Science topics: Mathematics

Science topic

# Mathematics - Science topic

Mathematics, Pure and Applied Math

Questions related to Mathematics

In current times we have a trend that many difficult tasks in practice got solutions on the basis of using AI. Before such tasks used mathematical techniques. What will be in the future? The human intellect and IQ will be decreased?

In radars use difficult mathematical techniques to estimation of signals sources parameters. But I think that the implementation of AI can be made unnecessary such an approach. For example, the task of detecting one target and the resolution of two targets can be have an effective solution by AI now. What do you think about this?

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.

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?

I have some complicated hints and clues, but I think their solutions should be much simpler.

Hi.

I have a data in which the relationship between two parameters seems to fit to a model that has two oblique asymptotes. Does any one have any idea about what type of function I should use? Please find attached a screenshot of the data. I appreciate any help.

Thanks.

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

Six Nobel Prizes are awarded each year, one in each of the following categories:

**literature**,**physics**,**chemistry**,**peace**,**economics**, and physiology & medicine. However Mathematics a subject mankind cannot do without is a strange omission and has remained excluded until today. Same with accounting. From 1901 doyens such as Albert Einstein, Marie Curie, Earnest Hemingway were honored with the prestigious Nobel. Do you think it’s time to rethink ?Hello,

I am searching the maximum Value a DIT Radix-2 FFT can have. I dont necessarily mean the end values, but the max value that could occur in all repetitions. The reason behind it is that I`m about to implement this in-place algorithm on a micro controller with very limited space and dont want to use unnecessary large variables.

I`m calculating the FFT in-place with the real and imaginary parts of the complex conjugates split to save memory. Also I`m just using real values as input.

Through some tests I found that when sampling an sinus with values between

**+2^n**and**-2^n**with**2^m**variables, all values will be**<=2^(m+n-1)**. I just found this through a bunch of tests and dont know if it will be always the case. Also I dont know why this applies if it is true.Furthermore I read about Parseval's theorem but cant draw a conclusion out of it.

So the main question is, what is the maximum Value that can occur in an Radix-2 DIT FFT when sampling any signal with amplitude

**2^n**with**2^m**sampling points.I hope it was understandable, but I`m open to further explanations if something is unclear.

Thank you

Much has been said about the differences between physics and mathematics, but less attention has been paid to the differences between physics and chemistry.

The question is, where does physics and chemistry work?

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

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.

According to a report published by UNESCO, 0.1% of the global population (in 2013) were researchers? Does anybody know the current numbers?

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.

Dear colleagues,

I am looking for a practical guide presenting the non-parametric tests intended for students without mathematical background (or very little) with if possible the codes SAS or R.

Thank you.

Good research is based on good relationship between the mentor or supervisor and the scholar. What are the qualities a supervisor or mentor must have to have a healthy and friendly environment in the laboratory?

I have found a beautiful technique to solve math problems such as:

- Goldbach’s conjecture
- Riemann hypothesis

The technique uses the notions of regular languages. The complexity class that contains all the regular languages is REG. Moreover, these mathematical proofs are based on if some unary language belongs to NSPACE(S(log n)), then the binary version of that language belongs to NSPACE(S(n)) and vice versa. The complexity class NSPACE(f(n)) is the set of decision problems that can be solved by a nondeterministic Turing machine M, using space f(n), where n is the length of the input.

We prove there are non-regular languages that define mathematical problems. Indeed, if those math problems are not true, then they have a finite or infinite number of counterexamples (the complement languages contain the counterexample elements). However, we know every finite language is regular. Therefore, those languages are true or they have an infinite number of counterexamples, because if they have a finite number of counterexamples, then the complement language should be in REG, that is, this complement must be a regular language. Indeed, we show some mathematical problems cannot have a finite number of counterexamples using the complexity result, that is, we demonstrate their complement languages cannot be regular. In this way, we prove these problems should be true or they have an infinite number of counterexamples as the remaining only option.

See more in my notions:

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.

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!!!

Many of the tools I saw and used were designed for measuring performance in a particular topic of mathematics. I am looking for a tool that can capture one's general mathematical thinking skills.

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

I searched a lot in googl and youtube for a step by step explanation for the Finite Elements Method. All throw a bunch of equations and mathematical terms without explaining why or where they came from.

Would you please suggest a good book or an article that clearly explains FEM?

Thanks

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

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.

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

Charles Sanders Peirce regarded mathematics as “the only one of the sciences which does not concern itself to inquire what the actual facts are, but studies hypotheses exclusively” (RLT, 114). Since, by contrast, “[w]e must begin with all the prejudices which we actually have when we enter upon the study of philosophy” (CP 5.265), the presuppositionless status of mathematics makes it more primitive than anything found in philosophy. Given that phenomenology falls under philosophy (CP 1.280), we get the result that mathematics is prior to phenomenology.

Yet, Peirce also held that “every deductive inference is performed, and can only be performed, by imagining an instance in which the premises are true and

*observing*by contemplation of the image that the conclusion is true” (NEM III/2, 968).We thus have two conflicting arguments:

On the one hand, one could argue that mathematics is prior to phenomenology because mathematics makes even less presuppositions than phenomenology.

On the other hand, one could argue that phenomenology is prior to mathematics because whatever happens during mathematical inquiry must perforce appear before (some)one.

Peirce's pronouncements notwithstanding, it is not obvious to me why the first argument should trump the second. In fact, I find considerations about the inevitability of appearing in mathematics to be decisive.

What do you think?

344/5000

Hi researchers, I have a problem with the mathematical formulation of the multi objectives model for solving the RFID planning problem network. Do you have any courses or documents or information that can help me achieve my mathematical model of RFID network optimization deployed in a body network. i didn't choose the approach and the algorithme of multi optimization yet, I am formulating my problem mathematically

how I do obtain in the mathematical expression "limiting current density used to reduce Fe+3(A/m2)"? actually how i find the i (Fe)?

i (c)= i (cu)+i (Fe)

Is there an encyclopedia of all the branching mathematical axioms, together with various ways of proving different theorems based on those axioms?

As you may be knowing that there are different mathematical tools and techniques which we can combine or hybridize with heuristic techniques to solve their entrapment in local minima and convergence issues. I know two techniques namely Chaos theory and Levy distribution as I have used them for increasing convergence speed of Gravitational Search Algorithm (GSA). So, my question is: can you name and briefly explain other mathematical techniques which we can combine with optimization algorithms in order to make them fit for solving complex real world problems.

Thank you.

The master Paul Erdos said "Mathematical may not be ready for such problem"

Terence Tao recently proposed a new and advanced approach for this conjecture and concluded: "Almost all orbits of the Collatz map attain almost bounded values".

The Collatz 's conjecture is infamous and very hard to solve

Take any positive integer, if it is even divide it by 2. If it is odd , multiply the number with 3 and add 1. Whatever the answer , repeat the same operations on the result.

Suppose the number is 5 then the operations wil be as follows: 5, 16, 8, 4, 2,1,4,2,1

Suppose the number is 7 then the operations will be as follows:7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1,4,2,1

The conjecture has been verified by computer for number as big as 10^18 and respects all the powers of 2. This is easely checked: 128, 64, 32, 16, 8, 4, 2, 1, 4, 2, 1.

How any positive integer reach some power of 2 in order to reach the loop of 4, 2, 1.?

We claim that any positive integer has a special numbber equal to a multiple of the positive integer. When the operation of 3n+1 is performed on that multiple it leads to some power of 2 .

N=1 gives special multiple 5=5*1.

3*5+1=16=2^4

N=3 gives special multiple 21=3*7

3*21+1=64=2^6

N=5 gives special multiple 85=17*5

3*85+1=256=2^8

The set (1, 5, 21, 85, 341.....) are called Collatz Numbers.

So we can claim that the Collatz's conjecture is almost solved.

A careful reading of THE ABSOLUTE DIFFERENTIAL CALCULUS, by Tullio Levi-Civita published by Blackie & Son Limited 50 Old bailey London 1927 together Plato's cosmology strongly suggest that gravity is actually a real world mathematics or in another words is gravitation a pure experimental mathematics?

In the preprint

W.-H. Li and F. Qi,

*A further generalization of the Catalan numbers and its explicit formula and integral representation*, Authorea Preprints (2020), available online at https://doi.org/10.22541/au.159844115.58373405I concluded two integral formulas indicated in the picture.

(1) Do you know the existence of these two integral formulas? Please give concrete and explicit references containing these two integral formulas.

(2) Can you find direct and elementary proofs for these two integral formulas?

why we plot absorbance vs wavelength although there is no direct formula between them and I also want to know that their is any direct or indirect relation between molar extinction coefficient and wavelength. I am trying to generate a theoretical plot between absorbance vs wavelength of single layer MoS2 by using python program,so I need mathematical formula for calculation .

The literature on public (and some school students') understanding of science and mathematics shows many have problems decoding relatively simple information, concepts and data such as from graphs. In the UK, and many other countries, the public have been exposed to unprecedented amounts of information, ideas, scientific findings, formulae, graphs and so on that purport to provide understanding of the global COVID-19 pandemic, so as to presumably advise on risk and guide personal decisions and influence behaviour. But what are the implications of this massive shift in communication for public understanding in general and for future science and mathematics education in schools?

FTIR technology is considered the most advance for the detection of adulterants in milk. Is there any mathematical relation that can describe the relationship between the amount of adulterants in milk using the absorbance from the FTIR? Please suggest any research articles that describe this or related areas.

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?

Hello fellow scientists,

I wish to determine the Dissociation Constant (K

_{D}) of a DNA polymerase binding dsDNA. I won't disclose what the DNA polymerase is because it is unpublished work. I have done some binding assays in Agarose gels, but due to the poor sensitivity of the available dyes I had to visualize the relative binding stoichiometrically, and I could not simply just set the protein or DNA concentration around the expected K_{D}.Previous work in our lab has determined a K

_{D}= 20 nm for our DNA polymerase binding a 33mer locked double stranded DNA hairpin.The purpose of using something so complicated was for kinetics assays. However, I am using a 13-mer dsDNA construct because my goal is to crystallize the DNA complex and a 33-mer is just way too large! My supervisor has advised that I don't believe that my K

_{D}is actually 20 nM for my small dsDNA construct.I am interested in using Isothermal Titration Calorimetry mainly to calculate the K

_{D}of my protein to binding this 13mer dsDNA construct. I would titrate my dsDNA into a fixed concentration of protein. I could guess that the K_{D}is 20 nM, but I actually don't know for sure.I have heard that when you determine the K

_{D}you have to have some estimate of the K_{D}and then scan ligand concentrations above and below the K_{D,}measure the response to get a curve of response vs ligand concentration and the K_{D}is mathematically fit or basically it is just the inflection point of the binding curve.However that advice doesn't tell me if the K

_{D}is say 20 nM, what should fixed concentration of my protein be? (I have appreciable amounts of 100 µM protein because I am a crystallographer so excessive protein isn't an issue.). What is the max and min range that I should scan the ligand concentrations? What if the K_{D}is way worse than we predicted and it is actually 1 µM? What fixed concentration of protein should I use and what min and max concentrations of ligand should I use?Is there a way that I can measure the K

_{D}with a certain fixed concentration of protein, and a huge range of ligand concentrations regardless of if the K_{D }is 20 nM or 1 µM? Is that possible?For any given function

*f : [a, b] → R*, there exists a sequence of polynomial functions converging to*f*at each point where*f*is continuous. (Note that we did not ask the convergence to be uniform).The acceptable practice is to validate a model used under any study. What validation methods are available and would we confirm one superior over others?

My question is: Is there any mathematical or empirical way to prove that given a dataset containing noisy signals y(t) [Y = X +N] and another dataset containing noise N and we want generator to generate clean signals X ̂ . How to prove other than experiments that generator will be able to generate clean signals from random noise vector z.

If the answer is yes, can one replace

*log n*by another sequence that approaches ∞ faster than*log n*?I have a query regarding data transformation if anyone can provide any guidance please?

I was wondering if, generally, it is possible to transform a variable's raw data twice, using 2 different methods, for the purpose of 2 different tests? I will provide you with a little background to my study first. I have a variable for 'Adverse Childhood Experiences' containing 1 score per participant. N = 113; however, 65 of these are 0 values and 3 are missing data - which I believe is disrupting my data considerably. I understand that it is not advised to simply remove the cases that read 0 just because there are many (however, if you recommend otherwise please let me know if so and why).

Useful to note here is that this variable has a skewness of 1.943, and because of this, I have made the decision to transform it.

I am carrying out a path analysis with 1 IV, one DV and 2 mediators. In the first instance I am carrying out a t-test (IV - gender, DV - ACE score) and then in the second instance I am carrying out a linear regression (IV age, DV - ACE score), to understand whether age and gender need to be included in my path analysis as covariates. In order to meet the assumptions of the t-test (namely, normal distribution across both levels of the IV: male and female) I have transformed the raw ACE data this using Tukey's formula, which brought the skewness to < 1 for each IV level - great. But then when I go to carry out the linear regression, and aim to meet the assumption of approx. normal distribution of residuals, the assumption is not met on the Tukey transformed ACE data. I have carried out a number of other transformations on the raw ACE data and the only one where the residuals are normally distributed for the regression is through a Log10 transformation.

My question is this: am I able to carry out the t-test with the Tukey transformed variable data, and then the linear regression with the Log10 transformed data? Or is it the case that I need to use the same transformed data for each stage of the analysis (ie. both Tukey or both Log10 for t-test and linear regression and then the same onward path analyses?)

If it is the case that I will need to use the Log10 ACE data to go back and carry out the gender t-test, it is useful to note here that I have done this already and when inspecting the Log10 transformed ACE data across the gender variable descriptives table the results come out very strange - for example, N for males goes down from 15 to 6, and N for females goes down from 115 to 59, and there are outliers, where there were none in the Tukey transformed data descriptives, so it is confusing me a little.

Any guidance welcome!

Thank you

In mathematical ecology, the recent trend is predator induced fear to prey which is an indirect effect of predator to prey. My question is how the prey populace are afraid of infected predator? Are they capable in inducing same level of fear as of healthy predator? Any efforts regarding this will be appreciated.

Hi all,

I am dealing with data with sevaral features and many of them are highly correlated with each other as well as with dependent variable.

In my research on this topics, I found that multicolinearity is harmful for regression problem and may not end up with good model. I got some suggestion that if the features are highly correlated then we have to remove them using VIF criterion.

But, logically when I think of removing correlated features from my analysis how can expect better model as I am not considering all the available information.

Is there any logical explaination or mathematical explaination is available for the above question?

Also, I am thinking that each features are somehow related to any of the other (May be nonlinearly) in that case, do we have problem of multicolinearity ?

The new Education Act (LOMLOE) that is now being prepared in Spain intends to make Mathematics an optional subject. The Mathematics Institute has issued a manifest that argues about the importance of Mathematics in society, and in favour of keeping Mathematics as a compulsory subject in high school. If you agree with this, please sign the manifest at the link below (the manifest is in Spanish; I don't remember if there is an English version):

There is also a petition at change.org:

Thank you very much in advance.

Hebert

In the midst of or post Covid-19, any suggestion(s) or (articles) on how best to implement blended teaching to optimize teaching and learning of mathematics

I need a documented answer with a mathematical derivation, please.

Hello

For typical dose-response assays, our lab usually uses steady state intervals for defining the difference between control and tested compound. For those assays, we typically use the angular coefficient or end-point value of given curve (within steady state) to estimate percentage of inhibition, or even kinetic constants

Now we have being working with an enzyme with strong 'sigmoidal' time curse reaction (hill n=3). How can I mathematically compare curves between control and inhibited reactions, or calculate constants?

If anyone could please point me to a good theorical reference or literature examples, I will be very thankful

Stay all safe

Let

*T*denote the circle group, that is, the multiplicative group of all complex numbers with absolute value*1*. Let*f : T → T*be a (sequentially) continuous map, and such that*f(z*for all^{2}) = f^{2}(z)*z ∈ T*. Then there is an integer*k*such that*f(z) = z*for all^{k}*z ∈ T*.Many informal settlements have insufficient capacity to forecast, check, handle and reduce disaster risk. These communities face a growing range of challenges including economic hardship, technological and social impediments, urbanisation, under-development, wildfire, climate change, flooding, drought, geological hazards and the impact of epidemics such as HIV/AIDS and COVID-19, sometimes termed ‘the burden of disease’. The inability of these communities to withstand adversities affects the sustainability of initiatives to develop them.

This is a question I would have asked during my masters degree research on Resilience in Disasters. I would like to know the opinions of other researchers as I would like to properly answer this question in a different research-related topic.

I am studying mass-spring-damper systems with coulombs friction. There are multiple discussions on simulating such systems using numerical methods and the problems that arise due the discontinuous excitation but I wanted to know if an analytical solution exists. To be mathematically clear about the problem, I am trying to analytically solve the following.

m*(d2x/dt2) + c*(dx/dt) + k*x = F*sign(dx/dt)

where the sign function is defined as:

sign(var) = 0 if var = 0

sign(var) = 1 if var > 0

sign(var) = -1 if var < 0

Note: I am aware of treating such systems as piece-wise linear nonlinear systems but I want to know whether a general solution exists that is capable of solving the problem without breaking it to a number of mini-problems.

If it makes easier, assume that f is continuous on [0,∞).

To avoid trivial solutions

*,*assume that*a*and*b*are non-zero real numbers.My feeling is that, for

*certain*values of*a*and*b*, there are no such functions.I am interested to solve a mathematical problem (MILP) using evolutionary algorithms but confuse about which one to choose as a beginner in the programming languages. Suggest an algorithm easy to implements with better results.

Thanks

Specifically, I know that there are discontinuous everywhere solutions

*f*of the given equation. I also know how to prove that, if*f*is continuous at 0, then*f*(x)=0 for all x∈ℝ. I don't know what gives the assumption of continuity of*f*at a non-zero point?What are the mathematical equations used to assess the environmental impact using some biological criteria in green algae?

Quadratic equations with complex root were considered unsolvable in secondary schools. this limitation is due to the lack of topic to address the idea of complex number in Nigerian secondary school Mathematics curriculum.

is it Okay to introduce the idea of the complex number so as to enable the student to solve a wide range of questions?

This question was raised by a student I coach when I told him that some quadratic equations do not have solutions in the realm of real numbers!

I understand that we can produce that number in MATLAB by evaluating exp(1), or possibly using exp(sym(1)) for the exact representation. But e is a very common constant in mathematics and it is as important as pi to some scholars, so after all these many versions of MATLAB, why haven't they recognize this valuable constant yet and show some appreciation by defining it as an individual constant rather than having to use the exp function for that?

UPDATE: The values of the variables that I am currently concerned with are:

a~65

V~3.887

While trying to solve a circuit equation, I stumbled onto a type of Lienard Equation. But, I am unable to solve this analytically.

x'' + a(x-1)x' + x = V-------------------------(1)

where dash(') represent differentiation w.r.t time(t).

The following substitution y =x-V and w(y) = y', it gets converted into first order equation

w*w' + a(y+V-1)w + y = 0; ---------------------- (2)

here dash(') represent differentiation w.r.t y.

if I substitute z = (int)(-a*(y+V-1), (int) represent integration. The equation gets converted into Abel equation of second kind.

w*w' - w = f(z). -------------------- (3) differentiation w.r.t z.

it get complicated and complicated.

I would like to solve the equation (1) with some other method or with the method that I had started. Kindly help in solving this,

Thank you for your time.

I am interested in including the inverse piezoelectric effect into my GaN HEMT simulation. Sentaurus Device provides a special feature that allows me to update the stress field by invoking the mechanic solver (Sentaurus Interconnect). But I don't have confidence in the results I got. Because from the mathematical point of view, solving the inverse piezoelectric effect is just a simple matrix multiplication (AB = C). However, the final matrix C I got was very weird - some components in C matrix should be zero but they are not. So I was wondering if there is anyone has the same situation about this?