Science topics: Mathematics
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Mathematics - Science topic

Mathematics, Pure and Applied Math
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In current times we have a trend that many difficult tasks in practice got solutions on the basis of using AI. Before such tasks used mathematical techniques. What will be in the future? The human intellect and IQ will be decreased?
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Advantages and Limitations of Artificial Intelligence
In book: Artificial Intelligence Applications of Critical Transportation Issues
Chapter: Why Artificial Intelligence?
by: Mashrur Chowdhury and Adel W. Sadek
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In radars use difficult mathematical techniques to estimation of signals sources parameters. But I think that the implementation of AI can be made unnecessary such an approach. For example, the task of detecting one target and the resolution of two targets can be have an effective solution by AI now. What do you think about this?
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A very strange view. You can, of course, ignore the mathematical algorithms embedded in AI and treat the AI carrier as a "black box". Nevertheless, the mathematics is there and it will work. Now, in the vast majority of cases, the operators of any modern equipment do not perform mathematical calculations, relying on the corresponding systems. Dream of a magic wand?
There are quite effective hunters in nature, for example, a cheetah (2D environment) or a falcon (3D), these really do not know mathematics, but solve practically problems similar to the one mentioned by the author of the question. But Is their efficiency sufficient in comparison with the efficiency of a modern radar complex?
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I am looking for a research paper about the mathematical or computational modelling of protein oxidation (caused by reactive oxygen species).. I would really appreciate that if someone helps me with this.
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Thank you so much for providing these papers.
Kind regards,
Faezeh
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In the education discipline, several leadership theory has been discussed but no such mathematical foundations are available to estimate them. More, especially how can I differentiate( in terms of Mathematical expressions ) the several leadership styles in decision making problems so that I could get the better one; and the decision maker would comfort to apply their industrial/ managerial/ organizational situation ? We may assume that, the problem is a part of fuzzy decision making/ intelligent system / artificial intelligent system/ soft system.
The leaders are manager of an industry/ organization/ corporate house, the ministry of a Government / the agents of a marketing system, the representatives of customers of a particular product in a supply chain management problem.
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In any leadership theory the " controlling power" of the management is the vital factor. The controlling power is that which can control the entire parameters and the decision variables of an objective function. First of all fuzzify the parameters/ variables which are more significant in the real time situations. Choose the fuzzy numbers as LOCK Fuzzy set, Then apply several strategies( as per Leadership Theory) of controlling keys of the fuzzy LOCK any one can get the Mathematical foundations of several Leadership Theory.
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what are the differences between mathematical modelling and realistic mathematic education?
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Five different perspectives on mathematical modeling in mathematics education By: Aline Abassian
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I have some complicated hints and clues, but I think their solutions should be much simpler.
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also i think their solutions should be much simpler.
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Hi.
I have a data in which the relationship between two parameters seems to fit to a model that has two oblique asymptotes. Does any one have any idea about what type of function I should use? Please find attached a screenshot of the data. I appreciate any help.
Thanks.
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Polynomial Division to Find Oblique Asymptotes. The idea is that when you do polynomial division on a rational function that has one higher degree on top than on the bottom, the result always has the form mx + b + remainder term. Then the oblique asymptote is the linear part, y = mx + b. https://magoosh.com/hs/ap-calculus/2017/oblique-asymptotes/
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What is the importance of Golden Ratio in nature and mathematics? Why the golden ratio is sometimes called the "divine proportion," by mathematicians?
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In the world of art, architecture, and design, the golden ratio has earned a tremendous reputation. Greats like Le Corbusier and Salvador Dalí have used the number in their work. The Parthenon, the Pyramids at Giza, the paintings of Michelangelo, the Mona Lisa, even the Apple logo are all said to incorporate it.
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Six Nobel Prizes are awarded each year, one in each of the following categories: literature, physics, chemistry, peace, economics, and physiology & medicine. However Mathematics a subject mankind cannot do without is a strange omission and has remained excluded until today. Same with accounting. From 1901 doyens such as Albert Einstein, Marie Curie, Earnest Hemingway were honored with the prestigious Nobel. Do you think it’s time to rethink ?
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Yes
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Hello,
I am searching the maximum Value a DIT Radix-2 FFT can have. I dont necessarily mean the end values, but the max value that could occur in all repetitions. The reason behind it is that I`m about to implement this in-place algorithm on a micro controller with very limited space and dont want to use unnecessary large variables.
I`m calculating the FFT in-place with the real and imaginary parts of the complex conjugates split to save memory. Also I`m just using real values as input.
Through some tests I found that when sampling an sinus with values between +2^n and -2^n with 2^m variables, all values will be <=2^(m+n-1). I just found this through a bunch of tests and dont know if it will be always the case. Also I dont know why this applies if it is true.
Furthermore I read about Parseval's theorem but cant draw a conclusion out of it.
So the main question is, what is the maximum Value that can occur in an Radix-2 DIT FFT when sampling any signal with amplitude 2^n with 2^m sampling points.
I hope it was understandable, but I`m open to further explanations if something is unclear.
Thank you
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Hello,
the worst case is not for sine but for constant value at either + or - 2^n for all 2^m variables.
Then one FFT value at least will be + or - 2^(m+n)
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Much has been said about the differences between physics and mathematics, but less attention has been paid to the differences between physics and chemistry.
The question is, where does physics and chemistry work?
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Differences in physics, mathematics, chemistry and biology
· The difference between physics and biology is in the study of inanimate and living systems, but in the physics of living systems (LSP) this difference disappears.
· There is a difference between physics and chemistry in the scales studied, but in physics the scales disappear.
· There is a difference between physics and mathematics in why and how, but in conceptual analysis this difference disappears.
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Dear Friends,
Kindly allow me to ask you a very basic important question. What is the basic difference between (i) scientific disciplines (e.g. physics, chemistry, botany or zoology etc.) and (ii) disciplines for branches of mathematics (e.g. caliculus, trigonometry, algebra and geometry etc.)?
I feel, that objective knowledge of basic or primary difference between science and math is useful to impart perfect and objective knowledge for science, and math (and their role in technological inventions & expansion)?
Let me give my answer to start this debate:
Each branch of Mathematics invents and uses complementary, harmonious and/or interdepend set of valid axioms as core first-principles in foundation for evolving and/or expanding internally consistent paradigm for each of its branches (e.g. calculous, algebra, or geometry etc.). If the foundation comprises of few inharmonious or invalid axioms in any branch, such invalid axioms create internal inconsistences in the discipline (i.e. branch of math). Internal consistency can be restored by fine tuning of inharmonious axioms or by inventing new valid axioms for replacing invalid axioms.
Each of the Scientific disciplines must discover new falsifiable basic facts and prove the new falsifiable scientific facts and use such proven scientific facts as first-principles in its foundation, where a scientific fact implies a falsifiable discovery that cannot be falsified by vigorous efforts to disprove the fact. We know what happened when one of the first principles (i.e. the Earth is static at the centre) was flawed.
Example for basic proven scientific facts include, the Sun is at the centre, Newton’s 3 laws or motion, there exists a force of attraction between any two bodies having mass, the force of attraction decreases if the distance between the bodies increase, and increasing the mass of the bodies increases the force of attraction. Notices that I intentionally didn’t mention directly and/or indirectly proportional.
This kind of first principles provide foundation for expanding the BoK (Body of Knowledge) for each of the disciplines. The purpose of research in any discipline is adding more and more new first-principles and also adding more and more theoretical knowledge (by relying on the first-principles) such as new theories, concepts, methods and other facts for expanding the BoK for the prevailing paradigm of the discipline.
I want to find answer to this question, because software researchers insist that computer science is a branch of mathematics, so they have been insisting that it is okay to blatantly violating scientific principles for acquiring scientific knowledge (i.e. knowledge that falls under the realm of science) that is essential for addressing technological problems for software such as software crisis and human like computer intelligence.
If researchers of computer science insist that it is a branch of mathematics, I wanted to propose a compromise: The nature and properties of components for software and anatomy of CBE (Component-based engineering) for software were defined as Axioms. Since the axioms are invalid, it resulted in internally inconsistent paradigm for software engineering. I invented new set of valid axioms by gaining valid scientific knowledge about components and CBE without violating scientific principles.
Even maths requires finding, testing, and replacing invalid Axioms. I hope this compromise satisfy computer science scientists, who insist that software is a branch of maths? It appears that software or computer science is a strange new kind of hybrid between science and maths, which I want to understand more (e.g. may be useful for solving other problems such as human-like artificial intelligence).
Best Regards,
Raju Chiluvuri
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Dear @Raju Chiluvuri
To my opinion, mathematics is the precursor to all the disciplines of science. And, in fact, mathematics is also a science.
Thanks!
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Hi
I am doing linear regression research assignment where I have to research how does mathematical scores and gender (independent variables) affect to natural history scores (dependent variable). I am not sure am I interpreting gender's dummy variable (female = 1, male = 0) right in the coefficients table.
Am I right by interpreting that females are getting on average 10.9 points less natural history scores than male?
Thank you in advance.
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Thanks for your answers.
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The mosque is in abu Dhabi
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Ok with the previous answers but the most important for such a huge building is not architecture but well engineering. It is not without reasons that engineers spend 4-5 years to study mathematics, physics, mechanics (including fluid mechanics), chemistry, resistance of materials, electricity, electronics, with plenty of mathematical equations, and so on.
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In fact, it is the fundamental defects in the work of “quantitative cognition to infinite things” that have been troubling people for thousands of years. But I am going on a different way from many people.
1, I analysis and study the defects in existing classical infinite theory system disclosed by the suspended "infinite paradox symptom clusters" in analysis and set theory from different perspectives with different conclusion: to abandon the unscientific (mistaken) "potential infinite and actual infinite" concepts in existing classical infinite theory system and discover the new concepts of "abstract infinite and the carriers of abstract infinite", especially to replace the unscientific (mistaken) "actual infinite" concept in existing classical infinite theory by the new concept of “carriers of abstract infinite" and develop a new infinite theory system with “mathematical carriers of abstract infinite and their related quantitative cognizing operation theory system ". From now on, human beings are no longer entangled in "potential infinite -- actual infinite", but can spare no effort to develop "infinite carrier theory", and develop comprehensive and scientific cognition of various contents related to "mathematical carrier of abstract infinite concept".
2, Abstract concept - abstract concept carrier theory, new infinite theory system, carrier theory, infinite mathematical carrier gene, infinite mathematical carrier scale,...The development of basic theory determines the construction of "quantum mathematics" based on the new infinite theory system.
3, I have up loaded 《On the Quantitative Cognitions to “Infinite Things” (IX) ------- "The Infinite Carrier Gene”, "The Infinite Carrier Measure" And "Quantum Mathematics”》2 days ago onto RG introducing " Quantum Mathematics". My work is not fixing here and there for those tiny defects (such as the CH theory above) but carrying out quantitative cognitions to all kinds of infinite mathematical things with "quantum mathematics" basing on new infinite theory system.
According to my studies (have been presented in some of my papers), Harmonic Series is a vivid modern example of Zeno's Paradox. It is really an important case in the researches of infinite related paradoxes syndrome in present set theory and analysis basing on unscientific classical infinite theory system.
All the existing (suspending) infinite related paradoxes in present set theory and analysis are typical logical contradictions.
The revolution in the foundation of infinite theory system determines the construction of "Quantum Mathematics" based on the new contents discovered in new infinite theory system: infinite mathematical carrier, infinite mathematical carrier gene, infinite mathematical carrier measure,... in new infinite carrier theory. So, the "Quantum Mathematics" mentioned in my paper is different from Quantum Logic and Quantum Algebras;
According to my studies (have been presented in some of my papers), “Non-Standard Analysis and Transfinite numbers” is all the infinite related things in unscientific classical infinite theory system based on the trouble making "potential infinite and actual infinite" --------- Non-Standard Analysis is equivalence with Standard Analysis while Transfinite is an odd idea of “more infinite, more more infinite, more more more infinite, more more more more infinite,…”).
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Search RG for Ed Gerck. I'm sure he'd be glad to discuss this topic.
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Mathematics differs from sensory science in that it draws its subject from structural construction to abstract abstraction of quantitative quantities, while other sciences rely on the description of actual sensory objects already in existence.
What do you think?
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Dear colleagues. A very interesting question, some years ago, in 2012, I published a work where I give a definition of Mathematics that can serve to answer the question.
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Computer Aided Design (Cad) subject deals with the backend mathematical calculation that happens in a 3D design.
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The book of Computer Aided Optimal Design: Structural and Mechanical Systems by the Mota Soares, C.A. and Templeman, A.B can be useful.
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Hello,
I am interested in the personalization of learning based on profiles, more specifically in mathematics.
Do you know any relevant references?
Thank you
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The fact that , electron can have only discrete energy level is obtained by solving schrodinger equation with boundary conditions, which is a mathematical derivation .
Physically, What makes the electron possess only certain energies ?
Or is there any physical insight or explanation or physical intution which can arrive at same conclusion(without math) that electron can have only discrete energy levels inside potential well
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When the electron's energy can take only certain values this just means that the states that would correspond to the other values don't exist, under those circumstances. These circumstances are described by the boundary conditions imposed, that are part of the physical description, too.
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Given a fixed volume where the relative humidity and temperature are known, how can you estimate how much water vapor will condense corresponding to a temperature decrease. I suspect it has to do with the dew point temperature but I'm having trouble finding mathematical relations.
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It is not very difficult, but some algebra needs to be involved.
The workflow is the following:
1. Knowing relative humidity at T=T0 (as an input), calculate the partial pressure of vapor at this temperature.
2. Calculate water vapor concentration rho_0 using the ideal gas equation.
3. Calculate saturated vapor pressure at T=T1 from tables or the Clausius-Clapeyron equation.
4. Calculate corresponding saturated vapor density rho_1 at T=T1 using the ideal gas equation.
5. If rho_1 < rho_0, there will be no condensation, otherwise the mass of water condensed in volume V will be V(rho_1 -rho_0).
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Hi every one,
here I have a problem in MATLAB, when I want to solve the following equation, relative to PI in the photo, or tau in the code, MATLAB will send me this error: Warning: Unable to find explicit solution. For options, see help.
I attached the question and the code below (in code, I rewrite pi in the photo with tau).
If you have any idea to solve this problem, analytically or numerically, I will be happy to hear it out.
NOTE:
> PI_0.1(X,t) = tau
> X = [x(t),y(t),psi(t)]^T;
** PROBLEM: Find tau in terms of X and t in which solve the mentioned equation.
Thanks in advance,
Arash.
code:
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clc;clear;
syms x y psi tau t
c1 = 1;c2 = 1.5;lambda = 0.1;
x_r(tau) = 0.8486*tau - 0.6949;
y_r(tau) = 5.866*sin(0.1257*tau + pi);
psi_r(tau) = 0.7958*sin(0.1257*tau - pi/2);
x_r_dot = 0.8486;
y_r_dot(tau) = 0.7374*cos(0.1257*tau + pi);
psi_r_dot(tau) = 0.1*cos(0.1257*tau - pi/2);
phrase1 = c1/2*(cos(psi)*(x - x_r) + sin(psi)*(y - y_r))*(cos(psi)*x_r_dot + sin(psi)*y_r_dot);
phrase2 = c1/2*(-sin(psi)*(x - x_r) + cos(psi)*(y - y_r))*(-sin(psi)*x_r_dot+cos(psi)*y_r_dot);
phrase3 = 0.5*(psi - psi_r)*psi_r_dot;
eq = -2*(1-lambda)^2*(phrase1 + phrase2 + phrase3) - 2*lambda^2*(t - tau)
sol = solve(eq == 0 , tau , 'IgnoreAnalyticConstraints',1)
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Pass x, instead of tau, as rightly pointed out by Saeb AmirAhmadi Chomachar
syms x y psi tau t
c1 = 1;c2 = 1.5;lambda = 0.1;
x_r(tau) = 0.8486*tau - 0.6949;
y_r(tau) = 5.866*sin(0.1257*tau + pi);
psi_r(tau) = 0.7958*sin(0.1257*tau - pi/2);
x_r_dot = 0.8486;
y_r_dot(tau) = 0.7374*cos(0.1257*tau + pi);
psi_r_dot(tau) = 0.1*cos(0.1257*tau - pi/2);
phrase1 = c1/2*(cos(psi)*(x - x_r) + sin(psi)*(y - y_r))*(cos(psi)*x_r_dot + sin(psi)*y_r_dot);
phrase2 = c1/2*(-sin(psi)*(x - x_r) + cos(psi)*(y - y_r))*(-sin(psi)*x_r_dot+cos(psi)*y_r_dot);
phrase3 = 0.5*(psi - psi_r)*psi_r_dot;
eq = -2*(1-lambda)^2*(phrase1 + phrase2 + phrase3) - 2*lambda^2*(t - tau);
eqn = rewrite(eq,'log');
sol = solve(eqn == 0 , x , 'IgnoreAnalyticConstraints',1);
pretty(sol)
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Hello,
I am doing research on HVLD detection capability.
From your experience, is there some mathematical formula to prove that HVLD machines can detect holes regardless of size or some other ways to prove it?
Thanks in advance !
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I am not expert in this subject , may be the following links are useful
High-Voltage Leak Detection of a Parenteral Proteinaceous Solution Product Packaged in Form-Fill-Seal Plastic Laminate Bags. Part 3. Chemical Stability and Visual Appearance of a Protein-Based Aqueous Solution for Injection as a Function of HVLD Exposure
Rasmussen, M., Damgaard, R., Buus, P., Guazzo, D. M.Journal:PDA Journal of Pharmaceutical Science and TechnologyYear:2013
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A question related to our cultural indebtedness to our mathematical forbears.
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Interesting question. However, the foundations that allowed calculus to evolve started long before Newton and Leibniz. The foundation is not calculus but the concept of the limit. Archimedes (287-212 BC) was probably the first to recognize what became the concept of the limit in is estimation pi and the area of the circle by taking inscribed and circumscribed polygons bounding the circle and using the simple fact that one approaches pi from below while the other from above. Of each sequence defines a Cauchy sequence - concept unknown at that time and the completion of the reals (also unknown at that time) show the limit of each sequence is the same and equal a the number pi. In reality the concept of infinitesimal - goes back to Archimedes although the formal concept of "infinity" was not accepted until long afterwards.
Roll backwards to the Greeks when faced with the proposition of an infinite number of prime number, was a problem as they believed the universe was finite. Infinity was not something the Greeks wanted to accept and Aristotle (385-348 BC). But Archimedes had just shown that infinity and infinitesimals had a role in mathematics - in fact a central role. It was not to the 1600's that mathematicians attack the problem of infinity to try to understand what it mean as they developed the concept of numbers that are used today.
As we better understood our real number system, the concept of point set or general topology was defined to abstract and better understand the structure. In general topology concepts like nets (generalizations of sequences required to define integrals for example), convergence, close to, in a neighborhood and limits are all defined through the concept of open sets which are used to define a topology on a set which now allows for the definition and study of the concept of limits and continuity and handle infinity. While the formulations of general topology came along after the "birth of the calculus" and known as Analysis Situs a term coined by Henri Poincaré through the work of Poincaré , Euler, Cantor, Lefschetz, Courant, Hilbert, etc., a firm foundation was laid not only to the real number system, but to limits, continuity all the foundations of what we now know as 'calculus."
Topology is so important to the foundations of calculus and the concept of a limit that in his classic text, "General Topology," John Kelley writes in the first paragraph of the preface he writes, "...I have, with difficulty, been prevented by my friends from labeling it: What Every Young Analyst Should Know." No truer words have been spoken or written as the foundations of topology has allowed the concept of calculus to be expanded far beyond its original intent.
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I am doing a research proposal i need answers on my topic. information must be from 2015-2020. relevant articles
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I believe that one of the most important reasons for low achievement in mathematics is their lack of basic mathematics and their belief that mathematics has no strong necessity in their lives, as there is a lack of training for students on questions that measure higher levels of thinking. As a result, students focus on memorization without understanding, as they remember in the time immediately preceding the test. As for students, they see that one of the factors for their low level of achievement in mathematics is the way the book is presented, as it does not allow them the opportunity to follow the course themselves, and the teaching methods of mathematics do not encourage research and benefit from mathematics, also the teacher does not use educational aids during the explanation In addition, they believe that the time difference between the tests is small and that the time allocated for answering is much less with what you need from these tests. They also admitted that they are worried about their test score, which will affect their achievement results
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Any bibliographic recommendations on the problem of routing vehicles with multiple deposits, homogeneous capacities? less than 10 nodes
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A multi-depot VRP with less than 10 nodes should be almost enumerable, as there exist less than 1024 possible subsets of customers. Given this fact, perhaps the simplest solution approach is to generate all feasible routes from each depot, discard those that are not TSP-optimal, and directly solve a set partitioning formulation based on these routes. Now, if you face larger problems (e.g., 15 nodes or more), you should use the formulations suggested by Adam and Noha, or even go for sophisticated branch-and-price approaches as described in
since the code associated with this paper is freely accessible at
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L'Huillier's theorem or calculation of spherical excess of "spherical triangle" formed between the unit vectors on unit sphere can find out the area, but how to explain this formula from purely plane trigonometry standpoint (i.e. without assuming any pre-requisite knowledge on spherical trigonometry)? The solid angle can be found by spherical trigonometry rules, and I am well aware of it. I want to introduce this problem to anyone with knowledge of plane trigonometry, but no knowledge of spherical trigonometry.
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According to a report published by UNESCO, 0.1% of the global population (in 2013) were researchers? Does anybody know the current numbers?
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I can imagine volumes of reasonings behind the eight-word response. Thank you Hermann Gruenwald !
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what is the mathematical expressions and equations used for the designing of antipodal structure of an antenna.
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Dear Sneha,
Please follow the paper in the link:
You will get the design formulas and an example of antipodal Vivaldi Antenna.
If you have more questions you can ask the first author of the paper.
Best wishes
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I hope for a global overview on mathematical giftedness and its support in school and/or on an extracurricular level. What programmes/opportunities are offered?
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First thanks , it is really an interesting question.
A problem is that gifted and talented students do not receive the necessary care
To meet their needs by remaining in regular classes. Therefore, I find it important to do the following:
- Staying away from traditional methods during teaching, this leads to boredom for students, especially talented people
- When constructing lessons conceptually, we take into account that gifted and talented students may also suffer
One of the weaknesses in understanding the curriculum and that they need to be considered. And when applying the teaching conceptually within
In the ordinary class, students of all levels will learn in a deeper way.
- Adding open-ended questions to both education and evaluation for their positive results on students ’understanding
As well as their attitudes towards the material.
The- direct and indirect financial support for talented people
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Quantum computing is the field that focuses on quantum computation/information processing, the mathematical and physical theory for which as well as the engineering required to realize different circuits and algorithms into hardware performance, as well as other contingent issues such as the whole “compute chain” (from software engineering to quantum machine code and then further on to the physical architecture) and device/hardware issues such as thermal, electrooptical and nanoengineering.
My question is how quantum computing is related to artificial intelligence?
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Quantum computing (QC) is the enabling technology for efficiently processing huge quantities of (quantum) information, in many cases outperforming "classical" computing (i.e. binary logic based). It provide you the "muscles" for data crunching, provided you feed it with quantum-coded information (qubits) and you get probabilistic results (with high likelihood if well designed).
Artificial Intelligence (and Machine Learning more specifically) is a discipline focused in performing data analysis with the objective of simulating human reasoning for achieving a certain goal. It can then definitively take advantages by a super fast computing capability provided by QC, both for speeding up "classical" algorithms or for running QC native ones, which are expected to open the door to a next level of AI capabilities beyond our current imagination.
Just be patient for few more years and wait for a working universal QC becoming available (at competitive price).
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Can any one suggest application(s) for $R_{\alpha}, R_{\beta}$ and $R_{m}$ -functions in mathematical or applied sciences; which is recently introduced in following research paper;
H. M. Srivastava et al. A family of theta- function identities based upon combinatorial partition identities and related to Jacobi’s triple-product identity, Mathematics 8(6)(2020), Article ID 918, 1-14.
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Interesting question. Following the discussion.
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Here I just want to know about the actual parameters to measure the content of happiness in a person. With the help of these parameters a neural network can be generated and maintained to achieve the maximum happiness. I am also expecting some better approach from the scholars.
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What a good question, dear Parul! I can tell you that, after 35 years of career in math & stats, I still fell rewarded when I solve a problem or finish a project. I do not know what chemicals are doing that for me, but they do. It is true, I did not have many frustrations to overcome, it worked well for me math & stats-wise, so I am pleased (and happy, as you say) by default. I am probably not the perfect subject for your study, you need people who had to struggle much more than me to achieve their goals.
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Dear colleagues,
I am looking for a practical guide presenting the non-parametric tests intended for students without mathematical background (or very little) with if possible the codes SAS or R.
Thank you.
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Hi Natacha,
rcompanion.org is a great source with many examples of non-parametric tests.
sthda.com is also good, but the author uses his own limited packages.
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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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1. Patience.
2. Knowledge of field and ability to impart that knowledge to others.
3. Ability to ask questions and define specific aims
4. Writing skills to produce grants and publications.
5. Research support in terms of grants or other types of research funding.
6. Contacts, perhaps a network of researchers with similar interests.
7. Foster attendance a scientific meetings, including presentations by students.
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I have found a beautiful technique to solve math problems such as:
  • Goldbach’s conjecture
  • Riemann hypothesis
The technique uses the notions of regular languages. The complexity class that contains all the regular languages is REG. Moreover, these mathematical proofs are based on if some unary language belongs to NSPACE(S(log n)), then the binary version of that language belongs to NSPACE(S(n)) and vice versa. The complexity class NSPACE(f(n)) is the set of decision problems that can be solved by a nondeterministic Turing machine M, using space f(n), where n is the length of the input.
We prove there are non-regular languages that define mathematical problems. Indeed, if those math problems are not true, then they have a finite or infinite number of counterexamples (the complement languages contain the counterexample elements). However, we know every finite language is regular. Therefore, those languages are true or they have an infinite number of counterexamples, because if they have a finite number of counterexamples, then the complement language should be in REG, that is, this complement must be a regular language. Indeed, we show some mathematical problems cannot have a finite number of counterexamples using the complexity result, that is, we demonstrate their complement languages cannot be regular. In this way, we prove these problems should be true or they have an infinite number of counterexamples as the remaining only option.
See more in my notions:
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Take, for example, such a concept as a minimum flow, that is, a gradient vector field, the level surfaces of which are the minimum surfaces. Then the globally minimal flow, evolving to an absolutely minimal state, could be compared with a quantum vacuum, and the locally minimal flow could be compared with fields and particles. At the same time, it is clear that it is necessary to correctly choose the space in which this minimum flow moves.
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Structure wave theory shows how mathematics as a structurally active language based on the release of structure waves is converted into physics.
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My dear friends, I am asking if some of your students are interested in applying a postdocotor position in China with me, here is the link and details!!!
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Age requirement l problem. If it was 40 better !!
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Many of the tools I saw and used were designed for measuring performance in a particular topic of mathematics. I am looking for a tool that can capture one's general mathematical thinking skills.
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Publications in good journals, either on old unsolved issues, or on novel paths and ideas.
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Hello all,
I am looking for an method / algorithm/ or logic which can help to figure out numerically whether the function is differentiable at a given point.
To give a more clear perspective, let's say while solving a fluid flow problem using CFD, I obtain some scalar field along some line with graph similar to y = |x|, ( assume x axis to be the line along which scalar field is drawn and origin is grid point, say P)
So I know that at grid point P, the function is not differentiable. But how can I check it using numeric. I thought of using directional derivative but couldn't get along which direction to compare ( the line given in example is just for explaining).
Ideally when surrounded by 8 grid points , i may be differentiable along certain direction and may not be along other. Any suggestions?
Thanks
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The answer to a question about the numerical algorithms for resolving the issue of differentiability of a function is typically provided by the textbooks on experimental mathematics.
I recommend in particular: Chapter 5: “Exploring Strange Functions on the Computer” in the book: “Experimental Mathematic in Action”.
For the review please see
You can also get a copy of the text in a form of a preprint from
Judging by the quote placed in the beginning of Chapter 5, the issue of investigation of the “strange functions” was equally challenging i 1850s as it is 170 years later:
“It appears to me that the Metaphysics of Weierstrass’s function
still hides many riddles and I cannot help thinking that enter-
ing deeper into the matter will finally lead us to a limit of our
intellect, similar to the bound drawn by the concepts of force
and matter in Mechanics. These functions seem to me, to say
it briefly, to impose separations, not, like the rational numbers”
(Paul du Bois-Reymond, [129], 1875)
The situation described in your question is even more complicated because the function is represented only by a few values on a rectangular grid and it is additionally assumed that the function is not differentiable at a certain point. In this situation I can suggest to use the techniques employed in the theory of generalized functions (distributions).
For a very practical example you can consult a blog: “How to differentiate a non-differentiable function”:
In order to answer your question completely I would like to know what is the equation, boundary conditions and the numerical scheme used to obtain a set of the grid point values mentioned in the question.
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the types of board game for mathematical literacy to make the learning and teaching fun
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You're welcome Rich Philp. For your information, I have a modest knowledge regarding programming, but still I made some games for PC. Here is a free one:
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I searched a lot in googl and youtube for a step by step explanation for the Finite Elements Method. All throw a bunch of equations and mathematical terms without explaining why or where they came from.
Would you please suggest a good book or an article that clearly explains FEM?
Thanks
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Dear;
The following documents show exemples of its application :
Automated Solution of Differential Equations by the Finite Element Method
Regards
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Electromagnetic (EM) waves have invoked a lot of interest among scientists and engineers over centuries. And this interest seems to be on the rise, in view of new applications of EM waves being explored and developed, particularly at newer and higher frequencies.
Propagation characteristics of EM wave depend on its frequency (or wavelength), to a large extent. And when an EM wave interacts with an object/material, it undergoes reflection, refraction, scattering, attenuation, diffraction, and/or absorption. Each of these effects are dependent on the frequency of the EM wave(s) because the size of wavelength (relative to the object/material) assumes great significance.
And due to the huge range of frequencies of EM waves employed in various applications these days, they undergo a variety of different effects. This confuses the scientific community sometimes as it is often unclear as to which effect is more dominant at what frequency.
Thus a single mathematical formula (or a small set of formulae) would/could be of great help if different effects (as listed above) and their relative weights can be known at different frequencies. This may be of great boon to young scientists and engineers as it would simplify things particularly for those who are mathematically minded.
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Not all these phenomena can be summarized in the permittivity of the material. For a start there is the permeability, which is as basic as the permittivity, then whole areas that these two do not cover at all, such as fluorescence, ionisation, photo-electricity, Rayleigh and Raman scattering, interaction with (other) fundamental particles, interaction with gravity/space-time, and more.
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By dynamical systems, I mean systems that can be modeled by ODEs.
For linear ODEs, we can investigate the stability by eigenvalues, and for nonlinear systems as well as linear systems we can use the Lyapunov stability theory.
I want to know is there any other method to investigate the stability of dynamical systems?
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An alternative method of demonstrating stability is given by Vasile Mihai POPOV, a great scientist of Romanian origin, who settled in the USA.
The theory of hyperstability (it has been renamed the theory of stability for positive systems) belongs exclusively to him ... (1965).
See Yakubovic-Kalman-Popov theorem, Popov-Belevitch-Hautus criterion, etc.
If the Liapunov (1892) method involves "guessing the optimal construction" of the Liapunov function to obtain a domain close to the maximum stability domain, Popov's stability criterion provides the maximum stability domain for nonlinearity parameters in the system (see Hurwitz , Aizerman hypothesis, etc.).
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Given:
1. The nearest neighbor of 𝑝𝑖 then 𝑝𝑖-𝑝𝑗 is a Delaunay edge.
2. In a 3D set of points, if we know that consecutive points ie... 𝑝𝑖-𝑝i+1 are nearest neighbors.
3. The 3D points do not form a straight line
Assumption:
Each Delaunay tesselation (3D) has at least 2 nearest neighbor edges.
Is my assumption true? If not can you please explain to me the possible exceptions?
Thanks,
Pranav
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Are you trying to play chess in 3D?
Your idea is a good one, but your assumptions are not.
You need to give a clear definition of paths, so I suggest for you to start in one 3D box, it includes 8 points. I prefer to give each point the following notation
P(i, j, k), so the locations of the 8 points are at
(0,0,0) (1,0,0), (0,1,0), (0,0,1), (1,1,0), (1,0,1),(0,1,1) and (1,1,1).
Study this cube carefully, define each Delanoy edge (axioms of the path), and then add another box, which means 12 points, etc.
If you find the closed formula that allows you to calculate all possible paths from the starting point at the origin to the farthest point at the upper corner of the rectangular box, then you are on the right track.
I wish you good luck.
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Any decision-making problem when precisely formulated within the framework of mathematics is posed as an optimization problem. There are so many ways, in fact, I think infinitely many ways one can partition the set of all possible optimization problems into classes of problems.
1. I often hear people label meta-heuristic and heuristic algorithms as general algorithms (I understand what they mean) but I'm thinking about some things, can we apply these algorithms to any arbitrary optimization problems from any class or more precisely can we adjust/re-model any optimization problem in a way that permits us to attack those problems by the algorithms in question?
2. Then I thought well if we assumed that the answer to 1 is yes then by extending the argument I think also we can re-formulate any given problem to be attacked by any algorithm we desire (of-course with a cost) then it is just a useless tautology.
I'm looking foe different insights :)
Thanks.
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exemple.docx
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I am currently studying the effect of atrophy of a muscle on the clinical outcome of joint injury. There is actually another muscle that was previously well established to have an effect on clinical outcome, and both these 2 muscles are closely related. The aim of the study was to shed some light on the previously ignored muscle to see if there is anything that can be done to help improve clinical outcomes in that aspect.
While doing univariate analysis, i wasnt sure if i should include the previously established muscle as well and when i included it into the multi-linear regression model, the initially significant primary variable became insignificant. I was thinking if this could be due to co-linearity but the VIF value was not high enough to show significant co-linearity in the two variables. (GVIF ^(1/(2*Df))=1.359987)
My question is, should these 2 variables be included in the same model if they are both highly correlated (clinically and mathematically) but was not determined to have co-linearity, or should these 2 variables be evaluated separately?
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Bryan Soh, your question is a good one. I think it's necessary to be familiar with the nature of your variables (which it seems you are). Unfortunately, I'm not, but might I suggest that you conduct your analyses both ways, look at the results, then think carefully about which results are likely to be most valid.
I also think it is a good idea to present both sets of results if that's permissible. As you are obviously aware, the world of research isn't black and white, and making other researchers, and consumers of research, aware of that could well be helpful. About 20 years ago, I read an article in a top psychological journal in which the author analysed her data in more than one way (from memory, it was more than only two ways), and she discussed the ins and outs intelligently and with insight. It was, for me, much more enlightening that the run-of-the-mill articles that seem to report clean-cut results but leave the reader wondering how much cleaning up and manipulation, and obscuring, occurred to obtain those results.
Every good wish as you plough on!
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Good evening all;
We are looking for literature on the mixed integer formulation of water distribution problems using Multi objective optimization methods.
Thanks
Nasiru Abdullahi
Mathematics Department
NDA Kaduna
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Sure. But you are not really helping by not being precise! And I am quite certain that there is one major goal - such as a quickest route of the water. I suggest that you check with the literature - which is quite big.
A search string might look like this, or with smaller adjustments:
water network [supply, distribution*, system*] problem*
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I know lots of composers have created works around mathematical constructs such as the Fibonacci sequence. I would like to learn if any composers have used mathematical constructs in their music to represent journeys.
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Tool - An American progressive rock band :)
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Dear all,
I am trying S parameter measurement _transmission_using TEKTRONIX DSA8300 oscilloscope. Initially, S parameters files are generated in LINEAR _magnitude format. Now S parameters transmission files are appearing in dB format from oscilloscope. Perhaps machine settings seem to be changed.
1)Kindly guide for appropriate setting button in TEKTRONIX DSA8300 oscilloscope, so as to receive the data from dB to linear magnitude format.
2) Also, alternative mathematical ways to receive data in LINEAR magnitude format are appreciated as well , kindly.
best thanks
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Charles Sanders Peirce regarded mathematics as “the only one of the sciences which does not concern itself to inquire what the actual facts are, but studies hypotheses exclusively” (RLT, 114). Since, by contrast, “[w]e must begin with all the prejudices which we actually have when we enter upon the study of philosophy” (CP 5.265), the presuppositionless status of mathematics makes it more primitive than anything found in philosophy. Given that phenomenology falls under philosophy (CP 1.280), we get the result that mathematics is prior to phenomenology.
Yet, Peirce also held that “every deductive inference is performed, and can only be performed, by imagining an instance in which the premises are true and observing by contemplation of the image that the conclusion is true” (NEM III/2, 968).
We thus have two conflicting arguments:
On the one hand, one could argue that mathematics is prior to phenomenology because mathematics makes even less presuppositions than phenomenology.
On the other hand, one could argue that phenomenology is prior to mathematics because whatever happens during mathematical inquiry must perforce appear before (some)one.
Peirce's pronouncements notwithstanding, it is not obvious to me why the first argument should trump the second. In fact, I find considerations about the inevitability of appearing in mathematics to be decisive.
What do you think?
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I don't understand the relationship of "is prior to" to ideas. Do you mean which idea came first to a human being? Or which idea has fewer presuppositions? Or which idea does not depend on the other? If that is the case, is your question a false either-or assertion, as can't two ideas be co-dependent, like chicken and egg?
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344/5000
Hi researchers, I have a problem with the mathematical formulation of the multi objectives model for solving the RFID planning problem network. Do you have any courses or documents or information that can help me achieve my mathematical model of RFID network optimization deployed in a body network. i didn't choose the approach and the algorithme of multi optimization yet, I am formulating my problem mathematically
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Thank you Dear Anatol Badach.
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how I do obtain in the mathematical expression "limiting current density used to reduce Fe+3(A/m2)"? actually how i find the i (Fe)?
i (c)= i (cu)+i (Fe)
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Armin,
Did you find the equation?
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Is there an encyclopedia of all the branching mathematical axioms, together with various ways of proving different theorems based on those axioms?
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Amauri Martins-Britto It is indeed helpful for me in other ways. Thank you.
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As you may be knowing that there are different mathematical tools and techniques which we can combine or hybridize with heuristic techniques to solve their entrapment in local minima and convergence issues. I know two techniques namely Chaos theory and Levy distribution as I have used them for increasing convergence speed of Gravitational Search Algorithm (GSA). So, my question is: can you name and briefly explain other mathematical techniques which we can combine with optimization algorithms in order to make them fit for solving complex real world problems.
Thank you.
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Optimization algorithms handling a fixed number of real correlated values (non-separable) can be of 2 types: gradient-based and derivative-free.
Gradient-based procedures seem to be significantly faster than derivative-free ones.
GRADIENT-BASED METHODS (some):
Stochastic Gradient Descent (SGD)
Nonlinear Conjugate Gradient
L-BFGS
Levenberg-Marquardt Algorithm (LMA)
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The master Paul Erdos said "Mathematical may not be ready for such problem"
Terence Tao recently proposed a new and advanced approach for this conjecture and concluded: "Almost all orbits of the Collatz map attain almost bounded values".
The Collatz 's conjecture is infamous and very hard to solve
Take any positive integer, if it is even divide it by 2. If it is odd , multiply the number with 3 and add 1. Whatever the answer , repeat the same operations on the result.
Suppose the number is 5 then the operations wil be as follows: 5, 16, 8, 4, 2,1,4,2,1
Suppose the number is 7 then the operations will be as follows:7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1,4,2,1
The conjecture has been verified by computer for number as big as 10^18 and respects all the powers of 2. This is easely checked: 128, 64, 32, 16, 8, 4, 2, 1, 4, 2, 1.
How any positive integer reach some power of 2 in order to reach the loop of 4, 2, 1.?
We claim that any positive integer has a special numbber equal to a multiple of the positive integer. When the operation of 3n+1 is performed on that multiple it leads to some power of 2 .
N=1 gives special multiple 5=5*1.
3*5+1=16=2^4
N=3 gives special multiple 21=3*7
3*21+1=64=2^6
N=5 gives special multiple 85=17*5
3*85+1=256=2^8
The set (1, 5, 21, 85, 341.....) are called Collatz Numbers.
So we can claim that the Collatz's conjecture is almost solved.
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Read my answer carefully.
I show the formula of your (trivial answer), and the second set is also trivial.
One can generate infinite sets of such families!!
Observe that each number n in the first family has the property
3n + 1 = 2k which satisfies Collatz's Conjecture.
And each number n in the second family has the property
3n + 1 = 7x 2k
therefore after removing 2k by k steps divisions, we reach the number 7
which satisfies Collatz's conjecture too.
The whole procedure is NOT PROOF.
All are elementary computations.
Regards
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A careful reading of THE ABSOLUTE DIFFERENTIAL CALCULUS, by Tullio Levi-Civita published by Blackie & Son Limited 50 Old bailey London 1927 together Plato's cosmology strongly suggest that gravity is actually a real world mathematics or in another words is gravitation a pure experimental mathematics?
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Very interesting question. To me, best answer is given by Roger Penrose using the paradigm "The three worlds of reality": the Physical World, the Mental World, and the Platonic World (Mathematics lives here).
The claim is that Platonic World "maps" onto Physical World and hence all possible physical universes are constructs of information consistent with Mathematics.
Obviously Physical World "maps" onto Mental World (because we live in the physical world); and Mental World "maps" onto Platonic World. But the three worlds are different.
For a much better explanation you can see Penrose's book "The Emperor's New Mind"
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In the preprint
W.-H. Li and F. Qi, A further generalization of the Catalan numbers and its explicit formula and integral representation, Authorea Preprints (2020), available online at https://doi.org/10.22541/au.159844115.58373405
I concluded two integral formulas indicated in the picture.
(1) Do you know the existence of these two integral formulas? Please give concrete and explicit references containing these two integral formulas.
(2) Can you find direct and elementary proofs for these two integral formulas?
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Dear Feng Qi
I am attaching a proof of the first formula.
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why we plot absorbance vs wavelength although there is no direct formula between them and I also want to know that their is any direct or indirect relation between molar extinction coefficient and wavelength. I am trying to generate a theoretical plot between absorbance vs wavelength of single layer MoS2 by using python program,so I need mathematical formula for calculation .
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Very interesting discussion and proposals to solve for calculating the absorbance of a single layer of MoS2 .
The absorbance is important to optically characterize the materials. The absorbance is the absorbed fraction of the incident light with a specific wavelength on a material with a given thickness. It is required for optical filters and for photodetectors and solar cells.
The dependence on the incident light wave length stems from the energy band structure of the material such that it is dependent on the probability of transferring of an electron from the valence band to the conduction band by the incident photons. Specifically it depends on the absorption coefficient as a function of the wavelength.
The key point for the solution is to calculate the energy band structure of the two dimensional material and from it you can get the absorption coefficient as a function of lambda. Then you can calculate the absorbance. As you have here a single layer the absorption coefficient will be equal to the absorbance.
You might benefit from the thesis given in the link: https://digitalcommons.mtu.edu/cgi/viewcontent.cgi?article=1049&context=etds
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The literature on public (and some school students') understanding of science and mathematics shows many have problems decoding relatively simple information, concepts and data such as from graphs. In the UK, and many other countries, the public have been exposed to unprecedented amounts of information, ideas, scientific findings, formulae, graphs and so on that purport to provide understanding of the global COVID-19 pandemic, so as to presumably advise on risk and guide personal decisions and influence behaviour. But what are the implications of this massive shift in communication for public understanding in general and for future science and mathematics education in schools?
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Thank you for sharing your paper Martin. I found it insightful - particularly your interpretation of graphs and your case for building 'critical STEM literacy'. From recent exploration, I notice that these graphs with data from the pandemic, present interesting outliers and multiple trend-lines which are ignored or cherry-picked in the final interpretation. Inferential stats while allowing decisive conclusions lead us to overlook these interesting data points. Critical graphicacy practices if nurtured from school will create this informed public, who will then find it difficult to simply accept the text interpretation, isn't it?
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FTIR technology is considered the most advance for the detection of adulterants in milk. Is there any mathematical relation that can describe the relationship between the amount of adulterants in milk using the absorbance from the FTIR? Please suggest any research articles that describe this or related areas.
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Relation between milk with adulterants . Many times urea is added in the milk as adulterant to increase the density. If you is isolated then in FTIR it shows the absorption for NH2(V NH = 3200-3350 cm-1) and C=O) at (v 1700 cmi1).
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NO. No one on Earth can claim to "own the truth" -- not even the natural sciences. And mathematics has no anchor on Nature.
With physics, the elusive truth becomes the object itself, which physics trusts using the scientific method, as fairly as humanly possible and as objectively (friend and foe) as possible.
With mathematics, on the other hand, one must trust using only logic, and the most amazing thing has been how much the Nature as seen by physics (the Wirklichkeit) follows the logic as seen by mathematics (without necessarily using Wirklichkeit) -- and vice-versa. This implies that something is true in Wirklichkeit iff (if and only if) it is logical.
Also, any true rebuffing of a "fake controversy" (i.e., fake because it was created by the reader willingly or not, and not in the data itself) risks coming across as sharply negative. Thus, rebuffing of truth-deniers leads to ...affirming truth-deniers. The semantic principle is: before facing the night, one should not counter the darkness but create light. When faced with a "stone thrown by an enemy" one should see it as a construction stone offered by a colleague.
But everyone helps. The noise defines the signal. The signal is what the noise is not. To further put the question in perspective, in terms of fault-tolerant design and CS, consensus (aka,"Byzantine agreement") is a design protocol to bring processors to agreement on a bit despite a fraction of bad processors behaving to disrupt the outcome. The disruption is modeled as noise and can come from any source --- attackers or faults, even hardware faults.
Arguing, in turn, would risk creating a fat target for bad-faith or for just misleading references, exaggerations, and pseudo-works. As we see rampant on RG, even on porous publications cited as if they were valid.
Finally, arguing may bring in the ego, which is not rational and may tend to strengthen the position of a truth-denier. Following Pascal, people tend to be convinced better by their own-found arguments, from the angle that they see (and there are many angles to every question). Pascal thought that the best way to defeat the erroneous views of others was not by facing it but by slipping in through the backdoor of their beliefs. And trust is higher as self-trust -- everyone tends to trust themselves better and faster, than to trust someone else.
What is your qualified opinion? This question considered various options and offers a NO as the best answer. Here, to be clear, "truth-denial" is to be understood as one's own "truth" -- which can be another's "falsity", or not. An impasse is created, how to best solve it?
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This way of thinking would support dictators and totalitarianism. It is rationalization to do nothing about it. But if one is aware then one is responsible. The legal theory is called, "participatory negligence." One can be guilty of a crime one does not commit. Hannah Arendt was instrumental in showing this, and it happened in a killing in New York. The attacker interrinterrupted, after around 80 people shouted that they woukd call the police. But the sttacker resumed, when no police help came, and finally killed the victim. All those 80 people were charged with the crime of negligence.
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Hello fellow scientists,
I wish to determine the Dissociation Constant (KD) of a DNA polymerase binding dsDNA. I won't disclose what the DNA polymerase is because it is unpublished work. I have done some binding assays in Agarose gels, but due to the poor sensitivity of the available dyes I had to visualize the relative binding stoichiometrically, and I could not simply just set the protein or DNA concentration around the expected KD.
Previous work in our lab has determined a KD = 20 nm for our DNA polymerase binding a 33mer locked double stranded DNA hairpin.The purpose of using something so complicated was for kinetics assays.
However, I am using a 13-mer dsDNA construct because my goal is to crystallize the DNA complex and a 33-mer is just way too large! My supervisor has advised that I don't believe that my KD is actually 20 nM for my small dsDNA construct.
I am interested in using Isothermal Titration Calorimetry mainly to calculate the KD of my protein to binding this 13mer dsDNA construct. I would titrate my dsDNA into a fixed concentration of protein. I could guess that the KD is 20 nM, but I actually don't know for sure.
I have heard that when you determine the KD you have to have some estimate of the KD and then scan ligand concentrations above and below the KD, measure the response to get a curve of response vs ligand concentration and the KD is mathematically fit or basically it is just the inflection point of the binding curve.
However that advice doesn't tell me if the KD is say 20 nM, what should fixed concentration of my protein be? (I have appreciable amounts of 100 µM protein because I am a crystallographer so excessive protein isn't an issue.). What is the max and min range that I should scan the ligand concentrations? What if the KD is way worse than we predicted and it is actually 1 µM? What fixed concentration of protein should I use and what min and max concentrations of ligand should I use?
Is there a way that I can measure the KD with a certain fixed concentration of protein, and a huge range of ligand concentrations regardless of if the KD is 20 nM or 1 µM? Is that possible?
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  • For statistically valid results and hyperbolic binding curves, the final ligand concentration should cover the range of 0.1 to at least 5, better 10 times Kd (if solubility permits), you need at least 12 ligand concentrations, which should be equal spaced (doi:10.1006/jtbi.1996.0023).
  • For method with reasonable sensitivity, the constant concentration of the macromolecule should be around Kd for best precision. For insensitive detection methods like ITC, you may need a higher macromolecule concentration for a well-detected signal.
  • If your binding curve is not hyperbolic, you'll need a wider ligand concentration range, in that case it may be worthwhile to space the data points logarithmically (1.0, 1.6, 2.5, 4.0, 6.3, 10, 16,...). From these guidelines it follows that you need to do an initial search study for rough determination of Kd. "Rough" means the order of magnitude.
  • Btw, the use of linearisation (say, Lineweaver-Burk or Scatchard plots) for the determination of Kd is outdated, although these methods still have use for data presentation. Use non-linear regression for determination instead, the Nelder-Mead simplex algorithm (doi:10.1093/comjnl/7.4.308) is more stable than Marquardt-Levenberg (doi: 10.1137/0111030), but requires bootstrapping for determination of error margins.
  • You may also wish to think about the detection method you use, ITC requires relatively large amounts of both macromolecule and ligand. Perhaps, surface plasmon resonance (SPR) would be a better choice. After all, you'll need lots of material for crystallisation later ;-)
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For any given function f : [a, b] → R, there exists a sequence of polynomial functions converging to f at each point where f is continuous. (Note that we did not ask the convergence to be uniform).
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Please see attached.
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The acceptable practice is to validate a model used under any study. What validation methods are available and would we confirm one superior over others?
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Welcome.
You can validate your analytical model by the following methods:
- running experiments under the same assumptions of the analytical mode
- By using numerical simulation where the the system is solved by the numerical methods. There are now powerful simulator for many disciplines of science such as electronic circuits , electronic devices, semicondcutor fabrication processing.
- In some statistical systems they can be validated by Monte Carlo simulations.
This is list may not be exhaustive
Best wishes
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My question is: Is there any mathematical or empirical way to prove that given a dataset containing noisy signals y(t) [Y = X +N] and another dataset containing noise N and we want generator to generate clean signals X ̂ . How to prove other than experiments that generator will be able to generate clean signals from random noise vector z.
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Thank you so much for your answers.
Janez Podobnik I have been workikng since your answer and found the optimality condition and also found the proofs of optimal estimator. I have minimized the summary as you can see here in the attached picture.
But I am stuck in linking the attached theory with my case. Since this is the general cndition for an optimal estimator (attached picture) and yes generator would be minimizing a cost function but how can I say that my generator would be able to generate clean signals?
I have changed the notations in main question for simplicity purpose.
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If the answer is yes, can one replace log n by another sequence that approaches ∞ faster than log n ?
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Good search, Romeo! It looks that the examples provided satisfy the unboundedness condition in our question. I did some search as well, and all the examples I found do satisfy that condition.
Thank you for the increased interest in this question, I'll leave it open of course, time is not of the essence here...
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I have a query regarding data transformation if anyone can provide any guidance please?
I was wondering if, generally, it is possible to transform a variable's raw data twice, using 2 different methods, for the purpose of 2 different tests? I will provide you with a little background to my study first. I have a variable for 'Adverse Childhood Experiences' containing 1 score per participant. N = 113; however, 65 of these are 0 values and 3 are missing data - which I believe is disrupting my data considerably. I understand that it is not advised to simply remove the cases that read 0 just because there are many (however, if you recommend otherwise please let me know if so and why).
Useful to note here is that this variable has a skewness of 1.943, and because of this, I have made the decision to transform it.  
I am carrying out a path analysis with 1 IV, one DV and 2 mediators. In the first instance I am carrying out a t-test (IV - gender, DV - ACE score) and then in the second instance I am carrying out a linear regression (IV age, DV - ACE score), to understand whether age and gender need to be included in my path analysis as covariates. In order to meet the assumptions of the t-test (namely, normal distribution across both levels of the IV: male and female) I have transformed the raw ACE data this using Tukey's formula, which brought the skewness to < 1 for each IV level - great. But then when I go to carry out the linear regression, and aim to meet the assumption of approx. normal distribution of residuals, the assumption is not met on the Tukey transformed ACE data. I have carried out a number of other transformations on the raw ACE data and the only one where the residuals are normally distributed for the regression is through a Log10 transformation. 
My question is this: am I able to carry out the t-test with the Tukey transformed variable data, and then the linear regression with the Log10 transformed data? Or is it the case that I need to use the same transformed data for each stage of the analysis (ie. both Tukey or both Log10 for t-test and linear regression and then the same onward path analyses?) 
If it is the case that I will need to use the Log10 ACE data to go back and carry out the gender t-test, it is useful to note here that I have done this already and when inspecting the Log10 transformed ACE data across the gender variable descriptives table the results come out very strange - for example, N for males goes down from 15 to 6, and N for females goes down from 115 to 59, and there are outliers, where there were none in the Tukey transformed data descriptives, so it is confusing me a little. 
Any guidance welcome!
Thank you
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I assume your data are count values (i.e., the number of adverse childhood experiences). If so, then use a count model (negative binomial is usually a good choice). Transfroming your data is not required at all. If excess zeros are a problem, consider a zero-inflated negative binomial model.
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In mathematical ecology, the recent trend is predator induced fear to prey which is an indirect effect of predator to prey. My question is how the prey populace are afraid of infected predator? Are they capable in inducing same level of fear as of healthy predator? Any efforts regarding this will be appreciated.
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I'm sorry, the answer was not for you. I posted by mistake !.
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Hi all,
I am dealing with data with sevaral features and many of them are highly correlated with each other as well as with dependent variable.
In my research on this topics, I found that multicolinearity is harmful for regression problem and may not end up with good model. I got some suggestion that if the features are highly correlated then we have to remove them using VIF criterion.
But, logically when I think of removing correlated features from my analysis how can expect better model as I am not considering all the available information.
Is there any logical explaination or mathematical explaination is available for the above question?
Also, I am thinking that each features are somehow related to any of the other (May be nonlinearly) in that case, do we have problem of multicolinearity ?
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The "mathematicaL" explanation is to examine the formula for the partial regression coefficient. It contains the covariance between the two independent variables, and if this is quite high, it will dominate the estimation of the coefficient. At the most extreme case, the two independent variables are identical, so neither one can make a separate contribution.
In my opinion, the best approach is to choose the most theoretically relevant variable from each set of highly correlated variables and use that one. This may well not cost you as much as you might think, because once you enter one of the variables, adding any of the other variables will amount to putting "the same thing" into the equation, so you R-sq is unlikely to increase.
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The new Education Act (LOMLOE) that is now being prepared in Spain intends to make Mathematics an optional subject. The Mathematics Institute has issued a manifest that argues about the importance of Mathematics in society, and in favour of keeping Mathematics as a compulsory subject in high school. If you agree with this, please sign the manifest at the link below (the manifest is in Spanish; I don't remember if there is an English version):
There is also a petition at change.org:
Thank you very much in advance.
Hebert
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This link talk about:
What arguments can I give a high school student why mathematics is important?
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In the midst of or post Covid-19, any suggestion(s) or (articles) on how best to implement blended teaching to optimize teaching and learning of mathematics
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I need a documented answer with a mathematical derivation, please.
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Check out Brian Hall's book, "Quantum Theory for Mathematicians" in the Springer Graduate Text in Mathematics series vol 267 In it he goes through the history and derivation of DeBroglie's theory.
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Hello
For typical dose-response assays, our lab usually uses steady state intervals for defining the difference between control and tested compound. For those assays, we typically use the angular coefficient or end-point value of given curve (within steady state) to estimate percentage of inhibition, or even kinetic constants
Now we have being working with an enzyme with strong 'sigmoidal' time curse reaction (hill n=3). How can I mathematically compare curves between control and inhibited reactions, or calculate constants?
If anyone could please point me to a good theorical reference or literature examples, I will be very thankful
Stay all safe
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The simplest way is to pick a specific time point as the point at which to calculate % inhibition. This is purely phenomenological. No theory.
If you have an enzyme reaction that shows a time lag before reaching maximal rate, you should investigate the reason for it. Maybe the enzyme autoactivates in the presence of its substrate, like an autophosphorylating kinase, or the substrate may slowly displace a competitive inhibitor. You may be able to preactivate the enzyme so as to get Michaelis-Menten behavior.
Time lags can also occur in coupled enzyme reactions if the concentration of the 2nd enzyme in the sequence is not high enough.
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Let T denote the circle group, that is, the multiplicative group of all complex numbers with absolute value 1. Let f : T → T be a (sequentially) continuous map, and such that f(z2 ) = f2 (z) for all z ∈ T. Then there is an integer k such that f(z) = zk for all z ∈ T.
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Another proof
let f(z)=exp(ig(a)), such that z=exp(i a), a belongs to [0,2pi]. From
f(z^2)=f^2(z), one concludes that there is an analytical function g(a) having the property as 2g(a)=g(2a)+2npi, for some integer number n, so n is zero. We must answer to this question which g(a) is only either linear function or not!
By power series, we could imply that g is linear function, then g(a)=k.a. indeed
f(z)=z^k, for any positive real number, are alone class functions, they satisfy at this property.
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Many informal settlements have insufficient capacity to forecast, check, handle and reduce disaster risk. These communities face a growing range of challenges including economic hardship, technological and social impediments, urbanisation, under-development, wildfire, climate change, flooding, drought, geological hazards and the impact of epidemics such as HIV/AIDS and COVID-19, sometimes termed ‘the burden of disease’. The inability of these communities to withstand adversities affects the sustainability of initiatives to develop them.
This is a question I would have asked during my masters degree research on Resilience in Disasters. I would like to know the opinions of other researchers as I would like to properly answer this question in a different research-related topic.
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i think the attitude and positivism of the community and their leaders is one big factor to add.
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I want Journals names or list
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Dear search for journal of Mathematics in Web of Science Journal Master list and you will see many journals for Mathematics.
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I am studying mass-spring-damper systems with coulombs friction. There are multiple discussions on simulating such systems using numerical methods and the problems that arise due the discontinuous excitation but I wanted to know if an analytical solution exists. To be mathematically clear about the problem, I am trying to analytically solve the following.
m*(d2x/dt2) + c*(dx/dt) + k*x = F*sign(dx/dt)
where the sign function is defined as:
sign(var) = 0 if var = 0
sign(var) = 1 if var > 0
sign(var) = -1 if var < 0
Note: I am aware of treating such systems as piece-wise linear nonlinear systems but I want to know whether a general solution exists that is capable of solving the problem without breaking it to a number of mini-problems.
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Dear Amir, this equation has the following ananlitics. It can be glue for v more than zero exact solution and for v less than zero. In both cases they are spirals and exactly solvable, but tends to different stationary points. You can even draw its phase space picture: you draw two spirals(exact solutions)each on proper halfspace and jump from one to another, when v=0.
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If it makes easier, assume that f is continuous on [0,∞).
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without loss of generality, you could assume that a=1. Also, exponential function classes are trivial solution of it.
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To avoid trivial solutions, assume that a and b are non-zero real numbers.
My feeling is that, for certain values of a and b, there are no such functions.
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For f(0) non-zero and t positive number,
f(x)=f(0)exp((2.\pi.i.x)/t) is a solution, with a=exp(-2.\pi.i.b)/t) and f(x+t)=f(x).
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I am interested to solve a mathematical problem (MILP) using evolutionary algorithms but confuse about which one to choose as a beginner in the programming languages. Suggest an algorithm easy to implements with better results.
Thanks
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It feels like you didn't try to use an exact method. Thus, I have to write here that all the beginers are suppose to listen to prof. Patriksson. So, at first try to find an optimal solution. Use CPLEX, learn to model. This will be one of your first sentences in the research paper: "We tried to solve this NP-hard problem... (provide some proof that you really tried)... Because we are not able to generate an optimal solution in reasonable amount of time we decided for a heuristic approach..." I hope this is clear. Otherwise, it is like working with machine learning without knowing about statistical tests. It is slightly embarrassing.
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Specifically, I know that there are discontinuous everywhere solutions f of the given equation. I also know how to prove that, if f is continuous at 0, then f(x)=0 for all x∈ℝ. I don't know what gives the assumption of continuity of f at a non-zero point?
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You are correct Romeo; a nice solution & discussion can be found here:
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What are the mathematical equations used to assess the environmental impact using some biological criteria in green algae?
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Dear professor,
The following article may provide inspiration to you about the subject.
Best wishes,
Tahir
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Quadratic equations with complex root were considered unsolvable in secondary schools. this limitation is due to the lack of topic to address the idea of complex number in Nigerian secondary school Mathematics curriculum.
is it Okay to introduce the idea of the complex number so as to enable the student to solve a wide range of questions?
This question was raised by a student I coach when I told him that some quadratic equations do not have solutions in the realm of real numbers!
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As long as the students are comfortable with algebra of real numbers and the quadratic equation, complex numbers should not be particularly challenging to them. These numbers follow rather naturally from a straightforward application of simple algebraic concepts, though novel at the same time. Humans crave novelty, and the younger they are the more so, I think.
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I understand that we can produce that number in MATLAB by evaluating exp(1), or possibly using exp(sym(1)) for the exact representation. But e is a very common constant in mathematics and it is as important as pi to some scholars, so after all these many versions of MATLAB, why haven't they recognize this valuable constant yet and show some appreciation by defining it as an individual constant rather than having to use the exp function for that?
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Dear brother and one of my best friends Mahmoud,
"you are really great researcher" This is how I see you.
Warmest regards,
Kareem
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UPDATE: The values of the variables that I am currently concerned with are:
a~65
V~3.887
While trying to solve a circuit equation, I stumbled onto a type of Lienard Equation. But, I am unable to solve this analytically.
x'' + a(x-1)x' + x = V-------------------------(1)
where dash(') represent differentiation w.r.t time(t).
The following substitution y =x-V and w(y) = y', it gets converted into first order equation
w*w' + a(y+V-1)w + y = 0; ---------------------- (2)
here dash(') represent differentiation w.r.t y.
if I substitute z = (int)(-a*(y+V-1), (int) represent integration. The equation gets converted into Abel equation of second kind.
w*w' - w = f(z). -------------------- (3) differentiation w.r.t z.
it get complicated and complicated.
I would like to solve the equation (1) with some other method or with the method that I had started. Kindly help in solving this,
Thank you for your time.
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I don't know about analytic solutions but this is the equation for a harmonic oscillator in a constant force field with nonlinear damping. It is a like a mass suspended by a nonlinear spring in a gravitational field. There is a single equilibrium point at x=V and x'=0 whose stability depends on the value of a. Solutions will either be unbounded (go to infinity), which is probably unphysical for your electrical circuit, or they will decay to the equilibrium point, following the usual exponential law for a linearly damped oscillator as they approach it. Only the case a=0 has (neutrally) stable oscillations whose amplitude depend on the initial conditions just as you would expect for a harmonic oscillator without damping. There are no limit cycles and no chaos.
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I am interested in including the inverse piezoelectric effect into my GaN HEMT simulation. Sentaurus Device provides a special feature that allows me to update the stress field by invoking the mechanic solver (Sentaurus Interconnect). But I don't have confidence in the results I got. Because from the mathematical point of view, solving the inverse piezoelectric effect is just a simple matrix multiplication (AB = C). However, the final matrix C I got was very weird - some components in C matrix should be zero but they are not. So I was wondering if there is anyone has the same situation about this?
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Dear Han-Wei,
welcome,
You want to validate your results.
you can make this validation by solving a known simple example where it can be solved analytically or its numerical solution is known with high confidence.
You can simplify the geometry of the device such that it can be solved analytically.
Than you can compare your numerical solution with the analytical solution.
You must not solve specifically for the HEMT.
Best wishes