Science topics: Mathematics
Science topic

# Mathematics - Science topic

Mathematics, Pure and Applied Math
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Fermat's last theorem was finally solved by Wiles using mathematical tools that were wholly unavailable to Fermat.
Do you believe
A) That we have actually not solved Fermat's theorem the way it was supposed to be solved, and that we must still look for Fermat's original solution, still undiscovered,
or
B) That Fermat actually made a mistake, and that his 'wonderful' proof -which he did not have the necessary space to fully set forth - was in fact mistaken or flawed, and that we were obsessed for centuries with his last "theorem" when in fact he himself had not really proved it at all?
Three more papers published by my purported to prove Fermat's Last Theorem are attached herewith.
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for different approach
What do we understand from the expression 'Vedic mathematics'?
Many Sanatana and Arya Smaj followers recite Veda even today. Are we still in Vedic period?
Vedic period, post Vedic period are expressions coined by ignorant foreigners for their convenience to understand History of people living in this region. They called them (us) Hindu.
I prefer dividing the period in two segments
1. When Veda were were written and updated from time to time.
As of now we are not sure when our sages started compiling the three Veda; Rug, Sama, and Yajur. A rough estimate is around 50,000 years BP. The last update in these three Veda was made by Maharushi Veda Vyasa, around 4500 BCE. He also compiled one more which we know as Athrva Veda.
I have sound reasons to believe that during this period ancient astronomers used very large numbers, simple arithmetical operations like addition, subtraction, multiplication, and division.
2. Period when there no more addition to four Veda, Post 4500 BCE.
We have internal evidence in Indian scriptures that around 2500 BCE, astronomers fixed the ratio of the square of circumference to the square of the diameter of a circle as equal to 10. They also started using sine and inverse sine tables during this period. These tables were of a limited number of angles which came up frequently in day-today astronomical calculations.
Much of the advancement in mathematics was done by Kerala school of mathematics in the CE era. A number of mathematical expansion series were developed by these mathematicians/astronomers.
Per my understanding, Vedic mathematics is like our ordinary arithmetic. Ancient astronomers had developed sutra/ready reckoners to complete complex arithmetical calculations with ease. In Ancient Indian astronomy one comes across 'rule of three'. This we know as the problems of ratio and proportion. When three quantities are known, the fourth is calculated by using this method. The oldest reference, I have seen this formula is in Vedanga Jyotisha. Many scholars have dated this book on ancient astronomy to around 2000 BCE. My findings suggest that this is about 35000 years old.
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Since numerical correlations were discovered in order to interpret these correlations, logical systems and methods are continually invented. Therefore I conclude that, according to me the reality is as below:
"MATHEMATICS IS BOTH DISCOVERED & INVENTED LOGICAL SYSTEMS ALSO BOTH ARTS & SCIENCE" Sinan Ibaguner
Dear Dr. Sinan Ibaguner,
The following sources should be helpful:
For a Platonist, a theorem is a provable assertion about something that is external to us (written on the wall of a cave, as it were) and which is discovered by us. Otherwise, for a non-Platonist, a theorem is a provable assertion that is invented by us concerning one or more relationships that we have put together. The relationships themselves can either be as a result of our experience, observations of natural phenomena, experiments in attempting to corroborate some hypothesis, perception of external events such as the time of sunrise or sunset (a posteriori) or can be purely abstract as a result of our understanding of definitions such as descriptively near sets, relations such as a traditional proximity relation, axioms such as those from Efremovic or Leader or Naimpally (a priori).
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Is Mathematics considered a science?
Science generally is analyzing information gathered from observing phenomena and coming up with theories to try and explain the phenomena. Then, attempting to predict a new phenomenon before it happens (when we can do that, we usually say that we have discovered "a fundamental law of nature"), and when we can consistently produce the same result, this is regarded as proof of the theory.
Mathematics is different. it does not rely on these experiments in order to claim the discovery of a new truth. There's a distinction between what Mathematics claims as proof in contrast to science. For a scientist, ten experiments with consistent results might constitute proof, for a mathematician, a million successful experiments are not enough proof. Instead, mathematicians rely on logic. Mathematics is very often inspired by nature, but it is a purely intellectual pursuit. It is just a bunch of ideas in our heads, like philosophy. Pure abstract reasoning.
Mathematics is so intricately related with science, Mathematics being the language used to describe scientific theories, but the difference between methods for arriving at proof appear to make the notion of mathematics as a science inconsistent. Is Mathematics considered a science?
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Lockdowns due to the COVID pandemic in last three years (2020-22) has played a significant role in the widespread of online based classrooms using applications like Zoom, MS teams, Webex and Google Meet. While substantial amount of the students were happy to complete their semester classes in due time without getting hampered by the lockdowns, thanks to the online based classrooms, there are also notable amount of students and parents who were complained regarding the online based classrooms that they have drastically distracted the academic performance of students.
Overall, I would like to leave it as an open-ended question. Dear researchers, what you think regarding the online based classroom? Is it an advantage for students or a disadvantage?
Everything has two sides dis/advantages. Please look at Table 3 and Table 4 of the attached file.
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How long does it take to a journal indexed in the "Emerging Sources Citation Index" get an Impact Factor? What is the future of journals indexed in Emerging Sources Citation Index?
Clarivate announced that starting with 2023 ESCI-indexed journals will also be assigned an impact factor. See: https://clarivate.com/blog/clarivate-announces-changes-to-the-2023-journal-citation-reports-release/
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I'm interested in the intersection of mathematics and social sciences, and I'm looking for expert opinions on ethical content in mathematical history.
23 November MMXXII
No.
Cordially...
ASJ
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My Awesomest Network, I am starting my Ph.D. studies and I have some questions and doubts concerning it. Could I write them down here, please? First of them is how can I join disciplines as sociology, management, economics, mathematics, informatics and other similar items to make a complex holistic interdisciplinary analysis and coherent study of pointed fields. I think personally that linking or joining et cetera aspects of artificial intelligence and computational social sciences would be interesting area of considerations. What are Your opinions?
Thank You very much for all in advance
There is even such a discipline called "COmputational Social Sciences"...
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I am a post graduate student presently writing my thesis in the department of curriculum and instructional designs.
I recommend research results from authors of the French group of Didactis of Mathematics as: Vergnaud, Bideaud, Meljac, Fischer, Brun. Also, from Oxford University Peter Bryant and Terezinha Nunes.
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I am working on meta-heuristic optimization algorithms. I would like to solve Image segmentation using Otsu’s method and my algorithm. I could not understand how to use meta-heuristic in image segmentation. Please help me in this regard. I am from maths back ground. If anybody have matlab code for the same, please share with me. I will be grateful to you.
Thank you, I have got some idea.
"An improved opposition-based marine predators algorithm for global optimization and multilevel thresholding image segmentation"
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Most statisticians agree that the minimum sample size to get any kind of meaningful result is 100.
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What is infinite? does this have any value? must there be an end or is it just our thoughts it can't imagine that there is no end to infinity! Aren't all things part of infinity? we too? is God an infinity that cannot be imagined but felt? is an infinity an energy that binds us and all things (reality and thought) together? Is there a physical explanation for infinity? Is the limitation by (infinity -1) or (-infinity + 1) legitimate or just a need to calculate it mathematically?
We can imagine any finite quantity to be halved, and then each half to be halved again, and so on, without end. You can then say the finite quantity has infinitely many parts. It's just a conceptual distinction.
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Which software is best for making high-quality graphs? Origin or Excel? Thank you
Both software solutions are superb. Next, many great suggestions regarding graphics software solutions you will find in this post:
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We see many theories in physics, mathematics, etc. becoming extremely axiomatic and rigorous. But are comparisons between mathematics, physics, and philosophy? Can the primitive notions (categories) and axioms of mathematics, physics and philosophy converge? Can they possess a set of primitive notions, from which the respective primitive notions and axioms of mathematics, physics, and philosophy may be derived?
Raphael Neelamkavil
Raphael Neelamkavil , you said, "But in your paper "The zero-dimensional physical theory (V): information, energy, efficiency, and intelligence" you exhibit enough awareness of the above facts. Hence, I do not understand what else you meant by the question at the end of your comment!".
The title of this forum topic is, "Can the Primitive Notions (Categories) and Axioms of Mathematics, Physics and Philosophy Converge?". When I said, "This is all a good question and debate, yet what is deliberate misinformation and ignorance, what is the drive for it, and can it be written about in a way so as not to promote it as being useful?" I am essentially asking whether or not the primitive notions are already granted by the contemporary ideas of mathematics, physics, and philosophy. My work highlights they are not, so a clear issue in this debate is all about what is assumed and what is not. My work with zero-dimensionality assumes nothing, and thence creates a new spectrum of ideas for mathematics, physics, and philosophy which has been, is, and perhaps still will be for most.
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I suppose so, it's true that physics is the special case of mathematics.
In physics, the existence and the uniqueness of the solution are ensured whereas in mathematics, it is the general case of physics, the existence and the uniqueness of the solution pass before all.
In Leon Lederman's wonderful book, "The God Particle" he comments about a pecking order in physics. It goes something like, "the experimental physicists only defer to the theoretical physicists who in turn only defer to the mathematician and the mathematician only defer to God..."
Physics is not mathematics. The role of physics like all sciences is to understand the universe. The theoretical physicists' role is to develop theories that explains all the experiments from the past plus allows predictions to be made to test the and potentially falsify the theory. The role of the experimental physics is to develop and perform those experiments. There is often as much deep mathematics used by an experimental physicists as a theoretical physicists.
The role of the mathematician is simple to expend the understanding of mathematics through rigorous logical reasoning. If a physicists or any other scientist finds these tools useful - then great.
Arguably the greatest theoretical physicists of the second half of the 20 Century was Richard Feynman. Here is what he said about physics.
"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong."
I would suggest for a better understanding of physics - what it is and isn't - a read of "The God Particle" would be recommended
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Right now, in 2022, we can read with perfect understanding mathematical articles and books
written a century ago. It is indeed remarkable how the way we do mathematics has stabilised.
The difference between the mathematics of 1922 and 2022 is small compared to that between the mathematics of 1922 and 1822.
Looking beyond classical ZFC-based mathematics, a tremendous amount of effort has been put
into formalising all areas of mathematics within the framework of program-language implementations (for instance Coq, Agda) of the univalent extension of dependent type theory (homotopy type theory).
But Coq and Agda are complex programs which depend on other programs (OCaml and Haskell) and frameworks (for instance operating systems and C libraries) to function. In the future if we have new CPU architectures then
Coq and Agda would have to be compiled again. OCaml and Haskell would have to be compiled again.
For instance suppose a formal mathematics Agda file started with
{-# OPTIONS --without-K --exact-split #-}
Both software and operating systems are rapidly changing and have always been so. What is here today is deprecated tomorrow.
My question is: what guarantee do we have that the huge libraries of the current formal mathematics projects in Agda, Coq or other languages will still be relevant or even "runnable" (for instance type-checkable) without having to resort to emulators and computer archaeology 10, 20, 50 or 100 years from now ?
10 years from now will Agda be backwards compatible enough to still recognise
current Agda files ?
Have there been any organised efforts to guarantee permanent backward compatibility for all future versions of Agda and Coq ? Or OCaml and Haskell ?
Perhaps the formal mathematics project should be carried out within a meta-programing language, a simpler more abstract framework (with a uniform syntax) comprehensible at once to logicians, mathematicians and programers and which can be converted automatically into the latest version of Agda or Coq ?
Clarence Lewis Protin `Writing "literate" .agda files in which code is mixed with an informal mathematical presentation of the formalisation seems the best option !`
There are software development practices akin to this. In the open-source projects that I have participated in (other than my own), comments are eschewed. There are variations on Literate Programming that some adopt, although it requires more mechanical support. In software, commentary helps differentiate what the software is for in contrast to what it is, establishing how the software is an interpretation of some conceptual model.
The risk used to justify the elimination of commentary is the problem of maintaining consistency between the commentary and the code as it is developed/maintained.
I have no objection to this approach, nevertheless. I find the commentary important for my own recollection of the purpose of some code and confirmation that the code accomplishes that.
I do not see how this methodology is a solution to the problem raised in this question though, unless it would be useful in maintaining the proof in the face of breaking changes up-level or down-level. Please say more about that.
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Assume we have a program with different instructions. Due to some limitations in the field, it is not possible to test all the instructions. Instead, assume we have tested 4 instructions and calculated their rank for a particular problem.
the rank of Instruction 1 = 0.52
the rank of Instruction 2 = 0.23
the rank of Instruction 3 = 0.41
the rank of Instruction 4 = 0.19
Then we calculated the similarity between the tested instructions using cosine similarity (after converting the instructions from text form to vectors- machine learning instruction embedding).
Question ... is it possible to create a mathematical formula considering the values of rank and the similarity between instructions, so that .... given an un-tested instruction ... is it possible to calculate, estimate, or predict the rank of the new un-tested instruction based on its similarity with a tested instruction?
For example, we measure the similarity between instruction 5 and instruction 1. Is it possible to calculate the rank of instruction 5 based on its similarity with instruction 1? is it possible to create a model or mathematical formula? if yes, then how?
As far as I understand your problem, you first need a mathematical relation between the instructions and rank. For instance, Rank x should correspond to some instruction value as y and vice versa; it means you require a mathematical function.
So there are various methods/tools to find a suitable (as accurate as you want) to find mathematical function based on given discrete values like curve fitting methods or the use of ML.
Further, Once you obtain the mathematical function, run your code a few times, and you will get a set for various combinations of (instruction, rank). These set values will work as the feedback for your derived function. Make changes based on the feedback, and you will get a much more accurate function.
I hope you are looking for the same.
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Hi frds,
Need a good weather probability calculator. Would like to calculate the probability of e.g. 10 degrees Celsius on a day above the average. Has anybody got good research/formulas?
Which distribution is assumed in the probability calculation? Normal one?
One possible approach is presented in the attached word document
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Hi all, I want to solve a system of simultaneous equations in which some equations are cubic and some are quadratic. How to solve such a system. The solution should consist of combinations of all solutions i.e., the positive as well as the negative solutions.
And this:
"Theoretically, such a system can be solved exactly; i.e. it can be determined whether the system has real solutions or not, and if it has, its solutions can be calculated exactly." is exactly what CAS-systems like Maple and Mathematica do. Good for Dudley J Benton to have a perpetual subscription. My experience is: the Maple syntax is simpler - and the sysmbolic solution of partial differential equations is better in Maple than in Mathematica. But for people wthout a license Mathematica is easier to rech - via wolframaplha.com. And there you need not to adhere to the syntax rules.
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I am thinking of the vector as a point in multidimensional space. The Mean would be the location of a vector point with the minimum squared distances from all of the other vector points in the sample. Similarly, the Median would be the location of the vector point with the minimum absolute distance from all the other vector points.
Conventional thinking would have me calculate the Mean vector as the vector formed from the arithmetic mean of all the vector elements. However, there is a problem with this method. If we are working with a set of unit vectors the result of this method would not be a unit vector. So conventional thinking would have me normalize the result into a unit vector. But how would that method apply to other, non-unit, vectors? Should we divide by the arithmetic mean of the vector magnitudes? When calculating the Median, should we divide by the median of the vector magnitudes?
Do these methods produce a result that is mathematically correct? If not, what is the correct method?
For vectors X1=[x1,1;x2,1;..,xn,1]; X2=[x1,2;x2,2;..,xn,2];,.., Xn=[x1,n;x2,n;..,xn,n]
M=[m1,m2,..mn] - vector median,
where
m1=med(x1,1; x2,1;..,xn,1)
m2=med(x1,2; x2,2;..,xn,2)
- - - - - - - - - - - - -
mn=med(x1,n; x2,n;..,xn,n)
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Any idea why the solution of the attached equation is always zero at r=0? It seems simple at first look, however, when you start solving, you will see a black hole-like sink which makes the solution zero at r=0 (should not be). I used the variable separation method, I will be happy if you suggest another method or discuss the reasons.
I also attached the graph of the solution, showing the black hole-like sink.
Thanks
I did give a physical explanation for why your boundary condition enforces the function f to become zero at r=0. In at least one physical interpretation, it models a system with infinite emission/absorption rate at r=0. This forces the temperature at this point to immediately become equal to the environmental temperature. In this interpretation f is (proportional to) the difference between body and environment temperatures. When you define a physcally unreasonable it is only fair that it provides you with physically unreasonable results ;-D
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I have no mathematical experience and no statistician to help me.
Thank you, Anton Vrdoljak.
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Is it possible to decompose a conditional probability with three or more elements (i.e. events) into conditional probability of only two elements or the marginal probability of one element? Knowing this decomposition, it would help to solve higher order Markov Chain mathematically. I also know that this decomposition can be solved if we add assumption of conditional independent.
To make it concrete here is a negative example:
P(c│a,b)=(P(a,b│c)∙P(c))/(P(a│b)∙P(b) ).
Notice that the RHS still contains a conditional probability with three elements P(a,b│c).
Assuming conditional independent on c, we have P(a,b│c)=P(a│c)∙P(b│c). Thus, the conditional probability decomposition becomes
P(c│a,b)≅(P(a│c)∙P(b│c)∙P(c))/(P(a│b)∙P(b) )
My question is whether this type of conditional probability decomposition into one or two element is possible without making assumption. If it is really unsolvable problem, then at least we know that the assumption of conditional independent is a must.
For my opinion we can use any product formulas only under condition of independence. For example the formula that you used P(a,b│c)=P(a│c)∙P(b│c) is valid if a and b are independent each from other. Both may be dependent from c. But it can be the case of so called "false dependence". For example a is the usage of energy, b is sale of warm clothes, c is decreasing of tempetature.
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During the lecture, the lecturer mentioned the properties of Frequentist. As following
Unbiasedness is only one of the frequentist properties — arguably, the most compelling from a frequentist perspective and possibly one of the easiest to verify empirically (and, often, analytically).
There are however many others, including:
1. Bias-variance trade-off: we would consider as optimal an estimator with little (or no) bias; but we would also value ones with small variance (i.e. more precision in the estimate), So when choosing between two estimators, we may prefer one with very little bias and small variance to one that is unbiased but with large variance;
2. Consistency: we would like an estimator to become more and more precise and less and less biased as we collect more data (technically, when n → ∞).
3. Efficiency: as the sample size incrases indefinitely (n → ∞), we expect an estimator to become increasingly precise (i.e. its variance to reduce to 0, in the limit).
Why Frequentist has these kinds of properties and can we prove it? I think these properties can be applied to many other statistical approach.
Sorry, Jianhing. But I think you have misunderstood something in the lecture. Frequentist statistics, which is an interpretation of probability to be assigned on the basis of many random experiments.
In this setting, on designs functions of the data (also called statistics) which estimate certain quantities from data. For example, the probability p of a coin to land heads is given from n independent trials with the same coin and just counting the fraction of heads. This is then an estimator for the parameter p.
Each estimator should have desirable properties, as unbiasedness, consistency, efficiency and low variance and so on. Not every estimator has these properties. But, in principle one can proof, whether a given estimator has these properties.
So, it is not a characteristics of frequentist statistics, but a property of an individual estimator based on frequentist statistics.
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Provide me the detail mathematical calculation for the measurement of uranium, thorium and potassium with their daughter progenies.
The solution is not a mathematical formula!
The question can be approached by two ways:
a) experimental: prepare homogenous standards having the same density and geometry as your samples, #1 material with low K,Th,U content, #2 same as #1 with known amount of K added, #3 same as #1 with known amount of Th added ,and #4 same as #1 with known amount of U added.
From the differences between measurements #N-#1 you may deduce the contribution of each of the three elements to the spectrum and, more specifically, the contribution of each of them to three regions of interest corresponding to strong peaks of each element, usually 1.46 MeV for 40K, 2.61 MeV for Tl208 (progeny of Th) and 609 keV for Bi214 (progeny of U), assuming secular equilibrium in Th and U families, or at least the same disequilibrium conditions in sample and standards.
It is then possible to calculate a matrix relating the measurements in the 3 ROIs to the three activities.
b) Monte Carlo simulation. The NaI detector is usually quite simple and can be simulated with a good accuracy. Experimental measurements are still necessary to evaluate the gaussian broadening of the peaks at the different energies, and an experimental validation of the MC model is always desirable.
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Hello,
For correlation analysis between body composition variables and blood hormone levels,
I have data from two different blood analysis methods but the same units; ECLIA & CLIA.
I wonder if there is any statistical and mathematical error when I run correlation analysis using the data together.
If it cannot,
Is there any suggestion for using these data together for statistical analysis?
Thank you very much.
If the methods are different, it is likely that there is no correlation ...
However, it would help a lot to know the datasets and the processing you say you have done.
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Mathematics is a subject most pupils love to hate; how did your journey into the world of mathematics proper begin?
My predisposition to mull with numbers and mathematical equations consistently, even though I do not specialize in the math field as a professional, is due to having FUN filled mentors early in life. They were so creative to attach images and anecdotes to math problems that my sense of wonder and fun was constantly tickled as I trundle along mathematical mines and problems. Missing the correct answer was not occasion for embarrassment but for more opportunities to discover funny and creative ways to approach math problems with new, innovative, and fun-filled attempts. My mentors showed me the short-cut methods, the winding methods, and the funny but sure fire methods. I do not believe I ever hated math. Math is FUN!
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Famous mathematicians are failing each day to prove the Riemann's Hypothesis even if Clay Mathematics Institute proposes a prize of One Million Dollars for the proof.
The proof of Riemann's Hypothesis would allow us to understand better the distribution of prime numbers between all numbers and would also allow its official application in Quantics. However, many famous scientists still refuse the use of Riemann's Hypothesis in Quantics as I read in an article of Quanta Magazine.
Why is this Hypothesis so difficult to prove? And is the Zeta extension really useful for Physics and especially for Quantics ? Are Quantics scientists using the wrong mathematical tools when applying Riemann's Hypothesis ? Is Riemann's Hypothesis announcing "the schism" between abstract mathematics and Physics ? Can anyone propose a disproof of Riemann's Hypothesis based on Physics facts?
Here is the link to the article of Natalie Wolchover:
The zeros of the Riemann zeta function can also be caused by the use of rearrangements when trying to find an image by the extension since the Lévy–Steinitz theorem can happen when fixing a and b.
Suppositions or axioms should be made before trying to use the extension depending on the scientific field where it is demanded, and we should be sure if all the possible methods (rearrangements of series terms) can give the same image for a known s=a+ib.
You should also know that the Lévy–Steinitz theorem was formulated in 1905 and 1913, whereas, the Riemann's Hypothesis was formulated in 1859. This means that Riemann who died in 1866 and even the famous Euler never knew the Lévy–Steinitz theorem.
I thought it would be better to type my work. Here is a link to the acceptable version of the article : https://www.researchgate.net/publication/364357359_A_contradiction_in_the_formula_of_Poisson_which_destroys_Riemann's_Hypothesis
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Everybody is eager to see the New winner of the Millenium Prize. Please share all your incomplete works about the Millenium Prize problems of Clay Mathematics Institute in order to collaborate for the solutions.
I am actually using the different nabla operator which I demonstrated mathematically in my published work: " A thesis about Newtonian mechanics rotations and about differential operators ".
This demonstrated differential tool enables to deal differently with the millenium problem about Navier-Stokes equation.
I also suggest that P=NP if the problem can be translated to a differential equation that has a solution. If your lucky friend finds and gives you an easy solution, than that solution leads directly to the general solution of the differential equation.
I will be waiting for your collaborations.
I thought it would be better to type my work. Here is a link to the acceptable version of the article : https://www.researchgate.net/publication/364357359_A_contradiction_in_the_formula_of_Poisson_which_destroys_Riemann's_Hypothesis
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Say I have a satellite image of known dimensions. I also know the size of each pixel. The coordinates of some pixels are given to me, but not all. How can I calculate the coordinates for each pixel, using the known coordinates?
Thank you.
Therefore, you have 20x20 = 400 control points. If you do georeferencing in Qgis, you can use all control points or some of them, like every 5 Km (16-points). During resampling, all pixels have coordinates in the ground system.
If you do not do georeferencing (no resampling), then you could calculate the coordinates of unknown pixels by interpolation. Suppose a pixel size a [m], then in one km, you have p = 1000/a pixels, and therefore known coordinates have the first(x1,y1) and the last(x2,y2) pixel. The slope angle between the first and last pixel is:
s = arc-tan[(x2-x1)/(y2-y1)]. Therefore, a pixel of a distance d from the first pixel has coordinates x = x1 + d.sin(s) and y = y1 +d.cos(s). You can do either row of column interpolation or both and take the average.
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Physics is a game of looking at physical phenomena, analyzing how physical phenomena changes with a hypothetical and yet mathematical arrow of time in 3D space, namely by plotting that physical phenomena with a mathematical grid model (typically cartesian based) assuming that physical phenomena can be plotted with points, and then arriving at a theory describing that physical phenomenon and phenomena under examination. The success of those physical models (mathematical descriptions of physical phenomena) is predicting new phenomena by taking that mathematics and predicting how the math of one phenomenon can link with the math of another phenomenon without any prior research experience with that connection yet based on the presumption of the initial mathematical model of physical phenomena being undertaken.
Everyone in physics, professional and amateur, appears to be doing this.
Does anyone see a problem with that process, and if so what problems do you see?
Is the dimension of space, such as a point in space, a physical thing? Is the dimension of time, such as a moment in time, a physical thing? Can a moment in time and a point of space exist as dimensions in the absence of what is perceived as being physical?
Ricardo Simão Pereira Lopes , indeed, your approach is the approach of many:
Physics is a game of looking at physical phenomena, analyzing how physical phenomena changes with a hypothetical and yet mathematical arrow of time in 3D space, namely by plotting that physical phenomena with a mathematical grid model (typically cartesian based) assuming that physical phenomena can be plotted with points, and then arriving at a theory describing that physical phenomenon and phenomena under examination. The success of those physical models (mathematical descriptions of physical phenomena) is predicting new phenomena by taking that mathematics and predicting how the math of one phenomenon can link with the math of another phenomenon without any prior research experience with that connection yet based on the presumption of the initial mathematical model of physical phenomena being undertaken.
My question is if you see a problem there and if so why and if not why not.
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Hello Friends and Colleagues,
Can anyone suggest a mathematical book that helps me to build my own mathematical equations and functions? I want to convert real-life problems(natural sciences) into mathematical formulations.
Note that I have basic knowledge of mathematics.
For me the following book is very useful
Functional Equations and How to Solve Them (Problem Books in Mathematics)
Springer
Christopher G. Small
Year:
2006
Language:
English
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Plz share if yes . I want to know how to get patent in vedic maths.
WO 2017/037729 A1: Concurrent architecture of Vedic multiplier-an accelerator scheme for high speed computing
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Applying mathematical knowledge in research models: This question has been in my mind for a long time. Can advance mathematics and applied mathematics solve all the problems in modeling research? Especially the formula derivation in the theoretical model part, can the analysis conclusion be obtained through multiple derivations or other methods? You have also read some mathematics-related publications yourself, and you have to admire the mystery of mathematics.
Mathematics is essentially one of the professional tools of science, including for physicists.
Admire the tool... If the cook says "Miracle saucepan", then the food will not get better...
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didactics of mathematics
Students should be shown the application of mathematics from a practical point of view. On the other hand, it is necessary to respect the theoretical side of mathematics, which is not easy for everyone to learn.@Peter Kepp Rickardo Gomes
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Hello everyone,
I would like to know how to locate mathematically a damage on a blade.
Usually a frequency analysis of the blade and a comparison with a similar healthy one helps to determine a default or damage on a blade. However, how could someone locate that damage?
Hi fellow researcher,
I think the answer depends on what kind of equipment you have on your disposition and what is your purpose. The simpler way is to have a model blade and compare it to the blade you want to determine the integrity using the physical properties of the blade.
For example, if you have an accurate sound sensor and a device that produces an specific sound profile in the model blade you can use this device to produce a similar sound in the test blade. Comparing the Fourier decomposition of frequencies of the sound produced by the test blade will give you information of cracks and non-uniformity in density produced by the forging process or even if the material the blade was made is of quality or not.
You can do a similar approach with thermodynamics. you can heat Specific spots on the test blade. As cracked regions do not conduct heat as well as non-cracked regions you will observe anomalies in the heat map of the blade.
Notice you don't really have to calculate something, but just know what to expect with a model blade data.
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I'm struggling to understand the method followed in the following analysis. Can someone please explain how the author got the values of Δ_1 and K_1 that justify its analysis?
I have tried to isolate "Δ" and "K" by setting Equation (B8) equal to zero. but I have failed to get similar conditions.
P.S: I'm new to mathematical modelling, so I really need to understand what's going on here. Thanks
The RHS is a fraction, whose numerator and denominator are quadratic expressions in Δ. Therefore the fraction takes positive values when numerator and denominator are of the same sign...
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why to quantize a Hamilton-Jacobi theory with fractional derivatives?, what are the physical or mathematical advantages?
Also, Hamilton-Jacobi theory can be applied with not only fractional derivatives but also, definition of fractional derivatives and integrals on time scale Yazen Alawaideh
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How to people propose a new optimization algorithm. I mean what is the baseline? Is there any intuition or mathematical foundation behind it?
The question is too general. To generate the basic idea of the algorithm, you need to know the detailed statement of the problem. Typically, the process of developing an algorithm starts with the identification of your problem complexity class. If there is no evidence or clear feeling that the problem is NP-hard, then it is reasonable to try to develop a polynomial algorithm for solving it. Such algorithms are usually based on the use of specific properties of the problem. Sometimes it is possible to construct a polynomial algorithm based on the general scheme of dynamic programming, taking into account the specific properties of the problem.
If the problem is known to be NP-hard, then branch-and-bound methods, dynamic programming, and their modifications often work well for a relatively small problem dimension. Sometimes it is possible to build a successful formulation of the problem in the form of an integer programming model, followed by the use of appropriate methods or ready-made software. For high-dimensional problems, you can either use well-known metaheuristics, or develop your own approximate algorithm. In the latter case, success is usually based on the use of the problem properties. As you can see, in any case, it is useful to start by studying the specific properties of your particular problem.
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When solving mathematical equations or system of equations there are things that are considerable; such as the Universe or domains...
Because, some equations may have no solutions or impossible to solve., at all. If a solution or some solutions exist for an equation or systems of equations, there are regions or intervals containing the solution(s). Such considerations may be important when applying numerical methods.
What are basins of attractions?
Dear, Tekle Gemechu basins of attraction comes from the dynamical system and chaos theory. It is related with systems behavior. There are several example of basins of attraction. Therefore, definition and examples of basins of attraction are given in scholarpedia. Below scholarpedia's link:
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The constants (G, h, c, e, me, kB), can be considered fundamental only if the SI units they are measured in (kg, m, s ...) are independent. However, if we assign numerical values to the SI units (kg = 15, m = -13, s = -30, A = 3, K = 20), then by matching the unit numbers, we can define (and solve) the least precise (CODATA 2014) constants (G, h, e, me, kB) in terms of the 3 most precise constants (c, μ0, R) ... (diagram #1). Officially this must be just a coincidence, but the precision is difficult to ignore.
We find further anomalies to equal precision when we combine the constants (G, h, c, e, me, kB) in combinations whereby the unit numerical value sums to 0 ... (diagram #2).
The methodology is introduced here
Is a simulation universe the best explanation for these anomalies?
Some general background to the physical constants.
Hi Hieram, youre welcome! Imho fun should be induced by fruitful scientific research supported by open commenting one other’s ideas (opposed to endless fruitless repeating discussions what presumingly not cannot ever workuntil it does) like iSpace („integer-Space„ or „complex-Space“ when treating the i as the one for a complex number) able to derive and decipher inter-relationships, dependencies and calculate exact arbitrary precision numerical values for most but all constants of nature.
Also recently a new true quantum geometric iSpace-IQ unit system has been developed, able to directly represent native quantum relations of contants while keeping strictly compatible to MKSA/SI system showing a single *time* based conversion factor, effective predicting quantization of time itself.
So - no - being a true long time Apple expert consultant i’d say we do not need to fear to be sued for (at least not in the foreseeable future ;-) ). And please all take the time to read thru the very short yet imho rreally convincing math of both of my newest papers to be found on my RG home.
Here is a link to RG summary of my iSpace project:
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I am aware of the facts that every totally bounded metric space is separable and a metric space is compact iff it is totally bounded and complete but I wanted to know, is every totally bounded metric space is locally compact or not. If not, then give an example of a metric space that is totally bounded but not locally compact.
Metric space A is said to be a totally bounded if every Cauchy sequence in A has convergent sub sequence
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What are the areas where mathematics are been applied medically.
Which type of mathematics? We use statistics in medical and biomedical research. We use artifial intelligance and use mathematical models in public health
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Does nature understand mathematics?
A connected question is -- How are theory, theorem, and truth related?
Theories and Theories of Truth | SpringerLink
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I am trying to model a business scenario mathematically for my research paper but I do not have the required skillset. What is a legitimate way to find and get help. Are there any online sources or paid services. Do I need to add the expert a co-author? What type of solutions exists.
I have many times served as an applied mathematician on a multi-disciplinary team, including, for instance, biologists, meteorologists, geologists, hydrologists, etc. The other team members possessed essential knowledge to the success of the project but not the math skills. This is good for you to recognize in the study of business because nobody knows everything. A diverse team can solve problems that a single individual cannot. I would have the biologists explain over and over again that part they understood (like fish behavior or metabolic needs) and I would create a model. Then we would run the model and ask, "Is it responding the way you expect it to?" One of these interesting projects considered production of peanut butter crackers and cheese crackers sold in vending machines manufactured on the same assembly line at a factory on the road from my house to the school. Walk over to the Mathematics Department and find a graduate student studying applied mathematics who is looking for a project. You can help each other.
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Why use metaheuristic algorithms when there are so many mathematical optimization tools available, like GAMS?
Ankur Maheshwari I agree with Ben Cardoen that a heuristic/partial search algorithm may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity where commercial solvers may struggle. But the key issue of heuristics is that they do not guarantee that a globally optimal solution can be found on some class of problems when compared with commercial solvers such as Ipopt, Cplex, Mosek, Gurobi,..., for NLP or LP or MILP or MINLP problems.
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1) What's the difference between SCILAB and MATLAB?
2) Which one would you recommend?
3) Which one is the most friendly user?
Hi Sunday Fadugba I have no experience with SCILAB (and very little with MATLAB). What I can recommend is using Mathematica (if you can afford it; or maybe you can use the free version on Raspberry Pi) or Julia (free). Hope it helps.
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Dear Colleagues, a recent trend in Fractional Calculus is in introducing more and more new fractional derivatives and integrals and considering classical equations and models with these operators. Thus, we have to think about and to answer questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. These and similar questions have remained mostly unanswered until now. To provide an independent platform for discussion of these trends in the current development of FC, the SI “Fractional Integrals and Derivatives: “True” versus “False””( https://www.mdpi.com/journal/mathematics/special_issues/Fractional_Integrals_Derivatives2021) has been initiated. In this SI, some important papers have been already published. However, you are welcome to share with the scientific community your viewpoint. Contributions to this SI devoted both to the new fractional integrals and derivatives and their justification and those containing constructive criticism of these concepts are welcome.
Best regards
Yuri Luchko
I like this new thinking. But for me it is difficult to say "true" or "false" since everyone has his own standard. I feel interested in the definition convenient both in the application and mathematical analysis.
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How can we analyze the propagation constant in slab waveguides? Is there a mathematical formula for this parameter?
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If interested you can send different articles from Piaget theory in the learning of mathematics through play.
I agree that it starts in Piaget's sensory-motor stage of play. Mary Reilly's Systems Explanation of play: Learning through play and the Third form of Information Processing theories mirror and expand on Piaget's Theory of play and learning.
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my article is about the relationship between playing and increasing intelligence via mathematics. this a longitudinal research which has done since 4 years ago until to year. it is a pre-test- post-test research with control group. results are wonderful. assessment tool in this research was Stanford-Binet test. I am following to a journal in grade Q1. I would be grateful if someone could help me.
Just based on the metrics I would suggest that you might have a look at:
Educational Studies in Mathematics https://www.springer.com/journal/10649 CiteScore 3.6 (SJR Q1 journal), Impact factor 2.853 (JCR Q2 journal)
ZDM – Mathematics Education https://www.springer.com/journal/11858 CiteScore 4.1 (SJR Q1 journal), Impact factor 2.481 (JCR Q2 journal)
Journal of mathematics teacher education https://www.springer.com/journal/10857 CiteScore 3.6 (SJR Q1 journal), Impact factor 1.786 (JCR Q2 journal)
Research in Mathematics Education https://www.tandfonline.com/journals/rrme20 CiteScore 3.4 (SJR Q1 journal), ESCI indexed (so no impact factor and Q ranking (yet))
Best regards.
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Chaos Theory, Chaotic dynamics
Dear Shireen,
There are data-driven and parametric that you can utilize to detect chaos. If the system is well-defined, a good starting point can be Lyapunov Exponent and Poincare map. If you have only output of the system then you need data-driven methods like 1/0 test or entropy-based methods.
Regards
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If any mathematical equations for coupling of pmsm and pmsg in matlab?
coupling equations available in ODEs and also built-on ode45, ode15, ect code in matlab.
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A study by Po-Shen Loh shows that quadratic equations can be solved using a clever trick that reduces guessing and cramming formula. Kindly follow this link to see examples of quadratic equations solve by Po-Shen Loh https://www.youtube.com/results?search_query=po+shen+loh+quadratic .
Could this idea be applied in class? if so, could it be generalized for other topics in mathematics?
By practical applications
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Can anyone please confirm whether there exists an explicit mathematical relationship between the gravitational instability growth rate and the corresponding structure (star) formation rate in molecular clouds?
Thanks a lot, dear Javad Fardaei, for the article
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I have formulated the mathematical equation of the vibration problem. The resulting equation is coupled nonlinear differential equation of 2nd order ODE. Please, anyone, suggest to me how to solve it using MATLAB.
Dear Sandip,
to answer your question, I agree with Abdelghani: you have 1) to transform the 2nd order equations into 1st order ones and then 2) to use a MATLAB ode solver to numerically solve the resulting 1st order system.
To do step 1), you have to introduce new variables that correspond to first derivatives. For instance, let us say that you have a system of two 2nd order ODEs in x=x(t) and y=y(t), e.g. x''=f(t,x,y,x',y') and y''=g(t,x,y,x',y'). Then you can introduce two dummy variables X=x' and Y=y' (for example) and get a system of four 1st order ODEs: x'=X, X'=x''=f(...), y'=Y, Y'=y''=g(...).
Then, in order to apply step 2), you have to define a variable vector, say v=[x,X,y,Y], and a function, say myFun, that defines the system. In this case:
function vder = myFun(t,v)
vder(1)=v(2); % this equation corresponds to x'=X
vder(2)=f( t, v(1), v(3), v(2), v(4) ); % you should actually write your original equation for x''=X'=...
...etc...
end
Then, choose an ODE solver (for example ode45) and solve the system by using the basic command [t,v] = ode45(@myFun,tspan,v0); where tspan is an interval for the independent variable (e.g. tspan=[0,10]) and v0 is a vector containing the initial values for x, X=x', y, and Y=y'. So please notice that you must provide initial values for the first derivatives!
You can find more details about all this stuff here: https://www.mathworks.com/help/matlab/math/choose-an-ode-solver.html
Hope this helps! :-)
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I am working on RIS aided communication. Whichever paper I go though, they cook up some complicated mathematics specially optimization problem, which seems to be unsolvable at first. But, then I see they are using some techniques which I have never seen anywhere. Can anyone from wireless comm background tell me, how you people proceed and get those sort of maths?
Optimization is a broad field of mathematics and not some mysterious quackery. I am not surprised that someone from another field entirely (wireless communications) might not be familiar with these topics. This is why I stress the importance of multi-discipline teams. Nobody knows everything. If you get smart people from different fields together in the same room to discuss a problem, you may find some clever solutions that any one person alone would never come up with.
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Hi!
I'm currently working on a Data Science project for optimizing the prices of the products one of the biggest supermarket chains in Mexico.
One of the things that we are working on, is finding the price elasticity of demand of such products. What we usually do, is that, apart from fitting an XGBoost model for predicting sales, we fit a linear regression, and we get the elasticity from the coefficient corresponding to the price (the slope).
However, it is abvious that linear regression is sometimes a poor fit for the data, not to mention that the execution times are way longer since it requires to run separately XGBoost and LR (which is not good considering that there are thousands of products to model).
Because of this, it ocurred to me that we could use numerical differentiation for finding the price elasticity. At last, calculating a numerical derivative is way faster than fitting another model.
However, I'm not sure if this is mathematically correct, since the data does not come from a function.
So the question would be, is this mathematically correct? Does it make sense?
From my experience, I would not use a linear predictor for elasticity. I know your question is asking about mathematically correct solutions but I don't think that's your issue. I would probably use logistic regression as a first choice.
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Dear colleagues,
I am researching in a topic related to philosophy and teaching methods. Please, could you point out me if are there any sources on dialectics or contradiction in mathematics education?
Regards
An activity theory perspective on contradictions in flipped mathematics classrooms at the university level, Helge Fredriksen and Said Hadjerrouit, 520-541, 2019
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Please look at the text of the section on random walk from page 9 to formula 4.7, where you will find mathematical calculations justifying the probabilistic interpretation of the Riemann zeta function.
If the distribution of the zeros of the Riemann zeta function is implicit in your question, then you may find the following paper exciting:
Regards,
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I will be glad if researchers and professors answer my question with mathematical formulas or explanations. Thank you so much.
Hi, it should be taken into account that it is actually 'stress' doing the deformation for us. So when you use a roll with a smaller radius, the contact area between the roll and the sheet/foil is also smaller, increasing the stress.
Stress = Force / Area
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I can't understand why each time we divide by the mass of oxidized NH4-N and multiply by the mass of treated NH4-N.
Look at the attached screenshot search and I think your question is answered if I understand you. Best wishes David Booth
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How can we mathematically calculate the critical thickness of polycrystalline(Sputtering) grown thin?
Thank you, Dr. Len
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Hello? Good evening, I would like to ask if there is a questionnaire aligned to the set of indicators on Mathematical Competence given by Sir Turner?
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Is multiverse a differential of possibility, a gradient of cross universe space time planes.
Do multiverses branch or all have separate beginnings.
Are multiverses different mathematical constants or is it different potentials.
How can we progress to a mathematical model of multiverse theory.
First we need a mathematical model of the universe and then we need to generalise it for the multiverse. Is this quantum physical, does this take into account the electromagnetic generation of mass and gravity in a recursive relationship?
Does Arc Length calculus change our notion of frequencies and therefor electromagnetism?
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I want to understand the mathematics of fluorescence process in terms of excitation and emission wavelengths. I want to develop a general mathematical model with certain specific parameters and without employing a spectrometer, I want to see the emission spectrum mathematically.
One can construct simple model (Shifted Harmonic Oscillator model) and derive tractable equations to obtain absorption and emission spectra.
1. Absorption and Emission Lite: Assume ground and excited states are shifted classical Harmonic Oscillator. Ground state |g> energy: Eg(R) = 1/2 ω2R2 & Excited state |e> energy: Ee(R) = 1/2 ω2(R - R0)2 + ΔE. Treating R classically one gets absorption (Ia) and emmision (Ie) spectra as:
Ia(e) = exp[(e-ΔE)2/2σ2] Ie(e) = exp[(E-ΔE + ω2R02)2/2σ2] (Arbitrary Units)
absorption and emission is peaked at different energies and the difference is ω2R02 --- stokes shift, see: https://en.wikipedia.org/wiki/Stokes_shift
σ is the linewidth caused by molecules coupling to environment (Homogeneous Broadening) caused because individual molecules see slightly different environment, e.g. ΔE (Inhomogeneous Broadening) is different for different molecule.
2. Absorption and Emission Pro: Same as 1, but treat R quantum mechanically,
this gives |g>|v0> , |g>|v1> ... |g>|vn> states and |g>|v0'> , |g>|v1'> ... |g>|vn'> where |vn> is nth vibrational state centered around 0 and |vn'> nth vibrational state centered around R0.
• Energy of |g>|vn> --> <vn|<g| H |g>|vn> = (n + 1/2)ℏω and
• Energy of |g>|vn> --> <vn'|<e| H |e>|vn'> = (n + 1/2)ℏω + ΔE
With this we write the absorption at T = 0K ( or ℏω >> kT)
Ia(e) = ∑n |<vn'|v0>|2 exp[(e-ΔE - nℏω)2/2σ2]
= ∑n (1/n!) * (ωR02/2)n exp[-(ωR02/2)2] exp[(e-ΔE - nℏω)2/2σ2]
Ie(e) = ∑n |<v0'|vn>|2 exp[(e-ΔE + nℏω)2/2σ2]
= ∑n (1/n!) * (ωR02/2)n exp[-(ωR02/2)2] exp[(e-ΔE + nℏω)2/2σ2]
|<v0'|vn>|2 are Franck-Condon factor,
|<v0'|vn>|2 = |<vn'|v0>|2 = (1/n!) * (ωR02/2)n exp[-(ωR02/2)2].
3. Absorption and Emission Pro Max: Same as 2 but at finite temperature T. Assuming instant thermalization --> states are population according to Bolzmann distribution,
Ia(e) = ∑mn |<vn'|vm>|2 exp[(e-ΔE - nℏω)2/2σ2] * Pm
= mn |<vn'|vm>|2 exp[(e-ΔE - nℏω)2/2σ2] * (exp[-βmℏω] /∑kexp[-βkℏω])
= ∑mn (1/n!) * (ωR02/2)n exp[-(ωR02/2)2] exp[(e-ΔE - nℏω)2/2σ2] * (exp[-βmℏω] /∑kexp[-βkℏω])
Ie(e) = ∑mn (1/n!) * (ωR02/2)n exp[-(ωR02/2)2] exp[(e-ΔE + nℏω)2/2σ2] * (exp[-βmℏω] /∑kexp[-βkℏω])
Pm = (exp[-βmℏω] /∑kexp[-βkℏω])
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Hello, this is my first post on this site. I'm an undergraduate student doing some Raman spectroscopy of CVD-grown graphene strained on silicon dioxide nanospheres. I notice that D and G' peaks show up in some measurements. The transfer process of the graphene to the silicon dioxide nanosphere-coated silicon chips I would think is far from perfect, as in certainly interferes with the structure of the graphene as there are rips and tears across the sample, as well as impurities and other things. You do however have "pristine" regions that only show G and 2D peaks.
On a loosely related tangent, I'm interested in how the molecular symmetry of graphene plays a role in its Raman spectra, and how that can be expressed mathematically. I wonder if perhaps the mathematical description of graphene in terms of group theory can possibly help explain the redshifts that occur in strained graphene versus unstrained graphene. If anyone has some advice or things to read about that, please let me know!
In perfect graphene, the D-peaks are by symmetry not Raman active. ideal graphene should only show the single G-peak. However, when there is anything disturbing the symmetry and structure, the condition is relaxed and the D-peaks become visible. Hence, their name D for "defect" peaks. Based on the relation of peak intensity or the integrated intensity below the modes, the quality of graphene layers can be quantified.
There are numerous reviews on Raman spectroscopy in graphene, explaining which information can be extracted and how they can be extracted from analyzing the spectra.
You should be able to quickly find numerous more articles.
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I have myself tried using the basic method but including incomplete ionization to figure out the depletion width however I failed miserably because of many mathematical roadblocks. I was wondering if this had been done in the literature before and I just missed it.
If anyone can help me in this regard then I would be very grateful. Thanks.
If you can send me a sample data file, I can have a look at it...
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please is there any mathematical function that relates the SMD (D32) to the mean diameter (D50)? I actually understand what each of them represent.
thanks
Thanks for this
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I am primarily interested in 2-player combinatorial games with perfect information. Useful wiki links are below.
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Is there a way to model the influence of pH on the electroosmotic EDL potential and velocity field inside the flat microchannel mathematically?
Thank you Masuduzzaman.
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How could one increase data values from weekly to daily observations using mathematical algorithm for interpolation?
Hello Nasiru,
What's the reason for wanting these values? That may have more to do with what sort of approach, if any, might make sense.
At first glance, doing this doesn't sound like a good idea to me. Among the reasons:
Any method for taking adjacent weekly values and inserting some estimate for the 6 six "missing" daily values will only bias the estimates of day-to-day variance in scores/values as well as increase the serial correlation across a lag from 1 to 6 days. As well, the presumption of a (perfectly) predictable day to day change is unlikely to be realized in actual measurements.
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The mathematical representation of both equations is same.