Science topics: Mathematics

Science topic

# Mathematics - Science topic

Mathematics, Pure and Applied Math

Questions related to Mathematics

Which software is best for making high-quality graphs? Origin or Excel? Thank you

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?

Lockdowns due to the COVID pandemic in last three years (2020-22) has played a significant role in the widespread of online based classrooms using applications like Zoom, MS teams, Webex and Google Meet. While substantial amount of the students were happy to complete their semester classes in due time without getting hampered by the lockdowns, thanks to the online based classrooms, there are also notable amount of students and parents who were complained regarding the online based classrooms that they have drastically distracted the academic performance of students.

Overall, I would like to leave it as an open-ended question.

**Dear researchers, what you think regarding the online based classroom? Is it an advantage for students or a disadvantage?**How long does it take to a journal indexed in the "Emerging Sources Citation Index" get an Impact Factor? What is the future of journals indexed in Emerging Sources Citation Index?

I'm interested in the intersection of mathematics and social sciences, and I'm looking for expert opinions on ethical content in mathematical history.

My Awesomest Network, I am starting my Ph.D. studies and I have some questions and doubts concerning it. Could I write them down here, please? First of them is how can I join disciplines as sociology, management, economics, mathematics, informatics and other similar items to make a complex holistic interdisciplinary analysis and coherent study of pointed fields. I think personally that linking or joining et cetera aspects of artificial intelligence and computational social sciences would be interesting area of considerations. What are Your opinions?

Thank You very much for all in advance

I am a post graduate student presently writing my thesis in the department of curriculum and instructional designs.

I am working on meta-heuristic optimization algorithms. I would like to solve Image segmentation using Otsu’s method and my algorithm. I could not understand how to use meta-heuristic in image segmentation. Please help me in this regard. I am from maths back ground. If anybody have matlab code for the same, please share with me. I will be grateful to you.

I need mathematical full solution.. Can anyone please help me..

What is infinite? does this have any value? must there be an end or is it just our thoughts it can't imagine that there is no end to infinity! Aren't all things part of infinity? we too? is God an infinity that cannot be imagined but felt? is an infinity an energy that binds us and all things (reality and thought) together? Is there a physical explanation for infinity? Is the limitation by (infinity -1) or (-infinity + 1) legitimate or just a need to calculate it mathematically?

We see many theories in physics, mathematics, etc. becoming extremely axiomatic and rigorous. But are comparisons between mathematics, physics, and philosophy? Can the primitive notions (categories) and axioms of mathematics, physics and philosophy converge? Can they possess a set of primitive notions, from which the respective primitive notions and axioms of mathematics, physics, and philosophy may be derived?

Raphael Neelamkavil

I suppose so, it's true that physics is the special case of mathematics.

In physics, the existence and the uniqueness of the solution are ensured whereas in mathematics, it is the general case of physics, the existence and the uniqueness of the solution pass before all.

Right now, in 2022, we can read with perfect understanding mathematical articles and books

written a century ago. It is indeed remarkable how the way we do mathematics has stabilised.

The difference between the mathematics of 1922 and 2022 is small compared to that between the mathematics of 1922 and 1822.

Looking beyond classical ZFC-based mathematics, a tremendous amount of effort has been put

into formalising all areas of mathematics within the framework of program-language implementations (for instance Coq, Agda) of the univalent extension of dependent type theory (homotopy type theory).

But Coq and Agda are complex programs which depend on other programs (OCaml and Haskell) and frameworks (for instance operating systems and C libraries) to function. In the future if we have new CPU architectures then

Coq and Agda would have to be compiled again. OCaml and Haskell would have to be compiled again.

For instance suppose a formal mathematics Agda file started with

{-# OPTIONS --without-K --exact-split #-}

Both software and operating systems are rapidly changing and have always been so. What is here today is deprecated tomorrow.

My question is: what guarantee do we have that the huge libraries of the current formal mathematics projects in Agda, Coq or other languages will still be relevant or even "runnable" (for instance type-checkable) without having to resort to emulators and computer archaeology 10, 20, 50 or 100 years from now ?

10 years from now will Agda be backwards compatible enough to still recognise

current Agda files ?

Have there been any organised efforts to guarantee permanent backward compatibility for all future versions of Agda and Coq ? Or OCaml and Haskell ?

Perhaps the formal mathematics project should be carried out within a meta-programing language, a simpler more abstract framework (with a uniform syntax) comprehensible at once to logicians, mathematicians and programers and which can be converted automatically into the latest version of Agda or Coq ?

Assume we have a program with different instructions. Due to some limitations in the field, it is not possible to test all the instructions. Instead, assume we have tested 4 instructions and calculated their rank for a particular problem.

the rank of Instruction 1 = 0.52

the rank of Instruction 2 = 0.23

the rank of Instruction 3 = 0.41

the rank of Instruction 4 = 0.19

Then we calculated the similarity between the tested instructions using

**cosine similarity**(after converting the instructions from text form to vectors- machine learning instruction embedding).Question ... is it possible to create a mathematical formula considering the values of rank and the similarity between instructions, so that .... given an

**un-tested instruction**... is it possible to calculate, estimate, or predict the rank of the new un-tested instruction based on its similarity with a tested instruction?For example, we measure the similarity between instruction 5 and instruction 1. Is it possible to calculate the rank of instruction 5 based on its similarity with instruction 1? is it possible to create a model or mathematical formula? if yes, then how?

Hi frds,

Need a good weather probability calculator. Would like to calculate the probability of e.g. 10 degrees Celsius on a day above the average. Has anybody got good research/formulas?

Which distribution is assumed in the probability calculation? Normal one?

Hi all, I want to solve a system of simultaneous equations in which some equations are cubic and some are quadratic. How to solve such a system. The solution should consist of combinations of all solutions i.e., the positive as well as the negative solutions.

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?

Any idea why the solution of the attached equation is always zero at r=0? It seems simple at first look, however, when you start solving, you will see a black hole-like sink which makes the solution zero at r=0 (should not be). I used the variable separation method, I will be happy if you suggest another method or discuss the reasons.

I also attached the graph of the solution, showing the black hole-like sink.

Thanks

I have no mathematical experience and no statistician to help me.

Is it possible to decompose a conditional probability with three or more elements (i.e. events) into conditional probability of only two elements or the marginal probability of one element? Knowing this decomposition, it would help to solve higher order Markov Chain mathematically. I also know that this decomposition can be solved if we add assumption of conditional independent.

To make it concrete here is a negative example:

P(c│a,b)=(P(a,b│c)∙P(c))/(P(a│b)∙P(b) ).

Notice that the RHS still contains a conditional probability with three elements P(a,b│c).

Assuming conditional independent on c, we have P(a,b│c)=P(a│c)∙P(b│c). Thus, the conditional probability decomposition becomes

P(c│a,b)≅(P(a│c)∙P(b│c)∙P(c))/(P(a│b)∙P(b) )

My question is whether this type of conditional probability decomposition into one or two element is possible without making assumption. If it is really unsolvable problem, then at least we know that the assumption of conditional independent is a must.

During the lecture, the lecturer mentioned the properties of Frequentist. As following

**Unbiasedness**is only one of the frequentist properties — arguably, the most compelling from a frequentist perspective and possibly one of the easiest to verify empirically (and, often, analytically).

There are however many others, including:

1.

**Bias-variance trade-off**: we would consider as optimal an estimator with little (or no) bias; but we would also value ones with small variance (i.e. more precision in the estimate), So when choosing between two estimators, we may prefer one with very little bias and small variance to one that is unbiased but with large variance;2.

**Consistency**: we would like an estimator to become more and more precise and less and less biased as we collect more data (technically, when n → ∞).3.

**Efficiency**: as the sample size incrases indefinitely (n → ∞), we expect an estimator to become increasingly precise (i.e. its variance to reduce to 0, in the limit).Why Frequentist has these kinds of properties and can we prove it? I think these properties can be applied to many other statistical approach.

Provide me the detail mathematical calculation for the measurement of uranium, thorium and potassium with their daughter progenies.

Hello,

For correlation analysis between body composition variables and blood hormone levels,

I have data from two different blood analysis methods but the same units; ECLIA & CLIA.

I wonder if there is any statistical and mathematical error when I run correlation analysis using the data together.

If it cannot,

Is there any suggestion for using these data together for statistical analysis?

Thank you very much.

Mathematics is a subject most pupils love to hate; how did your journey into the world of mathematics proper begin?

Famous mathematicians are failing each day to prove the Riemann's Hypothesis even if Clay Mathematics Institute proposes a prize of One Million Dollars for the proof.

The proof of Riemann's Hypothesis would allow us to understand better the distribution of prime numbers between all numbers and would also allow its official application in Quantics. However, many famous scientists still refuse the use of Riemann's Hypothesis in Quantics as I read in an article of Quanta Magazine.

Why is this Hypothesis so difficult to prove? And is the Zeta extension really useful for Physics and especially for Quantics ? Are Quantics scientists using the wrong mathematical tools when applying Riemann's Hypothesis ? Is Riemann's Hypothesis announcing "the schism" between abstract mathematics and Physics ? Can anyone propose a disproof of Riemann's Hypothesis based on Physics facts?

Here is the link to the article of Natalie Wolchover:

The zeros of the Riemann zeta function can also be caused by the use of rearrangements when trying to find an image by the extension since the Lévy–Steinitz theorem can happen when fixing a and b.

Suppositions or axioms should be made before trying to use the extension depending on the scientific field where it is demanded, and we should be sure if all the possible methods (rearrangements of series terms) can give the same image for a known s=a+ib.

You should also know that the Lévy–Steinitz theorem was formulated in 1905 and 1913, whereas, the Riemann's Hypothesis was formulated in 1859. This means that Riemann who died in 1866 and even the famous Euler never knew the Lévy–Steinitz theorem.

Everybody is eager to see the New winner of the Millenium Prize. Please share all your incomplete works about the Millenium Prize problems of Clay Mathematics Institute in order to collaborate for the solutions.

I am actually using the different nabla operator which I demonstrated mathematically in my published work: " A thesis about Newtonian mechanics rotations and about differential operators ".

This demonstrated differential tool enables to deal differently with the millenium problem about Navier-Stokes equation.

I also suggest that P=NP if the problem can be translated to a differential equation that has a solution. If your lucky friend finds and gives you an easy solution, than that solution leads directly to the general solution of the differential equation.

I will be waiting for your collaborations.

Say I have a satellite image of known dimensions. I also know the size of each pixel. The coordinates of some pixels are given to me, but not all. How can I calculate the coordinates for each pixel, using the known coordinates?

Thank you.

Physics is a game of looking at physical phenomena, analyzing how physical phenomena changes with a hypothetical and yet mathematical arrow of time in 3D space, namely by plotting that physical phenomena with a mathematical grid model (typically cartesian based) assuming that physical phenomena can be plotted with points, and then arriving at a theory describing that physical phenomenon and phenomena under examination. The success of those physical models (mathematical descriptions of physical phenomena) is predicting new phenomena by taking that mathematics and predicting how the math of one phenomenon can link with the math of another phenomenon without any prior research experience with that connection yet based on the presumption of the initial mathematical model of physical phenomena being undertaken.

Everyone in physics, professional and amateur, appears to be doing this.

Does anyone see a problem with that process, and if so what problems do you see?

Is the dimension of space, such as a point in space, a physical thing? Is the dimension of time, such as a moment in time, a physical thing? Can a moment in time and a point of space exist as dimensions in the absence of what is perceived as being physical?

Hello Friends and Colleagues,

Can anyone suggest a mathematical book that helps me to build my own mathematical equations and functions? I want to convert real-life problems(natural sciences) into mathematical formulations.

Note that I have basic knowledge of mathematics.

Thanks in advance,

Hadi

Plz share if yes . I want to know how to get patent in vedic maths.

**Applying mathematical knowledge in research models:**This question has been in my mind for a long time. Can advance mathematics and applied mathematics solve all the problems in modeling research? Especially the formula derivation in the theoretical model part, can the analysis conclusion be obtained through multiple derivations or other methods? You have also read some mathematics-related publications yourself, and you have to admire the mystery of mathematics.

Hello everyone,

I would like to know how to locate mathematically a damage on a blade.

Usually a frequency analysis of the blade and a comparison with a similar healthy one helps to determine a default or damage on a blade. However, how could someone locate that damage?

Thank you for your time.

I'm struggling to understand the method followed in the following analysis. Can someone please explain how the author got the values of Δ_1 and K_1 that justify its analysis?

I have tried to isolate "Δ" and "K" by setting Equation (B8) equal to zero. but I have failed to get similar conditions.

P.S: I'm new to mathematical modelling, so I really need to understand what's going on here. Thanks

why to quantize a Hamilton-Jacobi theory with fractional derivatives?, what are the physical or mathematical advantages?

How to people propose a new optimization algorithm. I mean what is the baseline? Is there any intuition or mathematical foundation behind it?

When solving mathematical equations or system of equations there are things that are considerable; such as the Universe or domains...

Because, some equations may have no solutions or impossible to solve., at all. If a solution or some solutions exist for an equation or systems of equations, there are regions or intervals containing the solution(s). Such considerations may be important when applying numerical methods.

What are basins of attractions?

The constants (

*G*,*h*,*c*,*e*,*me*,*kB*), can be considered fundamental only if the SI units they are measured in (*kg*,*m*,*s*...) are independent. However, if we assign numerical values to the SI units (*kg*=**15**,*m*=**-13**,*s*=**-30**,*A*=**3**,*K*=**20**), then by matching the unit numbers, we can define (and solve) the least precise (CODATA 2014) constants (*G*,*h*,*e*,*me*,*kB*) in terms of the 3 most precise constants (*c,**μ*0,*R*) ... (diagram #1). Officially this must be just a coincidence, but the precision is difficult to ignore.We find further anomalies to equal precision when we combine the constants (

*G*,*h*,*c*,*e*,*me*,*kB*) in combinations whereby the unit numerical value sums to**0**... (diagram #2).The methodology is introduced here

**Are these physical constant anomalies evidence we are in a simulation?**dx.doi.org/10.13140/RG.2.2.15874.15041/3**https://en.wikiversity.org/wiki/Physical_constant_(anomaly)**

Is a simulation universe the best explanation for these anomalies?

Some general background to the physical constants.

I am aware of the facts that every totally bounded metric space is separable and a metric space is compact iff it is totally bounded and complete but I wanted to know, is every totally bounded metric space is locally compact or not. If not, then give an example of a metric space that is totally bounded but not locally compact.

Follow this question on the given link

What are the areas where mathematics are been applied medically.

Does nature understand mathematics?

A connected question is -- How are theory, theorem, and truth related?

I am trying to model a business scenario mathematically for my research paper but I do not have the required skillset. What is a legitimate way to find and get help. Are there any online sources or paid services. Do I need to add the expert a co-author? What type of solutions exists.

Why use metaheuristic algorithms when there are so many mathematical optimization tools available, like GAMS?

1) What's the difference between SCILAB and MATLAB?

2) Which one would you recommend?

3) Which one is the most friendly user?

Dear Colleagues,
a recent trend in Fractional Calculus is in introducing more and more new fractional derivatives and integrals and considering classical equations and models with these operators. Thus, we have to think about and to answer questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. These and similar questions have remained mostly unanswered until now.
To provide an independent platform for discussion of these trends in the current development of FC, the SI “Fractional Integrals and Derivatives: “True” versus “False””( https://www.mdpi.com/journal/mathematics/special_issues/Fractional_Integrals_Derivatives2021) has been initiated. In this SI, some important papers have been already published. However, you are welcome to share with the scientific community your viewpoint. Contributions to this SI devoted both to the new fractional integrals and derivatives and their justification and those containing constructive criticism of these concepts are welcome.

Best regards

Yuri Luchko

How can we analyze the propagation constant in slab waveguides? Is there a mathematical formula for this parameter?

If interested you can send different articles from Piaget theory in the learning of mathematics through play.

my article is about the relationship between playing and increasing intelligence via mathematics. this a longitudinal research which has done since 4 years ago until to year. it is a pre-test- post-test research with control group. results are wonderful. assessment tool in this research was Stanford-Binet test. I am following to a journal in grade Q1. I would be grateful if someone could help me.

Chaos Theory, Chaotic dynamics

Please help me

If any mathematical equations for coupling of pmsm and pmsg in matlab?

A study by Po-Shen Loh shows that quadratic equations can be solved using a clever trick that reduces guessing and cramming formula. Kindly follow this link to see examples of quadratic equations solve by Po-Shen Loh https://www.youtube.com/results?search_query=po+shen+loh+quadratic .

Could this idea be applied in class? if so, could it be generalized for other topics in mathematics?

Can anyone please confirm whether there exists an explicit mathematical relationship between the gravitational instability growth rate and the corresponding structure (star) formation rate in molecular clouds?

I have formulated the mathematical equation of the vibration problem. The resulting equation is coupled nonlinear differential equation of 2nd order ODE. Please, anyone, suggest to me how to solve it using MATLAB.

I am working on RIS aided communication. Whichever paper I go though, they cook up some complicated mathematics specially optimization problem, which seems to be unsolvable at first. But, then I see they are using some techniques which I have never seen anywhere. Can anyone from wireless comm background tell me, how you people proceed and get those sort of maths?

Hi!

I'm currently working on a Data Science project for optimizing the prices of the products one of the biggest supermarket chains in Mexico.

One of the things that we are working on, is finding the price elasticity of demand of such products. What we usually do, is that, apart from fitting an XGBoost model for predicting sales, we fit a linear regression, and we get the elasticity from the coefficient corresponding to the price (the slope).

However, it is abvious that linear regression is sometimes a poor fit for the data, not to mention that the execution times are way longer since it requires to run separately XGBoost and LR (which is not good considering that there are thousands of products to model).

Because of this, it ocurred to me that we could use numerical differentiation for finding the price elasticity. At last, calculating a numerical derivative is way faster than fitting another model.

However, I'm not sure if this is mathematically correct, since the data does not come from a function.

So the question would be, is this mathematically correct? Does it make sense?

Dear colleagues,

I am researching in a topic related to philosophy and teaching methods. Please, could you point out me if are there any sources on dialectics or contradiction in mathematics education?

Thank you for your answers.

Regards

Please look at the text of the section on random walk from page 9 to formula 4.7, where you will find mathematical calculations justifying the probabilistic interpretation of the Riemann zeta function.

Preprint Chaotic dynamics on the sphere

I will be glad if researchers and professors answer my question with mathematical formulas or explanations. Thank you so much.

I can't understand why each time we divide by the mass of oxidized NH4-N and multiply by the mass of treated NH4-N.

How can we mathematically calculate the critical thickness of polycrystalline(Sputtering) grown thin?

Hello? Good evening, I would like to ask if there is a questionnaire aligned to the set of indicators on Mathematical Competence given by Sir Turner?

Is multiverse a differential of possibility, a gradient of cross universe space time planes.

Do multiverses branch or all have separate beginnings.

Are multiverses different mathematical constants or is it different potentials.

How can we progress to a mathematical model of multiverse theory.

First we need a mathematical model of the universe and then we need to generalise it for the multiverse. Is this quantum physical, does this take into account the electromagnetic generation of mass and gravity in a recursive relationship?

Does Arc Length calculus change our notion of frequencies and therefor electromagnetism?

I want to understand the mathematics of fluorescence process in terms of excitation and emission wavelengths. I want to develop a general mathematical model with certain specific parameters and without employing a spectrometer, I want to see the emission spectrum mathematically.

Hello, this is my first post on this site. I'm an undergraduate student doing some Raman spectroscopy of CVD-grown graphene strained on silicon dioxide nanospheres. I notice that D and G' peaks show up in some measurements. The transfer process of the graphene to the silicon dioxide nanosphere-coated silicon chips I would think is far from perfect, as in certainly interferes with the structure of the graphene as there are rips and tears across the sample, as well as impurities and other things. You do however have "pristine" regions that only show G and 2D peaks.

On a loosely related tangent, I'm interested in how the molecular symmetry of graphene plays a role in its Raman spectra, and how that can be expressed mathematically. I wonder if perhaps the mathematical description of graphene in terms of group theory can possibly help explain the redshifts that occur in strained graphene versus unstrained graphene. If anyone has some advice or things to read about that, please let me know!

I have myself tried using the basic method but including incomplete ionization to figure out the depletion width however I failed miserably because of many mathematical roadblocks. I was wondering if this had been done in the literature before and I just missed it.

If anyone can help me in this regard then I would be very grateful. Thanks.

please is there any mathematical function that relates the SMD (D32) to the mean diameter (D50)? I actually understand what each of them represent.

thanks

I am primarily interested in 2-player combinatorial games with perfect information. Useful wiki links are below.

Is there a way to model the influence of pH on the electroosmotic EDL potential and velocity field inside the flat microchannel mathematically?

How could one increase data values from weekly to daily observations using mathematical algorithm for interpolation?

The mathematical representation of both equations is same.

Hi

I'm solving nonlinear second order equation by using finite difference method . finally for calculating value at any desired node, knowing three preceding nodes is required however by knowing boundary condition just one of these nodes becomes obvious and still knowing two other values is necessary. it must be noted there are plenty of guesses for values of these nodes which lead to compatible response.

The 2023 ranking is available through the following link:

QS ranking is relatively familiar in scientific circles. It ranks universities based on the following criteria:

1- Academic Reputation

2- Employer Reputation

3- Citations per Faculty

4- Faculty Student Ratio

5- International Students Ratio

6- International Faculty Ratio

7- International Research Network

8- Employment Outcomes

- Are these parameters enough to measure the superiority of a university?

- What other factors should also be taken into account?

Please share your personal experience with these criteria.

Here I attached the journal and the mathematical solution of the Rayleigh number. I need to plot graph exactly in Figure 3 from the journal but I didn't know the command. I have tried using this command,

plot(subs(N1 = 0.5, N3 = 2, N5 = 1.5, a1 = 1, a2 = 3, a3 = 1, Q = 10, R), a = 0 .. 10, 11 .. 22);

but the results show only a single line 2D graph. Hopefully anyone could help me with this. Thank you in advanced.