousness in a form that relied more on energetic fields and maybe structures in unobservable matter than the stuff we made a brain from. There’s also some implication that quantum effects have something to do with our being aware. If that’s true for us, it was probably true for them.

Here, Elvi is vague but apparently pointing towards Roger Penrose's idea that humanlike intelligence exploits a successor to quantum physics as we understand it today, to make decisions that are literally uncomputable by any normal information-processing system. Though she seems to be focussing more on the idea that it's having experiences that is supported by quantum processes, which isn't Penrose's idea per se.
The reference to energetic fields and unobservable structures is referring to the PM builders' own consciousness and how it is supported, again hinting that they might be constructed out of exotic forms of matter, but ones that still inhabit our home universe - perhaps there is a connection to Dark Matter or energy here?

“My thesis—the one I was working on before I came here—explored the idea that our brains are kind of a field combat version of consciousness. Not too complex. Not a lot of bells and whistles, but takes a lot of punishment and keeps functioning. Our brain may actually have a kick-starting effect, so when the quantum interactions that underlie having experiences break down, they’re easier to start up again. Does that make sense?”

It does make sense, sort of - the idea that quantum interactions underlie consciousness is a big pill to swallow, given what we know about quantum physics as it is now. The idea that these interactions could be detached from the underlying physical structure; it would need new and very strange physics, but this is science fiction, so who am I to judge?

ER=EPR and AdS Space

In proto-Miller’s speech, the “nonlocal quantum hologram” was more likely referring to the AdS/CFT correspondence, and indirectly to the ER = EPR hypothesis (which is much more interesting as far as the protomolecule is concerned.
Five second explanation: ER = EPR is the idea that the EPR paradox (which seems to show that quantum entanglement transmits information faster than light), is explained by there existing a tiny wormhole that connects entangled particles.
AdS space is ‘anti de sitter space’, a type of solution to Einstein’s equations that describes a ‘bigger on the inside’ space with constant negative curvature - as you travel along it distances seem to grow. This is contrasted with ordinary positively curved ‘de sitter space’.
That really is significant because that would imply that AdS space is a thing in the Expanse's cosmology, and as far as I understand it an AdS layer is a common explanation given for how the 3+1 dimensional space described in conventional general relativity can sit embedded in a higher dimensional space without obviously being affected by it (i.e. why force laws are still mostly inverse square). That again points towards the ringspace being a brane world and the connections being not ordinary wormholes but running through some higher dimension. AdS explains why you can’t easily notice the gravitational effects of higher dimensions.
What about ‘ER=EPR’? the Protomolecule’s “instant communication” was actually communication via microwormholes, and isn’t really instantaneous at all. This isn’t directly stated in the books but it is alluded to in The Vital Abyss when Cortazar is describing what the Protomolecule does on a nanoscale, and he deduces that on a macroscale it would create a wormhole because it would be a fractal like elaboration of what it was already doing at a smaller level. This would also explain how the protomolecule is able to use quantum entanglement for FTL communication in the first place, given that this is absolutely impossible on conventional QM.

Which theory of Consciousness?

Orch-OR (the theory directly linking consciousness to quantum gravity) is not taken seriously, it isn’t even a hypothesis, it isn’t even falsifiable, and we have far better theories of consciousness based on information theory and neurophysiology that have already produced confirmed and clinically significant results.
But, that’s the way the Expanse is heading unfortunately. It is worth noting several things here: that the AdS/CFT correspondence and ER=EPR would be directly related to consciousness if Penrose and Hammeroff were actually correct, because both are describing in a fundamental way how quantum information affects the structure of spacetime. And secondly, even if we assume that consciousness is not quantum in origin directly, both may still be somehow related because consciousness appears to truly be a phenomenon of information processing, and information (albeit quantum information) appears to underlie the structure of space time if the above models are correct.
And finally, it’s worth noting that one of the actual legitimate (but still very, very incomplete) theories of consciousness that we have - Tononi’s IIT - has an interesting informational relationship with quantum mechanics as well. For further info on that, read Tegmark’s Perceptronium paper.
My point is, even if the phenomenon of consciousness is not specifically quantum in origin, it may still be related to the universe on a fundamental level and a true “theory of everything” would likely incorporate that. Most of my colleagues do suspect that consciousness has a deep root in physics, and it is particularly telling that there seems to be a confluence starting between neuroscience, information theory, and physics. So even though I disagree with the premise of how the Expanse interprets that part of the story, I can still get behind the general idea that beings with complete power over space time would also have complete power over consciousness, because it may actually be information (it-from-bit) that defines both the structure of reality and consciousness, albeit at different spatiotemporal scales and orders of magnitudes.

As far as I know the only line in either books or show that point to the objective wave-function collapse in microtubules a la Penrose explanation is that one line from Miller. Perhaps he was oversimplifying some vastly more complex theory of everything into English. Similarly, Elvi's own explanation doesn't go much further than "there seems to be some kind of deep connection between fundamental physics and consciousness, such that you need something more than information processing, and it might be related to quantum" - she doesn't specifically mention objective wave function collapse.
More here.

The USM Projector and Ring Builder Drive

Ring Builder technology seems to defy energy and momentum conservation, but those laws are absolutely involate. We must conclude that the energy and momentum goes somewhere.
Take the USM projector - although it's quite hard to calculate the energy needed to produce a field that strong, its is absurdly greater than anything we can conceive of coming from even an antimatter power source.
We know the field strength was on the order of 10^15 gauss (strength at a real magnetar) which is 10^11 T, and that the beam was extremely narrow and stretched out for at least a million km. A magnetic field which is like that, i.e. like a one way current, must have nonzero divergence so it breaks maxwell's equations which will require magnetic monopoles. The energy needed to create this has to come from somewhere.
It's hard to work out the exact area. Let's be generous and say the USM projector generates a cylindrical region with a cross-sectional area of 1mm and a length of 1 million km containing 10^11 Tesla, the field strength at a typical magnetar. Leaving aside the astounding power output needed to create this thing instantly, how much energy in total would it require? Just use the equation for stored magnetic field energy.
Energy = volume * 1/2 * B^2 / u_0 = volume * 3.979 * 10^27 J/m^3 = 3.979 *10^30 Joules(0.5(10%5E11Tesla)%5E2+%2F+permeability+of+free+space))
A USM shot is 1.6 percent of the gravitational binding energy of the entire Earth, or about 950 TRILLION MEGATONS of TNT. Every missile every fired by every faction that ever fought in all the wars in the Expanse's history wouldn't reach a thousandth the power output of one shot from the USM projector. The waste heat alone ought to explode the Tempest to less than atoms, the waste energy from the Pallas station shot ought to have given third degree burns to people watching the lightshow from Earth.
There is some kind of special exemption involved - my guess is that the Magnetar class is not actually directly inducing the field but rather generating some kind of self-perpetuating process, maybe a very specific kind of cosmic inflation, or some exothermic-type reaction like the conversion of matter to strange matter or vacuum collapse or something in that - I don't know, I'm not (really) a physicist. Aren't there theories that say cosmic strings or monopoles can produce more of themselves under the right circumstances?
It's the same deal as whatever moved Eros. That also exerted something on the order of 10^29 Joules to move the moon up to thousands of km/s, and the waste heat released was barely on the order of 10^19 Joules - like Naomi suggested all the way back in the first book, it was merely the faintest spillover of a vastly more energetic process.
If the tiniest fraction of the true power of the USM projector was released as waste heat it would have vaporised the Tempest and blinded people watching the lightshow on Earth. Again, maybe less than a billionth of the energy is released as waste heat, either on firing or on impact with the asteroid.
Where does that waste energy go? It goes to the same place that the ring gates open to, the same place that the Others come from: the higher dimensions of the Bulk, which is the reason that they are pissed at us.

That's why the goths are pissed, the waste heat probably gets piped to their dimension with fuck knows what consequences

Last night while binge drinking and reading through chains of articles on Wikipedia I had the best idea. I realized there are sections of the site I never explored. So I immediately closed List of animals with fraudulent diplomas and the n+1 articles on Permian fauna I had open, then went to the Wikipedia reference desk. Now the reference desk is pretty cool and it's one more reason why Wikipedia is an internet gem, anyone can ask a question about any topic, and anyone can answer.
Most of the questions in the mathematics section are what one would expect; people asking about things in homework assignments they don't understand, people asking for help deciphering arcane mathematics articles on the site, and people questioning their own understanding of things. Every now and then you'd find people asking why some proof of [insert famous conjecture here] published in [insert obscure journal here] wasn't cited on Wikipedia and why it wasn't accepted as a proof by the mathematical community. But I found something a little more spicy than that, I found a user that claims to have proven the Riemann hypothesis, the Collatz conjecture, the Goldbach conjecture, and created an elementary proof of Fermat's last theorem.
Is the following proof of Riemann Hypothesis correct?

Riemann Hypothesis states that the real part of all non-trivial zeros of the Riemann zeta function, or ζ(s) = Σ(k=1 to ∞) 1/k^s = 0, equals one-half. For the non-trivial zero, s, a complex number, we have s = a + bi where Re(s)= a = 1/2.

If I had $1 for every "proof" of the Riemann hypothesis I've seen where the writer starts by trying to find s such that 1+1/2^s+1/3^s+1/4^s+⋯=0 I'd probably be lounging on a beach in the Caribbean right now. The problem here is that the Dirichlet series for ζ(s) only converges when the real part of s is greater than 1, and this series is never 0 where it converges. So analyzing only this series will not be helpful.

Fact III: The sum of the complex conjugate pairs of non-trivial zeros, s = a + bi and s' = c + di where ζ(s) = Σ(k=1 to ∞) 1/k^s = 0 and ζ(s') = Σ(k=1 to ∞) 1/k^s' = 0, of the Riemann zeta function equals one according to the Fundamental Theorem of Arithmetic and the Harmonic Series (H):(Note: Euler and others have proven that there exists an infinite set of primes in H. And that the divergence of H is a key reason for that result.)

If s' is the complex conjugate of s=a+bi then why not just write s'=a-bi instead of s'=c+di? Or why not write s=σ+it instead, as this is a fairly standard way to write a non-trivial zero in literature on the topic? Sure, this isn't bad math per say, but it's pretty bad notation. Also, s+s'=1 always only if the Riemann hypothesis is true and this would have nothing to do with the fundamental theorem of arithmetic or the harmonic series! They have already assumed the Riemann hypothesis is true before they've done anything!
The bit where they talk about primes in the harmonic series is somewhat odd. It looks like they think the divergence of the harmonic series implies the divergence of the sum of reciprocal primes (which it doesn't, the implication is the other way around) and they seem to treat the harmonic series like a set.
After this our writer slaps his four facts together in some convoluted way that I can't decipher and declares victory.

Therefore, according to Facts I, II, III, and IV, we have:
k^(1/2) ≤ k^a ≤ k, k^(1/2) ≤ k^c ≤ k, and a + c = 1.
Hence, k^a = k^c = k^(1/2) which implies a = c = 1/2. Riemann Hypothesis is true! Riemann was right!

Then they make some final notes where they try to rewrite the harmonic series using some underexplained ideas about prime gaps and says

There are infinitely many more positive integers than there are prime numbers, or prime numbers have a zero density relative to the positive integers, and prime numbers generate the positive even integers efficiently so that gaps between two consecutive prime numbers increase without bound.

which is true in the sense of natural density for sure, so why not just say that? Using the phrase "infinitely many more" makes it sound like cardinality. Saying "so that gaps between two consecutive prime numbers increase without bound" makes it look like they're saying all prime gaps become larger as we increase through the sequence of primes, this isn't necessarily true although it's statistically something we should expect. The existence of arbitrarily large prime gaps is true though and isn't hard to prove, but they did not prove it in any of what was written and it's not the same as what they said.
Is the following proof of Goldbach Conjecture correct?

Keywords: π(*):= Odd Prime Counting Function and Fundamental Theorem of Arithmetic (FTA) Goldbach conjecture states every positive even integer is the sum of two prime numbers. (We count one as prime in the sense of additive number theory outside of the FTA.)

What? The parenthetical here is so strange. Additive number theorists don’t take 1 to be prime and they have no reason to do so.
The writer then tries to make a probabilistic argument from a system of linear equations defined over a set of odd primes less than an even number e>2,

Therefore, e ≠ p + q over S, (p,q є S) , implies the following system of equations over S, 1 = e - n1 * q1, 3 = e - n2 * q2, ..., pk = e - nk * qk, according to the Fundamental Theorem of Arithmetic where 1 < qj ≤ (nj * qj)^.5 ≤ nj for 1 ≤ j ≤ k where pj, qj є S and nj is a positive integer. Note: If qj = 1, then nj є S, or nj is an odd prime less than e.

and this last sentence is what they try to base their argument on. They attempt argue that for every even number e>2, the probability that an equation of the form p=e-1q doesn't show up goes to 0. Which would mean that it's likely that e=p+q.
Even if their probabilistic manipulations made sense this obviously still wouldn't prove the Goldbach conjecture. Showing that it's "probably true" isn't a proof that it's true. As if to attest to the writer's own doubt,

In addition, empirical evidence has confirmed the validity of the conjecture for all positive even integers up to at least an order of 10^18. Therefore, we conclude the conjecture is true.

If you proved it, why do you need to test it empirically?
Is the following elementary proof of Fermat's Last Theorem correct?

x^n+y^n=z^n for n > 2. I begin the proof by assuming there exists an integral (positive integer) solution to equation one for some n > 2. Equation one becomes with some algebraic manipulation, 2. x^n=z^n-y^n = (z^(n/2)+y^(n/2))*(z^(n/2)-y^(n/2)).

Okay.

Now that I have factored the right side of equation two, Fermat, the great French mathematician and respectable jurist, made I believe the next logical and crucial step.

Any evidence that Fermat did what you're about to do?

He factored the left side as well, x^n, with the help of an extra real variable, Ɛ, such that 0 < Ɛ < n . I have the following equation, x^n = x^(n/2+Ɛ/2)* x^(n/2-Ɛ/2) = (z^(n/2)+y^(n/2))*(z^(n/2)-y^(n/2) ). This equation implies x^(n/2+Ɛ/2)= z^(n/2)+y^(n/2) and x^(n/2-Ɛ/2) = z^(n/2)-y^(n/2).

Ah yes, if ab=cd then a=c and b=d. Everyone knows that! Eventually, after a few more lines, the author concludes

However, (1/4)^(1/n) is not a rational number, a ratio of two whole numbers, for n > 2. This implies the right side of equation five is not a positive integer. This contradicts my assumption that y is a positive integer. Thus, Fermat’s Last Theorem is true, and Fermat was right!

It's so easy now, Fermat's last theorem obviously just reduces to knowing 1/4^1/n is irrational for n>2. How did nobody see this before?
Is the following proof of the Collatz Conjecture correct?

Proof of the Collatz Conjecture: Suppose there exists a sequence, S’={n0, n1, n2, …} that does not converge to one, or nk ≠ 1 or nsub(k-r) ≠ 2^µ over S’ for all kϵ ℕ where r

It's obvious that hailstone sequences don't converge, so the “does not converge to one” bit is irrelevant. Here the fundamental error is same error as in their attempted proof of the Goldbach conjecture; they think making a probabilistic argument in favor of the conjecture being true is the same thing as proving it. Lots of other basic little details are also wrong, but I'll just look at one:

From a given positive integer, n, we obtain the maximum positive odd integer, n0 > 7, by repeated division of n by 2.

What is n here, the starting number? What if n is odd? We'd have to 3n+1 it first, not divide by 2. Even if n is even the first odd number we hit once we finish dividing by 2 is not the maximum odd number in its hailstone sequence, this is easy to see starting with n=22.

If a particle is acting as a wave does that mean it can teleport from different spots if we measured it once and then again immediately after? If so does that make a wave particle faster than light?

[https://pubchem.ncbi.nlm.nih.gov/periodic-table/png/Periodic_Table_of_Elements_w_Chemical_Group_Block_PubChem.png ] or [https://ptable.com/#Properties ]
If we are going off the Lewis definition of acids as electron pair acceptors and bases as electron pair donors, the problems of ion solubility (mostly H+ and OH- ions) can be appropriately distanced from the actual behavior of hydronium (H3O+) or hydroxide (OH-) complexes in water. In other words, we first ask what species exist in what concentrations in the solution of interest, then what will happen between the different species. However, we cannot completely separate the Brønsted-Lowry and Lewis definitions due to Le Chatelier’s principle, which would state that the presence of the products of dissociation tend to prevent additional dissociation events. However, if product ions start being consumed in other reactions, the effective result is to shift the equilibrium back towards the starting materials, and additional dissociation events will then become energetically favorable. The result of this is that the behavior of chemical reactions is best contemplated holistically and with a full set of executive functionality instead of being taught as a series of disconnected fragments that imply the existence of a much higher level of precision than is actually ever possible and must be stitched together by students working without the benefit of fully developed brains. As I go through the process of writing out this series of posts, I am getting the definite impression that the progress that has been made in our understanding of atoms and orbitals has mostly obsoleted the way that general chemistry is currently taught, and that the current state of teaching is centered around exams to the detriment of the students. My general chemistry education also had far too much emphasis on the Brønsted-Lowry definition of acids and bases instead of treating these as equilibrium problems.
So and before we go any farther, let’s get pH out of the way. A lowercase “p” denotes the mathematical operation of taking the negative log of a quantity for some reason, so pH is actually the negative (base 10) log of H where H is the ionic activity of “H+” in the solution of interest. As it turns out, this is actually the activity of hydronium complexes instead of lone protons, but unless you are trying to visualize what is actually happening in the solution the two can be treated as equivalent. Of course, if you’ve gotten so obsessed with applying equations to chemical processes that you are willing to ignore the three-dimensional picture, you’re probably also not doing anything of value, but anyway. In most cases, pH can be calculated with the concentration of hydronium in moles per liter instead of a more rigorous activity measurement, so in other words pH is mostly equal to -log([H3O+]). [I should also note that the difference between the concentration of hydronium and the concentration of protons is not particularly significant in acid-base problems because the protons in water will either react with other species or form hydronium. If you are calculating the concentration of protons in water at any given time, you are also calculating the concentration of hydronium.] If you’re willing to get pedantic there is a nearly infinite amount of additional complexity that can be brought in here, but I’m not emotionally invested in this and see no reason to care. Proceeding with pH=-([H3O+]), you may notice that we are only calculating the acidity of our solution and not the basicity.
However, due to the spontaneous dissociation/autoionization of water, acidity and basicity are closely related to each other. In a volume of water, the multiplication product of the concentrations in moles per liter of hydronium/H3O+ and hydroxide/OH- is a constant. At 25 degrees Celsius, this constant (Kw) is equal to 1.0x10^-14, and Kw=[H3O+]*[OH-]. In this notation scheme, the square brackets denote concentration in moles per liter, and square brackets are usually but not always moles per liter. In any case, the reason to care is that the assumptions here mostly hold true once we start adding additional chemical species to the volume of water we started with. As the number of ions in solution increase, other issues start to arise, but mostly what you need to remember is that this is a simplified model and not an absolute definition of what is happening on the molecular level. Where this model is valuable is in relating the concentration of hydronium to the concentration of hydroxide (both in moles per liter) in a mostly reliable manner, which means that if we know a value for one at a given time we can calculate the value of the other one. So, if you have a concentration of hydroxide and you want to know the pH, you can use Kw to calculate the concentration of hydronium, then take the negative base 10 log of the result to get to pH. The addition of the logarithm allows the comparison of numbers with vastly different orders of magnitude but also brings quite a bit of confusion. In any case, using these assumptions we can define interrelated pH and pOH scales to measure acidity and basicity as the density of hydronium and hydroxide in solution. You may notice that this aligns well with the Lewis definitions, although we are not considering any other possible Lewis acids or bases.
Once you get into organic chemistry and start trying to do reactions, having a trace amount of ions in your reaction mixture doesn’t get you anywhere, and all of the assumptions as previously defined get thrown out of the window. At high concentrations of ions/high ionic activities (which are mostly equivalent concepts), we get back to the idiosyncratic and non-intuitive behavior that we expect to see in chemistry. These conditions also favor the Lewis definitions, and if it seems like I am being a bit heavy-handed in mentioning the advantages of teaching the Lewis definitions to students as early as possible you would be quite correct. Fully embracing the Lewis definitions will require the more neurotic or tradition-bound individuals among the chemical community to let go of literally centuries of work that turns out not to be valid, but as before I have no particular emotional investment in Brønsted-Lowry and would much prefer to be taught the concepts in a way that actually makes sense.
In my list of topics I am supposed to cover acid-base equilibrium, which in the context of water (aqueous solutions) is how hydronium and hydroxide move into and out of solution. First looking at “HA” or a proton donor, we can either have the acidic proton attached to the conjugate base or not. The Lewis basic strength of “A-” determines how tightly the H+ is bonded and therefore how accessible it is to the surrounding water molecules. If the H+ is bonded too tightly, there is no chance of a water molecule ever removing it, and the compound is probably not going to be participating in any aqueous acid-base reactions. At this point I am really wanting to bring in some more organic chemistry concepts and talk about an example like ethanol (CH3CH2OH) as a compound with three distinct types of protons in three different chemical environments, with the hydrogen on the oxygen end (Eth-OH) as well as the two lone pairs on the oxygen being the most interesting electron pair acceptors and donors, but the current general chemistry syllabus as defined by the American Chemical Society (ACS) prevents this. Moving on to “BOH” in water, the strength of the bond between “B+” and hydroxide is also going to be important. As an example, the hydroxl group on ethanol has essentially no chance of being removed in an aqueous solution unless something quite energetic/violent happens, but the hydroxl proton can be stripped off or another proton can bond to one of the lone pairs on oxygen depending on the reaction conditions.
In the context of this post, I am basically trying to get into a decent position to talk about buffers. These are modeled by the Henderson Hasselbalch equation and are usually a combination of a weakly proton-donating “HA” with the “A-” part of that molecule paired with a positively charged counterion (counter-cation possibly). As an example cation, let’s choose sodium (Na+), which is a terrible electron pair acceptor because it is already in a noble gas valence electron configuration and adding electrons will be destabilizing. So, we can basically ignore the sodium ions unless we are interested in the total ionic activity for some reason, and at the same time the charges all balance out. If we select the correct “A-” and adjust the relative amounts of “HA” and “NaA”, we end up with a mixture that starts out at a pH that can be predicted via calculation. This is normal when adding proton or hydroxide donors to water, but where buffers are different is the ability to absorb proton or hydroxide inputs without the pH changing much. This is because of the presence of both protonated “HA” and deprotonated “A-” and is useful in situations were the molecules under study cannot tolerate large pH swings, which usually means proteins and other biological molecules. Selecting a buffer requires the concept of the constant of acidic dissociation (Ka) and the negative log of the same (pKa), but between this and Henderson Hasselbalch equation you should have plenty of keywords to play with. I am also supposed to be covering titrations here, but since these are as obsolete as Brønsted-Lowry and really shitty to have to carry out in the lab I’m not going to bother.

To help people decide what to read. I've left out most direct plot discussion, but that's usually easy enough to find out with a quick internet search.

推理/Mystery

Top entertainment genre in Japan.
Author, 東野圭吾: very talented, many novels, one of the most popular in Japan. One listed are highly readable, but some of his novels like 白夜行 have a lot of hard dialectal speech.

夜明けの街で also is a romance novel, movie-adapted. One of my first novels and I was quite able to keep up with it.
容疑者Xの献身 few characters, easy to follow. mathematics and logical discussions.
秘密 — psychologically very interesting, heated conflict.

Author, 湊かなえ: also one of the most popular authors. These first two novels are split into about 6 short story length chapters, with different narrators providing their interpretation of events in pseudo-monologue form. it will remind you of the story several times so its easier to keep track of the basic plot.

告白 — really popular, set in a school. At first a bit difficult to realize that its a teacher giving a speech, but watching the movie would make the scenes a lot easier to picture.
贖罪 — pretty gruesome subject matter. Some characters introduce a lot of new characters in their monologue so it can get hard to keep track. The final chapter is intentionally alienating.
リバース a bit less chaotic and more straightforward read.

村上春樹

Most well known Japanese author in the West, very translatable. often will go almost word for word with the translation. Pronouns used when most authors would drop them, so its really helpful when you are just starting to read and trying to keep track of who’s doing what in each sentence.

ノルウェイの森 one of the best-selling Japanese novel globally, iconic, and extremely engaging. Strong recommendation to start with.
海辺のカフカ talking cats (they speak in a cat accent). Two alternating narrators. Magical realism themes, some very strange things happen.
色彩を持たない田崎つくると、彼の巡礼の年 simple story, characters introduced early on, very engaging. If you liked Norwegian wood, I recommend this.
1973年ピンボール — one of his earlier novels. 2 concurrent stories. Not my favorite but also not bad.

Regarding Light Novels

Iseikai LNs will usually have a lot of vocab and (made-up) terms you will have to keep track off so keep that in mind. 読書好きの下剋上 is one I find to be quite readable.

君の膵臓を食べたい go to for your first LN: really engaging, emotional, few characters, simply written. No explicit place references (and few names) so you aren’t alienated due to lacking cultural knowledge. Lots of simple explicit sentences.

Older Literature

Author, 夏目漱石: Public Domain (can all be found free on Aozora Bunko). Meiji/Taisho era author, probably the most renowned national literary figure. Good if you want to engage in genuine literature. Maybe you’re intimidated, but he's not as hard as you think to read (mostly). Lots of furigana, so even though obsolete kanjis are used, you’ll quickly be able to keep track of what means what. Also lets you associate 漢語 (chinese-origin kanji words) with Japanese equivalents.

こゝろ — famous. simple language, few characters (all unnamed), most famous classic novel. Split into many very short chapters, so you don’t have to feel intimidated.
坊っちゃん — medium length, not too hard but there are more characters who have some quirks to keep track of, and short episodes or conversations that will take some concentration to fully grasp, but the basic establishment is easy so even if you miss out on some zones you can handle.
吾輩は猫である — very hard and long (~3x normal novel length). Narrator is a cat, lots of obscure grammars such as ざる and all the conjugations of べし and まい. Features traditional letters (✉️) (which use very obscure vocabulary, grammar, suffixes, kanji-use, sentence endings, particle dropping). The beginning isn’t too hard but the majority is conversations with a fairly large character pool. a lot of incomprehensible Buddhist references. Some poetry (also hard to get). The translation barely helps with the hard parts because its targeted towards western people so most specific japanesey references vanish. Its probably not worth the struggle, the chapters are about the length of a short-medium novel each. However, highly humorous and satirical at times (sometimes easier and harder to pick up).

破戒 older meiji novel, public domain, I could only find it in the old kana usage but you get used to it because its relatively intuitive. Cultural knowledge of social “castes” would help. Not the easiest read to get 100% but known as representative meiji novel.
死者の奢り・飼育 — Two (plus) short(ish) stories by author Kenzaburo Oe (Nobel Prize author). He has a very specific sentence style, and uses a wider range of descriptive vocabulary so he’s really good to sentence mine for higher-end vocabulary.
黒い雨: historical novel that follows events of Hiroshima, including real people. Uses diaries and letters to tell story. Not overly emotional. Gives good cultural insight (though also some difficulty if you want to know what the traditional plants, animals, tools, house parts, social organisations refer to). Very realistic. On the harder end, but well known literature.

Author, 三島由紀夫: well known post ww2 author. Pure literature. Lots of 漢語 and sentences with theoretical-reasoning.

潮騒 romance story, his easiest read, popular. Beautiful descriptions. Cultural knowledge of island life might help but its easy enough to pick up. Some obscure dialect but it doesn’t really hinder you. Seriously has like five movie adaptions so that could help you read along.
仮面の告白 good to compare with 人間失格 because they were written about the same time and the author’s had correspondence, and some similarities.
金閣寺：somewhat long. lots of buddhist terms and phrases, and you’ll lose sense of setting if you filter them out too much. Descriptions can at times be hard to follow. This difficulty made me underwhelmed at the end. Maybe read it twice and take notes if you want to get if fully (I haven’t been able to), because it’s supposedly up there with all time pure Japanese literature.

Contemporary Literature

Author 森見登美彦: popular Kansai author. Comedic.

夜は短し歩けよ乙女 and 四畳半神話大系 Campus life comedic stories. extremely entertaining, both split into about four sections of short-medium novel length. The word use is varied, using many adjectives, 四字熟語, and proverbs comedically which is really good to farm vocabulary for more advanced learners.
ペンギン・ハイウェイ easier (child narrated), light, magic realism elements.

コンビニ人間 high quality literature, not too long, simple plot. Go-to read if you want actual contemporary literature. Words aren’t too hard and the essential parts even easier.
限りなく透明に近いブルー not long, very popular novel, adult themes, a decent amount of characters. Sentences flow into each other, the meaning is not always explicit, dialogue is unmarked/unpunctuated a lot. Still enjoyable.
窓際のトットちゃん — Simple read. children-narrated text but highly well known, episodic.
何者 —Ave. difficulty. somewhat psychological, decent movie. About 就活 (job hunting). Uses a lot of tweets.
マチネの終わりに Mature Adults romance story, somewhat long but very captivating read. Follows recent (about 2000~2015) international events and settings across the world.
砂漠 Ave. difficulty. campus/youth novel following a friend group in college. Structured into 4 and a bit parts. The author is quite well known.
永遠の０: one of the highest selling novels, has a movie. About ww2, heroic themes. Its for general people so the war-terminology is well explained within it. Just a bit nationalistic so it would do with some caution that it might be a bit glorified
博士の愛した数式 and ことり both by 小川洋子. few characters, not really named, each follows the life of a quirky/bizarre person. Both have characteristic subject matter: math and birds respectively. Ave. difficulty.
サラバ！three part book of a person’s life story across several locations. References to notable events in recent decades such as earthquakes. Really engaging. Easy to follow, with a tiny bit of dialect.
あこがれ two medium length short stories using child narrators. The words are mostly basic, little kanji, and a lot of simple children's dialogue. Recommended for those who don't want to deal with a lot of kanji, and want more colloquial language. I think 川上未映子 (the author) generally does dialogue quite well, and her books seem to have a lot of it.

[https://pubchem.ncbi.nlm.nih.gov/periodic-table/png/Periodic_Table_of_Elements_w_Chemical_Group_Block_PubChem.png ] or [https://ptable.com/#Properties ]
In the last 14 posts, I have attempted to present the main points/useful information from a whole academic year of general chemistry. A significant fraction of the material taught in general chemistry is obsolete, but I am also skipping over any of the information that is actually beneficial to have somewhat memorized, all of the math, etc. Generally speaking, people don’t seem to have much trouble retaining information that is useful to them, so unless you’re having to pass a series of exams I would not worry about any of the details if you don’t want to. Maintaining a degree of rigor and intellectual honesty is important, but at the same time knowing a theory should enhance your understanding of the real world instead of detracting from it.
In any case, we have atomic nuclei with positively charged protons and non-charged neutrons surrounded by somewhat amorphous clouds of negatively charged electron density generated by a discrete number of negatively charged electrons moving around at high speed. How nuclei, orbitals, and electrons interact is chemistry, and given the complexity in chemical reactions that is evident (particularly in biology) it should come as no surprise that the behavior of electrons, elements, and molecules is also extremely complex. We as a species have spent many centuries of unified time and uncountable person-millennia of effort grappling with aspects of the complexity of chemical behavior, before discovering relatively recently that everything is derived from quantum mechanics and none of the simple mathematical models are particularly valid. The discovery of quantum mechanics started in the early 1900s to the 1920s or so in the physics community and has led to a progressive series of major improvements in the way we think about the world that is still underway. The information gained has led to our disastrous exploration of nuclear fission in heavy elements but also to the development of much more potent instrumentation, semiconductors, computers, and a better, if not necessarily more comforting, understanding of the universe that we live in.
Looking at chemistry specifically, our goal as a species needs to be to do as little chemistry as possible while still ensuring our survival. Where chemical reactions are unavoidable, we need to take care to ensure that the resulting waste is as non-toxic, biodegradable, and/or easily denaturable as possible. Simple molecules such as carbon dioxide can cause problems when emitted in bulk, and more complex molecules tend to be nastier in much lower quantities and concentrations (eg polychlorinated biphenyls/PCBs). As creatures with cellular machinery that is mostly made of organic molecules, we are going to be most interested in organic reactions despite our historical inability to make much sense of the complicated electronics and molecular orbitals of organic reactions. Unfortunately, this means that we will not be able to skip as many of the details, and if I want to try for complete coverage I would expect to see a few tens of posts. The main difference between general and organic chemistry is that a significant fraction (possibly even most) of the general chemistry material is obsolete and/or irrelevant, while the majority of organic chemistry material is both important and relevant. So this may take a while, and I’m going to wish that I still had access to the ChemDoodle software that is set up for organic structures. On ubuntu linux, the GChemPaint program seems similar and is free, and I guess that I’m about to find out how well that it works.
I will do my best to relate concepts back to the mental picture of how chemical compounds interact that you are hopefully building up as I introduce them, but as always things are usually going to be messy. The list of high level topics in organic chemistry as defined by my undergraduate study guide is as follows: structure, bonding, intermolecular forces of organic molecules, acids and bases in organic reactions, nomenclature, isomers, principles of kinetics and energy in organic reactions, preparation and reactions of (alkenes, alkynes, aldehydes, ketones, alcohols, sulfides, carboxylic acids, amines, aromatic compounds), organic reaction mechanisms, principles of conjugation and aromaticity, and spectroscopy. I have not yet decided if this is the order in which I would like to present these concepts, but hopefully you can see that this is a large amount of material. As a final note, organic chemistry is mostly the chemistry of hydrogen, carbon, nitrogen, and oxygen with trace quantities of several other elements participating at times. Organic molecules are interesting both because of the wide range of properties and behaviors that they exhibit and also because of our desire to understand our biology, and we are studying mainly the chemistry of the 1s, 2s, and 2p valence orbitals in small atoms.

CC according to Miriam Webster could be any of the following:
CC Country Club CC Carbon Copy (secondary email addressee) CC Cubic Centimeter CC Closed Captioning CC Courtesy Copy (email; for those who never used carbon paper) CC Community College CC Clone Commander (Star Wars) CC Cheat Codes CC Car Club CC Colorado College (Colorado Springs, CO) CC Cross Country CC Columbia College (part of Columbia University, New York) CC Character Code (ITU-T) CC Common Criteria CC Christian Church CC Clinical Center (NIH) CC Community Center CC Cruise Control CC City Council CC College Center CC Competition Commission CC Customer Care CC Clear Channel CC Commercial (Top-Level Domain introduced in 2000) CC Coupe Cabriolet (Peugeot 206 CC model) CC Computer Center CC Columbia County (various locations) CC Cable Connection CC Common Cause CC College Council CC Call Center CC Critical Care CC Common Carrier CC Case Closed CC Country Code CC Community Club CC Central Committee CC Comedy Central (cable channel) CC Clark College (Vancouver, WA) CC Centro Cultural (Spanish: Cultural Center) CC Commander CC Cotton Candy CC Center Console CC Committee Chair CC Circuit Current CC Common Control CC C Compiler CC Cruiser CC Computing Center CC Command Center CC Chief Counsel CC Cape Cod CC Chamber of Commerce CC Common Code CC Church of Christ CC Combined Cycle CC Copy Cat CC Color Code (Sprint) CC Code of Conduct CC Crowd Control (gaming) CC Clark County (various locations) CC Carroll College (Waukesha, Wisconsin) CC Command Code CC Change Control CC Cyber Cafe CC Creative Commons CC Communications Center CC Christian Coalition CC Closed Circuit CC Certificate of Completion CC Coca Cola CC County Council CC Cloud Cover CC Colon Cancer CC Catholic Charities CC Control Center CC Cyber Crime CC Carpet Cleaning CC Calling Card CC Cocos (Keeling) Islands (country code & Top Level Domain) CC Chevy Chase (Maryland) CC Constant Current CC Cancer Care CC Close Combat CC Chicago Cubs CC Conto Corrente (Italian: bank deposit) CC Contra Costa (California) CC Cross Cutting CC Call Control CC Contact Center CC Concealed Carry (weapons) CC Cable Channel CC Conference Call CC Cash Card CC Cash Credit CC Carbon-Carbon CC Contrast Color CC Common Cold CC Computer Crime (insurance) CC City Clerk CC Cubic Capacity CC Closed-Captioned CC Current Condition CC Cylinder Capacity CC Central Control CC Centro Comercial (Spanish) CC Commissioned Corps CC Cloud City (Star Wars) CC Come Closer CC Cash or Check CC Corpus Callosum (neurology) CC Canadian Club (whiskey) CC Coupled Cluster CC Crypto Currency CC Constructive Criticism CC Constitutional Court CC Common Client CC Clinical Chemistry CC Coco Chanel CC Course Change CC Chocolate Chips CC County Commissioner CC Cost Cutting CC Connecticut College (New London, CT) CC Cost Control CC Calvin College CC Counting Crows (band) CC Carabinieri (Italian Military Police) CC Code Control CC Cultural Competence CC Competence Center CC Consumer Confidence CC Central Computer CC Catalytic Converter CC Catholic Central High School (Redford, MI) CC Control Computer CC Custom Controls CC Charge Control CC Chrono Cross (video game) CC Chaco (Argentina Province, airline code) CC Complex Conjugate (mathematics) CC Carson City, Nevada (mint mark on some old silver dollars) CC Core Component CC Customs Clearance CC Cross-Connect CC Competent Communicator (Toastmasters) CC Caso Cerrado (Spanish TV show) CC Cashier's Check CC Corporate Center (Sprint) CC Control Channel CC Columbus Crew (Columbus, Ohio major league soccer team) CC Crew Chief CC Cesar Chavez (union activist) CC Community Chest CC Change Channel (Maple Story) CC Combination Chemotherapy (oncology) CC Cut Corner CC Charged Current CC Chief Complaint CC Cost Center CC Commerce Commission CC Cannibal Corpse (band) CC Control Console CC Command & Conquer (video game) CC Corporate Citizenship (various companies) CC Crack Cocaine CC Cult Classic (movie slang) CC Cris Carter (NFL player) CC Consultative Committee (various organizations) CC C.C. Sabathia (baseball player) CC Coordination Center CC Curriculum Commitee (various schools) CC COMSEC Custodian CC Cooling Coil (heating, ventilation, and air conditioning systems) CC Coco Crisp (baseball player) CC Core Competency CC Confined to Camp CC Career Counselor CC Conclave (online gaming community) CC Cheddar Cheese CC Cheshire Cat (Blink 182 album) CC Clearcase (software; IBM) CC Continuous Casting CC Calçada (Portuguese: sidewalk; postal use) CC Configuration Control CC Casual Collective (gaming) CC Código Civil (Civil Code) CC Copie Conforme CC Central Component CC Civic Centre (Singapore) CC Cycle Count CC Cybercity (Danish ISP) CC Combat Operations CC Control Language CC Condition Code CC Chief Clerk CC Clomiphene Citrate CC CardCaptors CC Climatic Change CC Cardiac Catheterization CC Climbers' Club (UK) CC CableCard CC Cavalera Conspiracy (band) CC Communications Coordinator CC Codice Civile (Italian: civil code) CC Coiled-Coil CC Compiler Construction CC Conseil Constitutionnel (French: Constitutional Council) CC Cornwall College (UK) CC Cheech and Chong (comedy duo) CC Chemical Control CC Carlton Cole (soccer player) CC Cluster Controller CC Consumer Cellular CC Coalicion Canaria CC Cranio-Caudal (view; mammography) CC Crystal Controlled CC Cybercom (computer company) CC Cour des Comptes (French: Court of Auditors) CC Camp Coordinator CC Comment Code CC Closing Capacity CC Columbus Circle (New York City) CC Courtesy Copy CC Close-Coupled CC Cold Cathode (UV emitting tubes) CC Code Civil (French: civil code) CC Chronic Cough CC Clearcut CC Capital Contribution CC Crown Colony CC Cuerpo Consular (Spanish: Consular Corps; various locations) CC Common Criteria for Information Technology Security Evaluation (international standard) CC Convolutional Code CC Consonant Cluster (speech) CC Corn Chip (food) CC Cholangiocarcinoma CC Corner Card (philately) CC Combat Command CC Cirrocumulus (cloud formation) CC Change of Course CC Class Clown (band) CC Component Command (NATO; US DoD) CC Component Carrier CC Clock Crew (Flash artists group) CC Collect Call CC Corrente Continua (Spanish: Direct Current) CC Continuous Commissioning (Texas Engineering Experiment Station) CC Core Client (computing) CC County Coordinator CC Casual Credit (gaming) CC Country Coordinator CC Chamilon Circuit (band) CC Crystal Cathedral (Robert Schuller Center) CC Cyanogen Chloride (inorganic compound) CC Command Ship CC Collagenous Colitis (inflammatory bowel disease) CC Cash Control CC Construction Component CC Cursor Control CC Company Commander CC Center Conductor CC Copy, Clear CC Cyber Chat (RPG chat server) CC Citizen Cope (band) CC Covenant Christian (High School) CC Correspondence Chess (long-distance chess) CC Clan Chat (Runescape gaming) CC Corte de Constitucionalidad (Spanish: Constitutional Court; Guatemala) CC Call Collect CC Cache Coherency CC Computacenter (European IT services company) CC Customer Contacts CC Channel Command CC Combatant Commander CC Connection Confirm CC Complications and Comorbid Conditions (medical coding) CC Channel Controller CC Communications Control CC Composite Component CC Constant Curve (bending of Windsurfing Masts) CC Corrosion Coupon CC Controlled Circulation CC Convoy Commander CC Component Check CC Crazy Cool CC Computing Curricula (education) CC Comfort Care (often seen with DNR order) CC Card Cage CC Coal Chamber (rock band) CC Coal Chamber (band) CC Continuity-Check (ITU-T) CC Correctional Custody CC Closed Corporation (South Africa) CC Central Controller (Cisco Wireless) CC Concrete Curb (public works) CC Carriage Control CC Carbon Composites CC Compassionate Conservatism (George W. Bush campaign) CC Concurrent Copy (disk storage management) CC Cross-Class (Dungeons & Dragons gaming) CC Companion of the Order of Canada CC Coast Is Clear CC Command Chief CC Computer Controller CC Cow and Calf (animal husbandry) CC Copper Citrate CC Complementary Color (fashion and design) CC Call Connected (ITU-T Rec I 451) CC Cheat City (gaming website) CC Carrier Current CC Computers and Composition (an International Journal) CC Chrono Crusade (anime) CC Close Captioned CC Congestion Controlled (IPV6) CC Closing Code CC Color Compensating CC Crazy Chicken CC Computer Community CC Crew Compartment (NASA) CC Centimetro Cubico (Spanish: Cubic Centimeter) CC Cédula de Ciudadanía (Colombia social securty equivalent) CC Constituent Code CC Canterbury College (Gold Coast, Australia) CC Carnivorous Carnival (Lemony Snicket) CC Cedarville College CC Canarian Coalition (Spain) CC Common Collector (transistors) CC Calculated Cost (pension benefit calculations) CC Coordinator Council (Maquis Forces International) CC Combat Control CC Chemical Corps CC Call Content CC Crimson Chin (Fairly Odd Parents TV show) CC Communications Central CC Carrier Control (modem information) CC Crew Commander CC City Confidential (TV show) CC Carl Czerny (classical composer) CC Cadet Commander CC Complaints Committee CC Celanese Corporation CC Card Column CC Command Caller (phone notification system) CC Combat Center CC Clow Card (Japanese Animé) CC Convoy Commodore CC Coin Collect CC Component Cooling CC Caring Connection CC Critical Characteristic (automotive) CC Common Controller CC Common Controller(s) CC Commander's Call (PHS-1 DMAT monthly meeting) CC Civil Commotions CC Clifford Chance LLP (UK law firm) CC Concord Coalition CC Chaos Castle (gaming) CC Construction Confederation (London, UK) CC Complications or Comorbidities (diagnosis related group descriptions) CC Captive Carry CC Compression Chamber CC Contracted Care CC Combat Challenge CC Conventional Campaign CC Criteria Check CC Coupled Cavity CC Combat Clothing CC Colon Classification CC Chaitanya Charitamrita (Gaudiya Vaishnava scripture) CC Competitive Category CC Command Controller CC Chefs Collaborative CC Carbonaceous Chondrite (meteorites).......

Here is the implementation in python of the algorithm in this article:

#! /usbin/python #---------- # This unusual and intriguing algorithm was originally invented # by Michael V. Klibanov, Professor, Department of Mathematics and Statistics, # University of North Carolina at Charlotte. It is published in the following # paper: # M.V. Klibanov, A.V. Kuzhuget and K.V. Golubnichiy, # "An ill-posed problem for the Black-Scholes equation # for a profitable forecast of prices of stock options on real market data", # Inverse Problems, 32 (2016) 015010. #---------- # Script assumes it's called by crontab, at the opening of the market #----- import numpy as np import pause, datetime from bs4 import BeautifulSoup import requests # Quadratic interpolation of the bid and ask option prices, and linear interpolation in between (https://people.math.sc.edu/kellerlv/Quadratic_Interpolation.pdf) def funcQuadraticInterpolationCoef(values): # There is 'scipy.interpolate.interp1d' too y = np.array(values) A = np.array([[1,0,0],[1,-1,1],[1,-2,4]]) return np.linalg.solve(A,y) # https://en.wikipedia.org/wiki/Polynomial_regression def funcUab(t,coef): return coef[2]*t**2 + coef[1]*t + coef[0] def funcF(s, sa, sb, ua, ub): return (s-sb)*(ua-ub)/(sa-sb) + ub # Initialize the volatility and option lists of 3 values optionBid = [0] # dummy value to pop in the loop optionAsk = [0] # dummy value to pop in the loop volatility = [0] # dummy value to pop in the loop # Initalization for the loop Nt = 4 # even number greater than 2: 4, 6, ... Ns = 2 # even number greater than 0: 2, 4, ... twotau = 2 # not a parameter... alpha = 0.01 # not a parameter... dt = twotau / Nt # time grid step dimA = ( (Nt+1)*(Ns+1), (Nt+1)*(Ns+1) ) # Matrix A dimensions dimb = ( (Nt+1)*(Ns+1), 1 ) # Vector b dimensions A = np.zeros( dimA ) # Matrix A b = np.zeros( dimb ) # Vector b portfolio = 1000000 # Money 'available' securityMargin = 0.00083 # EMPIRICAL: needs to be adjusted when taking into account the transaction fees (should rise, see the article p.8) # Wait 10mn after the opening of the market datet = datetime.datetime.now() datet = datetime.datetime(datet.year, datet.month, datet.day, datet.hour, datet.minute + 10) pause.until(datet) # Record the stock and option values and wait 10mn more def funcRetrieveStockOptionVolatility(): # Stock stock_data_url = "https://finance.yahoo.com/quote/MSFT?p=MSFT" stock_data_html = requests.get(data_url).content stock_content = BeautifulSoup(stock_data_html, "html.parser") stock_bid = content.find("td", {'class': 'Ta(end) Fw(600) Lh(14px)', 'data-test': "BID-value"}) print(stock_bid) stock_ask = content.find("td", {'class': 'Ta(end) Fw(600) Lh(14px)', 'data-test': "ASK-value"}) print(stock_ask) stockOptVol[0] = stock_bid.text.split()[0] stockOptVol[1] = stock_ask.text.split()[0] # Option option_data_url = "https://finance.yahoo.com/quote/MSFT/options?p=MSFT&date=1631836800" option_data_html = requests.get(option_data_url).content option_content = BeautifulSoup(option_data_html, "html.parser") call_option_table = content.find("table", {'class': 'calls W(100%) Pos(r) Bd(0) Pt(0) list-options'}) calls = call_option_table.find_all("tr")[1:] it = 0 for call_option in calls: it+=1 print("it = ", it) if "in-the-money " in str(call_option): itm_calls.append(call_option) print("in the money") itm_put_data = [] for td in BeautifulSoup(str(itm_calls[-1]), "html.parser").find_all("td"): itm_put_data.append(td.text) print(itm_put_data) if itm_put_data[0] == 'MSFT210917C00220000': # One single option stockOptVol[2] = float(itm_put_data[4]) stockOptVol[3] = float(itm_put_data[5]) stockOptVol[4] = float(itm_put_data[-1].strip('%')) else: otm_calls.append(call_option) print("out the money") print("bid = ", option_bid, "\nask = ", option_ask, "\nvol = ",option_vol) return stockOptVol # Record option and volatility stockOptVol = funcRetrieveStockOptionVolatility() optionBid.append(stockOptVol[2]) optionAsk.append(stockOptVol[3]) optionVol.append(stockOptVol[4]) # Wait another 10mn to record a second value for the quadratic interpolation datet = datetime.datetime.now() datet = datetime.datetime(datet.year, datet.month, datet.day, datet.hour, datet.minute + 10) pause.until(datet) stockOptVol = funcRetrieveStockOptionVolatility() optionBid.append(stockOptVol[2]) optionAsk.append(stockOptVol[3]) optionVol.append(stockOptVol[4]) tradeAtTimeTau = False tradeAtTimeTwoTau = False # Run the loop until 30mn before closure datet = datetime.datetime.now() datetend = datetime.datetime(datet.year, datet.month, datet.day, datet.hour + 6, datet.minute + 10) while datet <= datetend: datet = datetime.datetime(datet.year, datet.month, datet.day, datet.hour, datet.minute + 10) optionBid.pop(0) optionAsk.pop(0) optionVol.pop(0) stockOptVol = funcRetrieveStockOptionVolatility() stockBid = stockOptVol[0] stockAsk = stockOptVol[1] optionBid.append(stockOptVol[2]) optionAsk.append(stockOptVol[3]) optionVol.append(stockOptVol[5]) # Trade if required if tradeAtTimeTau == True or tradeAtTimeTwoTau == True: # sell if tradeAtTimeTau == True: portfolio += min(optionAsk[2],sellingPriceAtTimeTau) * 140 # sell 140 options bought 10mn ago tradeAtTimeTau = tradeAtTimeTwoTau sellingPriceAtTimeTau = sellingPriceAtTimeTwoTau sellingPriceAtTimeTwoTau = false else: # forecast the option when no trading # Interpolation coefa = funcQuadraticInterpolationCoef(optionAsk) # quadratic interpolation of the option ask price coefb = funcQuadraticInterpolationCoef(optionBid) # quadratic interpolation of the option bid price coefs = funcQuadraticInterpolationCoef(optionVol) # quadratic interpolation of the volatility sigma sa = stockAsk # stock ask price sb = stockBid # stock bid price ds = (sa - sb) / Ns # stock grid step for k in range (0, Ns+1): # fill the matrix and the vector for j in range (0, Nt+1): Atemp = np.zeros( dimA ) btemp = np.zeros( dimb ) print("k = {k}, j = {j}".format(k=k,j=j)) if k == 0: Atemp[ k*(Nt+1)+j, k*(Nt+1)+j ] = 1 btemp[ k*(Nt+1)+j ] = funcUab(j*dt,coefb) elif k == Ns: Atemp[ k*(Nt+1)+j, k*(Nt+1)+j ] = 1 btemp[ k*(Nt+1)+j ] = funcUab(j*dt,coefa) elif j == 0: Atemp[ k*(Nt+1)+j, k*(Nt+1)+j ] = 1 btemp[ k*(Nt+1)+j ] = funcF( k*ds+sb, sa, sb, funcUab(j*dt,coefa), funcUab(j*dt,coefb) ) elif j == Nt: # do nothing pass else: # main case akj = 0.5*(255*13*3)* funcUab(j*dt, coefs)**2 * (k*ds + sb)**2 dts = (twotau-dt)/Nt * (sa-sb-ds)/Ns #---------- #----- Integral of the generator L #---------- #----- time derivative #---------- Atemp[ (k+0)*(Nt+1)+(j+1), (k+0)*(Nt+1)+(j+1) ] = dts / dt**2 # k,j+1 ~ k,j+1 Atemp[ (k+0)*(Nt+1)+(j-1), (k+0)*(Nt+1)+(j-1) ] = dts / dt**2 # k,j-1 ~ k,j-1 #----- Atemp[ (k+0)*(Nt+1)+(j+1), (k+0)*(Nt+1)+(j-1) ] = - dts / dt**2 # k,j+1 ~ k,j-1 Atemp[ (k+0)*(Nt+1)+(j-1), (k+0)*(Nt+1)+(j+1) ] = - dts / dt**2 # k,j-1 ~ k,j+1 #---------- #----- stock derivative #---------- Atemp[ (k+1)*(Nt+1)+(j+0), (k+1)*(Nt+1)+(j+0) ] = akj**2 * dts / ds**4 # k+1,j ~ k+1,j Atemp[ (k+0)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j+0) ] = 4 * akj**2 * dts / ds**4 # k,j ~ k,j Atemp[ (k-1)*(Nt+1)+(j+0), (k-1)*(Nt+1)+(j+0) ] = akj**2 * dts / ds**4 # k-1,j ~ k-1,j #----- Atemp[ (k+1)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j+0) ] = -2 * akj**2 * dts / ds**4 # k+1,j ~ k,j Atemp[ (k+0)*(Nt+1)+(j+0), (k+1)*(Nt+1)+(j+0) ] = -2 * akj**2 * dts / ds**4 # k,j ~ k+1,j #----- Atemp[ (k-1)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j+0) ] = -2 * akj**2 * dts / ds**4 # k-1,j ~ k,j Atemp[ (k+0)*(Nt+1)+(j+0), (k-1)*(Nt+1)+(j+0) ] = -2 * akj**2 * dts / ds**4 # k,j ~ k-1,j #----- Atemp[ (k+1)*(Nt+1)+(j+0), (k-1)*(Nt+1)+(j+0) ] = akj**2 * dts / ds**4 # k+1,j ~ k-1,j Atemp[ (k-1)*(Nt+1)+(j+0), (k+1)*(Nt+1)+(j+0) ] = akj**2 * dts / ds**4 # k-1,j ~ k+1,j #---------- #----- time and stock derivatives #---------- Atemp[ (k+0)*(Nt+1)+(j+1), (k+1)*(Nt+1)+(j+0) ] = akj * dts / (dt*ds**2) # k,j+1 ~ k+1,j Atemp[ (k+1)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j+1) ] = akj * dts / (dt*ds**2) # k+1,j ~ k,j+1 #----- Atemp[ (k+0)*(Nt+1)+(j-1), (k+1)*(Nt+1)+(j+0) ] = - akj * dts / (dt*ds**2) # k,j-1 ~ k+1,j Atemp[ (k+1)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j-1) ] = - akj * dts / (dt*ds**2) # k+1,j ~ k,j-1 #---------- Atemp[ (k+0)*(Nt+1)+(j+1), (k+0)*(Nt+1)+(j+0) ] = -2 * akj * dts / (dt*ds**2) # k,j+1 ~ k,j Atemp[ (k+0)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j+1) ] = -2 * akj * dts / (dt*ds**2) # k,j ~ k,j+1 #----- Atemp[ (k+0)*(Nt+1)+(j-1), (k+0)*(Nt+1)+(j+0) ] = 2 * akj * dts / (dt*ds**2) # k,j-1 ~ k,j Atemp[ (k+0)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j-1) ] = 2 * akj * dts / (dt*ds**2) # k,j ~ k,j-1 #---------- Atemp[ (k+0)*(Nt+1)+(j+1), (k-1)*(Nt+1)+(j+0) ] = akj * dts / (dt*ds**2) # k,j+1 ~ k-1,j Atemp[ (k-1)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j+1) ] = akj * dts / (dt*ds**2) # k-1,j ~ k,j+1 #----- Atemp[ (k+0)*(Nt+1)+(j-1), (k-1)*(Nt+1)+(j+0) ] = - akj * dts / (dt*ds**2) # k,j-1 ~ k-1,j Atemp[ (k-1)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j-1) ] = - akj * dts / (dt*ds**2) # k-1,j ~ k,j-1 #---------- #---------- #----- Regularisation term - using alpha = 0.01 #---------- #---------- #----- H2 norm: 0 derivative #---------- Atemp[ (k+0)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j+0) ] += alpha # k,j ~ k,j #----- coef = funcF( k*ds+sb, sa, sb, funcUab(j*dt,coefa), funcUab(j*dt,coefb) ) btemp[ (k+0)*(Nt+1)+(j+0) ] += alpha * 2 * coef #---------- #----- H2 norm: time derivative #---------- Atemp[ (k+0)*(Nt+1)+(j+1), (k+0)*(Nt+1)+(j+1) ] += alpha / dt**2 # k,j+1 ~ k,j+1 Atemp[ (k+0)*(Nt+1)+(j-1), (k+0)*(Nt+1)+(j-1) ] += alpha / dt**2 # k,j-1 ~ k,j-1 #----- Atemp[ (k+0)*(Nt+1)+(j+1), (k+0)*(Nt+1)+(j-1) ] += -alpha / dt**2 # k,j+1 ~ k,j-1 Atemp[ (k+0)*(Nt+1)+(j-1), (k+0)*(Nt+1)+(j+1) ] += -alpha / dt**2 # k,j-1 ~ k,j+1 #----- coef = ( funcF( k*ds+sb, sa, sb, funcUab((j+1)*dt,coefa), funcUab((j+1)*dt,coefb) ) \ - funcF( k*ds+sb, sa, sb, funcUab((j-1)*dt,coefa), funcUab((j-1)*dt,coefb) ) ) / dt btemp[ (k+0)*(Nt+1)+(j+1) ] += alpha * 2 * coef btemp[ (k+0)*(Nt+1)+(j-1) ] += - alpha * 2 * coef #---------- #----- H2 norm: stock derivative #---------- Atemp[ (k+1)*(Nt+1)+(j+0), (k+1)*(Nt+1)+(j+0) ] += alpha / ds**2 # k+1,j ~ k+1,j Atemp[ (k-1)*(Nt+1)+(j+0), (k-1)*(Nt+1)+(j+0) ] += alpha / ds**2 # k-1,j ~ k-1,j #----- Atemp[ (k+1)*(Nt+1)+(j+0), (k-1)*(Nt+1)+(j+0) ] += -alpha / ds**2 # k+1,j ~ k-1,j Atemp[ (k-1)*(Nt+1)+(j+0), (k+1)*(Nt+1)+(j+0) ] += -alpha / ds**2 # k-1,j ~ k+1,j #----- coef = ( funcUab(j*dt,coefa) - funcUab(j*dt,coefb) ) / (sa - sb) btemp[ (k+1)*(Nt+1)+(j+0) ] += alpha * 2 * coef btemp[ (k-1)*(Nt+1)+(j+0) ] += - alpha * 2 * coef #---------- #----- H2 norm: stock and time derivative #---------- Atemp[ (k+1)*(Nt+1)+(j+1), (k+1)*(Nt+1)+(j+1) ] += alpha / (ds*dt) # k+1,j+1 ~ k+1,j+1 Atemp[ (k-1)*(Nt+1)+(j+1), (k-1)*(Nt+1)+(j+1) ] += alpha / (ds*dt) # k-1,j+1 ~ k-1,j+1 Atemp[ (k-1)*(Nt+1)+(j-1), (k-1)*(Nt+1)+(j-1) ] += alpha / (ds*dt) # k-1,j-1 ~ k-1,j-1 Atemp[ (k+1)*(Nt+1)+(j-1), (k+1)*(Nt+1)+(j-1) ] += alpha / (ds*dt) # k+1,j-1 ~ k+1,j-1 #---------- Atemp[ (k+1)*(Nt+1)+(j+1), (k-1)*(Nt+1)+(j+1) ] += -alpha / (ds*dt) # k+1,j+1 ~ k-1,j+1 Atemp[ (k+1)*(Nt+1)+(j+1), (k+1)*(Nt+1)+(j-1) ] += -alpha / (ds*dt) # k+1,j+1 ~ k+1,j-1 Atemp[ (k+1)*(Nt+1)+(j+1), (k-1)*(Nt+1)+(j-1) ] += alpha / (ds*dt) # k+1,j+1 ~ k-1,j-1 #----- Atemp[ (k-1)*(Nt+1)+(j+1), (k+1)*(Nt+1)+(j+1) ] += -alpha / (ds*dt) # k-1,j+1 ~ k+1,j+1 Atemp[ (k+1)*(Nt+1)+(j-1), (k+1)*(Nt+1)+(j+1) ] += -alpha / (ds*dt) # k+1,j-1 ~ k+1,j+1 Atemp[ (k-1)*(Nt+1)+(j-1), (k+1)*(Nt+1)+(j+1) ] += alpha / (ds*dt) # k-1,j-1 ~ k+1,j+1 #---------- Atemp[ (k-1)*(Nt+1)+(j+1), (k+1)*(Nt+1)+(j-1) ] += alpha / (ds*dt) # k-1,j+1 ~ k+1,j-1 Atemp[ (k-1)*(Nt+1)+(j+1), (k-1)*(Nt+1)+(j-1) ] += -alpha / (ds*dt) # k-1,j+1 ~ k-1,j-1 #----- Atemp[ (k+1)*(Nt+1)+(j-1), (k-1)*(Nt+1)+(j+1) ] += alpha / (ds*dt) # k+1,j-1 ~ k-1,j+1 Atemp[ (k-1)*(Nt+1)+(j-1), (k-1)*(Nt+1)+(j+1) ] += -alpha / (ds*dt) # k-1,j-1 ~ k-1,j+1 #---------- Atemp[ (k+1)*(Nt+1)+(j-1), (k-1)*(Nt+1)+(j-1) ] += -alpha / (ds*dt) # k+1,j-1 ~ k-1,j-1 #----- Atemp[ (k-1)*(Nt+1)+(j-1), (k+1)*(Nt+1)+(j-1) ] += -alpha / (ds*dt) # k-1,j-1 ~ k+1,j-1 #---------- coef = ( funcUab((j+1)*dt,coefa) - funcUab((j+1)*dt,coefb) \ - funcUab((j-1)*dt,coefa) + funcUab((j-1)*dt,coefb) ) / (dt * (sa - sb)) btemp[ (k+1)*(Nt+1)+(j+1) ] += alpha * 2 * coef / (ds*dt) btemp[ (k-1)*(Nt+1)+(j+1) ] += - alpha * 2 * coef / (ds*dt) btemp[ (k-1)*(Nt+1)+(j-1) ] += - alpha * 2 * coef / (ds*dt) btemp[ (k+1)*(Nt+1)+(j-1) ] += alpha * 2 * coef / (ds*dt) #---------- #----- H2 norm: stock second derivative #---------- Atemp[ (k+0)*(Nt+1)+(j+1), (k+0)*(Nt+1)+(j+1) ] += alpha / dt**4 # k,j+1 ~ k,j+1 Atemp[ (k+0)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j+0) ] += 4 * alpha / dt**4 # k,j ~ k,j Atemp[ (k+0)*(Nt+1)+(j-1), (k+0)*(Nt+1)+(j-1) ] += alpha / dt**4 # k,j-1 ~ k,j-1 #----- Atemp[ (k+0)*(Nt+1)+(j+1), (k+0)*(Nt+1)+(j+0) ] += -2 * alpha / dt**4 # k,j+1 ~ k,j Atemp[ (k+0)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j+1) ] += -2 * alpha / dt**4 # k,j ~ k,j+1 #----- Atemp[ (k+0)*(Nt+1)+(j+1), (k+0)*(Nt+1)+(j-1) ] += alpha / dt**4 # k,j+1 ~ k,j-1 Atemp[ (k+0)*(Nt+1)+(j-1), (k+0)*(Nt+1)+(j+1) ] += alpha / dt**4 # k,j-1 ~ k,j+1 #----- Atemp[ (k+0)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j-1) ] += -2 * alpha / dt**4 # k,j ~ k,j-1 Atemp[ (k+0)*(Nt+1)+(j-1), (k+0)*(Nt+1)+(j+0) ] += -2 * alpha / dt**4 # k,j-1 ~ k,j #---------- #----- H2 norm: time second derivative #---------- Atemp[ (k+1)*(Nt+1)+(j+0), (k+1)*(Nt+1)+(j+0) ] += alpha / ds**4 # k+1,j ~ k+1,j Atemp[ (k+0)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j+0) ] += 4 * alpha / ds**4 # k,j ~ k,j Atemp[ (k+1)*(Nt+1)+(j+0), (k+1)*(Nt+1)+(j+0) ] += alpha / ds**4 # k-1,j ~ k-1,j #----- Atemp[ (k+1)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j+0) ] += -2 * alpha / ds**4 # k+1,j ~ k,j Atemp[ (k+0)*(Nt+1)+(j+0), (k+1)*(Nt+1)+(j+0) ] += -2 * alpha / ds**4 # k,j ~ k+1,j #----- Atemp[ (k+1)*(Nt+1)+(j+0), (k-1)*(Nt+1)+(j+0) ] += alpha / ds**4 # k,j ~ k,j Atemp[ (k-1)*(Nt+1)+(j+0), (k+1)*(Nt+1)+(j+0) ] += alpha / ds**4 # k,j ~ k,j #----- Atemp[ (k+0)*(Nt+1)+(j+0), (k-1)*(Nt+1)+(j+0) ] += -2 * alpha / ds**4 # k,j ~ k-1,j Atemp[ (k-1)*(Nt+1)+(j+0), (k+0)*(Nt+1)+(j+0) ] += -2 * alpha / ds**4 # k-1,j ~ k,j #---------- coef = ( funcF( k*ds+sb, sa, sb, funcUab((j+1)*dt,coefa), funcUab((j+1)*dt,coefb) ) \ - 2 * funcF( k*ds+sb, sa, sb, funcUab((j+0)*dt,coefa), funcUab((j+0)*dt,coefb) ) \ + funcF( k*ds+sb, sa, sb, funcUab((j-1)*dt,coefa), funcUab((j-1)*dt,coefb) ) ) / dt**2 btemp[ (k+0)*(Nt+1)+(j+1) ] += alpha * 2 * coef / dt**2 btemp[ (k+0)*(Nt+1)+(j+0) ] += - alpha * 4 * coef / dt**2 btemp[ (k+0)*(Nt+1)+(j-1) ] += alpha * 2 * coef / dt**2 #---------- #---------- #----- Boundary de-computation #---------- if k+1 == Ns: Atemp[ (k+1)*(Nt+1)+(j+0), (k+1)*(Nt+1)+(j+0) ] = 0 # k+1,j ~ k+1,j Atemp[ (k+1)*(Nt+1)+(j+1), (k+1)*(Nt+1)+(j+1) ] = 0 # k+1,j+1 ~ k+1,j+1 Atemp[ (k+1)*(Nt+1)+(j-1), (k+1)*(Nt+1)+(j-1) ] = 0 # k+1,j-1 ~ k+1,j-1 btemp[ (k+1)*(Nt+1)+(j+0) ] = 0 # k+1,j btemp[ (k+1)*(Nt+1)+(j+1) ] = 0 # k+1,j+1 btemp[ (k+1)*(Nt+1)+(j-1) ] = 0 # k+1,j-1 if k-1 == 0: Atemp[ (k-1)*(Nt+1)+(j+0), (k-1)*(Nt+1)+(j+0) ] = 0 # k-1,j ~ k-1,j Atemp[ (k-1)*(Nt+1)+(j+1), (k-1)*(Nt+1)+(j+1) ] = 0 # k-1,j+1 ~ k-1,j+1 Atemp[ (k-1)*(Nt+1)+(j-1), (k-1)*(Nt+1)+(j-1) ] = 0 # k-1,j-1 ~ k-1,j-1 btemp[ (k-1)*(Nt+1)+(j+0) ] = 0 # k-1,j btemp[ (k-1)*(Nt+1)+(j+1) ] = 0 # k-1,j+1 btemp[ (k-1)*(Nt+1)+(j-1) ] = 0 # k-1,j-1 if j-1 == 0: Atemp[ (k+0)*(Nt+1)+(j-1), (k+0)*(Nt+1)+(j-1) ] = 0 # k,j-1 ~ k,j-1 Atemp[ (k+1)*(Nt+1)+(j-1), (k+1)*(Nt+1)+(j-1) ] = 0 # k+1,j-1 ~ k+1,j-1 Atemp[ (k-1)*(Nt+1)+(j-1), (k-1)*(Nt+1)+(j-1) ] = 0 # k-1,j-1 ~ k-1,j-1 btemp[ (k+0)*(Nt+1)+(j-1) ] = 0 # k,j-1 btemp[ (k+1)*(Nt+1)+(j-1) ] = 0 # k+1,j-1 btemp[ (k-1)*(Nt+1)+(j-1) ] = 0 # k-1,j-1 #---------- pass print("-----") print("Atemp = ") print(Atemp) print("-----") print("btemp = ") print(btemp) print("-----") print("-----") A = A + Atemp b = b + btemp print("-----") print("A = ") print(A) print("-----") print("b = ") print(b) print("-----") print("-----") input("Press Enter to continue...") # Conjugate gradient algorithm: https://en.wikipedia.org/wiki/Conjugate_gradient_method x = np.zeros(N).reshape(N,1) r = b - np.matmul(A,x) p = r rsold = np.dot(r.transpose(),r) for i in range(len(b)): Ap = np.matmul(A,p) alpha = rsold / np.matmul(p.transpose(),Ap) x = x + alpha * p r = r - alpha * Ap rsnew = np.dot(r.transpose(),r) if np.sqrt(rsnew) < 1e-16: break p = r + (rsnew / rsold) * p rsold = rsnew print("it = ", i) print("rsold = ", rsold) # Trading strategy sm = (sa + sb)/2 if x[Ns/2*(Nt+1)+Nt/2] >= optionAsk[0] + securityMargin: tradeAtTimeTau = True sellingPriceAtTimeTau = x[Ns/2*(Nt+1)+Nt/2] portfolio -= 140 * optionAsk # buy 140 options if x[Ns/2*(Nt+1)+Nt] >= optionAsk[0] + securityMargin: tradeAtTimeTwoTau = True sellingPriceAtTimeTwoTau = x[Ns/2*(Nt+1)+Nt] portfolio -= 140 * optionAsk # buy 140 options pause.until(datet) # Wait 10mn before the next loop pause.until(datet) datet = datetime.datetime.now() # Time should be around 20mn before closure datet = datetime.datetime(datet.year, datet.month, datet.day, datet.hour, datet.minute + 10) if tradeAtTimeTau == True: # sell stockOptVol = funcRetrieveStockOptionVolatility() optionAsk.pop(0) optionAsk.append(stockOptVol[3]) portfolio += min(optionAsk[2],sellingPriceAtTimeTau) * 140 # Wait 10mn more to sell the last options pause.until(datet) # it should be around 10mn before closure if tradeAtTimeTwoTau == True: # sell stockOptVol = funcRetrieveStockOptionVolatility() optionAsk.pop(0) optionAsk.append(stockOptVol[3]) portfolio += min(optionAsk[2],sellingPriceAtTimeTwoTau) * 140 # Market closure

Don't put money on this as I'm still debugging (I bet you half a bitcoin I have mistaken a few indices in the H_2 norm)... Here is the discretisation formula I used, to copy-paste on latexbase:

\documentclass[12pt]{article} \usepackage{amsmath} \usepackage[latin1]{inputenc} \title{Klibanov algorithm} \author{Discretisation formula} \date{\today} \begin{document} \maketitle Let $$ a_{k,j} = \frac12\sigma(j\delta_\tau)^2\times(255\times13\times3)\times(k\delta_s+s_a)^2, $$ then \begin{alignat*}{3} J_\alpha(u) = & \sum_{k=1}^{N_s} \sum_{j=1}^{N_t} \left| \frac{u_{k,j+1} - u_{k,j-1}}{\delta_\tau} + a_{k,j} \frac{u_{k+1,j} - 2u_{k,j} + u_{k-1,j}}{\delta_s^2}\right|^2\frac{2\tau - \delta_\tau}{N_t}\frac{s_a - s_b - \delta_s}{N_s}\\ & + \alpha \sum_{k=1}^{N_s} \sum_{j=1}^{N_t} \left| u_{k,j} - F_{k,j}\right|^2 \\ & \qquad + \left| \frac{u_{k,j+1} - u_{k,j-1}}{\delta_t} - \frac{F_{k,j+1} - F_{k,j-1}}{\delta_t}\right|^2 \\ & \qquad + \left| \frac{u_{k+1,j} - u_{k-1,j}}{\delta_s} - \frac{u_{a,j} - u_{b,j}}{s_a - s_b}\right|^2 \\ & \qquad + \left| \frac{(u_{k+1,j+1} - u_{k-1,j+1}) - (u_{k+1,j-1} - u_{k-1,j-1})}{\delta_s\delta_t} \right. \\ & \qquad \qquad \left. - \frac{(u_{a,j+1} - u_{b,j+1}) - (u_{a,j-1} - u_{b,j-1})}{(s_a-s_b)\delta_t}\right|^2 \\ & \qquad + \left| \frac{u_{k,j+1} - 2u_{k,j} + u_{k,j-1}}{\delta_\tau^2} - \frac{F_{k,j+1} - 2F_{k,j} + F_{k,j-1}}{\delta_\tau^2} \right|^2 \\ & \qquad + \left| \frac{u_{k+1,j} - 2u_{k,j} + u_{k-1,j}}{\delta_s^2}\right|^2 \end{alignat*} %% \left| \right|^2 with $\tau = 1$ unit of time (for example 10mn). \end{document}

Let me know if you see something wrong... And if you want to contribute, feel free

Not the best translation but interesting. Thanks to u/kokoniqq for the heads up!
1. Optical display scheme in AR glasses
Augmented reality technology, or AR technology, is to provide users with virtual information through images, videos, 3D models and other technologies while displaying real scenes, so as to achieve the ingenious integration of virtual information and the real world. It is the tipping point of the next information technology. According to authoritative predictions, augmented reality glasses will replace mobile phones as the next generation of collaborative computing platforms. Augmented reality technology represented by augmented reality glasses is currently emerging in various industries, especially in the security and industrial fields. Augmented reality technology embodies unparalleled advantages and greatly improves the way of information interaction. At present, the optical display solutions in the more mature augmented reality technology are mainly divided into prism solutions, birdbath solutions, free-form surface solutions, off-axis holographic lens solutions, and lightguide solutions.
1.1 Prism scheme
The prism scheme takes Google Glass as an example. As shown in Figure 1, the optical display system is mainly composed of a projector and a prism. The projector projects the image, and then the prism reflects the image directly into the human retina, superimposing it with the real image. Since the system is above the human eye, it is necessary to focus the eye to the upper right to see the image information, and this system has a natural contradiction between the field of view and the volume. The Google Glass system has a small field of view, with only a 15-degree field of view, but the optical lens has a thickness of 10mm, and the brightness is not enough, and the image has a large distortion, so the product was withdrawn by the company shortly after entering the market.

Figure 1. Physical image of Google Glass glasses products
1.2 Birdbath solution
The optical design in the Birdbath solution is to project light from the display source onto a 45-degree beam splitter. The beam splitter has reflection and transmission values (T), allowing the light to be partially reflected in the percentage of R, while the rest Transmitted in T value. At the same time, T allows users to see physical objects in the real world and digital images generated by the display at the same time. The light reflected from the beam splitter bounces onto the combiner. The synthesizer is generally a concave mirror that redirects light to the eyes. AR headsets using this optical display solution mainly include Lenovo Mirage AR headsets (Figure 2(a)) and ODG R8 and R9 (Figure 2(b)). Among them, ODG has a 50-degree field of view, and its thickness exceeds 20mm.

Figure 2. (a) Mirage headset device; (b) ODG R9 headset device
1.3 Free-form surface scheme
The free-form surface scheme generally uses a free-form surface mirror with a certain reflection/transmission (T) value. The free-form surface is a complex and unconventional surface shape that is different from a spherical or aspherical surface, which is used to describe the surface shape of the lens. The mathematical expression of is relatively complicated and often does not have rotational symmetry. The light from the display directly hits the concave mirrocombiner and is reflected back into the eyes. The ideal position of the display source is centered and parallel to the mirror surface. Technically speaking, the ideal position is for the display source to cover the user's eyes, so most designs move the display "off-axis" and set it above the forehead. The off-axis display on the concave mirror has distortion, which needs to be corrected on the software/display side. Since free-form surfaces can not only provide more degrees of freedom for the design of optical systems, significantly improve the optical performance of the system, but also bring more flexible structural forms to system design, so it has become a research hotspot in the field of optical design in recent years. Among the most representative companies are Epson of Japan (shown in Figure 3) and the Meta series of Dream Vision Corporation of the United States (shown in Figure 4). Although the AR glasses of Epson of Japan are gambling in terms of color, saturation and image quality, they only have a field of view of 23 degrees and a thickness of 13mm. Although the Meta2 series of AR glasses from American Dreamland Vision has a 90-degree field of view, its thickness exceeds 50mm, and the weight of the optical and mechanical system alone is about 420 grams.

Figure 3. AR glasses developed by Epson in Japan. (a) The actual product; (b) The imaging light path.

Figure 4. AR helmet developed by American Dreamland Vision. (a) The actual product; (b) The imaging light path.
From the above, it can be seen that there is an unavoidable contradiction in the prism scheme, birdbath scheme, and free-form surface scheme, that is, the larger the field of view, the thicker the optical lens and the larger the volume. It is precisely because of this. The irreconcilable contradiction limits its application in smart wear, that is, augmented reality glasses.
1.4 Holographic lens solution
The holographic lens solution uses the unique optical characteristics of the holographic lens. The principle is to record a holographic collimating lens (Hd) and a simple linear grating (Hg) on the same holographic dry plate, and the holographic collimating lens will emit the display source. The beam is collimated into a plane wave and diffracted into the substrate for total internal reflection transmission, while the line grating diffracts the beam into the human eye. This system uses holographic optical elements as coupling elements. It has a compact structure and reduces the difficulty of designing and processing holographic optical elements. At the same time, it reduces the dispersion of the holographic lens. It also has the advantages of large FOV and small size, so it is quickly adopted by people. accept. However, due to the relatively small eye movement range, and the holographic lens has complex aberrations and severe dispersion, the imaging effect of the holographic lens is not ideal. The representative manufacturer currently adopting the holographic lens solution is North. As shown in Figure 5, it is the physical map of North's AR glasses products based on the holographic lens solution and the schematic diagram of the imaging optical path.

Figure 5. AR glasses based on holographic lens solution developed by North Company. (a) The actual product; (b) The imaging light path.
1.5 Optical waveguide solution
The optical waveguide solution has advantages in terms of clarity, viewing angle, volume, etc., so it has become the best optical display solution in augmented reality glasses, and is expected to become the mainstream optical display solution for AR glasses. AR glasses based on waveguide technology are generally composed of three parts: display module, waveguide and coupler. The light emitted by the display module is coupled into the optical waveguide by the in-coupling device, travels forward in the form of total reflection in the waveguide, and when it reaches the out-coupling device, it is coupled out of the optical waveguide and enters the human eye for imaging. Because the optical path is folded by the waveguide, the general system volume is relatively small. According to the principle of the coupler, the optical waveguide technology used in AR glasses based on waveguide technology can be divided into two types: geometric waveguide and diffractive optical waveguide.
The geometric waveguide solution generally includes a sawtooth structure waveguide and a polarized film array mirror waveguide (referred to as a polarized array waveguide). Among them, the mainstream polarized arrayed waveguide uses multiple semi-transparent and semi-reflective film layers that are placed in parallel and have a certain split ratio to achieve image output and exit pupil expansion, thereby having a thin, thin, large field of view and eye movement range. And the advantage of uniform color. The diffractive optical waveguide schemes mainly include surface relief grating waveguide scheme and volume holographic grating waveguide scheme. The embossed grating waveguide solution is manufactured using nano-imprint lithography technology. Although it has the advantages of large field of view and large eye movement range, it will also bring challenges to field of view and color uniformity, and related micro-nano processing technology. It is also a huge challenge, and the production cost is high. The volume holographic grating waveguide solution has advantages in color uniformity (no rainbow effect) and realization of a single-chip full-color waveguide, so it has attracted great interest from AR optical module manufacturers.
Figure 6 is the basic display principle of the waveguide solution. The coupling area is used to couple the light beam of the micro-projector into the waveguide sheet, so that the light beam satisfies the conditions of total reflection propagation in the waveguide sheet, and the coupling area is used for total reflection. The propagating light beam couples out of the waveguide and reaches the human eye. The coupling area can be mirrors, prisms, relief gratings and volume holographic gratings. The decoupling area can be half mirrors, relief gratings and volume holographic gratings arranged in an array. This article will explain in detail the polarization array waveguide scheme in geometric optical waveguide technology and the surface relief grating waveguide scheme and volume holographic grating waveguide scheme in diffractive optical waveguide technology, and the preparation and processing technology of surface relief grating and volume holographic grating At the same time, it further introduces the research and development situation of Goolton Technology in this field.

Figure 6. Schematic diagram of the waveguide solution
2. Polarization array waveguide
2.1 Principle of Polarization Array Waveguide
The waveguide lens of the polarization array waveguide technology usually adopts a plurality of semi-transmissive and semi-reflective coatings placed in parallel and with a certain split ratio to achieve image output and exit pupil expansion. The semi-transparent and semi-reflective coating has angular selectivity. , And the array is arranged. The schematic diagram of its working principle is shown in Figure 7.After the light emitted by the image source is collimated by the eyepiece system, it is coupled into the waveguide by the reflective surface of the waveguide. The light in each field of view propagates in the waveguide according to the total reflection theorem, and the light enters the semi-transparent On the reverse side, part of it reflects out of the waveguide, and the other part of the transmission continues to propagate. Then this part of the advancing light meets another mirror, and the above-mentioned "reflection-transmission" process is repeated until the last mirror in the mirror array reflects all the remaining light out of the waveguide into the human eye. Since the waveguide can have multiple semi-transparent and semi-reverse surfaces, and each semi-transparent and semi-reverse surface forms an exit pupil, the exit pupil can be expanded when the substrate thickness is very thin to achieve a large field of view and large eye movement range. After multiple reflections, the emitted light can be "adjusted" to be more uniform.

Figure 7. Schematic diagram of the working principle of the array optical waveguide
The pupil dilation technology of this technology is more complicated in design. Full consideration should be given to stray light, human eye compatibility, and various performance indicators when designing. In addition, uniformity is also an intuitive indicator of the end user experience. How to control the reflection and transmittance of multiple coatings, how to optimize the whole machine, and how to control the coating process can ensure the uniformity of the entire eye movement range. the focus of research. For this reason, Goolton Technology independently developed and designed optical modules based on polarization arrayed waveguide technology, and after repeated attempts to summarize, obtained epoch-making results.
2.2 Goolton Technology-"Seven-fold, dodecahedron" ultra-short-focus AR optical module M3010
Recently, Goolton Technology released a new "seven-fold, dodecahedron" ultra-short-focus AR optical module M3010 (Figure 8), which uses specially selected materials and process combinations to successfully eliminate the inherent noise and streaks of peer products Difficult problems such as perception, ghosting, distortion, dispersion, etc., have broken through the limits of AR display technology at this stage in terms of imaging clarity, maximum brightness, color uniformity, weight, volume, power consumption, light leakage, etc., and all indicators are in In the forefront of the world, it truly integrates all the advantages of optical waveguide modules such as extremely thin, extremely light and extremely high color reproduction, and exerts its performance to the extreme. Figure 9 shows the product specifications of the optical module M3010 based on polarization array waveguide technology recently launched by Goolton Technology.

Figure 8. Goolton Technology-(a) Seven-fold optical path; (b) Product display diagram of optical module M3010 based on polarization arrayed waveguide technology

Figure 9. Goolton Technology-Product Specifications of Optical Module M3010 Based on Polarization Arrayed Waveguide Technology
Goolton Technology’s "seven-fold, dodecahedron" ultra-short-focus optical module M3010 has the following super performance. 1. Small: Based on the anisotropic characteristics of the crystal material, the multiplexing of optical devices is realized, and the light that originally propagated in one direction in the optical waveguide is folded into 7 segments, which reduces the volume of the projector unit by 85%; 2. : Weight is about 33 grams; 3. Transparency: The light transmittance of the waveguide lens exceeds that of ordinary architectural glass windows, which can reach more than 85%; 4. Thin: Refraction distortion is less than 2mm; 5. Color: ultra-high contrast, resolution, color reproduction The M3010 comes standard with LCOS as the image source, and the resolution can reach 1920*1080. It provides optical resolution close to the limit resolution of the human eye, completely eliminates the sense of screen boundary, and the image quality is clear and delicate, and the image contrast Sharp, no graininess. The maximum brightness can reach 5000nit, and the color gamut coverage is more than 100% RGB, reaching the level of professional monitors. 6. Zero light leakage: Thanks to the light splitting film array waveguide sheet and optical structure exclusively developed by Goolton Technology, the M3010 module will not leak light when working, and will not expose the content displayed on the screen to the outside world, regardless of the concealment requirements The extremely high military helmet is also the AR glasses for consumer entertainment, this feature is very important; 7.Super vision: M3010 adopts top-down structure, the horizontal field of view is completely unobstructed, and the entire field of view is fully visible. While improving the user experience, it also solves the problem of security risks caused by users wearing glasses to block the line of sight; 8. Low power consumption: battery life can reach about 10 hours; 9. Mass production reaches 10K pieces per year, and the mass production yield is stable. The cost has reached the world-class level; 10. Ultra-strict environmental testing standards: In the face of extreme high and low temperature environments, as well as high humidity and continuous salt spray, Goolton Technology’s "seven-fold, dodecahedron" ultra-short-focus AR optics The module M3010 can work stably with reliability far exceeding the industry average; 11. Fully accept customization: AR glasses have rich landing scenes, based on the powerful functions of M3010, technology companies from all walks of life can work in their familiar Customize a wide range of intelligent AR products in the field. We firmly believe that Goolton Technology’s "seven-fold, dodecahedron" ultra-short-throw optical module M3010 will definitely be able to kick off the next generation of display technology revolution, and provide better and more advanced technology for companies that also hold the spirit of craftsmanship. Powerful AR products and high-quality services.
3. Diffractive optical waveguide
3.1 Surface relief grating waveguide
The relief grating waveguide solution is to use relief grating (SRG) instead of traditional catadioptric optical device (ROE) as the coupling in, coupling out and exit pupil expansion device in the waveguide solution. The schematic diagram of its working principle is shown in Figure 10.

Figure 10. Schematic diagram of the principle of diffractive optical waveguide and surface relief grating
Commonly used relief gratings are mainly one-dimensional gratings, including tilted gratings, trapezoidal gratings, blazed gratings and rectangular grating structures. Figure 11(a) shows the scanning electron microscope (SEM) image of the tilted grating. The two-dimensional grating is mainly a hexagonal cylindrical grating structure commonly used in waveguides. Figure 11(b) shows the SEM image of the two-dimensional cylindrical grating structure. The feature sizes of the above grating structures are all nanometers. Currently, the most representative products of the embossed grating waveguide solution are Microsoft's HoloLens series 12(a) and WaveOptics' embossed grating waveguide series 12(b).

Figure 11. (a) Tilted grating structure diagram; (b) Two-dimensional cylindrical grating structure diagram

Figure 12. (a) HoloLens2 from Microsoft; (b) Embossed grating waveguide from WaveOptics
3.2 Volume holographic grating waveguide
The volume holographic grating waveguide solution uses a volume holographic grating as the coupling in and out of the waveguide. A volume holographic grating is an optical element with a periodic structure. It is generally exposed through a double-beam holographic exposure, directly on the micron-level thickness of the photopolymer The internal interference of the film forms interference fringes with light and dark distribution, which causes the periodic change of the refractive index inside the material. This period is generally a nano-scale grating structure, which is an order of magnitude with the wavelength of visible light, so the light can be effectively modulated, and the incident light can be diffracted to change the direction of light transmission. Combining the volume holographic grating and the waveguide film, the diffraction efficiency of the volume holographic grating can be adjusted by designing the relevant parameters of the volume holographic grating (such as material refractive index n, refractive index modulation factor and thickness, etc.).
The schematic diagram of the working principle of the volume holographic grating waveguide technology is shown in Figure 13.The image generated by the microdisplay becomes parallel light after passing through the collimating system. The diffraction effect changes the propagation direction of parallel light. When the light in the waveguide meets the condition of total reflection, it is confined to travel in the waveguide direction without loss. When the parallel light propagates to the holographic grating at the out-coupling end, the condition of total reflection is destroyed, and the light is diffracted again and becomes parallel light that exits the waveguide and enters the human eye for imaging. When the coupled holographic grating and the modulated out holographic grating have the same periodic structure and mirror symmetry, the dispersion can be effectively eliminated.

Figure 13. Schematic diagram of the working principle of volume holographic grating waveguide technology
The representative manufacturers that adopted volume holographic grating waveguide solutions in the early days were Sony and Digilens. With the maturity of this technology, the number of companies participating in the optical research of holographic grating diffraction waveguides is increasing, mainly including TruLife and WaveOptics in the United Kingdom, and Akonia in the United States. Wait. Sony has produced a high-brightness single-green volume holographic grating waveguide. As shown in Figure 14, the structure uses a double-sided volume holographic grating as the coupling end, achieving a transmittance of 85% and a display brightness of 1000cd/m2. However, due to the small thickness of the volume holographic grating, the efficiency of the system is low. In addition, it can only be used for monochromatic display and has been discontinued. Digilens launched a double-layer full-color volume holographic grating waveguide, as shown in Figure 15. This structure realizes color by using multiple monochromatic gratings, which can effectively reduce the crosstalk of system colors, but the efficiency of the system is not high, and because of its The double-layer waveguide structure makes the system more difficult to manufacture.

Figure 14. Sony's double-sided volume grating structure holographic waveguide. (a) The actual product; (b) The imaging light path.

Figure 15. Digilens full-color volume holographic grating waveguide. (a) The actual product; (b) The imaging light path.
Goolton Technology uses the holographic material exposure method to combine the RGB three colors into a diffractive waveguide, and uses the principle of coherent recording and diffraction to transmit the image to the human eye for display. There are three aspects: simulation design, materials, and process preparation. Simulation design requires self-written complex calculation models; materials mainly refer to the photosensitive materials in HOE. For holographic optical waveguides, low shrinkage ratio, high efficiency and high uniformity before and after manufacturing are required; in terms of process, more holographic technology is required Manufacturing light path and exposure experience, it is very related to the materials used. Figure 16 shows the corresponding display effect of the single-layer full-color volume holographic grating waveguide developed by Goolton Technology, with a field of view of 30°.

Figure 16. The display effect of the single-layer full-color volume holographic grating waveguide developed by Goolton Technology
4. Micro-nano manufacturing of diffractive optical waveguides
4.1 Micro-nano fabrication of surface relief grating waveguide
Surface relief gratings can be divided into one-dimensional and two-dimensional gratings from the dimension, and can be divided into straight gratings, blazed gratings and inclined gratings in structure. Since the augmented reality optical waveguide is used in the visible light band, in order to achieve greater diffraction efficiency and field of view, its characteristic size is generally hundreds of nanometers or even tens of nanometers, and its performance has a small tolerance for errors. Processing and preparation posed great challenges. The current preparation of diffractive optical waveguides is basically based on semiconductor preparation processes (such as photolithography and etching processes). However, because these methods are limited by their complicated and expensive equipment, the production cost is very high, and they are not suitable for mass production of optical modules.
Shown in Figure 17 is the process flow chart of surface relief grating template preparation or small batch preparation, including its scanning electron micrograph. For straight gratings, the process is relatively mature. First, a resist layer is spin-coated on the substrate, and the grating is patterned by interference exposure or electron beam exposure, and then reactive ion etching (RIE) or inductively coupled plasma etching is used ( ICP) transfer the pattern to the substrate and remove the resist layer to complete the preparation of the straight grating. Due to the uniformity problem, the oblique grating optical waveguide represented by HoloLens cannot be directly prepared by the reactive etching scheme, so the preparation process is more complicated, and focused ion beam etching (FIBE) and ion beam etching are required. Beam etching, IBE), reactive ion beam etching (reactive ion beam etching, RIBE) technology. Considering efficiency and uniformity comprehensively, RIBE is a more suitable solution. First, a hard mask (such as Cr) layer is plated on the substrate by physical or chemical methods, and then a resist layer is spin-coated. Also use interference exposure or electron beam exposure for patterning, and then transfer the resist pattern to the Cr layer through a chlorine dry etching process. After the etching process, the remaining resist layer is stripped by oxygen plasma method. Next, the fluorine-based RIBE process is used to incident the substrate with an ionized argon ion beam at an oblique angle. After the reactive ion beam etching, the Cr mask is removed by a standard wet etching process to obtain an oblique grating with excellent uniformity.

Figure 17. Surface relief grating template or small batch preparation process
The above-mentioned semiconductor-based manufacturing process is expensive and not suitable for mass production and processing of grating waveguides. Therefore, the replication process of diffractive optical waveguides was developed to achieve mass production, and this large-scale manufacturing process relies on optical resins with high refractive index. At present, Magic Leap and WaveOptics have carried out verification of related processes. The replication process includes hot embossing, UV-nano imprint lithography and micro contact printing (also known as soft lithography). Among them, ultraviolet nanoimprint lithography is a common method in mass production of surface relief grating waveguides.
The specific process flow is shown in Figure 18. The process can be divided into two stages: nanoimprint work mold preparation stage and mass production stage. First, the pattern is processed on the silicon wafer to be used as a template through the above-mentioned template preparation process, and UV resin is spin-coated on a larger silicon wafer through nanoimprint technology and more templates are printed on it. The printed structure is then exposed to ultraviolet light to fix the resin. Finally, the multi-pattern imprinting mold is mass-produced by repeating the above process. In the mass production process, multi-pattern molds are used to produce surface-relief grating waveguides, then functional coatings are used to cover the waveguides, and laser cutting technology is used to separate them, and finally the waveguides of different structures are stacked to realize the preparation of optical modules.

Figure 18. Mass production process flow of surface relief grating replication
4.2 Micro-nano manufacturing of volume holographic grating waveguide
The key element of the volume holographic waveguide is the volume holographic grating. The preparation of the volume holographic grating makes use of the characteristics of holographic technology. Two plane light waves with a certain angle excited by laser interfere with each other, and the interference pattern is exposed and attached to the substrate. It is obtained by forming interference fringes on the photosensitive material, and the material properties change according to the intensity distribution of light. Finally, a material with periodic changes in refractive index is obtained. The materials for preparing volume holographic waveguides include silver halide, dichromate gelatin, photosensitive polymers, holographic polymer dispersed liquid crystals, and other more exotic materials.
Holographic technology is a method that uses the principle of optical coherence to record and obtain the amplitude and phase information of an object light wave. It uses the principle of interference recording and diffraction reproduction to record the interference fringes generated by the interference of the object light wave with amplitude and phase information and the reference light wave into a hologram in the form of intensity distribution, thereby recording all the amplitude and phase information of the object light wave in On photosensitive materials. Holography is an active coherent imaging technology. The holographic recording optical path (as shown in Figure 19(a)) mainly completes two functions. One is to complete the coherent illumination of the measured object, which is formed by the transmission or reflection of the object. The object light wave; the second is to use the reference light wave to interfere with the object light wave to form a hologram.
Image
Among them, T0 represents the zero-order diffracted light, which corresponds to the transmitted light wave of the reference light wave; T+1 represents the +1-order diffracted light, which carries the information of the original object light wave; T-1 is the -1 order diffracted light, which carries the object light wave Conjugation information. In optical holography, the +1-order diffracted light can form a virtual image of the object, which can be directly observed with eyes, while the -1st-order diffracted light can form a real image of the object, which can be received by the screen.
Figure 19. Schematic diagram of the recording and reproduction process of optical holography
The diffraction order of the ideal holographic grating is only 0 and ±1 orders. The holographic optical waveguide display uses the 0th order light to be continuously totally reflected in the optical waveguide, while the -1 order light continuously emits from the waveguide surface. The geometrical schematic diagram of grating diffraction is shown in Figure 20.
Figure 20. Schematic diagram of holographic grating diffraction geometry
Image
From the above three equations, it can be concluded that for a specific wavelength, waveguide medium and light incident angle, the grating period that meets the total reflection condition should meet certain conditions.
According to its structure, holographic gratings can be divided into transmission type and reflection type holographic gratings. The fundamental difference between the two is that the recording method is different, that is, the propagation direction of the two recording lights is different, which causes the different orientation of the interference fringe surface in the recording material. When the transmission type holographic grating records, the object light and the reference light are incident from the same side of the recording medium, while when the reflection type holographic grating records, the object light and the reference light are incident from both sides of the recording medium.
Holographic gratings can be divided into surface holographic gratings and volume holographic gratings according to the relative thickness relationship between the thickness of the recording medium and the interference fringe spacing. The evaluation criteria of surface holographic grating and volume holographic grating are characterized by Q value. When Q≥10, it is volume holographic grating, otherwise it is surface holographic grating.
Image
The microstructure of volume holographic grating is inside the volume grating, so its diffraction is mainly the volume effect of the material. When the incident light satisfies the Bragg condition, the volume holographic grating will have extremely high diffraction efficiency, and if it deviates from the Bragg condition, the diffraction efficiency will drop rapidly. This characteristic makes the volume holographic grating have obvious angle and wavelength selectivity. When used as a coupling device, a volume holographic grating can couple light with a specific wavelength and angle in the waveguide out of the waveguide without blocking the view of the real scene from the outside, so it is an ideal coupling device.
The above-mentioned preparation process of volume holographic grating is only suitable for small batch verification, and for mass production, it is necessary to develop a more economical solution. Companies represented by Sony and DigiLens have developed the processing process of volume holographic waveguide. The roll-to-roll process for preparing volume holographic waveguides is shown in Figure 21. First, the double-beam interference exposure method is used to form volume holographic waveguides in the photosensitive polymer film attached to the roll; the second step is to form high-quality cycloolefin polymer plastic waveguides by injection molding. In order to obtain a qualified image, the warpage of the waveguide must be less than 5um, and the thickness change of the effective area should be less than 1um. Then the transfer process of the holographic optical element is carried out to accurately align and paste the holographic waveguide film with the plastic waveguide; then the plastic holographic waveguide is cut; finally in the color matching process, the red and blue plastic waveguides and the green plastic waveguide are aligned and used with UV The resin encapsulates and fixes it. The plastic substrate should remain flat before and after each processing is a challenge faced by both the stamping and color matching processes.

Figure 21. Preparation process of roll-to-roll holographic waveguide

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