Science topics: Mathematics

Science topic

# Mathematics - Science topic

Mathematics, Pure and Applied Math

Questions related to Mathematics

In this link shifted functions are defined as r*(x-o)/100 (where r is the original range)to keep the range between 100. But for optimizing the functions should I generate the values of X between [-100,100] or between [o-100,o+100]? If the function is shifted by o vector then the respective ranges should also change. Because if for 0<-100 or o>100, the global optimum won't fall in the range. And even if I generate the o values between [-100,100] then the function would be shifted in the range rather than being in the range where it is well defined.

Dear Colleagues,

I would like to invite you to submit both original research and review articles to the Special Issue on "Modern Applications of Numerical Linear Algebra" organised by Mathematics (IF=1.747) ISSN 2227-7390. For more details see https://mdpi.com/si/74727.

This is my very first encounter with functional equation of this kind, and methods of series solution and differential equations are of not much help. The solution to this problem, or at least the mathematical prerequisites to understand solution to this problem is asked.

This function is asymptotically zero at both +_ infinity, positive otherwise, and has a peak near zero.

If I am correct, then this is the frequency distribution of numbers fed to the sequence x

_{n+1}=a ln (x_{n}^{2}) as long as the sequence generated is chaotic and sufficiently large in number (value of a is usually limited to 0.2 to 1.3, Positive and negative signs of a are essentially immaterial except for the sequence is negated after first term) .The sequence is initiated or seeded with number roughly as the same order of magnitude of 1 in both positive and negative side, except for the values that eventually lead to zero or infinity in the sequence. The sequence is allowed to proceed, and frequency distribution of numbers in the sequence are noted, from which a continuous probability distribution may be numerically guessed but not analytically found. The expression to find out formula of the continuous probability distribution comes to me from the following reasoning- Suppose, the probability distribution is given by y=f(x). Now, if I consider a "dx" (infinitesimally) thin strip around x, then I come up with f(x) dx fraction of all points required to construct the probability distribution. When this fraction of all points are passed through yet another sequence of transformation through the recurrence x
_{n+1 }=a ln (x_{n})^{2}, the fraction of points involved must be unchanged. That is, when x is substituted with a ln x^{2}, the infinitesimal strip area, which changes to f( a ln x^2) d (a ln x^2), must be numerically equal to f(x) dx, thus the functional equation is postulated - I am not entirely sure about this reasoning, and experts are welcome to point out my fault of reasoning and show the correct equation , if I am mistaken.

Please see my related question https://www.researchgate.net/post/Can-you-figure-out-Chaos-of-the-recurrence-x-n-1lnx-n2 for further details.

Considering the majority of the population, as if, they do not know as to what is their strength. This perhaps is due to their considerably lesser exposure to various possibilities, as a result under exploitation of visible potential indicators being observed perceivably reflective. This is somewhat mathematically to be calculated based on the following generic formula which could further be deepened by incorporating a finer level of referrals and parameters as per the identified essentials during the study.

*Average calculated potential vs actual harvested potential vs differential potential = under or over harnessed potential*Over harnessed potential to be analyzed in terms of negative or positive impact in achieving socioeconomic equilibrium, so should be recommended to calculate in case of under harvested potential as well.

The above study should reflect socioeconomic loss vs gain due to under or overutilization of the human resource.

I would highly appreciate your view on the above.

For a function, usually sign of second derivative (and if it is zero, even/odd index of higher order derivative whose numerical value is zero) is enough to detect whether the extreme point is maximum/minimum/saddle point, if first derivative is zero. For a functional (NOT A FUNCTION), Euler-Lagrange equation plays the role of first "derivative" of Functional. However, it the RHS of Euler-Lagrange equation is set to zero and the resultant differential equation is solved, then how to find whether this function (as solution to differential equation) corresponds to minimum, maximum or saddle "point" of functional?

Unfortunately, the nature of extremum of a functional is usually declared to be "beyond the scope" of most preliminary/introductory functional analysis resources (I have not checked all). How difficult is that mathematics and what are the prerequisites to understand the mathematics involved in finding the nature of functional extremum?

Please note my knowledge on variational calculus, integral equations and transformations as well as group theory and advanced differential geometry is rudimentary.

In the definition of a group, several authors include the Closure Axiom but several others drop it. What is the real picture? Does the Closure Axiom still have importance once it is given that 'o' is a binary operation on the set G?

How to predict remaining useful life (RUL) on used aeroengine and its components level?

(or)

Any standard mathematical relations for RUL?

Mathematical programming is the best optimization tool with many years of strong theoretical background. Also, it is demonstrated that it can solve complex optimization problems on the scale of one million design variables, efficiently. Also, the methods are so reliable! Besides, there is mathematical proof for the existence of the solution and the globality of the optimum.

However, in some cases in which there are discontinuities in the objective function, there would be some problems due to non-differentiable problem. Some methods such as sub-gradients are proposed to solve such problems. However, I cannot find many papers in the state-of-the-art of engineering optimization of discontinuous optimization using mathematical programming. Engineers mostly use metaheuristics for such cases.

Can all problems with discontinuities be solved with mathematical programming? Is it easy to implement sub-gradients for large scale industrial problems? Do they work in non-convex problems?

A simple simple example of such a function is attached here.

I am on a quest to solve how a cell repairs itself through encoding-decoding of proteins. Is there any link to genetic algorithms to solve age old questions such as aging and how we heal?

I have calculated EVI2 using landsat 7 surface reflectance images and I am getting values above 1.25 (mathematical maximum for EVI2 based on the formula) in my study area (heavily vegetated). I get a range between 0.2 and 1.8. Many publications stipulate -1 to 1, especially based on MODIS data. I also did a check with Landsat 7 TOA images, and I get ranges from -1 to 1, as the publications say. Does this mean something is wrong with the Landsat 7 surface reflectance images, or should values above 1.25 still be okay?

I want to ask if I can get good resources that can explain the mathematical approach behind the Adaptive Model Predictive Control AMPC MATLAB toolbox?

am not be able to find the mathematical analysis behind this toolbox even on the MathWorks webpage.

thank you

Mohamed

Problem: 5 minutes of play are worth more than an hour of study

Knowing that: G = Game S = Gtudy 1 hour = 60 min

The mathematical formula that defines the statement is: 5 x G> 60 x S The quantitative ratio of the minutes expressed in the mathematical formula can be simplified: 60: 5 = 12,
therefore the simplified mathematical formula is: G> 12 x S

So, 1 minute of play is worth more than 12 minutes of study Or it can be said that: game G is worth more than 12 times than study S.

Therefore, the quantitative value of physical objects (or of spatial and / or temporal quantities) must be calculated differently from the qualitative value of human life experiences.

**Explain why it is possible**___________________________________________________________________

___________________________________________________________________________

(Exercise based on Fausto Presutti's Model of PsychoMathematics).

In several discussions, I have often come across a question on the 'mathematical meaning of the various signal processing techniques' such as Fourier transform, short-term fourier transform, stockwell transform, wavelet transform, etc. - as to what is the real reason for choosing one technique over the other for certain applications.

Apparently, the ability of these techniques to overcome the shortcomings of each other in terms of time-frequency resolution, noise immunity, etc. is not the perfect answer.

I would like to know the opinion of experts in this field.

In recent years, many new heuristic algorithms are proposed in the community. However, it seems that they are already following a similar concept and they have similar benefits and drawbacks. Also, for large scale problems, with higher computational cost (real-world problems), it would be inefficient to use an evolutionary algorithm. These algorithms present different designs in single runs. So they look to be unreliable. Besides, heuristics have no mathematical background.

I think that the hybridization of mathematical algorithms and heuristics will help to handle real-world problems. They may be effective in cases in which the analytical gradient is unavailable and the finite difference is the only way to take the gradients (the gradient information may contain noise due to simulation error). So we can benefit from gradient information, while having a global search in the design domain.

There are some hybrid papers in the state-of-the-art. However, some people think that hybridization is the loss of the benefits of both methods. What do you think? Can it be beneficial? Should we improve heuristics with mathematics?

Hi

I would really appreciate if someone helps me out with this MATLAB problem. I have uploaded both MATLAB file (which is not working properly) and the question.

Thank you very much in advance

#MATLAB

In the lands with ancient plain sediments, the courses of rivers change dramatically over time for easy movement and the arrival of rivers to an advanced geomorphic stage.

Are there mathematical arrays that achieve digital processing such as spectral or spatial improvements or special filters to detect buried historical rivers?

The mathematical relations how it comes.

List of unsolved problems in mathematics, engineering, industry, science, etc.

Hi, Prof and Dr. the following is my thesis title. Any comment, please.

"the study of predicted factors of teachers' intention in teaching Mathematics Problem Solving through online"

I am working on a research and i am looking for someone who can help with a mathematics matters.

**Abstract**

This paper studies the proof of Collatz conjecture for some set of sequence of odd numbers with infinite number of elements. These set generalized to the set which contains all positive odd integers. This extension assumed to be the proof of the full conjecture, using the concept of mathematical induction.

You can find the paper here:

Preprint Collatz Theorem

*(PDF) Collatz Theorem*. Available from: https://www.researchgate.net/publication/330358533_Collatz_Theorem [accessed Dec 21 2020].How i can extract mathematical function by the given data set

Some Mathematical expressions will be helpful.

I am looking for a research paper about the mathematical or computational modelling of protein oxidation (caused by reactive oxygen species).. I would really appreciate that if someone helps me with this.

I am looking for any book/article reference about the mathematical description of zero normal flux boundary condition for shallow water equations. My concern is that for a near-shore case how it is obvious to have zero normal flux. Physically, it does make sense that we have a near-shore case and on the boundary, there is no flow in the normal direction. How to mathematical explain it using the continuity equation in the case when there is a steady flow? The continuity equation suggests that $\partial h / \partial t + u. \partial h/ partial x = 0$. If we take steady flow then it is clear to me to get zero normal flux condition. But what if the first term is not zero? or do we say that at the boundary the flow is always steady?

I want to determine the success rate of an personnel selection instrument (interview, assessment center...) depending on the validity of the instrument itself, the selection rate and the base rate.

Thanks in avance for your answers!

If we are given that (x-2)(x-3)=0 and 0.0=0, then we can conclude that both x=2 and x=3 simultaneously. This is because x-2=0 and x-3=0, simultaneously, is consistent with 0.0=0. However, this leads to a contradiction, namely, x=2=3. So, generally we exclude this option while finding roots of an equation and consider that only one of the factors can be zero at a time i.e. all the roots are mutually exclusive. In other words, we consider 0.0 to be not equal to 0.

Now, if we are given that x=0 and asked to find out what x^2 is, then certainly we conclude that x^2=0. It is trivial to observe that this conclusion is made through the following process: x^2=x.x=0.0=0. That is, we need to consider 0.0=0 to make this simple conclusion.

Therefore, while in the first case we have to consider 0.0 not equal to 0 to avoid contradiction, in the second case we have to consider 0.0=0 to reach the conclusion. So, the question arises whether 0.0 is equal to 0 or not. As far as I know, mathematical truths are considered to be universal. However, in the present discussion it appears to me that whether 0.0 is 0 or not, is used as par requirement. Is that legitimate in mathematics?

How do you define uncertainty in an economic decision model? With this mathematical approach in mind, how should you make decisions?

My dear friends, I am asking if some of your students are interested in applying a postdocotor position in China with me, here is the link and details!!!

How does one get access to the Mizar Mathematical Library (MML) ? This refers

to the Mizar system for the formalisation and automatic checking of mathematical proofs based

on Tarski-Grothendieck Set Theory (mizar.org).

As we know,Strehl Ratio(SR) is a measure of turbulence is a medium.How to calculate SR of a medium mathematically?

Any decision-making problem when precisely formulated within the framework of mathematics is posed as an optimization problem. There are so many ways, in fact, I think infinitely many ways one can partition the set of all possible optimization problems into classes of problems.

1. I often hear people label meta-heuristic and heuristic algorithms as general algorithms (I understand what they mean) but I'm thinking about some things, can we apply these algorithms to any arbitrary optimization problems from any class or more precisely can we adjust/re-model any optimization problem in a way that permits us to attack those problems by the algorithms in question?

2. Then I thought well

*then by extending the argument I think also we can re-formulate any given problem to be attacked by any algorithm we desire (of-course with a cost) then it is just a useless tautology.***if we assumed that the answer to 1 is yes**I'm looking foe different insights :)

Thanks.

Dear scholars,

I am now struggling on a question.

Let's assume that there is a given line or a given arbitrary function defined on a z=0 plane. Now I twist the plane into a non-linear 3D surface that can be represented by any given continuous and differentiable equations. How could I represent this line or function in analytical equations now.

You could think this like "a straight line on a waving flag".

Much appreciated if you have any idea or suggested publications.

Thanks.

Can you help me create a source of type sinc in ADS

I found a mathematical function that plays the role (picture 1) but I do not know how to use it ?

thank you in advance

NO. No one on Earth can claim to "own the truth" -- not even the natural sciences. And mathematics has no anchor on Nature.

With physics, the elusive truth becomes the object itself, which physics trusts using the scientific method, as fairly as humanly possible and as objectively (friend and foe) as possible.

With mathematics, on the other hand, one must trust using only logic, and the most amazing thing has been how much the Nature as seen by physics (the Wirklichkeit) follows the logic as seen by mathematics (without necessarily using Wirklichkeit) -- and vice-versa. This implies that something is true in Wirklichkeit iff (if and only if) it is logical.

Also, any true rebuffing of a "fake controversy" (i.e., fake because it was created by the reader willingly or not, and not in the data itself) risks coming across as sharply negative. Thus, rebuffing of truth-deniers leads to ...affirming truth-deniers. The semantic principle is: before facing the night, one should not counter the darkness but create light. When faced with a "stone thrown by an enemy" one should see it as a construction stone offered by a colleague.

But everyone helps. The noise defines the signal. The signal is what the noise is not. To further put the question in perspective, in terms of fault-tolerant design and CS, consensus (aka,"Byzantine agreement") is a design protocol to bring processors to agreement on a bit despite a fraction of bad processors behaving to disrupt the outcome. The disruption is modeled as noise and can come from any source --- attackers or faults, even hardware faults.

Arguing, in turn, would risk creating a fat target for bad-faith or for just misleading references, exaggerations, and pseudo-works. As we see rampant on RG, even on porous publications cited as if they were valid.

Finally, arguing may bring in the ego, which is not rational and may tend to strengthen the position of a truth-denier. Following Pascal, people tend to be convinced better by their own-found arguments, from the angle that they see (and there are many angles to every question). Pascal thought that the best way to defeat the erroneous views of others was not by facing it but by slipping in through the backdoor of their beliefs. And trust is higher as self-trust -- everyone tends to trust themselves better and faster, than to trust someone else.

What is your qualified opinion? This question considered various options and offers a NO as the best answer. Here, to be clear, "truth-denial" is to be understood as one's own "truth" -- which can be another's "falsity", or not. An impasse is created, how to best solve it?

somebody, please elaborate on how to calculate exergy destruction in kW units. from Aspen HYSYS I found mass exergy with kJ/kg unit and i don't know how to calculate it by using Aspen HYSYS and if somebody has mathematical calculation with example please share with me. I know how to calculate by aspen plus but I need a mathematical or Aspen HYSYS solution.

thanks in anticipation

As we know, computational complexity of an algorithm is the amount of resources (time and memory) required to run it.

**If I have algorithm that represents mathematical equations , how can estimate or calculate the computational complexity of these equations, the number of computation operations, and the space of memory that are used.**

What happens to numbers with highest power and it's implication on the numbers last digit. How applicable is that in mathematical problem solving

In the education discipline, several leadership theory has been discussed but no such mathematical foundations are available to estimate them. More, especially how can I differentiate( in terms of Mathematical expressions ) the several leadership styles in decision making problems so that I could get the better one; and the decision maker would comfort to apply their industrial/ managerial/ organizational situation ? We may assume that, the problem is a part of fuzzy decision making/ intelligent system / artificial intelligent system/ soft system.

The leaders are manager of an industry/ organization/ corporate house, the ministry of a Government / the agents of a marketing system, the representatives of customers of a particular product in a supply chain management problem.

what are the differences between mathematical modelling and realistic mathematic education?

What is the importance of Golden Ratio in nature and mathematics? Why the golden ratio is sometimes called the "divine proportion," by mathematicians?

Dear Friends,

Kindly allow me to ask you a very basic important question. What is the basic difference between (i) scientific disciplines (e.g. physics, chemistry, botany or zoology etc.) and (ii) disciplines for branches of mathematics (e.g. caliculus, trigonometry, algebra and geometry etc.)?

I feel, that objective knowledge of basic or primary difference between science and math is useful to impart perfect and objective knowledge for science, and math (and their role in technological inventions & expansion)?

Let me give my answer to start this debate:

Each branch of Mathematics

**invents**and uses complementary, harmonious and/or interdepend set of valid**axioms**as core first-principles in foundation for evolving and/or expanding*internally consistent paradigm*for each of its branches (e.g. calculous, algebra, or geometry etc.). If the foundation comprises of few inharmonious or invalid axioms in any branch, such invalid axioms create*internal inconsistences*in the discipline (i.e. branch of math). Internal consistency can be restored by fine tuning of inharmonious axioms or by inventing new valid axioms for replacing invalid axioms.Each of the Scientific disciplines must

**discover**new falsifiable basic facts and prove the new falsifiable**scientific facts**and use such proven scientific facts as first-principles in its foundation, where a scientific fact implies a falsifiable discovery that cannot be falsified by vigorous efforts to disprove the fact. We know what happened when one of the first principles (i.e. the Earth is static at the centre) was flawed.Example for basic proven scientific facts include, the Sun is at the centre, Newton’s 3 laws or motion, there exists a force of attraction between any two bodies having mass, the force of attraction decreases if the distance between the bodies increase, and increasing the mass of the bodies increases the force of attraction. Notices that I intentionally didn’t mention directly and/or indirectly proportional.

This kind of first principles provide foundation for expanding the BoK (Body of Knowledge) for each of the disciplines. The purpose of research in any discipline is adding more and more new first-principles and also adding more and more theoretical knowledge (by relying on the first-principles) such as new theories, concepts, methods and other facts for expanding the BoK for the prevailing paradigm of the discipline.

I want to find answer to this question, because software researchers insist that computer science is a branch of mathematics, so they have been insisting that it is okay to blatantly violating scientific principles for acquiring scientific knowledge (i.e. knowledge that falls under the realm of science) that is essential for addressing technological problems for software such as software crisis and human like computer intelligence.

If researchers of computer science insist that it is a branch of mathematics, I wanted to propose a compromise: The nature and properties of components for software and anatomy of CBE (Component-based engineering) for software were defined as Axioms. Since the axioms are invalid, it resulted in internally inconsistent paradigm for software engineering. I invented new set of valid axioms by gaining valid scientific knowledge about components and CBE without violating scientific principles.

Even maths requires finding, testing, and replacing invalid Axioms. I hope this compromise satisfy computer science scientists, who insist that software is a branch of maths? It appears that software or computer science is a strange new kind of hybrid between science and maths, which I want to understand more (e.g. may be useful for solving other problems such as human-like artificial intelligence).

Best Regards,

Raju Chiluvuri

Hi

I am doing linear regression research assignment where I have to research how does mathematical scores and gender (independent variables) affect to natural history scores (dependent variable). I am not sure am I interpreting gender's dummy variable (female = 1, male = 0) right in the coefficients table.

Am I right by interpreting that females are getting on average 10.9 points less natural history scores than male?

Thank you in advance.

In fact, it is the fundamental defects in the work of “quantitative cognition to infinite things” that have been troubling people for thousands of years. But I am going on a different way from many people.

1, I analysis and study the defects in existing classical infinite theory system disclosed by the suspended "infinite paradox symptom clusters" in analysis and set theory from different perspectives with different conclusion: to abandon the unscientific (mistaken) "potential infinite and actual infinite" concepts in existing classical infinite theory system and discover the new concepts of "abstract infinite and the carriers of abstract infinite", especially to replace the unscientific (mistaken) "actual infinite" concept in existing classical infinite theory by the new concept of “carriers of abstract infinite" and develop a new infinite theory system with “mathematical carriers of abstract infinite and their related quantitative cognizing operation theory system ". From now on, human beings are no longer entangled in "potential infinite -- actual infinite", but can spare no effort to develop "infinite carrier theory", and develop comprehensive and scientific cognition of various contents related to "mathematical carrier of abstract infinite concept".

2, Abstract concept - abstract concept carrier theory, new infinite theory system, carrier theory, infinite mathematical carrier gene, infinite mathematical carrier scale,...The development of basic theory determines the construction of "quantum mathematics" based on the new infinite theory system.

3, I have up loaded 《On the Quantitative Cognitions to “Infinite Things” (IX) ------- "The Infinite Carrier Gene”, "The Infinite Carrier Measure" And "Quantum Mathematics”》2 days ago onto RG introducing " Quantum Mathematics". My work is not fixing here and there for those tiny defects (such as the CH theory above) but carrying out quantitative cognitions to all kinds of infinite mathematical things with "quantum mathematics" basing on new infinite theory system.

According to my studies (have been presented in some of my papers), Harmonic Series is a vivid modern example of Zeno's Paradox. It is really an important case in the researches of infinite related paradoxes syndrome in present set theory and analysis basing on unscientific classical infinite theory system.

All the existing (suspending) infinite related paradoxes in present set theory and analysis are typical logical contradictions.

The revolution in the foundation of infinite theory system determines the construction of "Quantum Mathematics" based on the new contents discovered in new infinite theory system: infinite mathematical carrier, infinite mathematical carrier gene, infinite mathematical carrier measure,... in new infinite carrier theory. So, the "Quantum Mathematics" mentioned in my paper is different from Quantum Logic and Quantum Algebras;

According to my studies (have been presented in some of my papers), “Non-Standard Analysis and Transfinite numbers” is all the infinite related things in unscientific classical infinite theory system based on the trouble making "potential infinite and actual infinite" --------- Non-Standard Analysis is equivalence with Standard Analysis while Transfinite is an odd idea of “more infinite, more more infinite, more more more infinite, more more more more infinite,…”).

Mathematics differs from sensory science in that it draws its subject from structural construction to abstract abstraction of quantitative quantities, while other sciences rely on the description of actual sensory objects already in existence.

What do you think?

Computer Aided Design (Cad) subject deals with the backend mathematical calculation that happens in a 3D design.

Hello,

I am interested in the personalization of learning based on profiles, more specifically in mathematics.

Do you know any relevant references?

Thank you

The fact that , electron can have only discrete energy level is obtained by solving schrodinger equation with boundary conditions, which is a mathematical derivation .

Physically, What makes the electron possess only certain energies ?

Or is there any physical insight or explanation or physical intution which can arrive at same conclusion(without math) that electron can have only discrete energy levels inside potential well

Given a fixed volume where the relative humidity and temperature are known, how can you estimate how much water vapor will condense corresponding to a temperature decrease. I suspect it has to do with the dew point temperature but I'm having trouble finding mathematical relations.

Hi every one,

here I have a problem in MATLAB, when I want to solve the following equation, relative to PI in the photo, or tau in the code, MATLAB will send me this error:

**Warning: Unable to find explicit solution. For options, see help**.I attached the question and the code below (in code, I rewrite pi in the photo with tau).

If you have any idea to solve this problem, analytically or numerically, I will be happy to hear it out.

*NOTE:*

*> PI_0.1(X,t) = tau*

*> X = [x(t),y(t),psi(t)]^T;*

**** PROBLEM: Find tau in terms of X and t in which solve the mentioned equation.**

Thanks in advance,

Arash.

**code:**

______________________________________

______________________________________

clc;clear;

syms x y psi tau t

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

x_r(tau) = 0.8486*tau - 0.6949;

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

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

x_r_dot = 0.8486;

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

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

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

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

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

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

sol = solve(eq == 0 , tau , 'IgnoreAnalyticConstraints',1)

______________________________________

______________________________________

Hello,

I am doing research on HVLD detection capability.

From your experience, is there some mathematical formula to prove that HVLD machines can detect holes regardless of size or some other ways to prove it?

Thanks in advance !

A question related to our cultural indebtedness to our mathematical forbears.

I am doing a research proposal i need answers on my topic. information must be from 2015-2020. relevant articles

**FYI:**"

*Is mathematics an effective way to describe the world?*",Any bibliographic recommendations on the problem of routing vehicles with multiple deposits, homogeneous capacities? less than 10 nodes

L'Huillier's theorem or calculation of spherical excess of "spherical triangle" formed between the unit vectors on unit sphere can find out the area, but how to explain this formula from purely plane trigonometry standpoint (i.e. without assuming any pre-requisite knowledge on spherical trigonometry)? The solid angle can be found by spherical trigonometry rules, and I am well aware of it. I want to introduce this problem to anyone with knowledge of plane trigonometry, but no knowledge of spherical trigonometry.

what is the mathematical expressions and equations used for the designing of antipodal structure of an antenna.

I hope for a global overview on mathematical giftedness and its support in school and/or on an extracurricular level. What programmes/opportunities are offered?

Quantum computing is the field that focuses on quantum computation/information processing, the mathematical and physical theory for which as well as the engineering required to realize different circuits and algorithms into hardware performance, as well as other contingent issues such as the whole “compute chain” (from software engineering to quantum machine code and then further on to the physical architecture) and device/hardware issues such as thermal, electrooptical and nanoengineering.

My question is how quantum computing is related to artificial intelligence?

Can any one suggest application(s) for

*$R_{\alpha}, R_{\beta}$ and $R_{m}$ -functions*in mathematical or applied sciences; which is recently introduced in following research paper;H. M. Srivastava et al.

*A family of theta*-*function identities based upon combinatorial partition identities and related to Jacobi’s triple-product identity,*Mathematics**8**(6)(2020), Article ID 918, 1-14.Here I just want to know about the actual parameters to measure the content of happiness in a person. With the help of these parameters a neural network can be generated and maintained to achieve the maximum happiness. I am also expecting some better approach from the scholars.

Take, for example, such a concept as a minimum flow, that is, a gradient vector field, the level surfaces of which are the minimum surfaces. Then the globally minimal flow, evolving to an absolutely minimal state, could be compared with a quantum vacuum, and the locally minimal flow could be compared with fields and particles. At the same time, it is clear that it is necessary to correctly choose the space in which this minimum flow moves.

Hello all,

I am looking for an method / algorithm/ or logic which can help to figure out numerically whether the function is differentiable at a given point.

To give a more clear perspective, let's say while solving a fluid flow problem using CFD, I obtain some scalar field along some line with graph similar to y = |x|, ( assume x axis to be the line along which scalar field is drawn and origin is grid point, say P)

So I know that at grid point P, the function is not differentiable. But how can I check it using numeric. I thought of using directional derivative but couldn't get along which direction to compare ( the line given in example is just for explaining).

Ideally when surrounded by 8 grid points , i may be differentiable along certain direction and may not be along other. Any suggestions?

Thanks

the types of board game for mathematical literacy to make the learning and teaching fun

Electromagnetic (EM) waves have invoked a lot of interest among scientists and engineers over centuries. And this interest seems to be on the rise, in view of new applications of EM waves being explored and developed, particularly at newer and higher frequencies.

Propagation characteristics of EM wave depend on its frequency (or wavelength), to a large extent. And when an EM wave interacts with an object/material, it undergoes reflection, refraction, scattering, attenuation, diffraction, and/or absorption. Each of these effects are dependent on the frequency of the EM wave(s) because the size of wavelength (relative to the object/material) assumes great significance.

And due to the huge range of frequencies of EM waves employed in various applications these days, they undergo a variety of different effects. This confuses the scientific community sometimes as it is often unclear as to which effect is more dominant at what frequency.

Thus a single mathematical formula (or a small set of formulae) would/could be of great help if different effects (as listed above) and their relative weights can be known at different frequencies. This may be of great boon to young scientists and engineers as it would simplify things particularly for those who are mathematically minded.

By dynamical systems, I mean systems that can be modeled by ODEs.

For linear ODEs, we can investigate the stability by eigenvalues, and for nonlinear systems as well as linear systems we can use the Lyapunov stability theory.

I want to know is there any other method to investigate the stability of dynamical systems?

Given:

1. The nearest neighbor of 𝑝𝑖 then 𝑝𝑖-𝑝𝑗 is a Delaunay edge.

2. In a 3D set of points, if we know that consecutive points ie... 𝑝𝑖-𝑝i+1 are nearest neighbors.

3. The 3D points do not form a straight line

Assumption:

Each Delaunay tesselation (3D) has at least 2 nearest neighbor edges.

Is my assumption true? If not can you please explain to me the possible exceptions?

Thanks,

Pranav

I am currently studying the effect of atrophy of a muscle on the clinical outcome of joint injury. There is actually another muscle that was previously well established to have an effect on clinical outcome, and both these 2 muscles are closely related. The aim of the study was to shed some light on the previously ignored muscle to see if there is anything that can be done to help improve clinical outcomes in that aspect.

While doing univariate analysis, i wasnt sure if i should include the previously established muscle as well and when i included it into the multi-linear regression model, the initially significant primary variable became insignificant. I was thinking if this could be due to co-linearity but the VIF value was not high enough to show significant co-linearity in the two variables. (GVIF ^(1/(2*Df))=1.359987)

My question is, should these 2 variables be included in the same model if they are both highly correlated (clinically and mathematically) but was not determined to have co-linearity, or should these 2 variables be evaluated separately?

Good evening all;

We are looking for literature on the mixed integer formulation of water distribution problems using Multi objective optimization methods.

Thanks

Nasiru Abdullahi

Mathematics Department

NDA Kaduna

I know lots of composers have created works around mathematical constructs such as the Fibonacci sequence. I would like to learn if any composers have used mathematical constructs in their music to represent journeys.

Dear all,

I am trying S parameter measurement _transmission_using TEKTRONIX DSA8300 oscilloscope. Initially, S parameters files are generated in LINEAR _magnitude format. Now S parameters transmission files are appearing in dB format from oscilloscope. Perhaps machine settings seem to be changed.

1)Kindly guide for appropriate setting button in TEKTRONIX DSA8300 oscilloscope, so as to receive the data from dB to linear magnitude format.

2) Also, alternative mathematical ways to receive data in LINEAR magnitude format are appreciated as well , kindly.

best thanks