I wanna know exactly what you know.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.
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.
“It’s about the nature of consciousness.” “That may be a wider context than I was looking for, Major.”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.
“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.”
“I don’t know what that means,” Trejo said.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.
“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.
“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?
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.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.
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.
That's why the goths are pissed, the waste heat probably gets piped to their dimension with fuck knows what consequences
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+1/2s+1/3s+1/4s+⋯=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!
Therefore, according to Facts I, II, III, and IV, we have:Then they make some final notes where they try to rewrite the harmonic series using some underexplained ideas about prime gaps and says
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!
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.
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.
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.
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?
Okay.
- 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)).
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 1/41/n is irrational for n>2. How did nobody see this before?
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 rIt'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.
FOREX StrategiesWhat are FOREX Strategies?https://preview.redd.it/ihmphstzguv51.jpg?width=960&format=pjpg&auto=webp&s=81f6b73c367d8695605514f8d32aaf3e2aeabc6e You may have noticed that most of people confuse the terminology and refer to FOREX Strategies in the wrong way. There are methodologies, systems, strategies, and techniques. The most effective methodology is Price Language (Trend Tracking). Combined with a correct reading of mass psychology presented by the charts. We know that in the Stock Markets there are thousands of strategies. FOREX, like the rest of the markets, presents you with the opportunity to apply similar strategies to win consistently. Taking advantage of repetitive psychological patterns. First, the Price Language methodology has created great fortunes in FOREX, and the next fortune may be yours. But this methodology must be implemented within a framework of advanced concepts of Markets. Without forgetting the basics. And working hard day by day. Second, a strategy is a set of parameters and techniques that together give you the advantage to act in any situation. Thus for example in war, generals have attack strategies and counterattack strategies. FOREX strategies alike are entry strategies and exit strategies. All beginners should know these FOREX strategies for beginners. That way you will get a general idea of the game and understand that trading is a war against the Market and its Specialists. Only applying FOREX strategies revealed by the same Specialists and using their own techniques, ... you can survive in this war. Do not fall into the trap of the many "systems" and "methods" that are offered on the internet about operating in the FOREX Market. They just don't work in the long run. They are strategies based on indicators for the most part. Using rigid parameters. That if they can work and give profitability during a certain period of time, they will always reach a breaking point when the market changes its dynamics. Instead, take advantage of your precious time and learn the Language of Price or Price Action. The Language methodology will allow you to adapt to each new phase of the Market. If you combine this knowledge with the appropriate psychological concepts, you can live comfortably from speculation in FOREX. Forex Trading Strategies Reddit - Basic FOREX StrategiesYou have two basic FOREX strategies, one entry, and one exit. Both follow a general strategy that helps you capitalize on the collective behaviors of the Market. That is, of the total of participating speculators.This behavior causes the formation of cycles that repeat over and over again. Driven by the basic emotions (uncertainty, greed, and panic) of the speculators involved that can be taken advantage of with the aforementioned FOREX strategies. Specialists identify these emotions in the order flow and capitalize on these events every hour, every day, and every month. Basic FOREX Strategies - The Price Cycle These repetitive cycles consist of 4 phases:
The two trends can be easily identified by their notorious breakdown. And the two areas of uncertainty (accumulation and distribution), due to their notorious range trajectories. This general behavior determines the core of our FOREX strategies. You buy when the price of a pair has broken and has come out of one of its congestion formations (accumulation or distribution). You implement one of the Forex strategies, in this case, the entry one. The multi-time technique will help you find the point of least risk when entering your initial buy or sell order. In the same way and using the same strategy but this time to close your position, the multiple timing technique will also show you how to close your operation obtaining the highest possible profit. The most consistent way to extract profits in the market is by trading the start of trends within a cycle . Once confirmed by their respective breaks from the areas of uncertainty. This is the mother of all FOREX strategies . And in a market that operates 24 hours, we have more frequent cycles and therefore more opportunities. Forex Trading Strategies Reddit - Advanced Forex StrategiesThere are many advanced FOREX strategies that are generally used by professional speculators working for large financial firms.Among these firms are banks, Investment Fund managers and Hedge Fund managers. The latter is an investment modality similar to Investment Funds, with the difference that Hedge Funds use more complex investment strategies. Its operations are more oriented to aggressive speculations in the short and medium-term. Among the most common strategies is hedging (hedging), carry trade, automated systems based on quantum mathematics. And a large number of combinations between the different option strategies. The Carry TradeThe central idea of Carry Trade is to buy a pair in which the base currency has a considerably higher interest rate than the quoted currency. To earn the difference in rates regardless of whether the price of the pair rises or falls.Suppose we buy a $ 100,000 lot of AUDJPY, which according to the rates on the chart would turn out to be the ideal instrument in this example to use the Forex carry trade strategy. As our capital is in US dollars we have to assume for our example, the following quotes necessary to perform the place calculations: AUD / JPY = 80.00 USD / JPY = 85.00 What happens internally in your broker is this.
The great advantage of carry trade FOREX strategies is that this percentage profit is applied to the $ 100,000 of the standard lot; the broker transfers all of the profit to you, even if you only contributed $ 1,000. On the other hand, if you carry out the inverse of this operation, this benefit of the Forex carry trade becomes a cost (swap), and you assume it completely. Remember that FOREX carry trade strategies are recommended for pairs with considerable interest rate differences, such as the one we have just seen in our example. These FOREX strategies should also not be used in isolation. The idea is that through technical analysis you identify when would be the ideal time to enter the market using your carry trade Forex strategy and multiply your profits considerably. What FOREX Strategies Do Hedge Funds Use?The FOREX strategies used by large fund managers do not constitute an advantage in terms of percentage results for them, nor do they constitute a competitive disadvantage for you.The vast majority of them fail because of their big egos. In fact, there was a firm made up of great financial geniuses, including 2 winners of the Nobel Prize in Economics, who developed a strategy based on quantum mathematical calculations. With an initial base capital of about 3 billion dollars, and after 3 successful years obtaining annual returns of over 40%, the firm Long-Term Capital Management, begins its fourth year with losses. To counteract these losses the geniuses decide to multiply the initial capital several times, while the losses continued. The year closed with the bankruptcy of the fund, and with a total accumulated loss of 1 trillion dollars, due to the great leverage used. And all for not admitting that the FOREX Strategies of Long Term Capital Management were not in line with the dynamics of the Market. There are an overwhelming number of opportunities in the stock markets to make money interpreting the Language of Price. You don't need to use complex "advanced" strategies that have been created to handle hundreds or billions of dollars. The reasons for using these FOREX strategies are very different from what a "retail trader" pursues with his small speculation business. As you can see, you should not worry about wanting to integrate any of these advanced strategies into your arsenal. They are only beneficial for managing hundreds or billions of dollars, where the return parameters are very different when you handle small amounts of capital. Do not worry about collecting hundreds of free FOREX strategies that circulate on the internet, that great accumulation of mediocre information will only serve to confuse you and waste your valuable time. Spend that time learning Price Action, … And you will always be one step behind the Specialists, identifying each new Market condition, and anticipating the vast majority of reversals of all prices. Ironically, the most successful fund managers indicate that their most profitable trades are those based on the basic trend-following strategies of the Price Language. The same ones that you will learn in this Free Course. Dedicate yourself to perfecting them and believe me you won't need anything else. As long as you have good risk management, taking into consideration the following points ... Styles of Investments in FOREXThe Investment FOREX long term is not recommended for small investors like you and me. If we take into account the term investing literally as large investors do who buy a financial product today to sell it years later.We both have a better niche in the short and medium-term. You may have noticed that the big multi-year trends in the Forex Market do exist. But minor swings within a big trend are usually very wide. These minor movements allow us to easily double and triple the annual return of the big general trend, motivating most traders to speculate in the short and medium-term. These minor oscillations or trends that occur within the large multi-year trends owe their occurrence mainly to two reasons. First, the FOREX Market presents 3 sessions a day each in different cities of the world with different time zones (Asia, Europe, and America). This causes more frequent trend changes than in the rest of the stock markets. Second, the purpose for which it was created also plays a role. The modern Foreign Exchange Market, since its inception in 1972, was conceived by the global financial system as a tool for speculation. To obtain benefits in the short and medium-term (from several days to 1 year). These two points are basically the reasons why we observe the immense speed with which the FOREX market changes trends. For example, for those who live in America, in the early morning (Europe) the EURUSD pair may be on the rise, in the morning or afternoon (America) it may be down, and then finally at night (Asia) it may return to the rise. Define your Own Style for your FOREX InvestmentsOne of the first decisions you will have to make is to choose your style as a trader or investor.There are 4 types of well-defined styles. Most professional traders tend to have multiple styles, although they always identify with one primary style for their FOREX investments. Study the characteristics of the 4 main styles to make your investments in FOREX : 1. Long Term: recommended for anyone who is going to enter the market for the first time and who can dedicate a minimum of one hour per month to their investments in Forex. The period of an open position ranges from 1 year to 5 years. 2. Medium Term: recommended for anyone who is going to enter the market for the first time and who can dedicate a minimum of one hour per week to their investments in Forex. The period of an open position ranges from 1 month to 1 year. 3. Short Term: recommended for anyone who is going to enter the market for the first time, or who already has a certain time operating in the long and medium-term, showing constant profits, and who can dedicate a minimum of one hour per day to your investments in FOREX. The period of an open position ranges from 1 day to 1 month. 4. Intraday : recommended only for people with a fairly solid earnings record in the short term, and with a capital greater than $ 50,000. As we have noted, this option constitutes a full-time job. People who start investing in FOREX , should start executing short-term (weeks) and medium-term (months) transactions only, and not pay attention to intraday oscillations (day trading). If you are interested in being an intraday speculator, I recommend that you first exhaust at least a year doing operations in the short and medium-term to assimilate the correct strategies and to develop the necessary mentality to carry out this work. The second option would be to participate in some kind of intensive training. I remind you that self-educating is almost impossible in speculation. You are likely to accumulate a lot of knowledge by reading books and attending courses. But you will probably never learn to make money with all the incomplete "systems" circulating on the internet. Mistakes to Avoid When Looking for Your StyleMany people who are new to FOREX investments make the mistake of combining these styles, which is a key to failure.I recommend that if you are not getting the results you expected by adopting one of these styles, do not try to change it. The problem sure is not in the style, but in your strategies or in your psychology. A successful investor is able to make a profit in any longer trading time than he is used to. I explain. If you are already a profitable operator in the short term, it is very likely that you will also be profitable in the medium and long term, … As long as you can interpret the Language of Price or Price Action. In the opposite case, the same would not happen. If you were a medium-term trader, you would need time to adjust to the intraday. The reality is that long, medium and short term traders have very similar personalities. The intraday trader is completely different. The Myth of the Intraday in Investments in FOREXIf you are already successful in the short, medium and long term, you will notice that the sacrifice and the hours necessary in front of the computer to operate intraday is much greater. The intraday style will be useful to increase your account if it is less than USD $ 100,000 in a very short time in exchange for 8 to 12 hours a day of hard work but ...You must first develop the necessary skills to operate the intraday. The ideal is to combine all the styles to get more out of the Market and carry out more effective transactions and have a diversification in your investments in FOREX. There are intraday traders that are very successful, but the reality is that there are very few in the world that make a profit year after year. If you want to become an intraday, you just have to prepare yourself properly through intensive training. Otherwise, I recommend that you don't even think about educating yourself to adopt the intraday style. It is not necessary to go against a probability of failure greater than 99%. Unless ... your ego is greater than your common sense. The main reason why this style of investments in FOREX is not recommended for the vast majority of us "retail investors" (the official term "retail traders"), is the high operational cost. The real commissions in this market range between $ 2.0 and $ 2.50 for each lot of 100,000 virtual units. This means that a complete operation (opening and closing) is approximately $ 5.00, for each standard lot traded ($ 100,000 virtual). Another fundamental reason is the advent of robotic traders (HFT = High-Frequency Trading), which tend to manipulate the market in the shorter intraday swings. Please do not confuse HFTs with automated systems that we find daily on the internet, and that can be purchased for a few hundred dollars and often for free on FOREX forums / groups. These HFTs to which I refer, they are effective. They cost millions of dollars and have been developed by the large Wall Street financial firms to manage their investments in FOREX. The reality of the intraday trader is that you execute orders for large lots at the same time, to profit from the smallest movements in the market. It is an activity based on reflexes. The slightest oversight or distraction can turn into a catastrophe for your FOREX investments. I recommend that you start investing in FOREX using slow time periods such as H4 or Daily. For some reason, all Goldman Sachs intraday FOREX investments are made with algorithms. Finally…To choose your style as a trader and manage your investments in FOREX, first determine what your degree of experience is, analyze the points mentioned below and the rest you will discover when you execute your first operations.The points that will affect your decision are:
And I hope you are one of those who get up over and over again. The next lesson will boost your confidence when you discover the main reason that moves currencies ... Fundamental Analysis in Forex Trading RedditThe fundamental analysis in Forex is used mostly by long-term investors. Players as we saw in the styles of operators, start a negotiation today, to close it years later.I always emphasize the importance that the mass media give to this type of analysis to distract the great mass of participants. It is all part of a great mass psychological manipulation. For centuries the ignorance of the masses has been organized before the great movements begin. The important news are the macroeconomic reports published by the Central Banks and other government agencies destined for this work. All reports are made up. 99% of them are corrected months later. These events are tools to justify fundamental analysis and price cleaning movements. Any silly headline does the job. With this, it is possible to absorb most of the existing liquidity, before the new trend phase is projected. Reaction!Except in rare situations, the result of an economic report of the fundamental analysis is generally already assimilated in the graph. In most cases, there are financial institutions that already have access to this information and are organizing and carrying out their operations in advance.The phrase buy the rumor and sell the news is a very old adage on Wall Street. And its meaning contains what we have just explained. For the investor who can interpret the Language of Price, fundamental analysis is of little importance. Well, in general, their disclosure does not indicate that you have to take any action in your open trades , as long as your entry strategy provides you with a good support cushion. This reality of fundamental analysis causes a lot of confusion for investors who lack in-depth knowledge of the forex market. Macroeconomic DataThe data published in these events is irrelevant. Both for speculators and for the people in general. They are false. They lack reliability.The price can go up or down with the same result of the data. The main ones are: - Interest Rates - GDP (gross domestic product) - CPI (inflation) - ISM (manufacturing index) - NFP (payroll) - Double Deficits (deficit = fiscal + balance of payments) If you are initiated, I recommend you avoid operating near these events. It is only a matter of having the time pending. Use the economic calendar for Fundamental Analysis of Forex Factory. There is a probabilistic advantage in operating these fundamental analysis events. But it takes preparation, experience, and practice. They represent a way of diversifying in the general operation of a speculator. The Uncertainty of Fundamental AnalysisOn many occasions after the disclosure of an economic report, the price movement of the currency pair that is going to be affected tends to move in the opposite direction to the logic of the report.I show you an example of a fundamental analysis report. Imagine that the EUR / USD pair is trading at 1.2500, and the FED (US Federal Reserve) issues a statement announcing that it has just raised inter-bank interest rates from 0.25 points to 0.75 points. Very positive news for the US dollar that logically implies an appreciation of the currency and consequently an instantaneous collapse of the EUR / USD pair (up the dollar and down the euro) However, minutes after the release of said fundamental analysis report, the pair after effectively collapsing to 1.2400, returns and returns to its levels prior to the report (1.2500). This situation is very common , but it is not so easy to identify it when it is occurring, but after the damage is done. Traps like these devour the accounts of beginners who approach the market with little experience, with weak strategies, and especially with very little experience. That is why I reiterate that you forget the fundamental analysis for now. Just keep in mind when operating, that there is no publication scheduled nearby. Just check the economic calendar for the day and forget about the numbers. Let the economists mess around with the data. FOREX Market CorrelationThe Forex market correlation exists between pairs with similar "base" currencies and not always under the same circumstances. The correlation in the Forex market that is most followed and that has the greatest impact on fundamental analysis is that of the US dollar (USD).The USD is the most traded monetary unit with a volume greater than 80% with respect to the rest of the currencies. This fact determines why their correlation is the most important, the most followed, and perhaps the only one worth following in the fundamental macro analysis. The 7 major pairs are usually in sync . These 7 pairs all include the USD and present a fundamental analysis correlation almost 75% of the time. Influencing the rest of the currency pairs. Advantages of the FOREX Market CorrelationIn the fundamental analysis the most basic FOREX correlation is the following. When the USD appreciates, the USD / CAD, USD / CHF, and USD / JPY pairs tend to go up in price. This indicates that the Canadian dollar (CAD), the Swiss franc (CHF), and the Japanese yen (JPY) are losing value against the USD.We must bear in mind that this correlation does not occur 100% of the time. In fact, the JPY generally tends to move in the opposite direction , since in recent decades this currency has been used as a source of financing to invest in other financial instruments. On the other side is the FOREX market correlation that generates a movement almost in unison in the other 4 major pairs EUR / USD, GBP / USD, AUD / USD, and NZD / USD. These tend to fall in price, homologous the appreciation of the USD. But not always. In this case the fundamental analysis correlation works most of the time, between 65 and 85% of the time. Small differences are noted in the extent that each of these pairs experiences. There is also a correlation in the secondary FOREX market, where the pairs of all currencies that do not include the USD participate, but I recommend you not to waste time on them for now. There are more important things about the Language of Price to know first. FOREX Commodity CorrelationIn this part I will explain to you in a basic way the Correlation Commodities - FOREX of the fundamental analysis.There are three currencies that have a direct correlation with commodities. They are usually called: "COMDOLLS" which is short for "Commodities Dollars" (Commodities Dollars), since all three obey the dollar denomination. These are: - The New Zealand Dollar (NZD) - The Australian Dollar (AUD) - The Canadian Dollar (CAD) These three currencies make up the group of the 8 largest together with the euro, the pound, the yen, the franc and the US dollar. Together, they merge to produce the major pairs traded in the FOREX Foreign Exchange Market. The FOREX Commodity Correlation has an affinity in most cases greater than 75%. And each of them has its different raw material of correlation. You will notice that the NZD and the AUD are two currencies that act practically in unison. Both present minimal discrepancies in their fluctuations in the short, medium and long term. This is mainly because their economies are very similar and their economic and fiscal policies are too. Their main production items also show great similarities, despite the fact that the Australian economy is much larger than the New Zealand economy. The raw materials that follow the movement of the AUD are mainly gold and copper. If you put the history of these three quotes during the last decade of the year 2,000 together on the same chart, you will notice a very similar upward movement between the three quotes. Pure correlation of fundamental analysis. This strong correlation with commodities in the metals area for the AUD has provided Australia with an economic advantage enviable over the other major powers that have seen their currencies devalue sharply against the AUD. At the same time, they experience a constant decrease in the purchasing power of their citizens. The NZD maintains a correlation with raw materials related to agriculture and livestock, mainly including milk and its derivatives. It is one of the countries that dominates the world export of these economic items, and also has important exports of metals , although in smaller quantities than Australia. Finally, you have a correlation with raw materials in the energy area. For historical reasons the CAD, which is not the largest oil producer in the world, but an important supplier to the largest consumer that is the US, has seen its currency oscillate in line with oil prices. To make long-term investments in the Foreign Exchange Market, it is necessary to take into consideration at least one Commodity Correlation - FOREX in your fundamental analysis. Forex Technical Analysis RedditThe technical analysis is the methodology that interprets the movements of the price. Specialists look for liquidity to fund their business. The repetition of the strategies used by the specialists in their work generate repetitive patterns.If you were an analyst, you would develop the visual ability to identify such patterns on a graph. If you were a programmer you would quantify them mathematically using complex formulas. And if you could learn to interpret the Language of Price, you would have the ability to anticipate 90% of all movements that occur on a chart. And in this business, anticipating is what will make you money. Market prices are reflected and framed on a horizontal time axis and a vertical price axis. Prices go up or down according to the aggressiveness of the participating operators. In an efficient or balanced market these oscillations should be imperceptible. But in reality this is not the case, since the Market works thanks to the digital printing of hundreds of billions of units of paper money systematically distributed by the Central Banks through the banking system. These resources serve as a tool to manipulate 100% of the movements that occur in the FOREX Market. Are you looking for Technical Indicators? All technical indicators were created from the 70's. How do you think that for more than 200 years the speculators of the past accumulated great wealth? With the Language of Price. The best timing is given by the price itself. Indicator-generated entry signals usually occur at the wrong time. The basis of technical analysis is human psychology. Unfortunately, human beings are not perfect and are loaded with emotions that dominate their behavior in similar situations, creating repetitive and highly predictable behavior when it occurs in masses. The study of technical analysis through indicators and subjective training, originates and shapes the collective thinking on which all the traps that specialists execute every day to maintain their business are designed. If the majority won, the Market would cease to exist. Although you already know that the patterns are not generated by the masses , but the repetitive behavior of the Specialists in the face of the action response of the masses. It is very easy for speculaists, because they can see everyone's orders in their books. And they also exert a great influence on the decisions of the masses through the mass media. It is what I call the war between the Egg and the Stone , if you hit me you win and if I hit you also you win. The Deception of Modern Technical AnalysisThrough the centuries thousands of people have been able to extract great benefits from the financial markets by applying the basic strategies of technical analysis and the psychology of the Price Language.More than 200 years ago when the markets began to operate officially, fundamental analysis predominated, which was only used by large financial institutions. As this analysis tool began to become popular, these institutions began to apply the strategies of technical analysis. In recent decades and with the massification of internet technology, technical analysis has begun to be handled by anyone who has a computer with internet access. The same financial institutions, which have been present for more than a century and as a result of this overcrowding , establish a strategy to confuse and misinform about the true strategies of technical analysis. This has been accomplished in the following manner. Currently there are hundreds, if not thousands of technical indicators that have been developed by so-called "gurus" of technical analysis and that sell their magic indicators packed in a "system" or "method" that usually cost thousands of dollars, or simply with the publication of a book with which they generate large profits. Double benefit. The aim is to confuse the initiates in speculation and create the collective mentality that will originate the same behaviors over and over again. About 95% of these new entrants completely lose all the capital they invest in their early stages as investors. Leaving them with a negative experience and creating the idea and the image that financial markets are an exclusive area for geniuses with high academic levels and that only they can produce returns in the markets year after year. The initiate, having lost all his original capital, turns to these “gurus” for help and teachings. You spend more capital on the products they offer you and the cycle repeats itself . Obviously, the vast majority do not relapse and completely forget to re-engage in the stock markets. I hope you have not been a victim of this drama. Now I will show you the simplicity of a FOREX technical analysis , without the need to resort to any indicator as a tool to determine an effective entry or exit strategy when planning your operations. The Price CyclePreviously you studied in the FOREX strategies lesson, that the typical price cycle when it is reflected in a graph, presents four very specific phases and very easy to identify if you perform a technical analysis with common sense . These are:
You will be surprised by the simplicity with which thousands of people around the world and over the centuries have accumulated large sums of money by drawing a few simple lines and applying responsible risk management with their capital. How to Identify Trends?Being able to determine the trend phases within the price cycle is the essence of technical analysis since it is these two phases that provide you with the probabilistic advantage you need to operate in the markets and obtain constant returns.In the most plain and simple language, in the world of technical analysis, there are only two types of formations: trends and ranges. The trends, in turn, can be bullish if they go up, or bearish if they go down. The ranges, on the other hand, can be accumulation if they are at the beginning of the cycle, or distribution if they are in the high part of the cycle. As I had indicated in the topic of FOREX strategies when describing the price cycle. This sounds more like a play on words, but I will show you the practical definition to simplify your life and then you will apply these definitions on the graph so that everything makes more sense to you.
Some key points from the graph:
The Common Sense, The Less Common of SensesThe central idea of technical analysis consists in determining the price situation of a market, that is, in which phase of the pattern of its cycle it is currently conjugated with the collective thinking of the masses and the possible traps that the market would have prepared to remove. the capital at stake by the public.To carry out a precise technical analysis, you will use the support and resistance lines, which can be static (horizontal) or dynamic (projecting an angle with respect to the horizontal axis). Your common sense prevails here. If you show a 10-year-old a chart, they will be able to tell you if the price is going up or down. You will most likely have no idea how to draw the lines, but you will be able to establish the general trend. Simply using your common sense. By introducing indicators and other gadgets , the simplicity and effectiveness of the technical analysis created by your common sense evaporates. The following graph conceptually shows you all the possible situations in which you could draw these lines to carry out your technical analysis of the place. You can clearly observe a downtrend delimited by its dynamic trend line and an uptrend on the right side with its respective dynamic delimitation. https://preview.redd.it/5iehg0r6guv51.png?width=500&format=png&auto=webp&s=84c265a5d35da7ea970792c4bf40fe20b33bd8bd Forex Charts AnalysisI want to remind you that the formations or patterns that develop on the charts (triangles, wedges, pennants, boxes, etc.) only work to execute trades that have initially been confirmed by the static support and resistance lines and to read the collective thinking of the masses.Chart formations work, but you must know the Language of Price to determine when the Specialists will exploit a chartist figure, or when they will allow it to run. In fact, you will learn with the Language that you can operate a chart figure in any direction. Much of the "mentalization" that the masses receive is to believe that the figures are made to be respected. Which is an inefficient way of working. Simply because you could wait days or months for a perfect chart figure to occur in order to perform a reliable trade. When in fact there are dozens every day. Japanese CandlesOf all the tools you have to carry out technical analysis, perhaps the best known and most popular is the Japanese technique of candles (candlesticks).Candles are mainly used to identify reversal points on the chart without resorting to confirmation of horizontal trend lines and only using a previous bar or candle breaks. Its correct use is subject to a multi-time analysis (multiple temporalities) and a general evaluation of the context proposed by the market in general at the time of each scenario. Later I will show you all the important details to take into account so that you use Japanese candles in a simple and very effective way. Do not forget ... Trading in your beginnings based on formations (chartism) and candlestick patterns conjugated with hundreds of tools and technical indicators, constitutes the perfect path to your failure. Before using any strategy or technique I recommend you focus on learning the Price Language, which includes 3 basic things:
Specialists make money every day at the expense of the collective behavior caused by the use of these strategies and techniques. With which you will only manage to lose your capital and your time by putting the cart in front of the horse. People who do the opposite, at best become, ... Philosophers of Speculation, or indocile Robot Assistants or Expert Advisors. To make money in any market condition, range or trend, you must use the technical analysis based on the Price Language and combine it with a correct psychological reading of the price. This knowledge can only be acquired through proper education and lots of supervised practice. Like any other career in life. I hope you've found this guide helpful! |
After years of development and brainstorming, I am happy to announce that my SemanTeX package for LaTeX has just been added to CTAN and is now part of TeX Live and MikTeX. The manual is available here. submitted by GanonZD to LaTeX [link] [comments] Its purpose is to allow for a more semantic, systematized way of writing mathematics, compared to the ordinary math syntax. The system is object-oriented and uses keyval syntax, and everything is highly customizable. An example from elementary analysis: Suppose we want to take the complex conjugate of a function f and then derive it n times, i.e. f̅ (n) . Using SemanTeX, we can write $ \vf[conj,der=\vn] $(The v in \vf stands for “variable”, so \vf is the variable f. It is usually best to create commands \va, \vA, \vb, \vB, ... for each variable you are using.) Or suppose you want to invert a function g and restrict it to a subset U, and then apply it to x, i.e. we want to write g-1|_U(x). This can be done by writing $ \vg[inv,res=\vU]{\vx} $An example from algebraic geometry: Suppose F is a sheaf and h a map, and that we want to typeset the equation (h -1F)_p = F_(h(p)), i.e. the stalk of h -1F at p is the stalk of F at h(p). This can be accomplished by writing $ \vh[inverseimage]{\sheafF}[spar,stalk=\vp] = \sheafF[stalk=\vh{\vp}] $(here, spar is the key that adds the parentheses around h -1F). All of these keys are defined by the user, and they can be modified and adjusted for all sorts of situations in all kinds of different branches of mathematics. Let us see how to set up SemanTeX to type the examples above: \documentclass{article} \usepackage{amsmath,semantex} \NewVariableClass\MyVar % creates a new class of variables, called "\MyVar" % Now we create a couple of variables of the class \MyVar: \NewObject\MyVar\vf{f} \NewObject\MyVar\vg{g} \NewObject\MyVar\vh{h} \NewObject\MyVar\vn{n} \NewObject\MyVar\vp{p} \NewObject\MyVar\vU{U} \NewObject\MyVar\vx{x} \NewObject\MyVar\sheafF{\mathcal{F}} % Now we set up the class \MyVar: \SetupClass\MyVar{ output=\MyVar, % This means that the output of an object % of class \MyVar is also of class \MyVar % We add a few keys for use with the class \MyVar: definekeys={ % we define a few keys {inv}{upper={-1}}, {conj}{command=\overline}, {inverseimage}{upper={-1},nopar}, }, definekeys[1]={ % we define keys taking 1 value {der}{upper={(#1)}}, {stalk}{seplower={#1}}, % "seplower" means "separator + lower", i.e. lower index % separated from any previous lower index by a separator, % which by default is a comma {res}{ rightreturn ,symbolputright={|}, lower={#1} }, }, } \begin{document} $ \vf[conj,der=\vn] $ $ \vg[inv,res=\vU]{\vx} $ $ \vh[inverseimage]{\sheafF}[spar,stalk=\vp] = \sheafF[stalk=\vh{\vp}] $ \end{document}https://preview.redd.it/pqftr2gz7g251.png?width=493&format=png&auto=webp&s=2273bb8139bbddfbd2cc51ff9135b711aade96ff See the manual for more details. Comments, bug reports, and ideas are more than welcome! :-) |
Hello all, submitted by seamoongames to gamedev [link] [comments] I've never learned about quaternions before, and it finally came up that I need to understand them to implement rotations in my game (being made in Unity). I decided to take the time to learn and understand them well, and one thing that helps me retain what I learned is to share/explain it to others in a way that is simple to understand. So that is why I'm making these posts. This first part will be explaining what quaternions are - i.e. their mathematical definition. The next part will be a simple tutorial on how to use quaternions to rotate game objects in Unity. DISCLAIMER: I myself have not gone in that much depth on the subject, I learned just enough to understand the basics, and this post will be a summary of that. Also, it's best to have a basic understanding of Linear Algebra and complex numbers to fully understand everything this post covers. While I will be linking the sources that I used to learn from, I want to give a special shout out to this site right here: https://eater.net/quaternions/. They explain quaternions beautifully and simply using interactive videos that greatly visualize the concepts. I highly recommend checking that out. That said, I hope you will find this and benefit from it. Please let me know in the comments if I have made any mistakes in my explanations or if I could improve on them in some way. Basic termsWhen discussing the rotation of an object, there are two types of coordinate frames that are important to know: the inertial frame, and the body frame.The inertial frame can be thought of as the fixed frame of reference of an object - the rotation will always be applied from the inertial frame. The body frame is the frame that shows the object's position and rotation relative to the inertial frame. So when applying a rotation, what it essentially means is to perform the mathematical transformation of a vector from the inertial frame to the body frame. See Figure 1 below for a simple visualization: Fig. 1: The inertial frame (blue) transformation to the body frame (yellow) [1] The need for quaternions3D rotation is much easier to understand when using Euler angles: you have the three separate axes that you can rotate on in 3D space: x, y, and z. For each axis, you would pretty much handle the rotation on the plane perpendicular to that axis - which essentially is like performing 2D rotation for each dimension.To rotate all 3 axes at once, you would basically put the formulas for rotating each individual axis in a matrix and multiply that matrix with the vector (from the right) to end up with the resulting rotated vector. See the figures below for a better understanding: Fig. 2: The inertial frame - the frame of reference of an object [2] Fig. 3: Rotation matrix from the inertial frame to body frame [2] However, Euler angles cannot solve every case of 3D rotation, as it can suffer from the "Gimbal Lock." This occurs when the angle on one axis approaches 90 degrees, which results in the object only being rotatable in 2 dimensions on the other axes, as they are positioned in a way such that rotating on one of the two remaining axes has the same range of angular motion as the other. To eliminate this problem and have the ability to rotate in all 3 dimensions at all times, we turn to What are quaternions?Mathematically speaking, a quaternion is a 4-element vector that can be used to encode any rotation in a 3D coordinate system. Generally speaking, it is actually a special kind of complex number, where the imaginary part is a 3-dimensional vector.Example: q = a + v => a is the real part, which is a scalar, and v is the imaginary vector defined as: v = (xi, yj, zk), where i, j, and k can be thought of as unit complex vectors in the x, y, and z axes, respectively. As a 4D vector, it can be represented like this: q = [a x y z] When used in the context of 3D rotations, you can think of the imaginary/vector part as being the axis that the body will rotate on, and the real/scalar part as being the angle of rotation. More specifically, if theta is the angle of rotation, and v is the axis vector, then the rotation quaternion q = [a b c d] - called the attitude quaternion - is defined as follows: Fig. 4: attitude quaternion [3] Before discussing the formula for quaternion rotation, we must discuss quaternion multiplication. Quaternion multiplication, although long and tedious to do by hand, is not very different from the multiplication of two complex numbers in rectangular form. NOTE: the following is only one way to define quaternion multiplication, but it is by far the simplest to understand. The Hamilton Product of two quaternions is essentially done by expanding each quaternion and multiplying them using the distribution law, similar to multiplying polynomials in algebra: Let q1 = a1 + b1i + c1j + d1k and q2 = a2 + b2i + c2j + d2k be two quaternions. Their resulting product is: q1q2 = (a1 + b1i + c1j + d1k)(a2 + b2i + c2j + d2k) = ... = (see result below) Fig. 5: resulting product of two quaternions [3] NOTE: order matters! Like matrix multiplication, quaternion multiplication is not commutative, meaning q1q2 != q2q1. All that said, the formula for rotating a vector from the inertial frame to the body frame is: Fig. 6: formula for quaternion rotation [3] Where qbi is the attitude quaternion as defined earlier, (0 vI) is the inertial frame vector to rotate, represented as a quaternion with a 0 real part, and (qbi)-1 is the inverse of the attitude quaternion. The inverse of a quaternion is similar to the conjugate of a complex number, where you simply invert the sign of the imaginary part. For a quaternion, you invert the sign of all the components of the vector part. Example: q = a + v => q-1 = a - v This all seems counter-intuitive...is what you might be thinking - because that's what I thought as well when I first read all this.My main questions were:
The second question is much more difficult to explain simply, so I will do my best to put it in my own words according to what I've learned: Before the actual explanation, I have to define what a stereographic projection is. In simple terms, a stereographic projection is a mapping of an entity of a higher dimension onto an entity of a lower dimension. A simple, practical example of stereographic projection is mapping the Earth's globe onto a 2D map of the world. When you perform a quaternion multiplication, geometrically speaking you're performing a stereographic projection of a 4-dimensional hypersphere (which is beyond our perception) onto 3-dimensional space. So when you perform the first multiplication from the right - i.e. the attitude quaternion by the input vector (0, v) - the resulting projection causes vector v is rotated by the angle of the attitude quaternion, which is 0.5 * theta, on the attitude quaternion's rotation axis - i.e. its "vector" part. However, the object represented by the input vector would be distorted due to that projection, if you were to apply that transformation on all the points that make up that object. Therefore, to undo the distortion effects of the hypersphere projection, we need to multiply the result mentioned above by the inverse of the attitude quaternion. This will rotate the object by the theta * 0.5 again while applying the "reverse" projection, undoing the distortions caused by the previous transformation. This results in the complete rotation of the object by angle theta. The overall multiplication first rotates it halfway while distorting it, and then it rotates it the rest of the way undoing the "damage" done by the first multiplication. You can get a better explanation and visualization of the above section at https://eater.net/quaternions/. Thank you for reading this whole thing if you got to this point, and I hope you benefit from this as much as I have benefitted from writing it! SourcesI will be splitting the sources in two sections: one for all the sources that I got information from to write this, and the other one for the figures that I directly took screenshots from. The one I can't stress enough to check out if you want to understand quaternions is: https://eater.net/quaternions/.Sources of Info
[1]: https://en.wikipedia.org/wiki/Inertial_frame_of_reference#Newton's_inertial_frame_of_reference [2]: http://www.chrobotics.com/library/understanding-euler-angles [3]: http://www.chrobotics.com/library/understanding-quaternions |
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Sign up to join this community. Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Home Questions Tags Users Unanswered Meaning of complex conjugate. Ask Question Asked 1 month ago ... Mathematics & Physics Any of a set of numbers that satisfy the same irreducible polynomial. 2. Chemistry A chemical compound that has been formed by the joining of two or more compounds. [Latin coniugāre, coniugāt-, to join together : com-, com- + iugāre, to join (from iugum, yoke; see yeug- in Indo-European roots ).] In Algebra, the conjugate is where you change the sign (+ to −, or − to +) in the middle of two terms. Examples: • from 3x + 1 to 3x − 1. • from 2z − 7 to 2z + 7. • from a − b to a + b. The meaning of this conjugate is given in the following equation. That is, must operate on the conjugate of and give the same result for the integral as when operates on . The definition of the Hermitian Conjugate of an operator can be simply written in Bra-Ket notation. Starting from this definition, we can prove some simple things. Taking the complex conjugate Now taking the Hermitian ... Conjugate. The conjugate is where we change the sign in the middle of two terms like this: We only use it in expressions with two terms, called "binomials": example of a binomial. Here are some more examples: A math conjugate is formed by changing the sign between two terms in a binomial. For instance, the conjugate of x + y is x - y. We can also say that x + y is a conjugate of x - y. In other words,... An example of conjugate is to show different forms of the word "be" such as was, were, being and been. (mathematics) An explementary angle. United in pairs; yoked together; coupled. (mathematics) Presenting themselves simultaneously and having reciprocal properties; said of quantities, points, lines, axes, curves, etc. Clearly, the word conjugate or conjugation is used for a myriad of different concepts across mathematics and even in science (see the Wikipedia page). Its meaning can range from the fraction used to rationalize a denominator in pre-algebra, to the $gNg^{-1}$ action in group theory. Complex numbers have conjugates, and harmonic functions can have “harmonic conjugates”. mathematics (of a complex number) A complex conjugate. mathematics More generally, any of a set of irrational or complex numbers that are zeros of the same polynomial with integral coefficients. mathematics An explementary angle. grammar A word agreeing in derivation with another word, and therefore generally resembling it in meaning. Comments. The concepts of conjugate harmonic functions and conjugate trigonometric series are not unrelated. Let $ u $ be a harmonic function on the closed unit disc and $ \widetilde{u} $ its harmonic conjugate, so that $ u = \mathop{\rm Re} ( \phi ) $, $ \widetilde{u} = \mathop{\rm Im} ( \phi ) $, where $ \phi $ is the analytic function $ u + i \widetilde{u} $.
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More resources available at www.misterwootube.com Remember when we talked about complex and imaginary numbers? All that a + bi stuff, it was a while ago. Well that can apply to matrices as well! We've been l... Get complete concept after watching this video Topics covered under playlist of Complex Variables: Derivatives, Cauchy-Riemann equations, Analytic Functions,... Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! The Conjugate Pair Theorem... This video lecture " Eigen Value and Eigen Vector in Hindi" will help Engineering and Basic Science students to understand following topic of of Engineering-... For early access to new videos and other perks: https://www.patreon.com/welchlabsWant to learn more or teach this series? Check out the Imaginary Numbers are... We talk about the number of ways to partition an integer.Visit our website: http://bit.ly/1zBPlvmSubscribe on YouTube: http://bit.ly/1vWiRxW*--Playlists--*Di... We use conjugates in the manipulation of imaginary and complex numbers. So it's important to understand what a conjugate is. This short video explains it. Conjugate of Matrix and it's Properties. To ask your doubts on this topic and much more, click here: http://www.techtud.com/video-lecture/lecture-conjugate-m... شرح دروس الماث للمراحل الابتدائيه والاعداديه واللغات بطرق تفاعليه جذابه مجانا
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