Science topics: Mathematics
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Mathematics - Science topic

Mathematics, Pure and Applied Math
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Is there any mathematical way/method to calculate GRF from kinematic data?
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Firstly you should calculate the equation at the centre of mass. And you can using reduction techniques in determinate system to reduce unknowns. exp: neglecting some parameters or some muscles.
Then using Newton laws to calculate forces and moment.
Consider summation of forces in the horizontal an vertical direction separately including GRF and external forces equal to m x a.
Finally consider summation of moments in centre of mass equal to mass moment of inertia x angular acceleration.
By solving these 3 equations by putting knowns, the unknown parameters are calculated.
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Have you ever wondered about using dimensional analysis in mathematics, as we do in physics.
For example, the Pythagoras formula is:
a^2+b^2=c^2
which relates the surface areas of squares resting on different sides of a right-angled triangle.
Therefore, based on a simple dimensional analysis, we may conclude:
a^2+b^2, could NOT be equal to c^3, due to conflict of dimensions.
This is a simple example. How about using dimensional analysis in other mathematics problems.
Please, feel free to share with me, your idea and comment.
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Yet another approach regarding dimensional analysis, for the proof of Pythagoras's Theorem:
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I am thinking of the vector as a point in multidimensional space. The Mean would be the location of a vector point with the minimum squared distances from all of the other vector points in the sample. Similarly, the Median would be the location of the vector point with the minimum absolute distance from all the other vector points.
Conventional thinking would have me calculate the Mean vector as the vector formed from the arithmetic mean of all the vector elements. However, there is a problem with this method. If we are working with a set of unit vectors the result of this method would not be a unit vector. So conventional thinking would have me normalize the result into a unit vector. But how would that method apply to other, non-unit, vectors? Should we divide by the arithmetic mean of the vector magnitudes? When calculating the Median, should we divide by the median of the vector magnitudes?
Do these methods produce a result that is mathematically correct? If not, what is the correct method?
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The components of random vector in your case are not independent, because they are connected with normalization condition. It means that you can calculate conditional expectations only. Say, M(X|Y) and M(Y|X) in 2D case. And the ME vector in this case consists of conditional components. You should verify, would it be unit vector or not. Concerning median I'm not sure. It is neccessary to think more. In any case it should be calculated using conditional probabilities.
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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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Oblique assymptote rule for rational function - https://www.storyofmathematics.com/oblique-asymptote
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Why the Chi-square cannot be less than or equal to 1 ?
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Adrianna Kalinowska There is no special meaning of the value 1 for the khi-square... As a probability function, continuous, the probability of a random variable following a khi-square law to be exactly 1 is 0. As a distance between two contingency tables, it's not clear why 1 should be given a special consideration.
So, I don't really understand the context of your question. Please could you detail?
(By the way, I don"t understand either the origin of the original question and this debate around the value « 1 » in the khi-square…).
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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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First of all, was the fitness (error) zero (0) at the end of the evolution?
If yes, it means that the skipped variables are not important for the data being analyzed.
If not, it can either mean that some variables are not important or that the evolution is stuck in a local optimum.
Note, that for real-world data, it is unlikely to obtain fitness 0 because of noise or other imperfections (in data collection or measurement).
regards,
Mihai
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Hello everyone,
Could you recommend papers, books or websites about mathematical foundations of artificial intelligence?
Thank you for your attention and valuable support.
Regards,
Cecilia-Irene Loeza-Mejía
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Mathematics enables AI scientists to address difficult deep abstract issues utilizing established methodologies and approaches that have been used for hundreds of years. Math, in reality, aids in the knowledge of logical reasoning and attention to detail.
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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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My intervention is limited to what Umberto Eco [who I met at the University of Urbino] thinks about Fermat's Theorem. Thank you Dear Dr. Mohamed Azzedine
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can you please tell how to solve the governing equation to obtain the frequencies to compare with the ansys result
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Hi
(I haven’t looked at your xml as I doing this from my iPad).
i guess the answer is Yes and No.
Yes, we can use analytical and numerical models, or tests, to find, as best possible natural frequencies. To what effect may be worth pondering.
There are some problem with pipelines.
1) they tend to be very long. Infinite, may be a reasonable approx. Unbounded systems don’t not have modes, they have wave propagation. They can be approximated using modes but you need a lot of them and the modal summation doesn’t always converge as one would want it to.
2) every frequency is a natural frequency for an infinite system, ie you get lots of closely spaced modes, which in turn provides a high modal overlap situation (search RG, it has been discussed before).
3) I imagine that numerical solvers may have a problem with closely spaced modal systems.
4) pipelines tend to lie on something, ie the couple to terrain, again a large system.
So, chasing this problem using modes may not be your best bet.
Wave propagation for analytical models and direct numeric solution for FE probably is the better way to go.
Hope this helps
claes
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Practical applications of special functions of mathematics in the oil and gas industry and related fields, thank you
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I put several 3D fields with animations here for you to see. They are all based on data beneath the ground. http://dudleybenton.altervista.org/projects/Field3D/Field3D.html
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If possible discuss the space, basis, dimension in the context of discreate mathematics and machine learning.
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Thank you Peter Breuer for your answer.
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I am looking for papers that provide explanation analytically as well as mathematically
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I hope the following paper are interested to you
1-Computer Vision-Based, Noncontacting Deformation Measurements in Mechanics: A Generational Transformation
Sutton, Michael A.
Journal:
Applied Mechanics Reviews
Year:
2013
2-Vision-based detection of loosened bolts using the Hough transform and support vector machines
Cha, Young-Jin, You, Kisung, Choi, Wooram
Journal:
Automation in Construction
Year:
2016
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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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Hi Solihu,
The orthometric height is hard to realize perfectly in practice because we need to know the exact path of the plumb line within the topography and the knowledge of gravity variations or mass-density distribution inside the topography at all points along the plumb line. So, the approximation (hypotheses) given by the Helmert (1890) orthometric heights is most used ( Heiskanen & Moritz, 1967, Chapter 4). Also, several refinements have been proposed to the Helmert method to improve models for the value of integral-mean gravity along the plumb line (Tenzer et al., 2005).
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Heiskanen, W.A. and Moritz, H. (1967) Physical Geodesy, WH Freeman & Co, San Francisco, USA, 364 pp.
Tenzer, R., Vaníček, P., Santos, M., Featherstone, W.E. and Kuhn, M. (2005) Rigorous determination of the orthometric height, Journal of Geodesy, vol. 79, nos 1-3, doi:10.1007/s00190-005-0445-2
Regards
Abdelrahim Ruby
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I want to know the calculation for following paper. I am attaching the paper. Please help me
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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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Unfortunately I missed your post. Possible implementation in Wolfram Mathematica is shown in the attached picture. Of course, Mathematica's native procedure Select looks much more elegant.
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How to linearize any of these surface functions (separately) near the origin?
I have attached the statement of the question, both as a screenshot, and as well as a PDF, for your perusal. Thank you.
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It seems the linearization is accomplished by replacing x1, for x1^2. And separately by replacing x2, for x2^2 & x2^4.
In this way, the surface function is linearized about the origin (0,0), it means we can find f1(x1,x2)=a*x1+b*x2, whilst a and b are calculable in terms of the algebraic parameters, k and c.
But my question transforms to another level. How, we can find a compact algebraic expression for f1(x1,x2), and f2(x1,x2), close enough to the origin. This algebraic expression, need NOT be necessarily linear (it could be a nonlinear function).
Question synopsis:
1--How to find another compact analytical expression equivalent to f1(x1,x2), f2(x1,x2)? (with fair accuracy)
2-- Is it possible to find an approximation near the origin (0,0), for f1(x1,x2), f2(x1,x2), as a function of only one of the two variables (either x1, or x2)?
Regarding the second synopsis, I am to cite another ResearchGate question linked below:
However, the gist of the idea in this link is not clear to me.
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International exchanges are inevitable in order to develop our projects and to ensure a sufficient critical base for the research. This confronts us with the problem of translating ideas, concepts and results that have developed in our local working language. As we know, English nowadays plays the role of the pivotal language in most conferences and publications. My intention is not to argue with this position -- a pivotal language is needed -- but to understand what are the main problems raised by writing and communicating in a language that is not the one in which the work is done.
English speakers themselves must question the meaning of words, sometimes neologisms, used by a non-English speaker. Of course, what is at stake is not the words but the meaning they convey. These issues are being addressed in the study of learning mathematics in a second language, or in the study of the variety and variability of teachers' vocabularies in different languages.
As researchers the issue is somewhat different. In particular, we must coin words and expressions to name phenomena or concepts in our own working language and then the challenge of translating them, or to understand words and expressions specific to the domain coming from another cultural and linguistic environment-- sometimes via the pivotal language.
I am preparing a short essay on these issues. I will appreciate your contributions, hence my questions:
Do you have examples to share or any particular experience? What do you think about the reasons for these difficulties and the impact they may have on your own communication?
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Teachers may assist students achieve academic success by explicitly communicating positive expectations for each student, providing equal opportunity for students to engage in class discussions, and conveying to students that they are confidence in their capacity to succeed in their courses.
This is not something you learn when you first start learning arithmetic. However, this is a fundamental skill that every student should master since it allows them to develop critical thinking. Certain situations in life need you to be analytical, which is critical when making judgments.
Mathematics is the systematic application of matter. Mathematics organizes and prevents chaos in our lives. Mathematics fosters certain abilities such as reasoning ability, creativity, abstract or spatial thinking, critical thinking, problem-solving ability, and even excellent communication skills.
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I want to model and simulate a tacho-generator in Matlab/Simulink. I keep on searching the mathematical expression for the same.
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The tachometer measures the speed of a rotating shaft in revolutions per min.
For non contact measurement, one uses a laser diode and a a photodiode as a photodetector. One mounts a circular disk having holes in its circumference which are equally spaced. Assuming one hole then the diode will detect only one pulse per one revolution. You need only then to count these pulses and display them numerically in one min.
So you can feed the laser diode with a pulse generator simulating the motor and the punched disk. Then you make the light from the diode to fall on the diode which senses the pulses. You need to amplify the pulses by an amplifier and and apply them on a counter to count the pulses for a time of one min.
This may be the proposal which you may elaborate on it.
Best wishes
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How to mathematically interpret the formula Kb=Kf (1−Rw)
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This article reveals how land surface temperature influences RUSLE based soil erosion. Please have a look-
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Which programming language is best for Mathematical simulation- Matlab or Fortran?
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Matlab is very good, a program with very great possibilities and for scientific applications.
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Measurement of foundational language skills
Measurement of foundational mathematical skills
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Not sure what the question is getting at.
Regarding mathematics, it is just arithmetic at primary grade. This involves skills like:
Addition and subtraction,
Multiplication and division,
Fraction of some number,
Fractions and percentages,
etc.
And some word problems involving the above skill.
It is easy to devise tests to evaluate the level in each of the above skills.
As regards language, the primary grade is just to be able to read simple descriptive essays, and simple children's poems. The vocabulary is determined by the prevailing essays and poems for primary grades. A good level to achieve is to be able to superficially read the local newspapers. Superficially in the sense that technical material discussed in the newspaper is not required; such as politics, economics, scientific terms, etc.
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It is a new type of mathematical explanation about the origin/existence of the universe. It is based on mathematical interactions of dimensional symmetries and fundamental technical aspects of the universe.
Can you accept (agree with) this solution?
(+0-0)^6 = (+1-(-1))^3 x (+0.0-0.0)^3
It is at the foundation of my research. Hint: "(a+b)^2 = a^2 +2ab +b^2"
My research is public as a preprint yet. I like to invite you to review it too.
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Sergey Trofimov, It was an initial condition in the universe for a moment (first infinite moment) because of the relative continuation of nothingness to the next level of nothingness (0.0-0.0, 0.00-0.00, etc) as an interaction. It represents a nothingness that shows a virtual gap (0 distance) related to the dimensions in the universe, which becomes dimensional moments with the continuation of it on the infinite nothingness. There is no big difference between +1-1 and +0-0 when there is something to measure relative to a direction, with or without anything inside it. But the universe continues that nothingness to the next level.
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  • Hello. I am struggling with the problem. I can measure two ratios of three independent normal random values with their means and variances (not zero): Z1=V1/V0, Z2=V2/V0, V0~N(m0,s0), V1~N(m1,s1), V2~N(m2,s2). These are measurements of the speeds of the vehicle. Now I should estimate the means and the variances of these rations. We can see it is Cauchy distribution with no mean and variance. But it has analogs in the form of location and scale. Are there mathematical relations between mean and location, variance and scale? Can we approximate Cauchy by Normal? I have heard if we limit the estimated value we can obtain the mean and variance.
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I will suggest you go through the attached materials by David. Alternatively, you can get more of this on search engine.
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Hello,
I am searching for auto tools that can be used to calculate the number of the real-consumed cycle or number of logical and mathematical operations for a code of thousands of lines?
Regards
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As long as you do not need a cycle accurate measurement, you can use profiling tools (such as Intel VTune, GPROF, or Valgrind as also suggested earlier). With VTune you find the number of cycles per function/class, number of operations, hotspots, memory usage, and several other factors.
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I would like to know how when we change the direction of the magnetic field, the refractive indices of left and right circularly polarized light reverses, can someone tell how that happens mathematically???
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This answer is from my research book (preprint):
"If the 0.5 Spin and the 6 dimensions in electrons (E:+-0.5x6/3) make an unstable dimension (`1`) on the interaction of the unstable Spin, and if there is another elementary particle with 1 dimension for Spin as a force and -5 dimensions in the dimensional set (M dimensional set/particle in the dimensional structure) while moving and replacing the Spin 1 dimension on the interactions of the -5 dimensions, then that elementary particle can try to attract 1 dimension from electrons as an entanglement between unstable dimensions making a cyclic process from that as making the Magnetic Monopoles. And that symmetric process could keep that elementary particle (M) as a relatively satisfied cyclic force, or Photons (P: -1x6/3) could give dimensions to fill M against electrons as an interaction between them (electromagnetism)."
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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 2^68 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 odd and positive integer has a special number 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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I find it very unlikely to be correct.
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Pursuing research in mathematical science through physical problem-solving is an art. More students of science and engineering can be attracted to learn mathematics in the process and apply the mathematical tools in solving real-world problems.
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^^ The book, which can be used as an overview and introduction to applied mathematics, is particularly suitable for sophomore, junior, and senior students in math, science, and engineering...
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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
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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:
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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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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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I think Cris Wellington was very lucky with the kids. Most children are unlikely to be able to get interested in the beauty of mathematics, all the more so in an ordinary classroom. Therefore, a pragmatic approach to the formation of curricula and methods is fully justified. Individual support for gifted children is needed. This is possible in small classes, with tutorial teaching.
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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.
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  • Asked 3 minutes ago
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
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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?
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I concur with Anton Vrdoljak
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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
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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.
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I am agree with Dr Komal Bansal
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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.
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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?
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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.
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Thank you, I'm here.
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What are the various fields
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Abstract Algebra
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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?
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Hamed Sadaghian Thank you, this is very useful for me.
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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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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.
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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.
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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
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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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Sure, but the question is narrowly as to whether you can substitute a y with e^rx, which is OK under those narrow terms owing to the bijection. Of course, there is an infinity of ways whereby you could substitute for y with other, legitimate forms .
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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
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Further to Peter's answer, another way of putting it would be to say that a set with a positive or nil number of elements can exist on its own, whereas a set with a negative number of elements can only be a virtual set that must exist in relation or combination with other more 'normal' sets, and may be engaged in operations affecting those sets. It cannot exist independently, but can take on a transient role as part of an operation or operator on those sets, or intermediate results.
By the way, if I may ? It's 'I dug into a theory..', not 'I have digged ...'
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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.
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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."
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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
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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.
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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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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.
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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?
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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!
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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.
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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?
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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
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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.
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I recently saw a question regarding the relationship between language and mathematical learning, but am interested in learning more about the opposite.
Can anyone recommend relevant readings that explore the relationship between mathematical ability/maths learning and language acquisition? I am primarily interested in second/foreign language acquisition, but also interest in first language acquisition and the relation to mathematics.
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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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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/
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Mob :+91 97522 95342
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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
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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.
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A performance task? A standardized test? Or some other means? Why?
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A question that needs more thought
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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
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is there any literature available on a kinetic study on the working of RO membrane with any software or simple mathematical simulation?
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Now some especially on simulation. David Booth
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I'd love to see a rough sketch of how the task would go.
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  1. Give students raw data and ask them to write an argument or analysis based on the data.
  2. Have students explore and write about unfamiliar points of view or “what if” situations.
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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
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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.
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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!
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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
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