Part 2 Mathematics Questions 26-50 Answers
Science topics: Mathematics
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Mathematics - Science topic
Mathematics, Pure and Applied Math
Questions related to Mathematics
Which programming language is best for Mathematical simulation- Matlab or Fortran?
I mean something strictly mathematical and not an algorithmic routine. For example The function f(n) produces 1,2,0,0,0,5,0,1,3,8,9,0,0, ... I need the function f(n) remove the zeros and produces: 1, 2, 5, 1, 3, 8, 9, ...
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Remark: in the case m=0 (i.e. when all fi=0), the transformed list is empty.
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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?
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My final &last paper entitled An elementary proof for Fermat's Last Theorem using Ramanujan-Nagell equation has been published in Turkish Journal of Computer and Mathematics Education Volume 12 No14 ( 2021) pp3631-3643
Why does the absorbance vary in a linear fashion, whereas the transmittance varies in an exponential fashion? Can this be explained mathematically/intuitively or are these results based on experimentation?
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Actually, absorbance changes neither linearly with length of the lightpath nor with concentration, just in a first approximation, which becomes exact, absurd as it may sound, in the limit of vanishing absorption. The reason why transmittance decays approximately exponentially is that the decrease of intensity is proportional to the intensity itself. Why only approximately? For details see this review:
how can i prove that mathematical proof about feasible solution is found at boundary point? also want to ask about why feasible region must be composed of a convex set. is there any mathematical proof about this?
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A feasible solution is any point in the feasible set, both interior points as well as boundary points can be feasible solutions, it depends on your optimization problem. For a Linear programming problem, the feasible region is a polyhedral set, which can have extreme directions and extreme points, if the polyhedron above is a bounded set, it can have a finite number of extreme points only. By representation theorem, for a bounded polyhedral set, any point in the set can be expressed as a convex combination of the extreme points of the set: substitute this expression in the expression for cost function as f= cT*x, cT is transpose of vector c, the cost vector. you can see that this linear form is bounded both above and below, the lower bound is fmin which is associated with the extreme point corresponding to lowest value of the objective function and upper bounded by fmax, which is associatef with that extreme point corresponding to the largest value of the objective function. A feasible region need not always be a convex set, but optimization of convex/concave functions over convex set, is called convex programming , it is mathematically very well studied and has many interesting features associated with it.
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Well the Cauchy distribution has all moments equal infinity. You might be interested in the attached Google search which is about robust Statisical methods but I would probably try the first ref in the second search first. Good luck if you do. David Booth
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At this moment, I have a nonlinear dataset that has X and Y-axis values. I want to come up with a nonlinear equation that represents the most values of this function without using a moving average filter.
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Without an idea of what the dataset represents, it doesn't make sense to look for an equation that could represent the data, there are many of them.
I have a problem. Measurements show the opposite of what convention assumes. It occurred in geotechnics, but could affect all material modelling branches. I tested soil specimens. Convention interprets materials as things where deformation is created (output) and force is applied (input). So, our task is: decode how much deformation a certain loading (force) will generate. After 6 years of testing, I noticed the convention is misleading. Reaction force behaves as a function of deformation. Not the other way round. Stiffness hysteresis loop shape, size and position stabilizes within deformation amplitudes. You can control the shape, size and position of stiffness loops - using deformation amplitude. All applied deformation values - have finite answers, unlike the "infinite displacement" paradox... It's a big problem. All software is designed to model deformation as a function of force applied. But in reality, force (reaction) behaves as a function of deformation. It could be we are stuck in a paradigm, where deformation is modelled as a function of force. But in reality, the reaction force is a function of deformation. F=f(U) not U=f(F). The observations (empirical evidence) pointed me to an abandoned theory from 40 years ago (strain-space plasticity, by P. J. Yoder 1980). His theory seems to be not only compatible with the observed physical properties, but also GPU - parallel computation compatible (there were no GPU units in 80's... so "parallel spring systems" in FEM caught no one's attention) So, we have something that is both: 1. Potentially more physically correct 2. For the first time makes elasto-plastic FEM is super computer compatible. I am stuck building robots for industrial projects at the faculty. For tests which are meant to provide "quick profit" to faculty. "fundamental" research is not funded. Tried applying for radical research EU grant... the topic is way too radical for them. All observations were made in spare time. Evenings, weekends, at times - using life savings... I tried showing test results to renown experts. They become red in the face, angry, and say "I have not seen anything like it". After an hour of questions - they find no flaws in the testing machines. And.. Leave. Never to hear from again. The theory of P. J. Yoder was defended in public defenses multiple times in the 80's. It seems "mathematically equivalent". As in - proven able to do "the same" as convention does. Without anyone ever testing what such "reversal of coordinate space" (strain instead of stress envelopes) would imply regarding interpretation of material properties. No one found flaws in it "mathematically". Never proves it wrong. But... Forgot, ignored and abandoned. I tried asking industries for opinion too. Industry asks for code compatible with existing software (return of investment). And I alone can not code a full software package. Frankly, I would rather keep testing, try to prove my assumptions wrong. But the more I test, the more anomalies and paradoxes are observed, exposed and resolved on the topic.. What is the "antidote" in such situation? Tests showing convention wrong. Nobody find any mistakes. Which leads to silence and being ignored.
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Tomas Sabaliauskas congratz you have fallen into one of the hardest human error traps to disprove: it is the exact opposite of what everyone believes, you can still hear an example daily: the Sun rises in the East. Fire is oxygen combining with the candle or the wood not releasing magic. The old Fire-air and dephlogistication controversy. There are so many examples. But as Fatemeh Khozaei sort of suggests... can you patent this idea etc. to make some money? Stellan Gustafsson is right that you can get the message out via youtube videos but if you want some scientific acknowledgement I would start by a preprint, presentation, or poster uploaded here and obtaining a DOI number so that technically others can cite you, or at Academia.edu, or both. A great many people are unaware of the revolution that is Researchgate. Look at us, we have an Iranian researcher, two Northern Europeans, and an American collaborating with no paperwork. (no pay either) For the moment, Researchgate has a no censor policy, and is very similar to the early days of Wikipedia when that site delivered more extensive, better quality articles, and was trusted over than paid encyclopedias. Understand search engines can not scan Researchgate, so our articles are ranked by Algorithms and compared to other scientific sites. Google and Scholar (if your paper is cited) rank the corpus (collection of documents) here on a par with Taylor and Francis, Springer, Elsevier and others. I can prove it Query Google with these key phrases Microbial Outsourcing or Plasma Water Theory and to see how important Check out the number of results or pages indexed by Google. BTW The former is a preprint and the latter is only a presentation. Then, once your paper or presentation is on line you can try to promote your idea even on Wikipedia itself. I hope this is of some help to you and perhaps Stellan as well. Sincerely Professor Christopher G. Yukna ps Stellan you might peruse Rutherford Conjecture too
Hi everyone, I have encountered a trouble about Zernik index when studing Zernik polynomials. This problem is equivalent mathematically as follows, Assume n=0,1,2,... With each given n, let m=-n,-n+2,-n+4,...,n Define j=[n(n+2)+m]/2 With a given j, for example j=16, how to calculate n and m?
Hello Researchers, I was working to check the validity of a mathematical equation. In doing so I have obtained a large data set values >50,000 experimentally. As the mathematical equation gives only a single value I was wondering is there any way to compare that data set to mathematical equation. Based on that comparison I am willing to assign a constant that is when operated (+,-,x,/) to mathematical equation results in values justifying the experimental data set. The constant could be more than one as the range of the data set is quite large compared to empirically obtained values through a mathematical equation.
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Thanks for your reply I would look at cross validation methods and see what is appropriate for your situation. Best wishes, David Booth
Hello everyone, I have a basic mathematical question. I designed a controller that can guarantee that variable z can remain zero or bounded for all time. Where z=s-r. Frome being zero or boundedness property of z can I conclude that s and r are also bounded? Any help will be appreciated. Best Regards.
Knowing orthometric height, latitude, longitude of a point and reduced level, latitude, longitude of a second point, what's the mathematical expression to compute for the orthometric correction to be applied to the reduced level of the 2nd point to get its corresponding orthometric Height?
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Basically, The distance along the plumb line from the reference surface (Geoid) to the point determines the orthometric height. Ellipsoid - a smooth mathematical surface that looks like a squashed sphere and is used to represent the Earth's surface. Kind Regards Qamar Ul Islam
Currently the only proof of Fermat's Last Theorem is very complex and certainly not the proof that Fermat had in mind. I wonder if it is possible to use a method that drastically simplifies Wiles' theory, a theory that has received much honors from the entire mathematical community.
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There's some sort of myth that Fermat had a proof. While he did have a proof for certain special cases, the approach doesn't work for the general case. ``Simplicity" is a subjective notion, what's simple for one person, is complicated for another. The only things that matter are, whether the proof is technically correct and what are its consequences. That's what the proof by Wiles and Wiles-Taylor accomplishes. This isn't about music on period instruments, certain notiins just weren't known in Fermat's time.
Hi I wanna solve partial differential equation in terms of x and t (spatial and time), As I know one of the most useful way for solving pde is variable separation. well explained examples about mentioned way are wave equation, heat equation, diffusion.... wave equation is Utt=C^2 .Uxx in other word; derivatives of displacement to time, equals to derivatives of displacement to spatial multiplied by constant or vice versa. however my equation is not like that and derivatives are multiplied to each other.for example : Uxx=(1+Ux)*Utt Im wondering how to solve this equation. I will be thankful to hear any idea.
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Dear Alireza Akbari looks like your equation is a nonlinear PDE, there are tables for those: However I could not find yours, but don't worry, I tell you a trick we use in MHD. 1. You linearized it, i.e., you solve the PDE as a function of ei(k.r - omega t) 2. You get a complex polinom, but I don't see any parameters in your equation. 3. Anyway you can try an algebraic manipulator such as math or maple and find the roots. However, I find it strange that there is not a parameter, you need it to scan the complex solution. Best Regards.
How can we determine the mathematical property of a high-dimensional benchmark problem? Take, for example, the n-dimension Rosebrock equation. It is a unimodal equation with localized behaviour in 2 dimensions (We can tell this from the 2D plot). However, if the dimension is taken greater than 3, the equation shows multimodal behaviour. In short, the mathematical characteristic may change according to the dimension change. How can we determine the mathematical characteristic of an equation with different dimensions using a small number of analysis results obtained in the design space? The n-dimensional Rosebrock equation is shared from the link below.
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As a method, we thought that the effect of the parameters in the high-dimensional equation on the result could be examined and the results would be decided by plotting the two-dimensional results for the two most dominant variables. But we are not sure whether it will give correct results for every equation. We will analyze the results by conducting experiments. Other than that, do you have any other suggestions?
The French mathematician Pierre de Fermat (1601-1665), conjectured that the equation x^n +y^n =z^n has no solution in positive integers x, y and z if n is a positive integer >= 3. He wrote in the margin of his personal copy of Brachet's translation of Diophantus' Arithmetica:"I have discovered a truly marvellous demonstration of this proposition that this margin is too narrow to contain". Many researchers believe that Fermat does not find a demonstration of his proposition but some others think there is a proof and Fermat's claim seems right. The search of a solution of equation x^n + y^n =z^n are splitted in two directions. The first one is oriented to search a solution for a specific value of the exponent n and the second is more general, oriented to find a solution for any value of the exponent n. - Babylonian (570,495 BC) studied the equation x^2+y^2=z^2 and found the solution (3,4,5). - Arabic mathematician Al-Khazin studied the equation x^3+y^3=z^3 in the X century and his work mentioned in a philosophic book by Avicenne in the XI century. - A defective proof of FLT was given before 972 by the Arab Alkhodjandi - The Arab Mohamed Beha Eddin ben Alhossain (1547-1622) listed among the problems remaining unsolved from former times that to divide a cube into two cubes.(refer Image of Arabic manuscript from British Museum. Problem N4 Red color at line 8 from top). - Fermat (1601, 1665), Euler (1707, 1783) and Dirichlet (around 1825) solved the equation for n=3, 4 and 5. - In 1753, Leonhard Euler presented a proof for x^3+y^3=z^3 - Fermat found a proof of x^4 +y^4 =z^4 using his famous "infinite descente". This method combines proof by contradiction and proof by backward induction. - Dirichlet (in 1825) solved the equation x^5+y^5=z^5 . - Sophie Germain (in 1823) generalized the result of Dirichlet for prime p if 2p+1 is prime.. Let p prime, x^p +y^p =z^p has no solution in positive integers if 2p+1 is prime. - In XIX century E.Kummer continued the work of Gauss and innovated by using numbers of cyclotomic field and introduced the concept of "prime factor ideal". -Andrew Wiles, a professor at Princeton University, provided an indirect proof of Fermat's Conjecture in two articles published in the May 1995 issue of Annals of Mathematics. Andrew Wiles solved a high level problem in modular forms about elliptic curves and the consequence is a solution for FLT. Thanks to the results of Andrew Wiles, we know that Fermat's Last Theorem is true. I think he opens a space for mathematicians to search proofs for FLT comprehensible by a normal student in mathematics and may be to find new concepts or ideas. This result should imply a direct proof of FLT. In this paper, I would like to suggest a direct proof of FLT using mathematical concepts (Parity Even or Odd of Numbers, forward and backward Induction,....) and tools of the Fermat's era. This direct proof is comprehensible for a student in mathematics and lovers of mathematics.
What are the various fields
If I wanted to link algebra and topology in order to specialize in algebraic topology (mathematics), what researches would you recommend me to start reading with?
Ablation studies is quite common in machine learning literature, especially those on neural network and deep learning. When a new architecture or method is proposed, the authors often perform an ablation study where they remove sub-components of their methods that they feel are important one at a time, and study how the performance of said method changes, to learn the actual importance of each of the sub-components. I find this approach quite useful for research on optimization algorithms, specifically heuristical algorithms, whose properties may not be easy or even possible to prove mathematically. However, I have only seen ablation study or the term "ablation study" (might be called something else in other fields) in machine learning research. Would it be appropriate to include in papers on mathematical optimization algorithms or other areas of research in general?
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These papers might be useful, have a look: Kind Regards Qamar Ul Islam
Physical insight can suggest a principle which in turn leads to mathematical modeling. Example might include Newton extending the falling of an apple to towards Earth's center, to the Moon falling around the Earth, and Einstein's free falling elevator compared to the effect of gravity. But mathematics can also give a powerful clue to a physical principle. Well known examples include Planck's 1900 or so work on energy packets implying discontinuous amounts of energy, and Dirac's prediction of the positron. From 2005 to 2008 studying networks, I found that the mean path length successfully scaled a lexical network, and the mathematical result implied some physical principles about the distribution of energy in a network, which by a circuitous route led to the idea of the principle of dimensional capacity around 2019. History, consistent with my own experience, suggests physical principles can imply the mathematics and vice versa. Your views? Do you have examples of each?
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Physics requires mathematics to prove physical theories and all hypotheses, but mathematics does not need physics. You should know that applied mathematics is physics and that applied physics is engineering and applied engineering is technology.
Need a journal published in German language in the fields of mathematics and programming indexed in scoups Q1?
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First of all, you can try to find the list of Scopus journals of this year, and then you can choose the Germany Journal, therefore, you can make contact.
I am interested in test anxiety and would like to dig into the seminal meta-analysis by Ray Hembree published in 1988. Does anyone has access to the bibliography file containing the list of studies included in the meta-analysis? Any help would be greatly appreciated! Meta-analysis (I have access) Hembree, R. (1988). Correlates, Causes, Effects, and Treatment of Test Anxiety. In Review of Educational Research (Vol. 58, Issue 1). https://doi.org/10.3102/00346543058001047 Bibliography (I do not have access) Hembree, R. (1987). A bibliography of research on academic test anxiety. Adrian, MI: Adrian College, Department of Mathematics. (ERIC Document Reproduction Service No. ED 281 779)
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I've seen this study before
Was Heisenberg a Third-Rate Natural Philosopher because he denied the reality of micro-objects that cannot be tracked by humans? Has this misled physics for 100+ years? Surely, because we have created a whole civilization from the manipulations of electrons, especially digital electronics, then "LOOKING" at an object is NOT a requirement for existence.? Electrons interact with everything; so surely quite sufficient, eh? Heisesenberg was educated in the Classical Philosophy of Aristotelian Classicism in the archaic German Education system. He failed to think for himself, substituting a Platonic idealist view of mathematics, as being superior to our imaginative/operational view of reality.
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Pity; just be careful near high edges.
Some, including Morris Kline, in a book dealing with uncertainty in the basis of mathematics, indicates that eachh definition in mathematics references some other or other definitions; but that this leads backwards to undefined terms, which must be there. Perhaps there are other problems, that whatever you are defining may not even exist. Given the historical roots of math, it is not so clear. That math ought to be based also on other disciplines, counting, land measurement and so on. Hence that defenitions may better hinge on a descriptive intuitive account that earn us the work of looking up every other definition made in mathematics, This is a great barrier in understanding a lot of work these days, the huge number of definitions one must absorb. This would best guide our intuition to see if the results are logical. But the comon practice these days are far from it, strait into having to prove everything, and know everything about very narrow specialties, meaningless to most outsiders. What is your opinion? Should we reform this?
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Borrowing from Whitehead and Russel (Principia Mathematica, Vol. I): "...the definitions are no part of our subject, but are, strictly speaking, mere typographical conveniences. Practically, of course, if we introduced no definitions, our formulae would very soon become so lengthy as to be unmanageable; but theoretically, all definitions are superfluous."
The temptation in all the remodeling of the study plans to train teachers that I have experienced, faced with a new strong point of interest, has been to introduce a subject that caters for it. Thus, environmental education, for example, has been the curriculum of Spain for more than 25 years. Now the SDGs are the focus of attention, and the university is committed to developing them. the challenge is to do it from the established curricular subjects Educational mathematics is developed in three or four subjects of each training curriculum, and has to embrace achieving the teacher's competence development to teach school mathematics and also, the purpose of working on the SDG, how can we do it?
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Sorry Ariful, it is not about technology to assume the question, it is about how in the knowledge that you must work on the subject you teach, you are able to integrate the SDG-2030 with meaning for the subject, for the students and for the degree or degree they study !! Thanks for your interest
I post this publication The 3x + 1 Problem and its Generalizations by Jeffrey C. Lagarias The American Mathematical Monthly, Volume 92, 1985 - Issue 1, pp. 3 - 23 and the following introductory video by Veritasium (which in my view is extremely well-produced -- in particular the adopted graphics are superlative) as I consider the links between this mathematical problem (the Collatz Conjecture) to physics to be noteworthy.
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Dear Markus Kreer, A5 R A53 means A5 is subset of A53. A53= { 53, 160,80,40,20,10,5,16,8,4,2,1} A5= {5,16,8,4,2,1} R is a relation Set inclusion. In set inclusion relation, the minimum element is the element having minimum cardinality.
Here we discuss about one of the famous unsolved problems in mathematics, the Riemann hypothesis. We construct a vision from a student about this hypothesis, we ask a questions maybe it will give a help for researchers and scientist.
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Riemann zeta function P
roblem.pdf
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I put together a solution of the RH myself. While it can't be considered a complete proof while not vetted by experts, it presents various strong arguments and a real breakthrough, which is the inversion formula for Dirichlet series. Given any Dirichlet F(s), you know a(n) from F(s). Unfortunately, it's impossible to have an integral representation for a(n) usually, it's a Taylor power series. Please head to my page for the paper.
I am getting immersed in The Kervaire-Milnor Formula, where each term of which connects with a different field in mathematics: "The number of differential structures on the 4k − 1-dimensional sphere is given by a quantity that is the product of three quantities: Elementary factor × "Non − J Classes" × Numerator of B2k/2k". Information read in https://people.math.harvard.edu/~mazur/papers/slides.Bartlett.pdf My research is focused on how to connect the Turán moments and coefficients of Jensen polynomials for the entire function Xi as I have noticed some valuable results. I would like to count with more articles or information about the Bernoulli numbers visible in topics of topology which could involve the Turán moments and Jensen coefficients as well. Thanks in advance! Carlos
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Is B2K a bug of the millennium sort of thing? is that what you're asking?
Is there a free academic online resource that can be used to look up and reference basic concepts and theorems in mathematics? I am esentially looking for a mathematical analogue to the Stanford Encyclopedia of Philosophy or the APA dictionary of Psychology, that can be cited in thesis work and the like, and that is suitable for researchers from other fields. (So basic information, not cutting-edge detailed research or whole discussions on current questions.) That is, it should be trustworthy and considered "respectable" enough to be cited in academic work. This would rule out Wikipedia - even though its articles on the subject are usually trustworthy - or things like github. But it should also be a freely accessible source. (Alternatively, if publishing sites like Springer host something similar which is accessible through university subscriptions, that might work for my purpose, too.) I know you can often find the correct answers to basic questions by googling, but the issue is it's a bit difficult to gauge sources and content as a non-mathematician. Thanks in advance!
I want to compute Ornstein-Uhlenbeck models using the OUwie() function in R. For this I'm using a set of 100 phylogenetic trees, so that each tree goes into one OUwie model, resulting in 100 models. The output of the OUwie gives estimates for a trait optimum and according SE. Now I want to describe this output over all 100 trees. For the estimates it's easy to simply give the average value, but as the standard error depends on the sample, I'm not sure if I can give the mean, or if I should give a range or if there is another (mathematically correct) way to communicate the information I get out of these models.
I am a homeschooling parent who came to realize that my young children (in grades 1 and 3 this year) are into mathematics for its beauty. They are amazed at the fact that adding two whole numbers in any order yields the same result (commutativity), grouping when adding may be helpful (associativity), that for particular numbers n, x, and y, we have that n = x^2 = y^3: 1 = 1^2 = 1^3; 64 = 8^2 = 4^3, etc. They are mesmerized by the fact that 1 = 1, 3 = 1 + 2, 6 = 1 + 2 + 3, 10 = 1 + 2 + 3 + 4, ...; special sequences of numbers such as (in this case) triangular numbers (which they know as "step shapes"). They don't take for granted that 1n = n for any integer (I don't think they are ready for real numbers in general). They can see that division is akin to factoring: 12/4 = 3 because 3 and 4 are factors of 12 (though they are not too up on the vocabulary yet)... They can see informally that a - b = - (b - a): 8 - 5 = 3 implies that 5 - 8 = -3. I hope I am fortunate enough to see them through their entire grade school through high school learning. My concern is: why do educators/teachers and parents a debate so much about basic skills versus critical reasoning as if these things removed from context of the ACTUAL beautiful ideas in mathematics will pull school children into understanding mathematics any more than knowing words alone is enough to make a great writer? Why do we either (a) think that its all basic skills, or (b) word problems about so-called everyday stuff that are more social studies than mathematics? How about focusing on mathematics as subject like we do Language Arts? We don't reduced Language Arts to writing letters and business contracts in which grammar and syntax are important? We want children to enjoy the beauty of language; shouldn't we do the same with mathematics?
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As a Pre-K to 12 levels schoolteacher in Math & Sciences, I used project-based learning/teaching approaches in teaching the disciplines to all levels. The students work in groups as in cooperative learning in designing, building, and presenting their scientific models/projects they built from scraps that they brought in the classroom lab from home. The presentation/s included the application of the corresponding math concepts/formulas/theorems, etc. involved in their projects' development. For example, Pythagorean theorem, isosceles triangle, etc. are applied in calculating their projects measurements. Hope this makes sense to my readers.
We use ALEKS-PPL for placement and co-requisite support for our math courses. Our institution is interested in using something similar for English composition: placement + adaptive learning co-requisite support. What is out there for us to review?
With the purpose of, to find out the pedagogical skills mathematics teachers use to identify and address students mathematics anxiety
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The effect of pedagogical evaluation and content evaluation on mathematics teachers
While solving differential equations in Mathematica.
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By using NDSolve to solve the equations. To do that it suffices to write the equations in the format that NDSolve uses. And to do that it suffices to read the manual, that provides rexamples of how to use NDSolve. But how to do so doesn't depened on the particular equations.
we substitute y=e^rx while solving constant coefficient linear differential equation. what is the reason behind this?. is there any proof?
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Let us suppose that y = e^(r·x) is a solution for a homogeneous linear differential equation with constant coefficients, i.e. for equation (1) a·y'' + b·y' + c·y = 0 (a, b, c are real), where r is a parameter which we have to determine. By formal inclusion y = e^(r·x), y' = r·e^(r·x), y'' = (r^2)·e^(r·x) in (1) we have: (2) e^(r·x)(a·r^2 + b·r + c) = 0 OR a·r^2 + b·r + c = 0 what is characteristic polynomial for (1). Because each quadratic equation have real or complex solutions, it is obvious that there exists number r, real or complex, such that y = e^(r·x) is a particular solution for equation (1).
Good research is based on good relationship between the mentor or supervisor and the scholar. What are the qualities a supervisor or mentor must have to have a healthy and friendly environment in the laboratory?
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Please have look on our(Eminent Biosciences (EMBS)) collaborations.. and let me know if interested to associate with us Our recent publications In collaborations with industries and academia in India and world wide. Our Lab EMBS's Publication In collaboration with Universidad Tecnológica Metropolitana, Santiago, Chile. Publication Link: https://pubmed.ncbi.nlm.nih.gov/33397265/ Our Lab EMBS's Publication In collaboration with Moscow State University , Russia. Publication Link: https://pubmed.ncbi.nlm.nih.gov/32967475/ Our Lab EMBS's Publication In collaboration with Icahn Institute of Genomics and Multiscale Biology,, Mount Sinai Health System, Manhattan, NY, USA. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/29199918 Our Lab EMBS's Publication In collaboration with University of Missouri, St. Louis, MO, USA. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/30457050 Our Lab EMBS's Publication In collaboration with Virginia Commonwealth University, Richmond, Virginia, USA. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/27852211 Our Lab EMBS's Publication In collaboration with ICMR- NIN(National Institute of Nutrition), Hyderabad Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/23030611 Our Lab EMBS's Publication In collaboration with University of Minnesota Duluth, Duluth MN 55811 USA. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/27852211 Our Lab EMBS's Publication In collaboration with University of Yaounde I, PO Box 812, Yaoundé, Cameroon. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/30950335 Our Lab EMBS's Publication In collaboration with Federal University of Paraíba, João Pessoa, PB, Brazil. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/30693065 Our Lab EMBS's Publication In collaboration with collaboration with University of Yaoundé I, Yaoundé, Cameroon. Publication Link: https://pubmed.ncbi.nlm.nih.gov/31210847/ Our Lab EMBS's Publication In collaboration with University of the Basque Country UPV/EHU, 48080, Leioa, Spain. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/27852204 Our Lab EMBS's Publication In collaboration with King Saud University, Riyadh, Saudi Arabia. Publication Link: http://www.eurekaselect.com/135585 Our Lab EMBS's Publication In collaboration with NIPER , Hyderabad, India. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/29053759 Our Lab EMBS's Publication In collaboration with Alagappa University, Tamil Nadu, India. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/30950335 Our Lab EMBS's Publication In collaboration with Jawaharlal Nehru Technological University, Hyderabad , India. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/28472910 Our Lab EMBS's Publication In collaboration with C.S.I.R – CRISAT, Karaikudi, Tamil Nadu, India. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/30237676 Our Lab EMBS's Publication In collaboration with Karpagam academy of higher education, Eachinary, Coimbatore , Tamil Nadu, India. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/30237672 Our Lab EMBS's Publication In collaboration with Ballets Olaeta Kalea, 4, 48014 Bilbao, Bizkaia, Spain. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/29199918 Our Lab EMBS's Publication In collaboration with Hospital for Genetic Diseases, Osmania University, Hyderabad - 500 016, Telangana, India. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/28472910 Our Lab EMBS's Publication In collaboration with School of Ocean Science and Technology, Kerala University of Fisheries and Ocean Studies, Panangad-682 506, Cochin, India. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/27964704 Our Lab EMBS's Publication In collaboration with CODEWEL Nireekshana-ACET, Hyderabad, Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/26770024 Our Lab EMBS's Publication In collaboration with Bharathiyar University, Coimbatore-641046, Tamilnadu, India. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/27919211 Our Lab EMBS's Publication In collaboration with LPU University, Phagwara, Punjab, India. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/31030499 Our Lab EMBS's Publication In collaboration with Department of Bioinformatics, Kerala University, Kerala. Publication Link: http://www.eurekaselect.com/135585 Our Lab EMBS's Publication In collaboration with Gandhi Medical College and Osmania Medical College, Hyderabad 500 038, India. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/27450915 Our Lab EMBS's Publication In collaboration with National College (Affiliated to Bharathidasan University), Tiruchirapalli, 620 001 Tamil Nadu, India. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/27266485 Our Lab EMBS's Publication In collaboration with University of Calicut - 673635, Kerala, India. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/23030611 Our Lab EMBS's Publication In collaboration with NIPER, Hyderabad, India. ) Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/29053759 Our Lab EMBS's Publication In collaboration with King George's Medical University, (Erstwhile C.S.M. Medical University), Lucknow-226 003, India. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/25579575 Our Lab EMBS's Publication In collaboration with School of Chemical & Biotechnology, SASTRA University, Thanjavur, India Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/25579569 Our Lab EMBS's Publication In collaboration with Safi center for scientific research, Malappuram, Kerala, India. Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/30237672 Our Lab EMBS's Publication In collaboration with Dept of Genetics, Osmania University, Hyderabad Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/25248957 Our Lab EMBS's Publication In collaboration with Institute of Genetics and Hospital for Genetic Diseases, Osmania University, Hyderabad Publication Link: https://www.ncbi.nlm.nih.gov/pubmed/26229292 Sincerely, Dr. Anuraj Nayarisseri Principal Scientist & Director, Eminent Biosciences. Mob :+91 97522 95342
I want to draw a bifurcation diagram using either maple,mathematical or Matlab. an example is the attached file.
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How to draw bifurcation Diagram for predator-prey model using maple
In Mathematics, some proofs are not convincing since the assumption fails in the Proofs. If equality is Changed to "approximately equal to" then the Proof becomes more Perfect. But Uniqueness cannot be guaranteed. In Page number 291, Introduction to Real Analysis Fourth Edition authored by Bartle and Sherbert, the Proof of Uniqueness theorem is explained. That Proof is not perfect. Reason : Initially epsilon is assumed as positive and so not equal to zero. Before Conclusion of the Proof, epsilon is considered as zero and written as two limits are equal. The equality cannot hold since epsilon is not zero. Only the possibility to write is Two limits are approximately equal. Since Epsilon is arbitrary, never imply epsilon is zero. I hope the authors and other mathematicians will notice this error and will change in new editions.
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The proof is fine. It is based on the following fact: If x < epsilon for every positive epsilon, then x ≤ 0. This is easily proved by contradiction. Suppose that x < epsilon for every positive epsilon and that x is not less or equal than 0. Then x>0, hence for epsilon=x/2 it is epsilon>0 and epsilon<x; this contradicts the hypothesis.
A performance task? A standardized test? Or some other means? Why?
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A question that needs more thought
What research is there (if any), about gifted students frequently getting easy questions on academic tests/exams INCORRECT and harder more challenging ones CORRECT – particularly in mathematics? Does anyone have any empirical evidence as to why this might occur? Thank you.
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Sorry, I have no such research
is there any literature available on a kinetic study on the working of RO membrane with any software or simple mathematical simulation?
I'd love to see a rough sketch of how the task would go.
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Every integer can be expressed as a sum of three triangular numbers. Given two integers N=a+b+c and M=x+y+z , how to express the product N*M as a sum of three triangular numbers. Example: 11=0+1+10 and 13=0+3+10 ; the product 11*13=143=10+28+105 How to write the product N*M=F(a,b,c,x,y,z) +G(a,b,c,x,y,z) +H(a,b,c,x,y,z) as three triangular numbers?
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Abdolrahman Razani The question is not clear. Could you give an example? Best regards M.AZZEDINE
I have digged into a theory established by D. Loeb from University of Bordeaux, and found an interesting way to represent the things you have (classical set) and the things you do not have and might need, want, be ready to acquire (new forms of set with negative number of elements) This fits very well in the extension of the matrices of sets which I needed to develop, se why and how here (see references below). I would be thrilled to know if you have use cases where this model of classical sets of what you have, and new negative sets of what you do not have, my help. Please share your input! REF: [3] D. Loeb, Sets with a negative number of elements, Advances in Mathematics, 91 (1992), 64–74.https://core.ac.uk/download/pdf/82474206.pdf
In a mathematical analysis of piezoelectric models, we use the terms "the electrically open and short circuit case" for which we have some mathematical definition as well. What is the physical significance of these boundary conditions in making sensors and other devices?
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Hi Sonal Nirwal, The surface is metallized (short circuit (CC)): corresponds to the vanish of the electric potential. The surface is non-metallized (open circuit (CO)): corresponds to the vanish of the surface charge density.
It is well confirmed that the nonlinear evolution equation (NLEE) is widely used as a mathematical leading equation for describing the physical issues in many branches of physics. But it is very difficult to solve. Recently, many researchers have proposed various types of solution methods. Unfortunately, most of the solutions methods lead to additional free parameters. In my opinion, the solutions with additional free parameters of NLEEs are not useful for further verification in the laboratory. That is why my discussion topic is "What is the best solution method for nonlinear evolution equations?".
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Hi, The short answer to your question is: there isn't one that can be applied in general. There may be only "satisficing" ones, for specific nonlinear (discrete or continuous), stable or unstable, equilibrium or non-equilibrium, single or multiple structural equilibria containing dynamical equations (problems) you either formulate yourself, or come across having been formulated by others. There are significant methodological and epistemological questions involved in your question; as well as yet unsolved (possibly unresolvable) mathematical problems. Good luck!
Although Bashkar II, in his Siddhantha Shiromani, critisized a Buddhist school of astrology who held the Earth is moving, I have not seen any mention about texts on Buddhist astrological or mathematical tradition in recent studies. Vedic and Jain sources are well known. Are there any primary textual resources on Buddhist astrology/mathematics?
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Japanese Buddhist Astrology and Astral Magic Mikkyō and Sukuyōdō Kotyk, Jeffrey.Japanese Journal of Religious Studies ; Nagoya Vol. 45, Iss. 1, (2018): 37-86,214. DOI:10.18874/jjrs.45.1.2018.37-86
Dear experts and colleagues, Hello, all! I recently received a reviewer's comment stating that the proposed network measures of graph theoretical analyses could be correlated by mathematical definition. So I ran the correlational analyses and global efficiency, characteristic path length, mean clustering coefficient (global measures) showed correlated to each other. I understand that Global efficiency is inversely related to characteristic path length, but I am quite confused about how characteristic path length is inversely correlated with mean clustering coefficient, while mean clustering coefficient is positively correlated with global efficiency. Or does my data is wrongly suggested? Briefly explaining my study, it is a neurological study using MR images (diffusion tensor imaging) to explore the structural networks. Any feedback and discussion are welcomed here!
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Look the link, maybe useful. Regards, Shafagat
hi, I have to get an inverse matrix of a square matrix (20*20) on excel , to make sure that calculation is right I Knew that multiplying the matrix with its inverse should yields a unity matrix which have a diagonal of ones and other cells are zeros but when i multiply the matrix with the inverse i got the result is a matrix with adiagonal of ones but not all other cells are zeros (some have values like 1,2,etc ... is this ok or what often is my mistake? thanks in advance
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To Manal Lotfy: I will suggest to try to solve your example in another program. For example, you may try Wolfram|Alpha (a computational knowledge engine):
In classical times there was a concept of pure science that was produced entirely in the intellect. More recently sciences were developed by testing the intellectual product with empirical data. These sciences are not regarded as being pure. Mathematics, often regarded as pure science, has for most of history been based on postulates of geometry that could not be proven. Then came relativity and other geometries. In the past century there was considerable effort to reformulate mathematics on a firmer basis of conditional sets. Math is now regarded as being somewhat more pure than before, while producing two generations of graduating students in some countries who are not able to do simple arithmetic. Fortunately I had some excellent teachers who explained the two systems and why they were both needed. Other teachers displayed the Gödel's incompleteness theorems. In academic settings there seems to be a difference of opinions about whether or not math is a science, and whether or not it is pure. Is Mathematics A Science?
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Mathematics is a science built on a theoretical basis through the occurrence of a phenomenon or an experiment and taking the data of these phenomena and making them a model, an equation or a system, and then it is solved according to the theoretical foundations.
About two years ago, I have submitted a manuscript to a reputed journal. After a couple of months of the peer review process, the response was "major revision has been requested". I made the necessary adjustments and resubmitted it again. The Journal's editor responded that my manuscript requires minor revision. Well, the decision was <<"Revise for Editor Only'' he claimed that revision should be quick and it will not undergo the entire review process>>. Again, I made the required edits in order to make the manuscript acceptable for publication. Afterward, I resubmitted it. It is the day 120 and the status is "With Editor". In fact, I did send two emails to the editorial team to update the status. Their response to both emails was the same, saying that they contacted the editor to accelerate the process. Dear readers, I need to have a piece of advice: what to do as a next step? Thank you in advance, Bassam
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This kind of situation can be frustrating, however, I would encourage you to keep calm and focus on other things while awaiting the editor's decision. Sorry about this experience
How to mathematically interpret the formula Kb=Kf (1−Rw)
I am combining fish abundance and biomass data collected from five locations which have utilised different transect dimensions: 15 x 4 m (60 m2; from one location) 30 x 5 m (150 m2; from three locations) 50 x 4 m (200 m2; from one location) When pooling data collected from transects of differing sizes, should you standardise your data down (to the smallest dimensions) or up (to the largest)? Or in this case, perhaps standardise according to the most commonly used dimensions (30 x 5 m/150 m2)? To me it seems as though there would be no difference, but I was wondering if there was some sort of mathematical explanation for why one way might be preferable over the others?
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Hi Joseph, Hope it's not too late to help. Because there is a general trend of larger fish to move more, your chance of sampling larger individuals with larger transects is also higher. If you scale down, you will be implicitly assuming that fish density wouldn't change, which may be inaccurate for very large and rare fishes, i.e., if you found 1 giant grouper on a 200m2 transect, would you really expect to find half a grouper on a 100m2 one? Scaling up brings the same assumption of fish density not changing, but it may be more acceptable because smaller fish tend to move less and be more homogeneously distributed. You would still have bias for small and rare species, but because the contribution of these to biomass should be negligible, the problem would dissolve away. Standardising to a mean dimension may bring both issues together, but may also mean that both of these biases are reduced. At the end of the day, it's about what you're willing to assume about fish distributions. One way of dealing with this is rescaling your data down or to a mid-dimension by subsampling your community based on the density of specific phases/types of fish. That's what I do in this paper: This, in essence, allows you to carry over uncertainty in density estimates to your further analyses, resulting in more 'messy' data, but in conservative estimates. Cheers, Renato
the VPL formula can be given here as, f(P)=sum((a+b*P+c*P^2)+abs(e*sin(f(Pmin-P)))) Can anyone please explain if the value from the term (Pmin-P) in the above formula is in degrees or radians?
Hi everyone, In engineering design, there are usually only a few data points or low order moments, so it is meaningful to fit a relatively accurate probability density function to guide engineering design. What are the methods of fitting probability density functions through small amounts of data or low order statistical moments? Best regards Tao Wang
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Good explanation is performed by Chao Dang, Best regards
Hello. I want to ask how can I translate weightages of "yes" or "no" of a criterion in terms of numbers in AHP calculations? for examples, my goal is to select most suitable construction material vendor (Alternative) according to the set criteria including "ASTM Standards", with 4 other criteria. This criterion means "Is the material vendor giving the material according to the Construction Standard ASTM, or not?" So the answer given to this by the alternative (vendor) would be a "Yes" or a "No", but not a value. First, I've sent a questionnaire to the experts to give me pair wise comparison weightages for one criteria vs the other. And I've got great response with consistency of 0.9. Acceptable! But when I ask the vendors to provide their responses, they put numerical values to the first four criteria, and I find the comparison matrix for these vendors (alternatives) for each criteria using simple maths division (value of one vendor divided by second vendor). It gives me the exact zero consistency, because I've found the alternatives weightages using exact math comparison. But I get numerical values of weightages to find ranks, so it works fine for me. But when it comes to the 5th criterion (ASTM Standards), the responses are in "Yes" or "No" terms! My question is that what numerical value should I give to a Yes and a No so that I can get their comparison by dividing with each other? for instance, if I use Yes =1 and No = 0, the system hangs because anything divided by zero gives an infinity answer, and it doesn't proceed further. If I want to use a scale of 1 to 9, saying Yes = 9, and No = 1, it gives me good results. But I've no reason to use 1 or 9, for it could be any numerical value say 1000 for Yes, and 1 for No. Please suggest me a reasonable value with a citation if possible. Thanks in advance.
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Dear Usman Very interesting your question. The problem lies in the fact that in AHP you determine artificial values, but if you use Yes or Nor, or 1 and 0, these are not only objective values but with only two possible answers Coincidentally, less than a week ago, another colleague put the same question, something that I had not seen in years This is one of the 'beauties' of AHP, so elemental a method, that does not allow for modelling frequently incidents like this. In other systems, you simply put 1 and 0 respectively
I want to learn fractal mathematics from scratch. What are the prerequisites and recommended resources for it? Thanks and regards. Nishanth
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Check the references from this resource: Perhaps you may start with this masterpiece: Mandelbrot, B. B. The Fractal Geometry of Nature. New York: W. H. Freeman, 1983.
Sometimes , we use term of "zero time" in a formulation but are we sure it is really "0" ? maybe it is 0,000......1 and is there a "zero" time(can we stop the time?), or sometimes, we say v =0 are we sure? On the other hand 1/0 = infinity. Well then, what's "infinity"? How does it work in all the other equations? infinity - infinity = 0? 1 + infinity = infinity? If we use closest number to zero-monad (basic thing that constitutes the universe-everything-)Gottfreid Leibniz, in his essay "Monadology," suggested that the fundamental unit of all things is the monad. He intended the monad to have some of the attributes of the atom, but with important differences. The monads Leibniz proposed are indivisible, indissoluble, and have no extension or shape, yet from them all things were made. He called them "the true atoms of nature." At the same time, each monad mirrored the universe. If we use monad instead of zero, every equations work I think Science says "Every Thing had originated from a basic thing"
Boolean and ZFC logic are constructed from fundamentally different foundations. Modern (20th century) mathematics appears to be dominated by the ZFC approach. I am not sure it is understood the two approaches are incompatible. Is this incompatibility studied?
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Es posible debo seguir profundizando y actuálizando me en Matemáticas pero según lo que he estudiado lo métodos matemáticos no se contradicen por diversas vías si son correctas se llega a los mismos resultados
I have done cropping attacks in visual (pictorial) form but, I want to do this test in mathematical form, i.e., I want to calculate values of cropping attack analysis in MATLAB.
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Puedes usar MATLAB, pero puedes indagar sobre otros métodos que podrían ayudarte con el objetivo que persigues
Hi, I am trying to write the motivation part for linearization of a non-linear mathematical formulation. I claim the mathematical model will be more simple and easier to solve. But, of course, I need a reference for that! Any suggested book chapters or articles that discuss this point please? Thanks in advance... Zak
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Linearization is one amongst most important problem solving methods, in science. This link may help you? Thanks
STEM fue el tema principal de la conferencia internacional ASTE 2019, con al menos 8 pósteres, 27 presentaciones orales y 3 talleres que promovieron las aulas STEM, la instrucción/enseñanza STEM, las lecciones STEM, los campamentos de verano STEM, los clubes STEM y las escuelas STEM sin proporcionar una conceptualización o definición operativa de lo que es STEM. Algunas presentaciones defendían la integración de las disciplinas, pero el ejemplo proporcionado fue principalmente prácticas "indagatorias" y de "diseño de ingeniería" que de hecho no diferían del tipo de actividades en el aula hands-on/minds-off mal conceptualizadas y epistemológicamente incongruentes. Por lo tanto, vale la pena considerar: (1) ¿Por qué lo llamamos STEM si no difiere de las prácticas aplicadas durante décadas (por ejemplo, indagación, actividades hands-on)? (2) ¿Qué beneficios (si los hubiere) puede aportar esta mentalidad/tendencia de STEMinificación a la educación científica y su investigación?
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1) Moda 2) Igualdad supuestamente.
Dear colleagues, please tell me a link to materials about mathematics of Dropout regularization in ANN. I perfectly understand how this algorithm works in practice, but I don't quite understand the mathematics.
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Thank you, dear Muhammad Ali!
I know that an infant's brain can repair itself when damaged but why doesn't the same happen in adults after stroke or brain injuries?
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With Regenerative Medicine, using stem cells, the ongoing Programs are doing it, with good results and promising expectations.
Hello everyone I would really appreciate it if anyone could give some idea of some mathematical techniques for developing correlation for a dependent variable, W which has to be defined as W=f(x,y,z) where the individual functions are in form of power-law, W=a(x^b), W=c(y^d) and W=e(z^f).
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The simplest advice via the remark: Logarithm of the equations implies linear formulas for the dependence of log W on log x , log y and log z.x,
In general in mathematics we work with groups that includ numbers, generally we work with constants. So for exempel: For any x from R we can choose any element from R we will find it a constant, the same thing for any complex number, for any z from C we will find it a constant. My question say: Can we find a group or groups that includ variabels not constants for exemple, we named G a group for any x from G we will find an x' it's not a constant it's another variabel ? and if it exisit can you give me exempels ? Thank you !
While working in both the software, after loading the training and validation data for the prediction of a single output using several input variables (say 10), it skips some of the inputs and delivered an explicit mathematical equation for future prediction of the specific parameter but it skips some of the input variables (say 2 or 3 or maybe greater). What criteria are these software uses in the back for picking the most influential parameters while providing a mathematical predictive model?
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Look the link, maybe useful. Regards, Shafagat
Hello Can someone help me to solve this? Because I really don't know about these problems and still can't solve it until now But I am still curious about the solutions Hopefully you can make all the solutions Sincerely Wesley
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Hi In what area was the issue raised? Euclidean space, Hilbert space, Banach space?
Austrian-born mathematician, logician, and philosopher Kurt Gödel created in 1931 one of the most stunning intellectual achievements in history. His shocking incompleteness theorems, published when he was just 25, proved that within any axiomatic mathematical system there are propositions that cannot be proved or disproved from the axioms within the system. Such a system cannot be both complete and consistent. The understanding of Gödel's proof requires advanced knowledge of symbolic logic, as well as Hilbert and Peano mathematics. Hilbert's Program was a proposal by German mathematician David Hilbert to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent. Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic. Gödel's 1931 paper proved that Hilbert's Program is unattainable. The book Gödel's Proof by Ernest Nagel and James Newman provides a readable and accessible explanation of the main ideas and broad implications of Gödel's discovery. Mathematicians, scholars and non-specialist readers are invited to offer their interpretations of Gödel's theory.
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The idea is you have to go out of the system in order to prove some results. Like the Fermat problem needed things like Eliptic curves also, foreign to just plain integer arithmetic. That is if you mix up a bunch of rules, there are also unexpected side effects which might be true, but cannot be proven. Some results are random (prime numbers) Many other problems are still open.
When I observed mathematics education in preservice teachers at my university, I found that What students learn in mathematics classes does not match what is needed in school mathematics classes. That led to my initiation to do design research, a Hypothetical Learning Trajectory that contains a sequence of learning processes related to elementary school mathematics learning. I consider starting with observations in elementary math class to identify misconceptions, then jointly reviewing issues on campus, conducting literature reviews, designing lessons to address identified problems, implementing them in class and evaluating the results. The final result is a Local Instructional Theory on Learning about Teaching Mathematics for prospective teachers to overcome misconceptions that occur in elementary mathematics classes. I need so many suggestions to do this research.
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From my experience your idea has been voiced by every teacher in every subject from the beginning of teaching. In addition, myself and very teacher wants a concept close to what you describe. So much so that they have refined it and set it in place as a curriculum goal at all levels of education. And it usually fails in real-world classrooms. Especially teaching students from 5 to 18 years old. These are people in their early stages of developing skills to learn. And by their nature never at the same levels. To me those needs come first. You can be successful as a teacher and at same time put aside the obvious theory and hopeful goals. Like someone else here suggested, spend a few years with the children you hope to help and find out what their needs are and those of their families and community VS what you think they are. First experience helping people to learn before you decide how they should learn and how to organize the curriculum. Mathematical skills, concepts and facts - like anything else - are easily learned. With a big "if"...if the child likes to learn and has had people help them along the way.
In 2010, Dr. Khmelnik has found the suitable method of resolving of the Navier-Stokes equations and published his results in a book. In 2021, already the sixth edition of his book was released that is attached to this question for downloading. Here it is worce to mention that the Clay Mathematics Institute has included this problem of resolving of the Navier-Stokes equations in the list of seven important millennium problems. Why the Navier-Stokes equations are very important?
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I finally could check the PDF, Prof. Aleksey Anatolievich Zakharenko Dr. Khmelnik uses a variational principle to solve the NS equation, which is very powerful indeed. He also discusses and gives examples & a reason for turbulence. I know that the solution of NS is a non-linear problem that involves several modes and that it depends on the source. However, my knowledge of the foundations of NS is very limited to a few linear/non-linear problems on non-equilibrium gas dynamics& MHD solved by the method, Prof. Miguel Hernando Ibanez had. Thank you for sharing the link. I recovered my account.
According to the resources; there is used to algorithm in HOMER sotware, grid search algorithm and derivative-free algorithm. So how can I find the mathematical formulas of these algorithm ? Please if you know the way or source help me Thank you
Hello! I have an exercise to do and I am struggling with it for a week ago. I have a 2D flow with the initial velocity at the inlet=0.01m/s. And I want to calculate the numerical results of the velocity which is the function of x and y direction (U(x,y)) in the domain of the water flow. For example if I want to calculate the velocity at the distance x1 and x2 (as in the figure) in the function of x and y., how can I calculate it? Please note that it is incompressible flow. It is fully developed after it passed the entrance length. The height of the domain is 0.02 m and the length is 1 m. Please help me! You can see the following figure. Thank You in advance! I will appreciate your help !
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Finally, I did it after I know how to use 1st Simpson Rule to apply this problem!
According to the resources; there is two algorithm used in HOMER sotware optimization process; grid search algorithm and derivative-free algorithm. So how can I find the mathematical formulas of these algorithm ? Please if you know the way or source help me Thank you
Mathematical about the work-related with graphene or any other type of films/coatings. Lubrication equations in solid films.
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The thesis "Aspects of Flow and Viscoelasticity in a Model Elastohydrodynamically Lubricated Contact" by Ellen van Emden at UT Twente, might give you some ideas!
using BTE how do we get mobilities and conductivity ,more calculation(mathematics) oriented answers would be helpful.
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Found this useful, Refer to chapter 1(Low field electron transport) of Rode's book 'semiconductor and semimetals' . It has a thorough explanation for mobility and conductivity calculations.
I mean the mathematical component of said process.
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What exactly is not clear?
I am interested in TPACK and mathematics education, can you share recent research articles on both topics here?
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Of course Yes, give me a little time
Physical reality can be observed. At least part of the structure and behavior of physical reality is perceivable. Humans can communicate about these experiences. Curious humans want to comprehend these perceptions. Humans have designed linguistic tools to be able to communicate about the perceived structure and behavior of physical reality and with these tools, they have constructed structures and models of mechanisms that might explain the perceived structures and mechanisms that physical reality exposes. Some of these structures and models of mechanisms seem to be successful. People discuss the success of these approaches and call this activity exact science. Other humans discuss this activity and call themselves philosophers. Humans are interested in the structure and mechanisms of physical reality because this knowledge helps them survive as individuals and as communities. Part of the exact sciences is formed by mathematics. Mathematics contains structures and models of mechanisms that are not directly derived from perceptions of physical reality. These concepts are derived from abstract foundations. Examples are empty space and point-like objects. Scientists use these concepts to construct vector spaces, number systems, and coordinate systems. The scientists apply these higher-level concepts to construct a model of their living space. The philosophers will immediately indicate that it is impossible to prove that these models are correct. However, these models feature structure and behavior. If the structure and behavior of the models agree more with the perceived models and behavior, then there is a larger chance that the model fits reality. Since reality appears to be very complicated, little chance exists that good correspondence will ever end the dispute. One of the aspects of the dispute concerns what the best inroad will be for comprehending most of the structure and the mechanisms of physical reality. That is the background of the posed question.
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The paper "Sticky Space Coverage" relies on the results of David Hilbert, John von Neumann, and Cantor. I consider them better and deeper-looking mathematicians than the EPR team. They all worked on set theory, vector spaces, and Hilbert spaces. Hilbert cooperated with Einstein on gravitation theory. The paper "The Standard Model of Elementary Fermions and the Hilbert Repository" ; https://vixra.org/abs/2106.0135 offers an explanation for the phenomenon of entanglement.
US Fed's balanced sheet has recently doubled up from $4T to $8T (see the monthly chart) – not to mention it used to be $800B around 2008. It seems like to me, that is highly inflating the housing markets, pushing the housing prices higher as well as the inflation rates higher – regardless of taking economic productions much into consideration. Fed refers to the situation as "transitory". I'm sure that there should be solid mathematical rations behind it. Does this parabolic Quantitative Easing approach a mathematically and/or economically sound strategy, considering the current economic situations? Any other alternative strategy? Any upsides and downsides? Thank you! --------- PS: A bit outdated visual components of Fed's balanced sheet:
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From the perspective of monetary system stability it is ( ), so I'm supposing that provides a mathematical justification. But that's not the only perspective to be looked at in my opinion. The question also needs to be asked where all that money went to. Since debt is bought on the financial markets by the central banks I'm supposing most of the money is going to investors and investment funds. How much of it is then used to contribute to something which is beneficial to our society? What are the effects on inequality?
Dear colleagues, I would like to know if there is a mathematical equation or model to calculate the Soxhlet number of cycles by varying the following parameters: - the type of solvent - the volume of the extractor - the temperature of the solvent heating if yes how can we apply it? and how much uncertainty it has? thank you so much best regards
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Suggested reference: D.A. Ellis, "Prediction of multistage solvent extraction operation from limited data", Industrial and Engineering Chemistry, 52(3) March 1960, 251-252.
I need mathematical formula to measure public service quality and organizational impact
such as Fourier , Hilbert or Laplace transforms in order to analysis and studies in the field of music acoustics.
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You my see 1-Transform methods in applied mathematics: An introduction Wiley-Interscience Peter Lancaster, Kestutis Šalkauskas Year: 1996 Language: english 2-Integral transforms in applied mathematics Cambridge University Press John Miles Year: 1971 Language: english
Please look at the mathematical construction of theta and zeta functions in the representation of a winding sphere. In this paper, based on the representation of the winding of a sphere, we construct a proof of the Riemann hypothesis of nontrivial zeros. Could you check this proof?
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Dear Bayak, Your idea is certainly interesting, but unfortunately, I am not an expert on topolog,y. I strongly suggest you first meet a professor and talk to him on how you have tackled the problem. Then give him the paper to study. This procedure will make a good beginning. Also, you can start by giving seminars/ lectures on the proof. You will get suggestions for improvements ( if any) And then you get a few people to recommend your paper to a Journal. Best of Luck and God Bless! Regards Dr Kumar Eswaran.
Hi researchers, I need to find a method of proving a mathematical equation that exist in attached file. This mathematical equation is about Bessel function. I will be thankful to hear your helps and advises.
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This link might be useful, have a look: Kind Regards Qamar Ul Islam
Dimensional rules for Homogeneous Diophantine equations A Diophantine equation is an algebraic equation with several unknowns and integer coefficients. Those are equations whose solutions must be whole numbers. The only solutions of interest are integers In mathematics and physics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it or the minimum number of sides to build a physical area or volume. To build a geometrical rectangle (square) we require 2 orthogonal sides (x, y are independent indeterminates) area = x*y (or area = x*x) To compute a numerical square (square number) we require 2 numbers p and q coprime with gcd(p,q)=1 or independent numbers. Let we introduce a dimension for nature of numbers like I (for integer), R (for real), C (for complex) and so on. n^2 = p^2 +q^2 ; 5^2=3^2 +4^2 Dimensional analysis gives for n^2= p^2 +q^2 I*I =I*I +I*I ; The sum of square might be equal to a square in some conditions. Then the equation n^2 = p^2 +q^2 may have integer solutions. A dimension is anything we can independently adjust, it is based on some geometric or algebraic definition. In any correct mathematical equation representing the relation between physical quantities or mathematical objects (length, area, volume,….,.simplex), the dimensions of all terms must be the same on both sides. Terms separated by '+' or '–' must have the same dimensions. The degree of freedom is the number of free components : how many components need to be known before the « objects » is fully determined?. For example: - a point in the plane has two degrees of freedom : its two coordinates; - a square has two degrees of freedom : its two sides ( length and breadth). - A point in 3-dimensional space has three degrees of freedom because three coordinates are needed to determine the position of the point. Law of Degree of Freedom The degree of freedom of a Diophantine equation is the number of parameters of each side that may vary independently. The degree of freedom must be the same on both sides. - The equation n^2= p^2 +q^2 LHS is a square number with two degrees of freedom (its two multipliers or components) . RHS is a sum of two squares with two degrees of freedom p^2 and q^2 which vary independently. The degree of freedom is defined as the dimension of a mathematical object. When the degree of freedom is used instead of dimension, this usually means that the object is only implicitly defined. Attempt to answer to Hilbert 10th problem Hilbert's Tenth Problem Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it can be determined in a finite number of operations whether the equation is solvable in rational integers. The problem was solved in 1970 by Yuri Matiyasevichwho in his doctoral dissertation proved that a general algorithm for solving all Diophantine equations cannot exist. I think the concept of dimensional analysis is an attempt to answer Hilbert 10th problem related to homogeneous Diophantine equations . It works very well and allows to know if a homogeneous Diophantine equation has integer solutions but it remains to calculate these solutions using modular arithmetic or algebraic method…. The most important thing is to answer Yes/No and affirm that the integer solutions exist or not.
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Hello A.H Sheikh, The question is very clear. Can we use dimensional analysis for Diophantine equation? 1/x+1/y =1/z with x, y, z integers. x^2 + y^2 =z^2 with x, y, z integers 1/x^2 + 1/y^2 = 1/z^2 with x, y, z integers 1/x +1/y =1/z (called optic equation) which has integer solutions (2,2,1), (4,4,2)….. The physical interpretation shows this equation is used for distances in thin lens equation (1/d1 + 1/d2 = 1/f ) , (1/L + 1/L= 1/L dimensional equation is correct) electrical engineering (1/R1 + 1/R2 =1/R3).(1/R + 1/R= 1/R dimensional equation is correct) 1/x^2 + 1/y^2 = 1/z^2 (in a right triangle) with x, y, z integers has integer solutions (15,20,12), (20,15,12) ,(80, 60, 48),…. In the right triangle we have the equality 1/a^2 + 1/b^2 =1/h^2 where a and b are the integer sides of the right triangle and h the integer altitude to the hypotenuse (geometric interpretation (1/L^2 + 1/L^2 =1/L^2 dimensional equation is correct) If the dimensional equation is right, correct then the Diophantine equation has integer solutions. Greetings M.AZZEDINE
Dear Community, I want to center (subtract the mean) my data in order to lower my intercept (as close as possible to zero). However, as I have categorical data as well, which I don't know how I can possibly center, I can't seem to lower my intercept. And the thing is that my dummy variable drive up the intercept... So I don't know to fix the issue. When I enter only continuous variables that are centered, the intercept is close to zero. I thank you in advance?
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Not sure why you want the intercept being zero, but one way you could easily achieve this is by first finding the (non-zero) intercept and the subtract this value from the response variable.
Dear Colleagues! I hope you are all doing well. I have a question to all of you. I love to teach and so far I have been teaching everything from international business, marketing, management to organisational psychology. I feel ambivalent towards this however.I love to teach and Im curious in my nature and what better way to learn new things than to teach? However I also feel that if I continue being a generalist It might also be bad since I risk loosing touch with my main specialisation. What are your thoughts? Your experiences? My speciality is this : Best wishes Henrik and professor Hugo 3 months old who keeps me company when Im trying to work :-) Ps stay safe.
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Teaching one subject is more scientific and it will give you more academic background.
I have seen that some equation sets have an explicit way of defining the substrate consumption whereas others have an implicit way. I would like to know how to convert the former into the latter. For instance, in the attached file, it can be seen that there are two ways to describe the growth of bacteria. In the first (explicit), the presence of a half-saturation constant suggests that the model is a Michaelis-Menten case. The second is straight a logistic model. I was wondering if I can convert the first into the second, that is explicit to implicit. Considering that the Monod term says that μ = μᵢ[S/(S + K)] then I can write Ṅ = μN * logistic term My question is: Would this modification be mathematically and biologically sound? If yes, how can I estimate the carrying capacity? For instance, if I know the amount of limiting substance, can I estimate the number of cells that a system can sustain? Thank you
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I'm working on constructing a field based on finite undirected and unlabeled graphs. I've selected graph join and graph Cartesian product. But I'm trying to figure out if the latter distributes over the former (or simple graph union).
I want to know how we can relate magnetostriction with Applied magnetic field mathematically? Or if there is any way to derive it using mechanical equations?
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There are some classic thermodynamic models to discuss the influence of an external magnetic field on magnetostriction. And we can discuss the influence of external magnetic field on magnetostriction in ferromagnetic materials with different initial stress states. 【1】Shi Pengpeng. One-dimensional magneto-mechanical model for anhysteretic magnetization and magnetostriction in ferromagnetic materials. Journal of Magnetism and Magnetic Materials 2021, 168212. https://doi.org/10.1016/j.jmmm.2021.168212
Hi All, Can anyone please tell me which mathematical equation can be used to normalize the single ion monitoring quantitation in GC-MS? Thanks in advance!
The field equations originally starting as Maxwell distributions graphs configure a velocity variable. Understanding that in connection to wave theory requires a mathematical transformation of velocity variable into wave function parameter. This may help mathematically to define particle wave quantum relativity quantitatively. Legendre transform theoretically will have a way to provide link among functionality of parameter-variable systems.
There is a contradiction between the natural width of the energy transition, which is determined by the lifetime at the corresponding energy level and the spectral line width of the radiation line, which is determined by the duration of the wave train. For example: For the Mössbauer transition, whose lifetime is of the order of 2 years, while the interaction time at the receiving end is about 10^(-10) sec. Mathematically, this interaction is expressed by the Feynman diagram of the electron - electron interaction, which integrates over the internal photon line, which, together with the delta functions of the vertex parts, limits the photon spectrum. By the way, the same paradox applies to any other type of collision. So, is exist (really) the electromagnetic field?
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Dear Pratik, dissatisfaction with quantum theory, among physicists, lies in the fact that it, like any statistical theory, does not allow describing the dynamic processes of individual physical objects. The only physical substantiation of quantum theory is that the exchange of energy between objects occurs (according to Max Planck) in portions of the integer Planck action per oscillatory cycle. Thus, the phase space of coordinates / impulses (time / energy) is divided into cells, inside which any processes can occur without violating the Planck prohibition (the classical model of the hydrogen atom), and at the border between the cells, the Fourier transform degenerates to the zero component. The space of classical c-numbers is partitioned into symmetric and antisymmetric components. It is possible that this corresponds to splitting the wave functions into even and odd parts (fermions and bosons). Thus, the task is to construct an internally consistent building of classical mechanics that is compatible with the quantum theory, taking into account the properties of symmetry and interaction parameters.
When we derive the formula for length contraction, we use the direct Lorentz transformation. But for solving the formula for time dilation, we use the inverse transformation. Why is that so?
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The Modification of Special Relativity:
A question from far away worlds...Life Sciences (cricket) and an hyperbolic function from history of mathematics are trivially juxtaposed to encourage whatever reply. [The antennas of the cricket roughly complete the less frequently represented branches of the hyperbola in the photographed virtual third and fourth quadrant of the Cartesian coordinate system].
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They say the best educators are able to make a complex subject easily understood by a child. Perhaps this is a challenge to us all. Quarternion mathematics can be quite complex to wrap your head around. For educators out there how are you explaining this to your students from high school. Is a pictorial method the most appropriate under these circumstances.
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Hey Joseph, In my opinion sticking with unit quaternions would be the way to go. At a high school level it may be a good idea to skip the complex math definitions and instead focus on the intuitive "definition" of a unit axis and a rotation about that axis. Depending on the context you could run through an animation/example in 2D or 3D to show how multiplication works, then give the multiplication rules as formulas -- the same way one might do for dot and cross products at the high school level. I would guess another important question to answer is why a roboticist would use quaternions instead of other representation. Having a short discussion on gimbal lock could be a great motivator, especially if there audience is interested in aerospace applications or robotic arms. Thanks, Logan
I have read that time is defined in terms of entropy (entropy of the universe maybe? I'm not sure). But entropy is a macroscopic quantity which makes time a macroscopic quantity. Yet time is a parameter in Schrodinger's equation. So we have a macroscopic quantity appearing in a microscopic equation. That makes me think that this microscopic equation is really a statistics equation. It produces deterministic solutions but maybe these deterministic solutions are just mathematical procedures for statistical calculations. That would be consistent with the fact that these solutions actually are used for statistics calculations. Does it makes sense for a macroscopic quantity (time) to appear in a microscopic equation, unless it is a statistics equation? Or, am I mistaken in calling time macroscopic? My primary question is whether Schrodinger's equation can be derived from some set of statistical postulates. The question is not whether the equation was historically obtained from statistical arguments (we already know it wasn't), the question is whether the same equation can be derived from statistical arguments. What Schrodinger was thinking at the time of producing his equation is not relevant to this question.
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Interesting, I still remember that my QM physics teacher in Moscow told us in a lecture that the SE came from a more general theory. I just found this on a Wikipedia commons article that remains me of what he said in 1990: I always have been impressed more with the old quantum method of quantization that the same SE, systems such as superfluidity in He4 can be predicted by the old method quite nicely.
Mathematics is the basis of exact sciences. The development of mathematics consists in the fact that, among others, new phenomena of the surrounding world, which until recently were only described in the humanistic perspective, are also interpreted in mathematical terms. However, is it possible to write down the essence of artistic creativity in mathematical models and create a pattern model for creating works of art, creative solutions and innovative inventions ? If that was possible, then artificial intelligence could be programmed to create works of art, creative solutions and innovative inventions. Will it be possible in the future? Do you agree with my opinion on this matter? In view of the above, I am asking you the following question: Will mathematics help to improve artificial intelligence so that it will achieve human qualities of artistic creativity and innovation ? Please reply I invite you to the discussion Best wishes
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DISCUSSION_D.Prokopowicz_.Will mathematics help to improve artificial intelligence...artistic creativity and inno
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Dear Stan Sykora, Boris Pérez-Cañedo, Baidaa Mohammed Ahmed, Thank you for answering the above question and participating in this discussion. Regards, Dariusz Prokopowicz
what are other possible ways to convert a CW laser to a pulsed laser. Please give all the theoretical and mathematical details.
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Output optical power can be achived by optical phase shift in one arm of Mach Zehnder interferometer. π/2 phase shift will lead to destructive interference and lower values of output intencity. If we consider integrated structure of silicon Mach Zehnder modulator, the phase shift is induced by changing electron and hole concentration along with the effective refractive index. The attached picture represents output power equation of MZM with a phase shifter in one arm. Indices 1 and 2 corresponds to MZM arms with and without the phase shifter. Index 3 denotes the phase shifter itself. L - length, betta - propagation constant, alfa - absorption coefficient.
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Part 2 Mathematics Questions 26-50 Answers
Source: https://www.researchgate.net/topic/Mathematics
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