Mathematics - Science topic

I think "International Journal of Differential equations" is suitable for it.

Dr.Salahuddin

It may be useful to make a distinction between 'global' optimisation (where one is given an explicit, non-convex objective function) and 'black-box' optimisation (where the function is not given explicitly). The methods for them are very different.

Dear Mohamed Albira,

I suggest you to see links and attached files on topic.

Best regards

We're all faced throughout our lives with decisions and choices, some on a grand scale, most of them on lesser points. We define ourselves by the total sum of decisions and choices we have made.

Yes, your assumption is right. I am using a Likert- Scale. The same participants rated the same statements for both learning context. The number of respondents of my study is more than 30. Well, thank you for responding my question Anna-Gesina Hülemeier .

Long and boring solutions are attached. If anyone can provide a nicer argument, please share.

A not too complicated solution, please see attached.

Excellent Omran, your construction solves my inquest, with the minimal continuity set for f.

Utkarsh Singh There is an esthetic reason in why a mathematical method is of interest in signal processing:

-a beautiful algorithm is well articulated, says what it does in few instructions, and does it in a stable and reliable manner

-this hints to the underlying algebra

With powerful and minimal computation, we go deep into algebra structures: group, rings, fields (see references on Evariste Galois as the inventor of "group" as we know it)

-Fourier transform is an interesting invention: it allows to decompose a signal into resonating modes (as for piano music: you produce a sound at frequency F, but also its harmonic NxF...). Naturally there is the aliasing question and the Nyquist theorem for reconstruction

There are many more time-frequency representations: Fourier, Laplace, discrete or continuous, cosine transform, wavelet transform, etc.

The interesting feature of discrete algorithms for those transforms is that you can implement a butterfly structure.

The key idea is to replace a very large number of multiplications (in brute force "non-esthetic" programming) by a smaller number of additions.

This idea worked for me for developing a codec system using underlying GF(n) properties.

See this patent:

The regularity in the processing and the efficiency of the representation go hand in hand.

Let me go back to a very basic mathematical method: the Gram-Schmidt decomposition: take a sequence of n vectors v(1),..., v(n), and the matrix of cross-products m(i,j)=<v((i),v(j)>. The Gram-Schmidt method diagonalises this matrix. It extracts eigenvalues, and eigen vectors. In frequency terms, it extracts modes (resonating modes present in the signal).

This algorithm highlights the efficiency side of the representation: it's projecting the signal onto something found "in itself", call it principal components if you want.

There are only two reasons for choosing a technique in engineering:

-(i) it addresses the problem completely

-(ii)it's economically implementable.

Both criteria are equally important and a good way to find these is to look for elegant, esthetic solutions (minimal and complete at the same time).

Does it help?

I am surprised that a known scholar with a long experience in the transportation domain maintains such a hard stance on heuristic search. Obviously, we live in a world where extreme opinions are those which are the most echoed. Truth is, assuming that all practical optimization problems can be solved to optimality (or with approximation guarantees) is essentially wishful thinking. Given this state of art, better integration of exact and heuristic algorithms can largely benefit the research community. At the risk of repeating myself, here are some important remarks to consider:

• CPLEX and Gurobi (the current state of the art solvers for mixed integer programming optimization) rely on an army of internal heuristics for cut selection, branching, diving, polishing, etc... Without these heuristic components, optimal solutions could not be found for many problems of interest. CPLEX has even recently made a new release permitting a stronger heuristic emphasis (https://community.ibm.com/community/user/datascience/blogs/xavier-nodet1/2020/11/23/better-solutions-earlier-with-cplex-201). MIP solvers also heavily depend on the availability of good (heuristic) initial solutions to perform well. For many problems, cut separation is also done with heuristics. In the vehicle routing domain, we have a saying: heuristics are the methods that find the solutions, exact methods are those that finally permit to confirm that the heuristics were right (sometimes many decades later, and only for relatively small problems with a few hundred nodes despite over 60 years of research on mathematical models)...

• The machine learning domain is quickly taking over many applications that were previously done with optimization. Among the most popular methods, deep learning applies a form of stochastic gradient descent and does not guarantee convergence to optimal parameters. Neural networks currently face the same scrutiny and issues as the heuristic community, but progress in this area has still brought many notable breakthroughs. Decision-tree construction and random forests are also largely based on greedy algorithms, same for K-means (local improvement method) and many other popular learning algorithms.

• Even parameter tuning by the way is heuristic... I'm sorry to say that, but most design choices, even in the scientific domain, are heuristic and only qualify as good options through experimentation.

Hi, you can directly use the following MATLAB function : fminsearch that uses the Nelder-Mead simplex (direct search) method instead of trying to implement your own version. Best

Ruqaya Ameen The digital elevation model (DEM) is a good component in the field of remote sensing and GIS. The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM). The ASTER GDEM needs further error-mitigating improvements to meet the expected accuracy specification. The RMSE values can be used to represent the DEM errors, in addition to mean error and standard deviation (stddev).

Vinayak - this is just a preprint, the authors are allowed to write whatever they like and how they like it; I would follow the printed version (in a journal, conference proceedings etc) - usually it gets better when reviewed & printed.

Dear Aziz Elghazouani

It gains its importance due to the strong relationship between the Riemann Zetta function and prime numbers distribution.

Also, it is one of the Millenium open problems.

The Riemann Hypothesis is

See the attached file.

Best regards

An Euler brick is a cuboid that possesses integer edges a>b>c and face diagonals. If the space diagonal is also an integer, the Euler brick is called a perfect cuboid, although no examples of perfect cuboids are currently known.

Example 19. “A function with a dense set of points of continuity, and a dense set of points of discontinuity no one of which is removable.”

Example 22. “A function whose points of discontinuity form an arbitrary given closed set.”

Example 23. “A function whose points of discontinuity form an arbitrary given F_σ set.”

Example 24. “A function that is not the limit of any sequence of continuous functions.”

(See Examples 19, 22, 23 and 24, Chapter 2, pages 28, 30 and 31 in the book: B.R. Gelbaum and J.M.H. Olmsted, Counterexamples in Analysis, Dover Publications, Inc. Mineola New York, 1964.)

I don´t understand you. It´s no trivial to find two prime numbers whose sum +1 will be other prime number. In fact my formula have a success of the 80%

As a mathematician & statistician, I can say that, when modeling reality, we make compromises; and, when validating the models, we have lots of surprises.

I was thinking of defining k(n) := sup { k ≥ n : x_k - x_n < c }. Then

x_k(n) - x_n < c ≤ x_k(n)+1 - x_n , and the length of the interval containing c is x_k(n)+1 - x_n , which → 0 as n → ∞ by hypothesis.

Is this OK for all c > 0?

Design optimization, fabrication, and performance evaluation of solar parabolic trough collector for domestic applications

Attached for your kind perusal@Miss. A.M

Dear Dagnachew Jenber

The first 11 theorems in your article provide a limit family of numbers that obey the Collatz conjecture and the number of steps needed to reach 1.

Unfortunately, in theorem (12), you have assumed that Collatz conjecture is true!!

In fact, your assumptions of the existence of b₁ , b_{2 ,} ....b_k-1 where k is finite

is exactly the Collatz conjecture, and the rest is an elementary computation of the number of steps to reach 1.

Can you prove that k is finite?

Obviously, if one assumes k is finite, then he assumes that Collatz conjecture is true.

Anyway, you have determined a nice family of numbers that satisfy the Collatz conjecture.

I wish you good luck to show k is finite.

Best regards

Ajit - if you are not interested in statistical analyses (regressions etc), a polynomial interpolation will do just fine.

Bernard Di Martino Many thanks for this detailed explanation.

No

These days, as I study the internal structure of matter, I find it interesting to know how a chemist looks at atoms or molecules.

For example, does a chemist, like me, who examines fundamental actions and states of equilibrium between protons and electrons, do the same, or does he only deal with the bonds between them and not with details or actions?

Or, for example, how does a chemist look at water molecules? Is only the bond between hydrogen and oxygen important to him, or why and how do two or more atoms reach a stable state?

Of course, these can be examined from the point of view of a biologist.

consult

I suppose you are considering some special cases where the PDE can have locally such an effect, for example as happens for the governing equation in transonic steady flows.

The appearence of complex eigenvalues means that there are no longer characteristic lines in the physical plane but only in the mathematical complex plane. This is the case of elliptic equations and the physics associated to such a mathematical character is generally of an equilibrium state, that is a perturbation in a point is propagated, istantaneoulsy, in isotropic way along all the directions.

see

Anh C.T., Hung P.Q., Ke T.D., Phong T.T.: Global attractor for a semilinear parabolic equation involving Grushin operatot. Electron. J. Differ. Equ. 32, 1–11 (2008)

D’Ambrosio L.: Hardy inequalities related to Grushin type operators. Proc. Am. Math. Soc. 132, 725–734 (2004)

Thanks Maged Gumaan Bin-Saad

Boris,

Your description of MPM is exactly what I mean by a focusing method. MPM requires the observer to select the data that is understood as relevant to particular phenomena. The reason I use the term "focus" is to signal the effect on the notion of a "lens." However we want to formulate the question, we cannot escape the need to choose what we want to see. Therefore, human choices must dominate what humans see. By the way, look at how many Americans literally choose not to believe in the Covid pandemic. Some disbelieve, i.e. cannot see Covid, even as they are dying from it.

@Pedro, I don't understand why the word or is emphasised . As per my understanding , a quadratic equation must possess exactly 2 roots so this equation (x-2)(x-3)=0 contains two distinct roots which are x=2 and x=3. For better visualisation , one can easily plot that equation to find the roots where the function cuts the x-axis. It does not mean that x=2=3. Do I miss any necessary information?

Thank you Ebrahim for sending all these articles.

check

Once the economical model reduces to a statistical one, the entire machinery of the latter is at the disposal of the former. Alternatively, a stochastic processes can be the solution to an economical model, so there's another machinery that can handle uncertainty.

See here: (PDF) Folding and Bending Planar Coils for Highly Precise Soft Angle Sensing (researchgate.net)

A little more further evaluation is required.

hello , you can use Verilog A to create this source.

"Only dead fish swim with the current implies that those who swim against the current are those who wish to invoke change; who want to control, manipulate, and improve their environment. People who swim upstream make things happen. They are the movers and shakers; the innovators and inventors; the disruptors of the world. There is nothing new downstream; only that which is old and boring, ancient history, the past, the been there and done that... the tried and true. One must swim upstream to find and explore new territory; learn new stuff, have new experiences. To create; fly; soar."

We read this in https://www.psychologytoday.com/us/blog/the-main-ingredient/201705/upstream-vs-downstream

But those who try, find it hard to not "go with the flow." The solution maybe to swim like a salmon, making the least waves. With the same principle, it works on a swimming pool, trying to improve personal "best times" -- and tells one why a deeper pool is faster.

Check the following papers:

Muhammad Ali Thank you for answer

see

Saif ur Rehman ... thanks for your response.

x=x(t)=m/cos(t), y=y(t)=n(tan(t) - t),

I think what you want is in this book

Mathematical modeling is the process of a problem solving by the mathematical expression of real life event or a problem. This process enables learners to relate mathematics to real life and to learn it more meaningfully and permanently.

Realistic Mathematics Education – RME – is a domain-specific instruction theory for mathematics, which has been developed in the Netherlands. Characteristic of RME is that rich, “realistic” situations are given a prominent position in the learning process.

Mathematical Modelling Approach in Mathematics Education BY:Ayla Arseven

Best regards

Good job,

Cheers

Andrea Rossi

Dear @Raju Chiluvuri

To my opinion, mathematics is the precursor to all the disciplines of science. And, in fact, mathematics is also a science.

Thanks!

Thanks for your answers.

Search RG for Ed Gerck. I'm sure he'd be glad to discuss this topic.

The answer relies on lmatalogical Godel's axioms: The answwer is YES you need it, in case implicity you haven't inserted previously.

Dear colleagues. A very interesting question, some years ago, in 2012, I published a work where I give a definition of Mathematics that can serve to answer the question.

The book of Computer Aided Optimal Design: Structural and Mechanical Systems by the Mota Soares, C.A. and Templeman, A.B can be useful.

see links

When the electron's energy can take only certain values this just means that the states that would correspond to the other values don't exist, under those circumstances. These circumstances are described by the boundary conditions imposed, that are part of the physical description, too.

It is not very difficult, but some algebra needs to be involved.

The workflow is the following:

1. Knowing relative humidity at T=T0 (as an input), calculate the partial pressure of vapor at this temperature.

2. Calculate water vapor concentration rho_0 using the ideal gas equation.

3. Calculate saturated vapor pressure at T=T1 from tables or the Clausius-Clapeyron equation.

4. Calculate corresponding saturated vapor density rho_1 at T=T1 using the ideal gas equation.

5. If rho_1 < rho_0, there will be no condensation, otherwise the mass of water condensed in volume V will be V(rho_1 -rho_0).

Pass x, instead of tau, as rightly pointed out by Saeb AmirAhmadi Chomachar

syms x y psi tau t

c1 = 1;c2 = 1.5;lambda = 0.1;

x_r(tau) = 0.8486*tau - 0.6949;

y_r(tau) = 5.866*sin(0.1257*tau + pi);

psi_r(tau) = 0.7958*sin(0.1257*tau - pi/2);

x_r_dot = 0.8486;

y_r_dot(tau) = 0.7374*cos(0.1257*tau + pi);

psi_r_dot(tau) = 0.1*cos(0.1257*tau - pi/2);

phrase1 = c1/2*(cos(psi)*(x - x_r) + sin(psi)*(y - y_r))*(cos(psi)*x_r_dot + sin(psi)*y_r_dot);

phrase2 = c1/2*(-sin(psi)*(x - x_r) + cos(psi)*(y - y_r))*(-sin(psi)*x_r_dot+cos(psi)*y_r_dot);

phrase3 = 0.5*(psi - psi_r)*psi_r_dot;

eq = -2*(1-lambda)^2*(phrase1 + phrase2 + phrase3) - 2*lambda^2*(t - tau);

eqn = rewrite(eq,'log');

sol = solve(eqn == 0 , x , 'IgnoreAnalyticConstraints',1);

pretty(sol)

I am not expert in this subject , may be the following links are useful

High-Voltage Leak Detection of a Parenteral Proteinaceous Solution Product Packaged in Form-Fill-Seal Plastic Laminate Bags. Part 3. Chemical Stability and Visual Appearance of a Protein-Based Aqueous Solution for Injection as a Function of HVLD Exposure

Rasmussen, M., Damgaard, R., Buus, P., Guazzo, D. M.Journal:PDA Journal of Pharmaceutical Science and TechnologyYear:2013

Interesting question. However, the foundations that allowed calculus to evolve started long before Newton and Leibniz. The foundation is not calculus but the concept of the limit. Archimedes (287-212 BC) was probably the first to recognize what became the concept of the limit in is estimation pi and the area of the circle by taking inscribed and circumscribed polygons bounding the circle and using the simple fact that one approaches pi from below while the other from above. Of each sequence defines a Cauchy sequence - concept unknown at that time and the completion of the reals (also unknown at that time) show the limit of each sequence is the same and equal a the number pi. In reality the concept of infinitesimal - goes back to Archimedes although the formal concept of "infinity" was not accepted until long afterwards.

Roll backwards to the Greeks when faced with the proposition of an infinite number of prime number, was a problem as they believed the universe was finite. Infinity was not something the Greeks wanted to accept and Aristotle (385-348 BC). But Archimedes had just shown that infinity and infinitesimals had a role in mathematics - in fact a central role. It was not to the 1600's that mathematicians attack the problem of infinity to try to understand what it mean as they developed the concept of numbers that are used today.

As we better understood our real number system, the concept of point set or general topology was defined to abstract and better understand the structure. In general topology concepts like nets (generalizations of sequences required to define integrals for example), convergence, close to, in a neighborhood and limits are all defined through the concept of open sets which are used to define a topology on a set which now allows for the definition and study of the concept of limits and continuity and handle infinity. While the formulations of general topology came along after the "birth of the calculus" and known as Analysis Situs a term coined by Henri Poincaré through the work of Poincaré , Euler, Cantor, Lefschetz, Courant, Hilbert, etc., a firm foundation was laid not only to the real number system, but to limits, continuity all the foundations of what we now know as 'calculus."

Topology is so important to the foundations of calculus and the concept of a limit that in his classic text, "General Topology," John Kelley writes in the first paragraph of the preface he writes, "...I have, with difficulty, been prevented by my friends from labeling it: What Every Young Analyst Should Know." No truer words have been spoken or written as the foundations of topology has allowed the concept of calculus to be expanded far beyond its original intent.

I believe that one of the most important reasons for low achievement in mathematics is their lack of basic mathematics and their belief that mathematics has no strong necessity in their lives, as there is a lack of training for students on questions that measure higher levels of thinking. As a result, students focus on memorization without understanding, as they remember in the time immediately preceding the test. As for students, they see that one of the factors for their low level of achievement in mathematics is the way the book is presented, as it does not allow them the opportunity to follow the course themselves, and the teaching methods of mathematics do not encourage research and benefit from mathematics, also the teacher does not use educational aids during the explanation In addition, they believe that the time difference between the tests is small and that the time allocated for answering is much less with what you need from these tests. They also admitted that they are worried about their test score, which will affect their achievement results

A multi-depot VRP with less than 10 nodes should be almost enumerable, as there exist less than 1024 possible subsets of customers. Given this fact, perhaps the simplest solution approach is to generate all feasible routes from each depot, discard those that are not TSP-optimal, and directly solve a set partitioning formulation based on these routes. Now, if you face larger problems (e.g., 15 nodes or more), you should use the formulations suggested by Adam and Noha, or even go for sophisticated branch-and-price approaches as described in

since the code associated with this paper is freely accessible at

Dear Sumit Bhowmick

I hope you find the following discussion is useful

https://math.stackexchange.com/questions/202261/solid-angle-between-vectors-in-n-dimensional-space#:~:text=The%20formula%20of%203D%20solid,c)%7C%E2%86%92a%7C.

Best regards

I can imagine volumes of reasonings behind the eight-word response. Thank you Hermann Gruenwald !

Dear Sneha,

Please follow the paper in the link:

You will get the design formulas and an example of antipodal Vivaldi Antenna.

If you have more questions you can ask the first author of the paper.

Best wishes

First thanks , it is really an interesting question.

A problem is that gifted and talented students do not receive the necessary care

To meet their needs by remaining in regular classes. Therefore, I find it important to do the following:

- Staying away from traditional methods during teaching, this leads to boredom for students, especially talented people

- When constructing lessons conceptually, we take into account that gifted and talented students may also suffer

One of the weaknesses in understanding the curriculum and that they need to be considered. And when applying the teaching conceptually within

In the ordinary class, students of all levels will learn in a deeper way.

- Adding open-ended questions to both education and evaluation for their positive results on students ’understanding

As well as their attitudes towards the material.

The- direct and indirect financial support for talented people

Quantum computing (QC) is the enabling technology for efficiently processing huge quantities of (quantum) information, in many cases outperforming "classical" computing (i.e. binary logic based). It provide you the "muscles" for data crunching, provided you feed it with quantum-coded information (qubits) and you get probabilistic results (with high likelihood if well designed).

Artificial Intelligence (and Machine Learning more specifically) is a discipline focused in performing data analysis with the objective of simulating human reasoning for achieving a certain goal. It can then definitively take advantages by a super fast computing capability provided by QC, both for speeding up "classical" algorithms or for running QC native ones, which are expected to open the door to a next level of AI capabilities beyond our current imagination.

Just be patient for few more years and wait for a working universal QC becoming available (at competitive price).

Interesting question. Following the discussion.

What a good question, dear Parul! I can tell you that, after 35 years of career in math & stats, I still fell rewarded when I solve a problem or finish a project. I do not know what chemicals are doing that for me, but they do. It is true, I did not have many frustrations to overcome, it worked well for me math & stats-wise, so I am pleased (and happy, as you say) by default. I am probably not the perfect subject for your study, you need people who had to struggle much more than me to achieve their goals.

Hi Natacha,

rcompanion.org is a great source with many examples of non-parametric tests.

sthda.com is also good, but the author uses his own limited packages.

1. Patience.

2. Knowledge of field and ability to impart that knowledge to others.

3. Ability to ask questions and define specific aims

4. Writing skills to produce grants and publications.

5. Research support in terms of grants or other types of research funding.

6. Contacts, perhaps a network of researchers with similar interests.

7. Foster attendance a scientific meetings, including presentations by students.

Age requirement l problem. If it was 40 better !!

The answer to a question about the numerical algorithms for resolving the issue of differentiability of a function is typically provided by the textbooks on experimental mathematics.

I recommend in particular: Chapter 5: “Exploring Strange Functions on the Computer” in the book: “Experimental Mathematic in Action”.

For the review please see

You can also get a copy of the text in a form of a preprint from

Judging by the quote placed in the beginning of Chapter 5, the issue of investigation of the “strange functions” was equally challenging i 1850s as it is 170 years later:

“It appears to me that the Metaphysics of Weierstrass’s function

still hides many riddles and I cannot help thinking that enter-

ing deeper into the matter will finally lead us to a limit of our

intellect, similar to the bound drawn by the concepts of force

and matter in Mechanics. These functions seem to me, to say

it briefly, to impose separations, not, like the rational numbers”

(Paul du Bois-Reymond, [129], 1875)

The situation described in your question is even more complicated because the function is represented only by a few values on a rectangular grid and it is additionally assumed that the function is not differentiable at a certain point. In this situation I can suggest to use the techniques employed in the theory of generalized functions (distributions).

For a very practical example you can consult a blog: “How to differentiate a non-differentiable function”:

In order to answer your question completely I would like to know what is the equation, boundary conditions and the numerical scheme used to obtain a set of the grid point values mentioned in the question.

You're welcome Rich Philp. For your information, I have a modest knowledge regarding programming, but still I made some games for PC. Here is a free one:

Mohammad Esmail Aryaee Panah

Not all these phenomena can be summarized in the permittivity of the material. For a start there is the permeability, which is as basic as the permittivity, then whole areas that these two do not cover at all, such as fluorescence, ionisation, photo-electricity, Rayleigh and Raman scattering, interaction with (other) fundamental particles, interaction with gravity/space-time, and more.

An alternative method of demonstrating stability is given by Vasile Mihai POPOV, a great scientist of Romanian origin, who settled in the USA.

The theory of hyperstability (it has been renamed the theory of stability for positive systems) belongs exclusively to him ... (1965).

See Yakubovic-Kalman-Popov theorem, Popov-Belevitch-Hautus criterion, etc.

If the Liapunov (1892) method involves "guessing the optimal construction" of the Liapunov function to obtain a domain close to the maximum stability domain, Popov's stability criterion provides the maximum stability domain for nonlinearity parameters in the system (see Hurwitz , Aizerman hypothesis, etc.).

Dear Pranav Khade

Are you trying to play chess in 3D?

Your idea is a good one, but your assumptions are not.

You need to give a clear definition of paths, so I suggest for you to start in one 3D box, it includes 8 points. I prefer to give each point the following notation

P(i, j, k), so the locations of the 8 points are at

(0,0,0) (1,0,0), (0,1,0), (0,0,1), (1,1,0), (1,0,1),(0,1,1) and (1,1,1).

Study this cube carefully, define each Delanoy edge (axioms of the path), and then add another box, which means 12 points, etc.

If you find the closed formula that allows you to calculate all possible paths from the starting point at the origin to the farthest point at the upper corner of the rectangular box, then you are on the right track.

I wish you good luck.

exemple.docx

Bryan Soh, your question is a good one. I think it's necessary to be familiar with the nature of your variables (which it seems you are). Unfortunately, I'm not, but might I suggest that you conduct your analyses both ways, look at the results, then think carefully about which results are likely to be most valid.

I also think it is a good idea to present both sets of results if that's permissible. As you are obviously aware, the world of research isn't black and white, and making other researchers, and consumers of research, aware of that could well be helpful. About 20 years ago, I read an article in a top psychological journal in which the author analysed her data in more than one way (from memory, it was more than only two ways), and she discussed the ins and outs intelligently and with insight. It was, for me, much more enlightening that the run-of-the-mill articles that seem to report clean-cut results but leave the reader wondering how much cleaning up and manipulation, and obscuring, occurred to obtain those results.

Every good wish as you plough on!

Sure. But you are not really helping by not being precise! And I am quite certain that there is one major goal - such as a quickest route of the water. I suggest that you check with the literature - which is quite big.

A search string might look like this, or with smaller adjustments:

water network [supply, distribution*, system*] problem*

Tool - An American progressive rock band :)

You may check