Science topics: Mathematics
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Mathematics - Science topic

Mathematics, Pure and Applied Math
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How tolerance factor in ABO3 ceramics is related to spontaneous polarization? Is there any mathematical relation between them?
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Spontaneous polarization happens in non-centro-symmetric crystal structures, which are not cubic. Take, for instance, barium titanate which has 3 ferroelectric phases, none of which are cubic. The tolerance factor, however, demonstrates how much crystal structure is close to the "ideal" cubic structure. Therefore, its being deviated from unity is desirable for spontaneous polarization.
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In the python library Scipy, the optimization.minimize() API has several algorithms which we can use to optimize our objective functions. But in my case, when I use this API with those algorithms it doesn't give me an expected optimal value. I just want to know whether that API has the ability to converge into a global minimum.
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Indeed I recognize the names from my previous work as a bachelor and PhD student. These functions will, in general, not give you optimal solutions, but perhaps a near-stationary point.
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I wish to understand the mathematical relationship between the land surface temperature and air temperature.
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I wanted to know if it is possible to generate random numbers using GAN and what mathematical background is necessary.
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If a GAN can accept Non-Parallel data then it has the ability to generate random numbers.
1. They may have a sequence in past to predict new numbers. OR
2. Just a random sequence .
I worked with non parallel voice data using GAN and it worked, then this has also the ability to work for random numbers as well. But this method may not be the best choice as there are other models SVM,LSTM(for exmple). But your question is "whether we can ?" Then you can give it a try.
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One remembers, first, that all matter used in anything is constructed of atoms, where atoms are made of particles, where quantum mechanics (QM) physically works.
Any physics, chemistry, engineering, computer science, even mathematics -- where the electrons, light, wave, and number behaviors are determining these fields by Nature -- will obey quantum rules, such as NO "law of the excluded middle" and NO "axiom of choice", and where QM principles play main roles.
One reads, for example, at Stanford U. that: the concepts and techniques of quantum mechanics are essential in many areas of engineering and science such as materials science, nanotechnology, electronic devices, and photonics.
Nominations by participants here (in order of appearance) include:
Superfluidity, superconductivity, HVDC with QM rectification by a thyristor (semiconductor), incandescence, laser, quantum decoherence, entanglement, P-type or N-type semiconductors, transistor radio, and the entire known universe for 13.8 billion years so far.
What is your reasoned opinion? What is your best example of QM having visible effects on microscopic and macroscopic scales?
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One thing that comes to mind in regards to your primary question is hydrodynamic quantum analogs. These experiments were done at MIT in July of 2013 published in Physical Review Letters E. Dr. Daniel M. Harris displayed that "a coherent wavelike statistical behavior emerges from the complex underlying dynamics and that the probability distribution is prescribed by the Faraday wave mode of the corral." I hope this helps!
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Interested in looking at aviation-centred training and use of latest ideas in neuroscience and maths/science education for improving learning outcomes.
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Thanks - I'll folow up later in the week.
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It all started with the Normalized Difference Vegetation Index (NDVI). I am curious to know how a researcher gets to derive or modify such mathematical (sometimes complicated equations) equations by making use of two bands (absorbing and reflecting bands)? Is it by trial and error method?
For example, NDVI seems to be a simple normalization of NIR and RED bands. MSAVI has NIR and red bands along with mathematical operations both in numerator and denominator. How do we come to such a relatively complex formula?
Thank you very much in advance.
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The modified vegetation indices (such as EVI and MSAVI) are generally aimed to reduce the effects of atmosheric attenuation and soil background. The form of these complex formula can be determined or inspired by radiative transfer theory and also soil line theory. The coefficients are determined empirically or based on training datasets.
Trial and error method can be used to develop new indices, but the new indices should in most cases be supported by physical principles. Even for the machine learning method, those important independent variables (related to the dependent variable) are generally selected for learning.
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Dear All,
Greetings. I am looking for reader-friendly books that explain tensors analysis for Fluid Mechanics. The objective to be comfortable dealing with tensors.
Thanks in advance.
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Dear All,
Thanka a lot for the suggestions.
Much appreciated.
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As The First Generation of Infinite Set Theory is based on present classical infinite theory system, contradictory concepts of "potential infinite” and “actual infinite" make people unable to understand at all what the mathematical things being quantitative cognized in set theory are-------- are they "potential infinite things” or “actual infinite things " or the mixtures of both or none of both? People have been unable to understand at all what kind of relationship between the quantitative cognizing theory and the unavoidable concepts of "potential infinite, actual infinite" in set theory: If the mathematical things being quantitative cognized are "potential infinite”, what kind of "potential infinite” cognizing idea, operations and results should people have; if the mathematical things being quantitative cognized are "actual infinite”, what kind of "actual infinite” cognizing idea, operations and results should people have; if the mathematical things being quantitative cognized are the mixtures of both or none of both "potential infinite” and "actual infinite”, what kind of mixing cognizing idea, operations and results should people have? Are there "one to one correspondence" theories and operations for "potential infinite elements” or “actual infinite elements" or the mixtures of both or none of both? Why?
Therefore, it is very free and arbitrary for people to conduct quantitative cognitions to any infinite related mathematical things in The First Generation of Infinite Set Theory: It can either be proved that there are as many elements in Rational Number Set as there are in Natural Number Set or that there are more elements in Rational Number Set than that in Natural Number Set; the T = {x|x📷x}theory can either be used to create Russell’s Paradox or to create "Power Set Theorem", make up the story of “the Hilbert Hotel forever with available rooms” ------- strictly make all the family members of the Russell's Paradox mathematicization and turn all the family members of Russell's Paradox into all kinds of Russell's Theorems; ...
However, because it has a little to do with applied mathematics; it is impossible to verify the scientificity of many practical quantitative cognitive operations and results in set theory. So, there are far more unscientific contents (more arbitrary quantitative cognizing behaviors) in the quantitative cognitive process of present classical infinite set theory than in present classical mathematical analysis.
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You have raised many simultaneous questions about the (finite) and (infinite) concepts. Indeed the latest (infinite) is full of paradoxes in mathematics.
One can observe that :
(*) the part may include the whole,
(*) many infinite sums rearranged to obtain different answers,
(*) Hilbert Hotel paradox,
(*) ambiguity of Cantor sets,
(*) Zeno's paradoxes,
(*) infinity is not real,
All terms: inf - inf, 0xinf, inf/inf, inf^inf, inf^0 1^inf all are undefined!!
So one can stay with such paradoxes years without any clear answer.
And this doesn't mean that we can't use infinity. It is useful to find particular answers for a given mathematical problem. Also, we can construct new definitions that should be consistent with the axioms of the set theory and all other branches of current modern mathematics. All are considered valid based on the added axiom. This is very similar to change the fifth postulate of Euclid's to construct hundreds of non-euclidean geometries; all are consistent and accepted.
So, you can say that the sum of the angles of the triangle is 180 degrees or > 180degree, or < 180 degrees all are correct but in different geometries.
All agree with the initial axioms, but they differ by one axiom.
We can do the same for the set theory.
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Does it make sense to discuss this?
Learning through and with art?
Can an imaginative teaching model be the solution to multiple forms of learning and divergent production?
In my doctoral thesis, I assigned students the task of imagining a text math assignment and trying to draw it or present and solve it using instruments / sounds. Mathematical musical and visual representation of mathematical textual tasks and vice versa ..
From sound to image / icon / symbol.
The results are impressive ... What do you think about it ..
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We are discussing the Mozart effect in our review:
The influence of music on the surgical task performance: A systematic review
  • November 2019
  • International Journal of Surgery (London, England)
  • DOI:
  • 10.1016/j.ijsu.2019.11.012
  • 📷Michael El Boghdady
  • 📷Béatrice Marianne Ewalds-Kvist
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(1) In mathematics, among the various "infinite related number forms with cognizable quantitative properties (such as infinitesimal variables and monads in present classical mathematical analysis)", some are with Half Archimedean Property, while others are not ------- this determines that people need to carry out various necessary qualitative cognitions and studies on them [14-28].
(2) In mathematics, certain infinite related Half Archimedean number forms (such as infinitesimal variables and monads in present classical mathematical analysis) sometimes can join any quantitative calculation process (formula) with “mathematical contents with Archimedean property (such as finite number forms)”, but sometimes can not --------- this determines that during the necessary qualitative cognizing process to them, people sometimes need to put this kind of "Half Archimedean number forms" together with "mathematical contents with Archimedean property (finite number forms)" on the same quantity calculation process (formula), and carry out many calculations of “mathematical contents with Archimedean property” but sometimes need to use certain "scientific reasons" suddenly to drive such quantitative forms out of the exactly same quantitative calculation process (formula) to terminate the very calculation for the "differential" operation results (unfortunately, the fatal defects in the basic theory has been preventing mankind from finding this "scientific reason" for more than 2,500 years). Otherwise, there would be no the subject mathematical analysis in our science.
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Not familiar with the terminology, can you give some example? With infinitesimals I could guess, but monad is more a philosophical entity, I think.
If you think some numbers are matrices, you can do more with real alone.
For example i may be
0 -1
1 0
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Hai.. im curently doing study on mathematical resilience among success student. i am thinking to use survey to select the participant that has gain success from failure and in depth interview to the selcted student that obligate the criteria. But im confuse either this research is called a qualitative or mixed method study?
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My impression is that interpretive structural modeling is a qualitative technique, so if the initial research interview was quantitative, this would probably be QUANT --> qual. If so, this is known an explanatory sequential design in mixed methods.
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We have understood from the studies of infinite related mathematics’ history that present classical infinite theory system is based on the concepts of "potential infinite and actual infinite", which cannot be defined scientifically and contradict each other. This fatal flaw in the basic theory deeply affects the scientific nature of mathematical behavior of mathematical workers in the field related to the concept of "infinite". So, one cannot escape the constraint of the two false concepts of "potential infinite and actual infinite", and one cannot stop the emergence of various infinite related paradoxes. In addition, these paradoxes must exist in the form of "family (infinite paradox syndrome)". In different historical periods, the constantly emerging paradox family members repeatedly reveal the fundamental defects in the classical infinite theory system from different perspectives and call on people to solve these very defects. The fatal fundamental defects in present classical infinite theory system are the source of the second and the third mathematical crisis: more than 2500 years, no one can get rid of a kind of disease in the infinite related fields of mathematics --------- a diseases produced by the confusion of "potential infinite and actual infinite" concepts in set theory diagnosed clearly by Poincare, Frege, and Weyl more than 100 years ago. Studies have proved that this is the common "disease" existing in many infinite related mathematical disciplines with the foundation of present classical infinite theory system: the various "number and non--number mathematical things” -------- “variables of not only potential infinite but also actual infinite (the ‘ghost’ disappearing and reappearing at any time?)" for all the family members of Zeno's Paradox and Berkeley's Paradox in mathematical analysis [1-6]; the mathematical things with the property of "elements belonging and not belonging to a set ---------- T = {x|x📷x} (variable elements of not only potential infinite but also actual infinite: the ‘ghost’ disappearing and reappearing at any time?) " for all the family members of Russell paradox in set theory;…
This is why we are so sure to say that the Third Mathematical Crisis in present scientific theory system is unsolvable and the Third Mathematical Crisis is another manifestation of the Second Mathematical Crisis in set theory. They are "twins".
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Answer see parallel-topic. (Why two at the same time?). Please no answer here.
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I know we use CPA in maths (concrete, pictorial and abstract) but I feel visualisation needs some attention as it may be a bridge from pictorial to abstract. Does anyone know of any research with regards to enhancing children’s visualisation in their minds eye in maths? Thanks
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Thank you. I will begin to read!
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Hi
I am translating an early mathematics Inventories from English to Persian and was having trouble with the word "co-normed" in the following sentence:
The TEMI-O was co-normed with the TEMI-PM.
"Early Mathematics Inventories - Progress Monitoring" and "Early Mathematics Inventories Outcome"
Please help me understand the meaning of this concept.
Thanks!
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Hi,
you might be looking for this explanation:
CO-NORMINGCo-norming entails the process where two or more related, but different measures are administered and standardised as a unit on the same norm group.
B.R.,
Ari
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I am looking for compact formula for approximation of Mittag Lefller function.
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See the attached file of Prof. J. C. Prajapati.
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I want to calculate properties of metal foam by a mathematical formula without destruction of material and without use of any software is it possible
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May be the following papers help you, hope
(1)Manufacturing routes for metallic foams
John BanhartJournal:JOM Journal of the Minerals, Metals and Materials SocietyYear:2000
(2)Metal foams: a design guide: Butterworth-Heinemann, Oxford, UK, ISBN 0-7506-7219-6, Published 2000, Hardback, 251 pp., $75.00
Michael F Ashby, Anthony Evans, Norman A Fleck, Lorna J Gibson, John W Hutchinson, Hayden N.G WadleyJournal:Materials & DesignYear:2002
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To integrate a mathematical function from -inf to inf in MATLAB, I am using from trapz but i am finding it difficult as the variable like d(X), X has to be like ( -1000,1000,2000), but since i have to integrate it from -inf to +inf, if you have any suggestions to look into please let me know
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Good question...
That should help, there are some good examples
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33, is a number surrounded by a special mystique. For many years, 33 has fascinated the mathematical community by starring in one of the apparently simpler cases of a diophantine equation, but which is nevertheless pending resolution.
Diophantine equations are defined as “polynomial equations that involve only sums, products and powers and in which both the coefficients and the only valid solutions are whole numbers.” In short, nothing less than the ABCs of mathematics.
It might seem easy to express the number 33 as the sum of the cubes of three whole numbers – that is, to find a solution for the equation a3 + b3+ c3= 33 – but no one had yet succeeded since 1955 when mathematicians set out to solve this mathematical mystery.
This challenge has been on the table since the 3rd century AD, when the equations were enunciated by the Greek mathematician Diofante of Alexandria.
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33 is not a Lucky number, as you may check:
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mathematical solution , please find attached file
computer vision , linear algebra , mathematics , grey level co-occurrence matrix
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I hope that the attached article helps you to do your assignment.
Best regards
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The article is in French with the title "essai sur le probleme des trois corps".
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Could you paraphrase your question so that it can become clearer.
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Mathematics is crucial in many fields.
What are the latest trends in Maths?
Which recent topics and advances in Maths? Why are they important?
Please share your valuable knowledge and expertise.
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For me, as well as for majority of other researchers, Mathematics is the language of Science!
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this is axiomatic set theory . these axioms are needed for set theory and not for mathematics. so can we avoid them since the involve use of predicate and property. will experts guide in detail. can the use be restricted by using a mapping rather than property or predicate notion ? 
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You mentioned in your question that "these axioms are needed for set theory and not for mathematics", but this is not a simple claim.
Separation and replacement axioms are needed for establishing many important results dear to mathematicians. For instance, it is fundamentally necessary to prove recursion theorem for natural numbers. Replacement, on the other hand, is necessary for establishing transfinite recursion.
(Note: one do not need separation, for it is provable using replacement)
Further, you asked about using mappings instead of properties. This is indeed possible for replacement:
One can use functions directly in replacement axiom.
Replacement: if F is a function and A any set, then {F(x) | x in A} is a set.
However, the stronger version would be provable using the other axioms of ZF and the weak version of replacement.
Strong replacement:
If F(x, y) is a property the behaves like a function, then for any A, {F(x) | x in A} is a set.
********
In the chapter Constructible Sets of Set Theory: Third Millenium Edition (Thomas Jech), Jech defines Godel operations for building the contructible universe. This can be seen as a strategy for considering the generation of sets as operations. This may interest you.
About your question: I keep hearing that some subtheory of "hereditarily finite" set theory is OK that way, but I have only a fuzzy idea what it is and am too lazy to look it up ...
Hereditarily finite sets axiomatization is known as the 'set theory equivalent of peano arithmetics'. These theories are very closely connected: they are bi-interpretable. The idea is: you remove the infinity axiom, say that every set is finite and that every member of each set is finite. In this theory, the axiom of separation and replacement become the equivalent of the axiom of induction in arithmetics.
Notably, it is known that ZF can provide a model construction for PA and thus it can provide a model construction for this set theory. Using completeness theory for first order logic, it means that ZF proves consistency of this theory.
But, this is even more general. ZF has a property called reflection. It means that ZF provides truth predicates for any set-size part of itself. In particular, the class of hereditarily finite sets is a set in ZF. Therefore, ZF provides a truth predicate for it, i.e. ZF proves the consistency of hereditarily finite set theory.
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As "the first generation of infinite set theory" is based on present classical infinite theory system, contradictory concepts of "potential infinite” and “actual infinite" make people unable to understand at all what the mathematical things being quantitative cognized in set theory are-------- are they "potential infinite things” or “actual infinite things " or the mixtures of both or none of both? People have been unable to understand at all what kind of relationship between the quantitative cognizing theory and the unavoidable concepts of "potential infinite, actual infinite" in set theory: If the mathematical things being quantitative cognized are "potential infinite”, what kind of "potential infinite” cognizing idea, operations and results should people have; if the mathematical things being quantitative cognized are "actual infinite”, what kind of "actual infinite” cognizing idea, operations and results should people have; if the mathematical things being quantitative cognized are the mixtures of both or none of both "potential infinite” and "actual infinite”, what kind of mixing cognizing idea, operations and results should people have? Is there "one to one correspondence" theories and operations for "potential infinite elements” or “actual infinite elements" or the mixtures of both or none of both? Why?
As it turns out, the quantitative cognizing theories and operations (including the theory and operations of one to one correspondence and limit theory) for those infinite related mathematical things in "the first generation of infinite set theory" are lack of scientific foundations: It is impossible to know at all what the relationship among all the quantitative cognizing behaviors in infinite set theory and the concepts of "potential infinite” and “actual infinite" is and how to carry out scientific and effective operations specifically to different kinds of infinite related mathematical things. Therefore, it is very free and arbitrary for people to conduct quantitative cognitions to any infinite related mathematical things in "the first generation of infinite set theory" : It can either be proved that there are as many elements in Rational Number Set as there are in Natural Number Set or that there are more elements in Rational Number Set than there are in Natural Number Set; the T = {x|x📷x}theory can either be used to create the Russell’s Paradox or to create "Power Set Theorem", make up the story of “the Hilbert Hotel forever with available rooms” ------- strictly make all the family members of the Russell's Paradox mathematicization and turn all the family members of Russell's Paradox into all kinds of Russell's Theorem; ... However, because it has nothing to do with applied mathematics, it is impossible to verify the scientificity of many practical quantitative cognitive operations and results in set theory. Therefore, there are far more unscientific contents in the quantitative cognitive process of present classical infinite set theory than in present classical mathematical analysis, because it can be more arbitrary!
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Dear Geng Ouyang,
Read word by word, paragraph by paragraph, chapter by chapter the book "Set Theory and it's Logic" by Willard Van Orman Quine, and you will understand my reaction to your writings. Good luck!
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What is the most accurate way of calculating wind direction (2D NESW), wind speed and vertical wind movement using 3D Ultrasonic Anemometer data in the form of uX-uY-uZ m/s (or U-V-W vector) data? I am looking for calculations, methods and/or sources for these approaches.
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I am planning to do research in text classification but , how can I improve the performance of the chosen machine learning algorithm by enhancing classification through derivation of mathematical equation.
I am not perfect in mathematics , can anybody suggest me, what i have to do to, what study i need to do in order to derive a new mathematical equation which improves the performance of a chosen ML algorithm .
Please help me out!!!!!!!!!!!
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In statistics, Cramér's V is a measure of association between two nominal variables, giving a value between 0 and 1 (inclusive). It was first proposed by Harald Cramér (1946).
It is actually considered in many papers I came accross that a threshold value of 0.15 (sometimes even 0.1) can be considered as meaningful, hence giving hints of a low association between the variables being tested. Do you have any reference, mathematical foundation or explanation on why this threshold is relevant ?
Regards,
Roland.
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Hello Roland,
There are guidelines, of course, but these may well be useless for many variable sets or contexts. I don't know of any mathematical reason to suggest that .15 (ir any other value) is magically better as a threshold for a relationship being judged as noteworthy.
Jacob Cohen, in his 1988 text, Statistical power analysis for the behavioral sciences (2nd ed.), proposed these levels for the simpler version of V, the phi coefficient (in which one of the two dimensions has 1 df):
"Small" effect size = phi of .10; "medium" ES = phi of .30; "large" ES = phi of .50.
However, Cohen would be the first to admit that such guidelines may be meaningless in specific data/variable/population contexts; there is no substitute for intimate understanding of these features.
Here's a simple example of how a very low correlation can still be useful: Consider a correlation of .01 between a no-cost, one-question cancer screener and the subsequent occurrence of cancer within a year. Sounds useless, right?
(With these hypothetical values from 100,000 cases: screen+/cancer+ = 6,472; screen+/cancer- = 57,922; screen-/cancer+ = 3,356; screen-/cancer- = 32,250; the chi-square = 10.114, and phi = .01). In this scenario, the one-question screener would potentially save nearly 6,500 lives. So, is it useful?
Good luck with your work.
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How to estimate the resonating modes by looking surface current in CST Microwave studeo ? I am attaching a surface current Image. I am not able to determine the higher order modes here at 40 G Hz. The fundamental mode is at 6.8 G Hz i.e. TM10 and matching to mathematical calculations.
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From navigation tree go to
2D/3D results--->Port Modes--->Port
Click on e1, if it is perpendicular to direction of propagation,than it's TE. As well as you will see the mode type (wheather TE/TM/TEM) will appear at the left-bottom corner of the screen.
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Please give a mathematical description
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There are multiple ways of doing so:
* Train the model to generate point forecasts, and then use simulations of multiple predictions to then calculate the prediction intervals. You can use MCMC or Dropout at prediction time to perform the simulation. Uber for example uses Dropout to calculate the uncertainty of their LSTM forecasts.
* You can train the LSTM to predict the parameters of a predefined distribution (Normal, Poisson, etc...) and then calculate both your forecasts and your intervals by sampling from the distribution. Amazon's DeepAR model uses this approach.
* You can also train the model to predict forecast quantiles directly - i.e. instead of the output of the LSTM being the mean or the median, the output can be the 85% quantile or the 95% quantile, etc...Amazon's MQ-RNN forecaster uses this approach.
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Chaos exists not only in the mathematical world, but also in real life. From the quote: "All creativity begins in chaos, progresses in chaos and ends in chaos" ( Ralph Abraham), it follows that creating starts from chaos. Since the connection between imagination and creativity is obvious, can a direct connection be made between chaos and imagination?
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Yes the imagination will be autom,atically converted to chaos thru the term MISUNDERSTANDING .
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I have a signals of force over a contraction period. I hoping to fit my signal to a mathematical function. I have been exploring models of the muscle. Does anyone have pointers, suggestions or advice?
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This really depends on how the force was measured and whether you have any additional information i.e. position, movement, other physiological signals etc.
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Perron's paradox, emphasizes the danger of assuming a solution to a mathematical problem exists, if the solution is actually nonexistent.
For example, if we assume the largest natural number exists and it is N, therefore if N>1, then N^2>N, and this contradicts our hypothesis that N is the largest natural number, hence the largest natural number is N=1, and this is illogical, hence it emphasizes the danger of assuming a solution exists while it is actually nonexistent.
I think there is a glitch under its underpinning. Let's ponder it again:
If you do not know what is the largest natural number, or you do not know the largest natural number does not exist, then you have no basis for your mathematical operations, and you have no insight on anything in the naïve mathematics. You would not also understand the sign lesser or greater (< or >), hence you cannot conclude N^2>N, is a paradox (contradiction), because you have no insight on foundation of mathematics, it means you do not know natural numbers (alphabet of mathematics) and the sign > or < is meaningless to you and you cannot conclude N^2>N, is a contradiction because you cannot interpret the inequality N^2>N when you do not understand the comparison sign (> or <) and hence you are helpless!
Hence, Perron's paradox will tell you nothing about the largest natural number, it means Perron's paradox cannot lead you to contradiction and to get the result that N=1. It only makes you dizzy about your assumption, and can one by one rebuff all your assumptions and make you assume another assumption. You assume N=2, and again reach contradiction, and hence N=3, and so on, until you fathom the answer reaches infinity, or probably conclude it does not exist. Also using mathematical induction, you can move from N=1 to N=2 and hence forth from N to N+1, and conclude (limit N) goes to infinity hence the largest Natural number in infinity or actually does not exist.
Perron's paradox does not underline the danger of assuming a solution exists to a math problem, while it is actually nonexistent. It actually highlights the danger of not having any information, insight and realistic idea about a math problem. Consider you've assumed the solution to a differential equation is twice continuously differentiable (it means it is C2), whereas actually it is not C2, but it is probably C1. Then there is no danger to hinder your assumption, except you would probably face a contradictory conclusion. But this is no danger, only this contradiction would tell that you should modify your assumption and narrower your hypothesis, it means you should again assume another solution or hypothesis, probably you should revamp your hypothesis to C1 continuity of the solution to the differential equation under investigation. If this again led you to contradiction, you should assume the solution is discrete or else.
Hence, I think Perron's paradox is not resourceful, whilst it is only a sophistry, while too many mathematicians believe the proof for existence of a solution to a math problem is only mathematical detail, nothing helpful, as any problem would have some type of solution: continuous/discrete/smooth/jagged or so on…
Let me know your viewpoints on this discussion.
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Thank you for the comments. Regards.
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Hi!
I'm a math teacher.
I think and I believe that starting with kindergarten math and music must be almost a whole for the student.
In fact, the education without the culture, and the culture without the education are nonsenses.
So, the mathematics without the music and the music without the mathematics (in sense that the last is the music of the knowledge) are nonsenses too.
I believe in a future world which will understand such trues.
In short, I am very curious about this project.
Sincerely yours,
BNN
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Music activities as well as medicine, drama, etc. can have an extremely divergent charge for thinking. Children need to learn to think and more to create. Through music, they can put maths as I asked in a problem recently. Also through play, specially designed didactic music games I designed. If you are interested contact me freely.
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I'm interested in digging deeper about the question : What are the affordances of video to research and practice in education?
Please feel free to suggest a good paper on this theme. If it is connected to mathematics education, it would be even better...
Thank you for your consideration.
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Hello, Mathieu
I really like this chapter by Rogers Hall:
Hall, R. (2000). Videorecording as theory. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 647–664). Mahwah, NJ: Lawrence Erlbaum.
I appreciate his argument and examples that our choices of video recording methods are based in our theories of learning, activity, and mathematical/science practice. If you search in the same time period, you will find several related pieces published by Rogers and Reed Stevens. Much of that research was focused on mathematics and/or science learning.
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A reasonable method of defining an integral that includes the HK integral is to say a Schwartz distribution $f$ is integrable if it is the distributional derivative of a continuous function $F$. Then the integral $(D)\int^b_a f=F(b)-F(a)$. The resulting space of integrable distributions is a Banach space that includes the space of HK integrable functions and is isometrically isomorphic (with Alexiewicz norm) to the continuous functions vanishing at $a$ (with uniform norm).
If $F=C$ is the Cantor(the Devil's staircase) function and $\langle C'\rangle$ (we use notation $\langle C'\rangle$ to avoid confusion and in some situation $C'$) is the distributional derivative of $C$, then
$(D)\int^0_1 \langle C'\rangle=C(1)-C(0)=1-0=1$. Note that $\langle C'\rangle$ is a measure.
If here $C'$ denotes derivative in classical sense then $C'=0$ a.e. and $(HK)\int^0_1 C'=0$.
Suppose $F$ is continuous on $[a,b]$. Also suppose $f(t)=F'(t)$ exists except on a countable set $Q=(c_k)$; define $f$ arbitrarily on $Q$. Then
Then $\int_a^t f(x) dx $ exists and equals $F(t)-F(a)$.
See for example
"An Open Letter to Authors of Calculus Books". Retrieved 27 February 2014.
NEWTON–LEIBNIZ FORMULA AND HENSTOCK–KURZWEIL INTEGRAL ZVONIMIR \v SIKI\'C, ZAGREB
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Dear Miodrag,
Fist here is definition of the Henstock–Kurzweil integral :
The set of KH-integrable functions forms an ordered vector space and the integral is a positive linear form on this space. On a segment, any Riemann-integrable function is KH-integrable (and of the same integral).
For relation between the gauge integral and the Lebesgue and Riemann integrals, i suggest you to see links and attached file on topic.
Best regards
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I need a definition for a search.
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I have searched TIMSS high and low but cannot find out what they base their questions for students' engagement and attitudes in Maths on...is it the Self-Description Questionnaire? If so, is it Marsh's SDQ III (1990)
Many thanks
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Many thanks Jack Son
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What would be the logical mistake if indicial equation roots are actually different by an integer, but still mathematically one solves the equation following the route of non-integer difference, still evaluated at ordinary singular point? Suppose,the ODE is of second order. Would doing so might result in two linearly independent solutions whose one particular linear combination in a terminating series? I am following textbook on Ordinary and Partial differential equations by Dr. M.D. Raisinghania, but logic behind the method is not mentioned in the book.
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The logic is that we need to find two independent solutions. If they differ by an integer, one can be obtained from others by setting few zero coefficients on series. You can find the proof of it from Kreyszig Advanced Engineering Mathematics book (Appendix 4)
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While reading FEM by J .N Reddy I have notice that the shear strain term is taken as sum of (dw/dx) and Ф for mathematical convenience. I didn't understand why we should take slope in negative instead of positive. Cant we solve the problem in other way round?
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As Ф is negative around axis y, see the attached figure
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I was wondering if there is a connection between exponential function and reciprocal function, because if we look at the graph of reciprocal function, horizontal and vertical asymptote looks like exponential function.
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Using the Maclaurin power expansion, for |x| < 1
x/(1-x) = x{1+ x + x² +..+ xⁿ+..}
= x + x² + .. + xⁿ + ..
The exponential function has an approximation
ex = 1 + x + (1/2)x² + (1/6)x³+....
Notice that
|ex - 1 - (x/(1-x))| = O(x²)
therefore, for small values for x
the given rational function is a good approximation of an exponential function.
Best regards
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I am looking for the mathematical formula for calculating the sample size.
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The following equation shows the formula
n=[ 4r (1-r) (f) (1.1)] / [(0.12r )^{2} p(n_{h})]
where: - n: the sample size required for the main indicator expressed by the number of households (see the following sub-sections below) Identify the main indicator). 4: - The factor necessary to achieve a 95% confidence level. - r: the expected or potential spread (coverage rate) of the indicator to be. Estimation 1.1: Factor to increase sample size by 10% for non-response. deff abbreviation: f - - 12r.0: maximum margin of error at a confidence level of 95%, defined as 12% of r (therefore representing 12% of the relative sampling rate, r.) - h: average household size. If the sample size in the survey is calculated using the baseline indicator based on the smallest target group by percentage of the total population, the accuracy of the survey estimates for most other key indicators will be better.
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what is the important factors that affects in student achievement in (TIMMS) in Eighth Grade Science in (Alain - Abu Dhabi )
Which Factors are more influential on student achievement in international study (TIMMS)ز
Will these factors for mathematics differ from the factors for science on the one hand and will they differ for the fourth grade from the eighth grade on the other hand ?
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I develop only my MINT and MINT-Wigris program and have no testing except for problem solving in mathematics.
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Some time, I could not find the abbreviated names of some journals.
Is there any website contains all of them.
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No, but in a wide range..
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Nowadays, so many people are concerned with converting CGPA to Percentage on a 4.0 scale. There is a common method in which they multiply the CGPA by 25 since one CGPA is equivalent to 25 in Percentage system but this is clearly not scientific and accurate since the CGPA is calculated in a range base. So, I would be grateful if anyone can come up with a statistical or mathematical equation to convert CGPA to Percentage?
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Hello all,
The "multiply by 25" works so long as: (a) you've created a GPA that is weighted by the number of credit hours (as indicated in my earlier post); and (b) the maximum value of a mark is 4.0, since the conversion of proportion: GPA/max GPA to a percent (e.g., multiplying by 100) may be re-expressed as (100/4)*GPA, which equals 25*GPA. The fact that the full equation is algebraically equal in this case does not make it (the shortcut) incorrect!
I don't see that an alternate method is called for, but perhaps there is some other goal that Rebwar Mala Nabi may have had in mind that wasn't clear in the query.
Cheers,
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Is it possible to patent a mathematical (with algorithm ) model used for variables calculation of a chemical process, knowing that there are different models patented for the same chemical process ?
and what if my model is based on another model but with major equations modifications and improvements, can I still patent it ? (of course, while citing the prevuous work).
Thank you.
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Hey all, in order to open the discussion, you'll need to be aware of a few basic principles: a) patentability conditions, b) freedom-to-operate & doctrine of equivalence and c) exceptions of patentability.
a) a patent can be granted when your 'technical' invention is 1° new, 2° inventive and 3° industrial applicable. This third condition is 'here' important here because when talking about algorithms and mathematical formulae, they should be implemented in a particular application, such as a device, an apparatus, a process, etc. More particularly it is not enough to explain only the theoretical background, then you can choose for a scientific publication.
b) be aware of these already patented models, and you'll have to determine their scope of protection. When they claimed broadly and you use these already claimed features (in valid patents, covering your geographical market), you can be attacked for infringement, when entering these markets! So, you'll have to check your freedom-to-operate (FTO) for vending your product, with or without your own patent. Moreover, you can also be accused based on the doctrine of equivalence, when not exactly the same features of the patented technologies of others, but applying the spirit of invention even with your own slight differences. When you solve the same problem in a small different way, applying the fundamentals of the patented technologies, you'll need their authorisation to commercialize, like a license. A profound patent study is required here.
c) some 'non-technical' issues are not patentable, or at least open for discussion. This is i.a. the case with computer implemented inventions (software). This is mentioned in art.52 EPC (European Patent Convention): https://www.epo.org/law-practice/legal-texts/html/epc/2016/e/ar52.html. More specifically, art. 52 (2) (a) en (c) are important here. In the US: https://www.uspto.gov/web/offices/pac/mpep/consolidated_laws.pdf, art. 35 U.S.C. 101 and 103 are important. However, it could give you the impression that patentability is easier, less exclusions, etc... Case law in US states that abstract ideas and just data can be patented. Here again, the condition of a specific applications is required.
To finish my small intervention , a practical approach in a patent database. One of the patent classes that be used to search for models is: https://worldwide.espacenet.com/classification#!/CPC=G05B17/00. An example of a granted patent in this field is https://worldwide.espacenet.com/publicationDetails/originalDocument?FT=D&date=20190925&DB=EPODOC&locale=en_EP&CC=EP&NR=2556414B1&KC=B1&ND=4#. In order to select the granted patents (or thus those that are patentable by the EPO) you'll have to choose EPB in the field of the publication number and combining this with the CPC field: G05B17/low. Another very important Class is https://worldwide.espacenet.com/classification#!/CPC=G16C
Another example: https://worldwide.espacenet.com/publicationDetails/originalDocument?FT=D&date=19990811&DB=EPODOC&locale=&CC=EP&NR=0494110B1&KC=B1&ND=4#. When looking at the claims: claim 1 describes a process for the estimation of the physical parameters....using a computer. The classifications G06F17/50: https://worldwide.espacenet.com/classification#!/CPC=G06F17/50 (which is broader for multiple applications) and G06F19 can also be very useful to search. https://worldwide.espacenet.com/classification#!/CPC=G16B are related to ICT applications (bioinformatics).
So, to conclude: 1° try to find similar granted patents and have a look at the claims what they exactly claim, 2° detect patents that you can infringe and check their legal status (preferably with professional assistance) in the framework of your FTO. If you don't have FTO, your are blocked for your future steps, if FTO think about step 3, 3° ask for a patent professional to analyze your model in order to evaluate the novelty and inventive step, and the techncial application. When you solve the problem with a feature that is not obvious for a skilled person and you don't use the fundamentals of earlier valid patents, unless you can agree a cross-license or an agreement of use, patentability is on the floor. The best.
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I’m trying to make a 4:1 ratio of two solutions. One solution is a 5mL soln. at 20% (w/v) and the other is a 100mL soln at 10% (w/v), respectively. Normally this is easy when both concentrations are the same, but how do I do the ratio with different concentrations? A mentor is recommending diluting the 20% solution to 10%, but this would defeat the purpose right? I’m sure there is a mathematical formula that would make things easier to understand. Thanks all.
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Ok but you want the concetration of the chemical species in the two different solutions to be the same?
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I am looking for mathematical framework to calculate the co-ordination number of any element in a given compound.
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The coordination number of Al be 4, with whole charge -2.
The coordination number of Na be 1 since this is neutral.
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Every common source avoids the derivation, saying it to be too difficult. Where can i fiend volterra's original derivation? Knowing which mathematics would be necessary?
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In the inhomogeneous viscid Burgers' equation:
u_t+m u_x+λg(u)=νu_xx,
what is the significance of λ(coefficient of source term)?
what is the significance of m(associated to flux function)
Which of the following statements is mathematically correct?
1.When λ=0 the Burgers' equation becomes homogeneous
or
2. When g(u) tends to zero then the Burgers'equation becomes homogeneous
3.Both statement 1. and 2 can be used
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First of all, if you talk about the Burgers equation then m can only be the velocity u(x,t). The Burgers equation indeed is also rewritten with the convective term in the conservative form d/dx(u^2/2).
The source term is generally a forcing term such that the solution is statistically steady (in equilibrium) with the action of the diffusive term (RHS) whne periodic boundary conditions are prescribed. Without such forcing, the final solution would be the rest.
For homogeneity of the non-linear equation, any function u(x,t) satisfying u(λx,λt)=λnu(x,t)" where n is any integer, is a homogeneous function and differential equation which involves homogeneous function is called homogeneous differential equation.
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We know that mathematicians study different mathematical spaces such as Hilbert space, Banach space, Sobolev space, etc...
but as engineers, is it necessary for us to understand the definition of these spaces?
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Yes, we do have to know about the spaces, at least during our university studies, to enables us to expand our mind into abstact level, that will be very usefull for design activities
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In field theory, a primitive element of a finite field GF(q) is a generator of the multiplicative group of the field. In other words, α ∈ GF(q) is called a primitive element if it is a primitive (q − 1)th root of unity in GF(q); this means that each non-zero element of GF(q) can be written as αi for some integer i.
For example, 2 is a primitive element of the field GF(3) and GF(5), but not of GF(7) since it generates the cyclic subgroup {2, 4, 1} of order 3; however, 3 is a primitive element of GF(7).
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can you using turbo pascal of simple programming..if have a problem can calling me or sending a message to help
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Where can I find validated protocols of teaching mathematics to healthy elderly and to elderly with moderate dementia as an independent variable in a longitudinal research study testing the synergy of cognitive training and physical exercise in preventing dementia or slowing the onset of dementia?
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Math protocols is a good start to snurge the memory , while unless there is a inner interest on individuals depending on format or framework of mathematic game.
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"PSNR of image increase an the entropy of image increase (in watermarking)". How one can prove this statement mathematically.
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Sanjay Kumar In my opinion, obviously PSNR is somehow proportional to the Entropy. But, I think if the PSNR increases (which means the image has lesser noise components) then Entropy should decrease. As noises only add randomness and undecidability to the original signal which in turn increases the Entropy. Therefore, I beg to differ with the statement "PSNR of image increase an the entropy of image increase (in watermarking)".
Please feel free to correct me if I don't get your question.
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Not established at all ! who is the first founder of algebra in mathematical history ? Websites below are very interesting but not satisfactory !
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The scientist is characterized in that they is interested in everything (“how?” Or “who?”). But the next questions are: "why?" and "for what?".
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Brain signals Analysis for fMRI images.
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From the literature I am familiar with, I can say that the most numerous are studies of brain activity in the reading process. This is probably due to the great interest in his disorders and the problems of dyslexia. I have practically never encountered such studies of brain signals when performing various mathematical tasks. At the same time, the claim is that the left hemisphere dominates this type of operation.
In your study, you should consider the different involvement of the brain departments in solving arithmetic (non-verbal) and verbally-assigned (text-based) tasks. I'm sure you'll find a difference in the organization of brain signals in these two types of tasks.
I wish you success and look forward to seeing the results of your experiment!
Neli
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Respected Researchers,
Is it right to submit a mathematical paper on arXiv before it is submitted to any journals? Please help.
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It is right also because, in case of unfair and predatory behaviour on part of the reviewers, or of anybody else who might have got a preview of your work, one can always point out to your arXiv preprint, which has an official submission date on which you can base a priority claim. On the other hand, people who engage in such behaviour would often also be ready to just copy from your arXiv preprint without quoting. Personally, I feel safer putting everything on arXiv. I also have several contributions which, for different reasons, were never published on peer-reviewed journals, but I am happy that they are accessible on arXiv all the same. It also gives immediate visibility to your work, since arXiv preprints pop up almost immediately on e.g. Google Scholar profiles, which saves one a lot of effort in terms of letting people know what one is doing.
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The musical melody is a structure consisting of a series of two types of entities: tones and pauses. Each tone has two properties: pitch and duration; each pause has one property - duration. According to these properties, they can compare to each other. The result of a comparison can be identity or difference.
Hypothesis: some combination of tones and pauses give us a sense of beauty, others don’t. Let us assume that beauty is proportional to the quantity and variety of the identity relations that the melody structure contains.[1]
Question: how can we determine the quantity and variety of identity relations in a given melody structure if we know that there are:
1. identity relations between individual tones and pauses;
2. identity relations between relations. (example: A and B are different in the same (identical) way as B and C; duration of A is half of the duration of B just like (identically) the duration of C is half of the duration of D; etc.)[2]
3. between groups of tones (and pauses)
And a second question: by which method can we create structures that contain maximum quantity and variety of identity relations?
*********
[1] About the reasons behind this hypothesis seePreprint , part 3.
[2] The structure must be observed throw time. If we play the tones and pauses of a beautiful melody in random time order the beauty will be lost. These types of relations allow us that.
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Quite true. There is a danger that rationalization of beauty can lead to its destruction. Explaining a joke just makes it not funny. However, curiosity, desire for knowledge, seems to be stronger.
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Dear Colleagues
Hope you all will be fine
The optical carriers can be written in mathematical form as shown in attached figure.Please let me know how we can write/show linearly polarized LP modes in mathematical form such as shown in attached figure?
I will be very thankful for your kind help.
Regards
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Let (X1, p1) and (X2, P2) be metric spaces and define metrics on X1 x X2 as follows: For x = (x1,22), y := (41,42) E X1 x X2, let (a) di(x,y) := pı (x1, y1) + P2(x2, y2), (b) dz(x, y) := V(21(x1, yı))2 + (P2(x2, y2))2. (i) Prove that di and d2 define identical topologies. (ii) Prove that (X1 x X2, dı) is complete if and only if Xi and X2 are complete. (iii) Prove that (X1 * X2, dı) is compact if and only if X, and X, are compact.
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I am just wondering why bachelor degree programme in Statistics is run in the department of Mathematics in some universities. Mathematics is a major tool in Physics, just like in Statistics, but I have never heard or seen any Mathematics Department running a bachelor degree in Physics. Is this practice doing more harm than good to the training of statisticians?
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Mathematics is a major tool in statistic
Yes, there are subtle differences between mathematics and statistical thinking. This writing distinguishes between the types of thinking during the test and the classification of mathematical and statistical tasks. In statistics, we use mathematics tools to solve problems (such as using algorithms and formula, theoretical probability models, and many forms of graphical representations). However, we rely heavily on data and context in statistical thinking. Statistical questions begin with a context in which individuals must make decisions about how to collect data to investigate problems. In some cases, data are already collected, and statistical questions stem from interest in the data set. In all cases, it is impossible to do a sense of statistical problem without knowing the details of the situation surrounding the data. Context can help shed light on why there are extreme groups or certain groups within the data or whether we should exclude outliers. For example, when studying the typical value of foot length, one can determine the extreme values ​​by looking at the data. The age of people whose feet have been measured (in inches) may be noticeable contributing to understanding how data is disseminated and divided. If the data value of 26 inches is present, the context is the foot length of students aged 11 to 13 years may warrant a decision to exclude the value in the analysis and interpretation of the results. The question of measurement is another important distinction between statistics and mathematics. In mathematics, measurement usually refers to an understanding of units and accuracy in problems that deal with most concrete measures such as length, area and size. But, in statistics, measurement can be more abstract. For example, when thinking about how to measure intelligence or the speed of city life, there is no obvious way. Instead, researchers and statisticians should decide how best to measure what is being studied and often do it in different ways.
Variance and uncertainty in conclusions is another major difference between statistics and mathematics. In mathematics, the results are usually reached by deduction, logical evidence, or mathematical induction and usually there is one correct answer. Statistics, however, uses inductive inductive and conclusions are always uncertain. This is largely due to the interpretation of the context and methods surrounding data collection and analysis. It also stems from the nature of heterogeneity of problems. For example, “How old are teachers in my school?” Is a statistical question that predicts age variation. One will need to decide where to get data from (school teachers), to measure (age) and choose appropriate statistics (central tendency or variation measures) and graphical presentations to answer the question. In contrast, given the set of data
Teacher age points and asking students to find the average data set is not a statistical issue since the answer is definitely finding the number one using an algorithm. Another example in bivariate data is the appropriate linear function between height and weight. In mathematics, students are often asked to find a (deterministic) job through a set of points. In contrast, statistical questions focus on the level of certainty one can achieve when using the "most appropriate" function to predict one variable based on the other. In particular, one looks at the extent to which such extrapolation can be made based on the context and the amount of error associated with the prediction. In summary, some of the salient features we bring in statistical questions include the role of context, measurement, volatility, and uncertainty. Mathematics serves as a tool to help statistical inquiry questions, but not the only end of the statistics themselves.
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Is a physical basis that necessarily requires constancy of the speed of light a logical impossibility, or is the constancy of the speed of light the result of ideas not yet found or applied?
Does isotropy require constancy of the speed of light?
Jensen’s inequality for concave and convex functions, implies for a logarithmic function maximal value when the base of the log is the system’s mean. Mathematically, this implies that the speed of light must be uniform in all directions to optimize distribution of energy. This idea has a flaw. Creation of the universe happened considerably before mathematics and before Jensen’s inequality in 1906. Invert the conceptual reference frame and suppose that Jensen’s inequality is mathematically provable in our universe because it is exactly the type of universe that makes Jensen’s inequality mathematically true in it. A mathematical argument based on Jensen’s inequality goes around in a circle. Are there reasons, leaving aside Jensen’s inequality (or even including Jensen’s inequality), that require constancy of the speed of light?
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The discussion is about the light speed in the same medium(in general, the space vacuum). For example, does the light speed affected by the gravity
(Diffraction phenomenon) when passing near black holes? It has no meaning to study the light speed in a medium where light can not penetrate.
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I wanna calculate the value of Magnetic susceptibility and magnetic permeability form my characterization graph in origin. Is there any related video can you suggest??
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You can find out the permeability from the slope of the initial curve.
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If we have: z = f (x,y) and z = f (t), could you please answer to my below questions:
1) Can I say: x = f (t) and y = f (t)?
2) How can I analyze dz/ dt?
Thanks in advance for your help.
Best Regards
Gholamreza Soleiman
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Z is a function of x,y and z is also function of t.this is exists only when x,y are functions of t.
by total derivative we can analyze dz/dt .
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I have found that some mathematicians disagree with meta-heuristic and heuristic algorithms. However, from a pragmatic point of view such algorithms often can find high-quality solutions (better than traditional algorithms) when tackling an optimization problem but the success of such algorithms usually depend on tuning the algorithms' parameters. Why some mathematicians are against these algorithms? is it because they don't posses a convergence theory?
I am looking for different arguments on the situation.
Thank You!
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This question is similar to another one that I have seen. My response to that one was basically this:
1. I don't know any mathematicians who are prejudiced against heuristics per se. Many of them (myself included) use them regularly.
2. I do know a lot of mathematicians who are fed up with people claiming to invent dozens of "new" meta-heuristics every year (like harmony search or the bat algorithm), when really they are just old ideas expressed in fancy new words. Actually, many people in the heuristics community are unhappy with it as well.
3. I also know people working in combinatorial and/or global optimisation who are fed up with people saying "problem X is NP-hard, and therefore one must use a heuristic". This shows a breathtaking ignorance of the (vast) literature on exact methods (and approximation algorithms) for NP-hard problems.
(By the way, I agree with Michael's comment about "matheuristics" being a very interesting research direction.)
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I'm trying to design a wavelet. I extracted signal from transient for my wavelet. How to calculate coefficients of low-pass and high-pass filters for wavelet transform filter bank?
Maybe you can recommend some literature. I have read many literature about wavelet (Mallat, Daubechies and other mathematical books) but it's require deep knowledge in mathematics.
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Dear Valery,
To calculate the coefficients for a wavelet filter you can check:
To use custom wavelets for a filter bank you can check:
If you would like to like to read some additional wavelet literature together with some tutorials and practice assignments to better understand the "deep knowledge in mathematics," I would recommend:
Hope this helps!
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Many are saying that statistics is not a branch of mathematics. They say that statistics is just partly using mathematics while the other parts are on language skills especially in the interpretation of results.
Thanks.
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Preferably conference scheduled for early 2020.
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Also
ENUMATH 2019 — European Numerical Mathematics and Advanced Applications Conference 2019
30 Sep 2019 - 04 Oct 2019 • Egmond aan Zee, Netherlands
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It would seem that the answer should be negative. However, if you think about it, the answer is not so obvious. Indeed, it is enough to take the vector field of accelerations (velocities) of particles as ether and we will get a mathematical definition of moving matter. Another question is where and how it moves this matter and why we do not see it, but this question may already have an answer1. Matter moves on the surface of the seven-dimensional sphere, and it is invisible because we move with it.
1)
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In simple words, the ether is a flow of particles whose motion obeys the principle of least action. This flow (ether) moves from a less stable position to a more stable position, and its geometry is given by minimal surfaces. In addition, minimal flows form topological singularities that are associated with elementary particles. Closed minimum flows (elementary particles) have different degrees of stability, and the minimum flow as a whole also fluctuates.
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Hello everyone,
I am thinking how the function should look like in order to generate this kind of curve shown below.
I am guessing the variables should be :
  • the radius that increases by "x" after every half-rotation,
  • how many rotations should take place before stopping.
Can anyone shed some light on this?
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t = 20:0.1:40;
x = t.*cos(t);
y = t.*sin(t)
plot(x,y)
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In quasicrystal, a different set of tilling can form the quasicrystal. However, most of the mathematical theory is trying to explain the quasicrystal tilling from one starting point and not from a different setpoint ( 2 or 3 points with some specific distance) to explain the tilling pattern, which these set points can expand at the same time. This will bring a question of what is the best tilling, packing density, the maximum area of QC tilling, ...
My question is how we can explain this by the relation between the degree of packing and tilling pattern?
Regards,
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this book is interesting
Metamaterials - Beyond Crystals, Noncrystals, and Quasicrystals – CRC-Taylor & Francis
Cui T.J., Tang W.X., Yang X.M., Mei Z.L., Jiang W.X., (2016)
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Let us have Minkowski space-time, which must be curved so that its metric does not change, and the coordinates cease to be straight lines. How can I do that? In this matter, a hint can be found in the mathematical apparatus of quantum mechanics. Indeed, if we take the Pauli matrices and the Pauli matrices multiplied by the imaginary unit as the basis of the Lie algebra sl2(C), then the four generators of this algebra can be associated with the coordinates of Minkowski space-time not only algebraically, but also geometrically through the correspondence of the elements of the algebra sl2(C) and linear vector fields of the 4-dimensional space. Then the current lines of the vector fields of space-time become entangled in a ball, which, when untangled, surprisingly turns into Minkowski space-time.
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In fact, in the previous post, the path from Dirac's quantum geometry to Einstein's geometry was indicated, and the mathematical apparatus for successfully passing this path must be found in the mechanism of local algebras of vector fields1.
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Visuals are commonly used to help the low level students understand maths but who's to say it can't benefit everyone.
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We, humans, are essentially a visual animal. So, it is no surprise that everybody benefits from visual representations.
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If we have a fourth order polynomial as follows:
f(X)=a*X^4+b*X^3+c*X^2+d*X+e
how to make this equation on the following form:
f(X)=-(m*X^2+n*X+y)^2. I tried to extract the all terms of the second equation and compare the terms coefficients but it didn't work.
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To get your request you need the following conditions to be satisfied:
(3b²-8ac)/(bd-16ae) = (bc-6ad)/(cd-6be) = (bd-16ae)/(3d²-8ce)
with all coefficients a,b,c,d and e are negative values.
The proof ( Using the resultant techniques)
Example:
f(x) = -(x²+3x+1)² = -x⁴ - 6x³ -11x² - 6x -1
a = -1, b = -6, c = -11, d = -6, e = -1
Check the conditions:
(3(-6)²-8(-1)(-11)/(-6)(-6)-16(-1)(-1))= 1
((-6)(-11)-6(-1)(-6))/(-11)(-6)-6(-6)(-1))= 1
((-6)(-6)-16(-1)(-1))/(3(-6)²-8(-11)(-1))= 1
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The attached file is such a proof.
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The first file below is an updated published version of the above. If are interested in the impacts of this look at the other attached files.