Science topics: Mathematics
Science topic

# Mathematics - Science topic

Mathematics, Pure and Applied Math
Questions related to Mathematics
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Question
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?
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.
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Computer Aided Design (Cad) subject deals with the backend mathematical calculation that happens in a 3D design.
The book of Computer Aided Optimal Design: Structural and Mechanical Systems by the Mota Soares, C.A. and Templeman, A.B can be useful.
Question
Hello,
I am interested in the personalization of learning based on profiles, more specifically in mathematics.
Do you know any relevant references?
Thank you
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Quran = Key + Message
The Key has 139 letters, 124 diacritics (harakat), and 56 letter dots.
139 + 124 = 263 = 56th prime number.
Letter diacritics and dots always existed mathematically before they were added to the Quran's Text.
عدد حروف سورة الفاتحة = 139
عدد حركات حروف سورة الفاتحة = 124
عدد نقاط حروف سورة الفاتحة = 56
139 + 124 = 263 وهو العدد الأولي السادس والخمسون (عدد النقاط)!!!
حركات ونقاط القرءان موجودة رياضياً من قبل أن تضاف الى الرسم القرءاني
This topic lacks the simplest scientific research methods, so we do not know what Quran = Key + Message means
And how did you get to this equation? Just unproven conclusions.
The Qur’an is the word of God, and it makes no sense for you to say that the movements and points of the Qur’an exist mathematically before they are added to the Qur’anic drawing.
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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
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.
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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?
The difference between physics and chemistry is revealed in Nobel 2020
Nobel Prize in Physics for a fantasy illusion called a black hole
Nobel Prize in Chemistry for a Beneficial Bio synthetic Method of Genetic Scissors (development of a method for genome editing)
Which are closer to reality and which are closer to life?
I'm ashamed of this physics.
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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.
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).
Question
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.
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)
______________________________________
______________________________________
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)
Question
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?
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
Question
A question related to our cultural indebtedness to our mathematical forbears.
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.
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I am doing a research proposal i need answers on my topic. information must be from 2015-2020. relevant articles
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
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Any bibliographic recommendations on the problem of routing vehicles with multiple deposits, homogeneous capacities? less than 10 nodes
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
Question
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.
I hope you find the following discussion is useful
Best regards
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According to a report published by UNESCO, 0.1% of the global population (in 2013) were researchers? Does anybody know the current numbers?
I can imagine volumes of reasonings behind the eight-word response. Thank you Hermann Gruenwald !
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what is the mathematical expressions and equations used for the designing of antipodal structure of an antenna.
Dear Sneha,
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
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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?
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
Question
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?
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).
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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.
Interesting question. Following the discussion.
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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.
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.
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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.
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.
Question
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?
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.
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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:
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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.
Structure wave theory shows how mathematics as a structurally active language based on the release of structure waves is converted into physics.
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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!!!
Age requirement l problem. If it was 40 better !!
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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 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”.
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.
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the types of board game for mathematical literacy to make the learning and teaching fun
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:
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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
Dear;
The following documents show exemples of its application :
Automated Solution of Differential Equations by the Finite Element Method
Regards
Question
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.
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.
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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?
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.).
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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
Are you trying to play chess in 3D?
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.
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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 if we assumed that the answer to 1 is yes 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.
I'm looking foe different insights :)
Thanks.
exemple.docx
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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?
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!
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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
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*
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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.
Tool - An American progressive rock band :)
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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
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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?
I don't understand the relationship of "is prior to" to ideas. Do you mean which idea came first to a human being? Or which idea has fewer presuppositions? Or which idea does not depend on the other? If that is the case, is your question a false either-or assertion, as can't two ideas be co-dependent, like chicken and egg?
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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
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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)
Armin,
Did you find the equation?
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Is there an encyclopedia of all the branching mathematical axioms, together with various ways of proving different theorems based on those axioms?
Amauri Martins-Britto It is indeed helpful for me in other ways. Thank you.
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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.
Optimization algorithms handling a fixed number of real correlated values (non-separable) can be of 2 types: gradient-based and derivative-free.
Gradient-based procedures seem to be significantly faster than derivative-free ones.
L-BFGS
Levenberg-Marquardt Algorithm (LMA)
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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.
I show the formula of your (trivial answer), and the second set is also trivial.
One can generate infinite sets of such families!!
Observe that each number n in the first family has the property
3n + 1 = 2k which satisfies Collatz's Conjecture.
And each number n in the second family has the property
3n + 1 = 7x 2k
therefore after removing 2k by k steps divisions, we reach the number 7
which satisfies Collatz's conjecture too.
The whole procedure is NOT PROOF.
All are elementary computations.
Regards
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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?
Very interesting question. To me, best answer is given by Roger Penrose using the paradigm "The three worlds of reality": the Physical World, the Mental World, and the Platonic World (Mathematics lives here).
The claim is that Platonic World "maps" onto Physical World and hence all possible physical universes are constructs of information consistent with Mathematics.
Obviously Physical World "maps" onto Mental World (because we live in the physical world); and Mental World "maps" onto Platonic World. But the three worlds are different.
For a much better explanation you can see Penrose's book "The Emperor's New Mind"
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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.159844115.58373405
I 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?
Dear Feng Qi
I am attaching a proof of the first formula.
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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 .
Very interesting discussion and proposals to solve for calculating the absorbance of a single layer of MoS2 .
The absorbance is important to optically characterize the materials. The absorbance is the absorbed fraction of the incident light with a specific wavelength on a material with a given thickness. It is required for optical filters and for photodetectors and solar cells.
The dependence on the incident light wave length stems from the energy band structure of the material such that it is dependent on the probability of transferring of an electron from the valence band to the conduction band by the incident photons. Specifically it depends on the absorption coefficient as a function of the wavelength.
The key point for the solution is to calculate the energy band structure of the two dimensional material and from it you can get the absorption coefficient as a function of lambda. Then you can calculate the absorbance. As you have here a single layer the absorption coefficient will be equal to the absorbance.
You might benefit from the thesis given in the link: https://digitalcommons.mtu.edu/cgi/viewcontent.cgi?article=1049&context=etds
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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?
Thank you for sharing your paper Martin. I found it insightful - particularly your interpretation of graphs and your case for building 'critical STEM literacy'. From recent exploration, I notice that these graphs with data from the pandemic, present interesting outliers and multiple trend-lines which are ignored or cherry-picked in the final interpretation. Inferential stats while allowing decisive conclusions lead us to overlook these interesting data points. Critical graphicacy practices if nurtured from school will create this informed public, who will then find it difficult to simply accept the text interpretation, isn't it?
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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.
Relation between milk with adulterants . Many times urea is added in the milk as adulterant to increase the density. If you is isolated then in FTIR it shows the absorption for NH2(V NH = 3200-3350 cm-1) and C=O) at (v 1700 cmi1).
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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?
This way of thinking would support dictators and totalitarianism. It is rationalization to do nothing about it. But if one is aware then one is responsible. The legal theory is called, "participatory negligence." One can be guilty of a crime one does not commit. Hannah Arendt was instrumental in showing this, and it happened in a killing in New York. The attacker interrinterrupted, after around 80 people shouted that they woukd call the police. But the sttacker resumed, when no police help came, and finally killed the victim. All those 80 people were charged with the crime of negligence.
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Hello fellow scientists,
I wish to determine the Dissociation Constant (KD) 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 KD.
Previous work in our lab has determined a KD = 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 KD is actually 20 nM for my small dsDNA construct.
I am interested in using Isothermal Titration Calorimetry mainly to calculate the KD 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 KD is 20 nM, but I actually don't know for sure.
I have heard that when you determine the KD you have to have some estimate of the KD and then scan ligand concentrations above and below the KD, measure the response to get a curve of response vs ligand concentration and the KD is mathematically fit or basically it is just the inflection point of the binding curve.
However that advice doesn't tell me if the KD 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 KD 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 KD with a certain fixed concentration of protein, and a huge range of ligand concentrations regardless of if the KD is 20 nM or 1 µM? Is that possible?
• For statistically valid results and hyperbolic binding curves, the final ligand concentration should cover the range of 0.1 to at least 5, better 10 times Kd (if solubility permits), you need at least 12 ligand concentrations, which should be equal spaced (doi:10.1006/jtbi.1996.0023).
• For method with reasonable sensitivity, the constant concentration of the macromolecule should be around Kd for best precision. For insensitive detection methods like ITC, you may need a higher macromolecule concentration for a well-detected signal.
• If your binding curve is not hyperbolic, you'll need a wider ligand concentration range, in that case it may be worthwhile to space the data points logarithmically (1.0, 1.6, 2.5, 4.0, 6.3, 10, 16,...). From these guidelines it follows that you need to do an initial search study for rough determination of Kd. "Rough" means the order of magnitude.
• Btw, the use of linearisation (say, Lineweaver-Burk or Scatchard plots) for the determination of Kd is outdated, although these methods still have use for data presentation. Use non-linear regression for determination instead, the Nelder-Mead simplex algorithm (doi:10.1093/comjnl/7.4.308) is more stable than Marquardt-Levenberg (doi: 10.1137/0111030), but requires bootstrapping for determination of error margins.
• You may also wish to think about the detection method you use, ITC requires relatively large amounts of both macromolecule and ligand. Perhaps, surface plasmon resonance (SPR) would be a better choice. After all, you'll need lots of material for crystallisation later ;-)
Question
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?
Welcome.
You can validate your analytical model by the following methods:
- running experiments under the same assumptions of the analytical mode
- By using numerical simulation where the the system is solved by the numerical methods. There are now powerful simulator for many disciplines of science such as electronic circuits , electronic devices, semicondcutor fabrication processing.
- In some statistical systems they can be validated by Monte Carlo simulations.
This is list may not be exhaustive
Best wishes
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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.
Janez Podobnik I have been workikng since your answer and found the optimality condition and also found the proofs of optimal estimator. I have minimized the summary as you can see here in the attached picture.
But I am stuck in linking the attached theory with my case. Since this is the general cndition for an optimal estimator (attached picture) and yes generator would be minimizing a cost function but how can I say that my generator would be able to generate clean signals?
I have changed the notations in main question for simplicity purpose.
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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
I assume your data are count values (i.e., the number of adverse childhood experiences). If so, then use a count model (negative binomial is usually a good choice). Transfroming your data is not required at all. If excess zeros are a problem, consider a zero-inflated negative binomial model.
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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.
I'm sorry, the answer was not for you. I posted by mistake !.
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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 "mathematicaL" explanation is to examine the formula for the partial regression coefficient. It contains the covariance between the two independent variables, and if this is quite high, it will dominate the estimation of the coefficient. At the most extreme case, the two independent variables are identical, so neither one can make a separate contribution.
In my opinion, the best approach is to choose the most theoretically relevant variable from each set of highly correlated variables and use that one. This may well not cost you as much as you might think, because once you enter one of the variables, adding any of the other variables will amount to putting "the same thing" into the equation, so you R-sq is unlikely to increase.
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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
What arguments can I give a high school student why mathematics is important?
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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
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Check out Brian Hall's book, "Quantum Theory for Mathematicians" in the Springer Graduate Text in Mathematics series vol 267 In it he goes through the history and derivation of DeBroglie's theory.
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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
The simplest way is to pick a specific time point as the point at which to calculate % inhibition. This is purely phenomenological. No theory.
If you have an enzyme reaction that shows a time lag before reaching maximal rate, you should investigate the reason for it. Maybe the enzyme autoactivates in the presence of its substrate, like an autophosphorylating kinase, or the substrate may slowly displace a competitive inhibitor. You may be able to preactivate the enzyme so as to get Michaelis-Menten behavior.
Time lags can also occur in coupled enzyme reactions if the concentration of the 2nd enzyme in the sequence is not high enough.
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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 think the attitude and positivism of the community and their leaders is one big factor to add.
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I want Journals names or list
Dear search for journal of Mathematics in Web of Science Journal Master list and you will see many journals for Mathematics.
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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.
Dear Amir, this equation has the following ananlitics. It can be glue for v more than zero exact solution and for v less than zero. In both cases they are spirals and exactly solvable, but tends to different stationary points. You can even draw its phase space picture: you draw two spirals(exact solutions)each on proper halfspace and jump from one to another, when v=0.
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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
It feels like you didn't try to use an exact method. Thus, I have to write here that all the beginers are suppose to listen to prof. Patriksson. So, at first try to find an optimal solution. Use CPLEX, learn to model. This will be one of your first sentences in the research paper: "We tried to solve this NP-hard problem... (provide some proof that you really tried)... Because we are not able to generate an optimal solution in reasonable amount of time we decided for a heuristic approach..." I hope this is clear. Otherwise, it is like working with machine learning without knowing about statistical tests. It is slightly embarrassing.
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What are the mathematical equations used to assess the environmental impact using some biological criteria in green algae?
Dear professor,
The following article may provide inspiration to you about the subject.
Best wishes,
Tahir
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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!
As long as the students are comfortable with algebra of real numbers and the quadratic equation, complex numbers should not be particularly challenging to them. These numbers follow rather naturally from a straightforward application of simple algebraic concepts, though novel at the same time. Humans crave novelty, and the younger they are the more so, I think.
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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?
Dear brother and one of my best friends Mahmoud,
"you are really great researcher" This is how I see you.
Warmest regards,
Kareem
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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,
I don't know about analytic solutions but this is the equation for a harmonic oscillator in a constant force field with nonlinear damping. It is a like a mass suspended by a nonlinear spring in a gravitational field. There is a single equilibrium point at x=V and x'=0 whose stability depends on the value of a. Solutions will either be unbounded (go to infinity), which is probably unphysical for your electrical circuit, or they will decay to the equilibrium point, following the usual exponential law for a linearly damped oscillator as they approach it. Only the case a=0 has (neutrally) stable oscillations whose amplitude depend on the initial conditions just as you would expect for a harmonic oscillator without damping. There are no limit cycles and no chaos.
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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?
Dear Han-Wei,
welcome,
You want to validate your results.
you can make this validation by solving a known simple example where it can be solved analytically or its numerical solution is known with high confidence.
You can simplify the geometry of the device such that it can be solved analytically.
Than you can compare your numerical solution with the analytical solution.
You must not solve specifically for the HEMT.
Best wishes
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Heat transfer problem: what mathematical calculations apply to estimate the net current yield in a (TEG HV3-based) thermoelectric panel system where the source emits 5 Mjoule/h at 100°C, and cooling is aimed at by blowing air at 28°C as depicted in the attached drawing. How would you mathematically define a function to maximize net electricity yield by controlling blower speed? What heat exchange design tips are advisable? Thank you.
Good discussion
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I don't find mathematical problem-solving skills which i can call them my dependent variable. can you please suggest me the mathematical problem-solving skills that work as dependent variable. My research topic is "comparison of students' mathematical problem solving skills taught by guided practice and problem-solving approach"
I agree with Gilbert Lacroix
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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.
In fact mathematics is the major tools in applied sciences the best way of measuring academic performance in mathematics is what Prof. Muhammad Ali have mentioned.
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Hallo,
there is a new proof of the 3n+1-Problem !
The paper ist available

Perhaps there is a flaw in the proof

The Collatz-conjecture (the famous 3n+1-problem):
we construct a sequence of integers starting with integer n = a_0
If a_j is even, the next number ist a_(j+1) = a_j/2.
If a_j is odd, the next number ist a_(j+1) = 3*a_j+1.
Example n = 6:
6, 3, 10, 5, 16, 8, 4, 2, 1
The Collatz-conjecture: the sequence with a every positive starting-integer ends always in the sequence 4,2 1
Hello, I observed just this fact, don't know whether or not it can be interesting.
Just analysing the variations: in "even" case the iteration converges (0.5n) and in the odd case the iteration diverges (3n). So calling the f(n)=n/2 the "C" phase and f(n)=3n+1 the "D" phase we have initially the same probability that algorithm start with C or D phase (because even and odds are equally distributed).
The C1 phase will equally (probabilistically) call another C2 phase or a D2 phase (even numbers are equally distributed among multipliers of 4 and not) and so does the D1 phase: numbers that are not multipliers of 3 are equally distributed among even and odds.
The answer seems to be strongly initial conditions dependant, so the algorithm for me is unstable, hence the conjecture is false.
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Matlab based ANN toolbox provides to platform to simulate the following relationship using different algorithms (LM, SCG and so on)
Ypredicted = function(Xi) (1)
Then, a plot of Ypredicted to Yobserved to validate the ANN work.
However, is there a way to obtain the mathematical function behind on the above relationship (1)? I know, it has to be highly complex and non-linear function. But is there any specific way to get that function?
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I want to correlate real time application to I newly defined Topology that named Tiny Topology.
I am not in this area. Please remove me from your list.
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Dear Sirs,
I think many knows the ideas due to Jules Henri Poincaré that the physics laws can be formally rewriten as a space-time curvature or as new geometry solely without forces. It is because the physics laws and geometry laws only together are verified in the experiment. So we can arbitrary choose the one of them.
Do you know any works, researchers who realized this idea. I understand that it is just fantasy as it is not proved in the experiment for all forces excepting gravitation.
Do you know works where three Newtons laws are rewritten as just space-time curvature or 5D space curvature or the like without FORCES. Kaluzi-Klein theory is only about electricity.
Force, mass, and energy are a parallel set of descriptions of the effects of special relativistic Thomas Precession. All matter and space, and their interactions are described with distance in three dimensions, time, and their derivatives.
Newton's first law of motion is , "Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it."
Yet the concept of motion requires at least two objects, and if there are two objects, then there is always an external force, which is gravitation.
So the idea of rewriting Newton's laws without force (or mass or energy) is good, but it should be extended to incorporate the most basic non-linear effects of motion in space time, which are special relativity and Thomas Precession.
See my article describing the recent discovery of the effects of Thomas Precession the particle and galactic scales.
Article Thomas Precession is the Basis for the Structure of Matter and Space
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I realized that students do not understand integral conceptually.
Before formalizing the concept of definite integral, from the graph of the speed of a mobile, I build rectangles whose area is the space traveled (remember that s = v.t), that allows me to properly introduce this concept. This class is in one of the presentations that I have uploaded, you can consult it.
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We would like to follow the progress in students’ learning through the development of their mathematical skills and are looking thus for an appropriate classification of learners related to their achievements.
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Perhaps one of the hardest subjects in distance education applications is mathematics courses. If we dont have an IPAD everthing is very hard. Do you have suggestions for online question solving platforms that I can use in Distance Education Courses?
You could use MathCityMap@home (www.mathcitymap.eu). You can create a learning path with hints and immediate solution check and chat synchronously with the students in the Digital Classroom!
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Dear all :
I need to solve the following integral (attached as an image file)
The context is on the calculation of View Factors in Radiation Heat Transfer
I worked out the this expression from the general formula, working out my configuration of two bodies in cylindrical coordinates (for one of the bodies) and using spherical coordinates (for the other body).
But I'm not sure if I ended with a well defined Integral, since I used two different coordinated systems on a same problem.
I used Cylindrical Coordinates for one of the dA and Spherical Coordinates for the other dA, however both dA are part of the same integral.
Hopefully someone out there can give me some help !
Regards and Thank you !
When is an integral well defined? First, if the integrating function is integrable (in this case it is); second, if the domain of integration makes sense and is non-contradictory, then the final answer is that it depends on domains A1 and A2. What I do not understand is what the two additional integration variables mean, therefore I suppose that in the domains A1 and A2 the limits for z and η are included. If not, it is a meaningless integral.
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Hi. I'm currently working on my masters' thesis. I will analyse Grade 2 and 3rd (elementary level) maths textbooks and teachers' guides to discover how teaching and learning materials promote students conceptual understanding in mathematics especially the area of number and place value concepts. This will be completely desk-based research.
In order to analyse the materials, Should I use someone's framework or is it okay that I create some kinda criteria on my own to judge. I'd prefer make my own, but I'm not sure I can do that or not.
I would be very appropriated if you could give me an advice.
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Distribution dominates policy. Resources are injected at a point and distribute across communities. Can the distribution be almost instantaneous as in the heat equation? Do the resources morph and distribute, drawing in the wave equation? Where is stability (cf. Laplace equation)? These seem basic questions of public policy. Yet, the big three rarely feature in scholarship on public policy. Why?
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I would like to fit a curve of my steady-state anisotropy results in Origin, which revealed weak binding between two proteins. I tried quadratic equation but it turned out that it is used for strong interction, so I would like to reevaluate my results. I tried to find information about weak binding fits, but could not find detailed infos.
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Hello, I am a beginner in PARAFAC, and I am following Murphy et al. (2013) and using “drEEM” toolbox to process my data. However, I came up against some questions while dealing with the data and applying the method, and I really hope that I can get some advice from here! Thanks!
1. I am running RANDINITANAL to obtain the least-square model, but it seems like there are two components in my dataset often appear together, and PARAFAC don’t always decompose(?) them into separate components. The output of 100-run RANDINITANAL for 6 and 7-component model shows that there is a chance of 69% and 91% that PARAFAC will treat them as individual components. However, the runs that didn’t decompose them nearly always have smaller SSEs, though the relative difference in SSE is only about 1%, and will be chosen as the least-square model. I’ve read about that “There is no way to say, from the decomposition whether component one is rightfully the first, second or fifth component.” from the online PARAFAC tutorial “Interactive introduction to multi-way analysis in MATLAB (Bro, 1998)”. What about the difficulty(?) for PARAFAC to resolve a particular combination of components during the random process? And is it normal for PARAFAC to resolve a combination of components more easily(?) but with higher SSE? Should I just simply use the output “LSmodel” from RANDINITANAL?
2. Some low-signal samples are included in my dataset, and the contours of the corrected EEMs, especially those with low signal, seem very fragmental. I think this is the reason why I am getting some abruptly-changing excitation and emission spectra. And I think these abruptly-changing spectra are also making my model extremely difficult to validate in split-half analysis. Since I can’t really distinguish the true fluorescence signal from the noise (blank subtraction is done in FDOMCORRECT), removing faulty parts using ZAP or SUBDATASET might not be suitable. I’ve been thinking about smoothing my dataset, however, the instructions of function EEM_SMOOTH in the R package “staRdom” mentioned that smoothing is not advised in PARAFAC analysis. I’m wondering are there any other options when processing these kind of low-signal samples?
3. I’ve read about that the score (concentration) and loadings (spectra) of a component are “only determined up to a scaling (Andersen and Bro, 2003)”, for example, multiplying the excitation spectra by 2 and dividing the emission spectra by 2 at the same time doesn’t change the contribution to the model. What about the relative magnitudes between components? Do the relative magnitudes between components have any mathematical (or physical, or chemical, perhaps?) interpretation? I am asking this because those abruptly-changing spectra mentioned above sometimes feature peaks (or spikes) that have greater value than the spectra of other normal-looking components.
If any further explanation for my questions is needed, please let me know. If any of my questions is too basic, or there is any literature I need to read before continuing, please let me know, too.
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is there any criteria for evaluation or content analysis in early childhood's mathematics textbook?
What kind of criteria you want to analysis the book according to it?? You mean Quality Criteria or What?? You should determine which criteria.
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While most governments try to hide the facts and manipulate statistics about COVOD-19 due to political/economical/stupidity reasons, many physicians and scientists are currently working on finding cures for COVOD-19. I am curious whether there is any center/platform to use experts from different areas of research in this fight.
To be clearer, let me ask this:
I work in biomedical engineering department. I, my colleagues and our students are familiar with optimization, data analysis, artificial intelligence, time-series analysis, modeling, control and …
I hope there might be a center which can provide some data, plus some tasks, so we can do some real and useful research and have a share in this fight.
Just a saying: maybe a proper deep neural network can suggest best combination of drugs according to the available history.
-----------------------
P.S.
My question is about the direct fight. I don’t mean helping in e.g. producing masks, cloths and …
There are two fronts:
1) Short-time efforts that can ease the crisis management, e.g., alternative ways to use/adapt equipment to healthcare needs, taking notes of new empirical knowledge, check the mathematical models, etc.
2) Medium and long term efforts: remediate the healthcare, political and economic by-products the pandemic. I particularly think production engineering can be of great help because several practices could be reorganized to ease all economic sectors.
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I have been receiving complaints from different universities in Germany that master students from countries like India, Nepal, Pakistan can't cope up with the standard of mathematics and the majority of students struggling to pass such courses. Since the Indian Engineering colleges/ universities are divided into IITs, NITs, Government colleges, Private Engineering colleges and so on..the differences in the quality of education are so high that it is difficult for foreign universities to define the qualification criteria in an admission process. Eg. The grades of such students look pretty good on a marks sheet but students' performance in maths exam at German University/FH is poor. Are there any criteria to decide the potential of students during the admission process? Any recommendations to tackle this problem? How other universities in Germany addressing this issue?
In Nigeria many universities admit students into Preparatory classes called Basic Studies. During this programme the students are properly drilled preparatory to their admissions into the matriculation year
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related literature in my chosen topic
Are you asking for a list of references related to technology-based pedagogies in mathematics education? If so, get started with ...
Svela, A., Nouri, J., Viberg, O., & Lechen, Z. (2019). A Systematic Review of Tablet Technology in Mathematics Education. International Journal of Interactive Mobile Technologies, 13(8), 139-158. doi:10.3991/ijim.v13i08.10795
Donnelly-Hermosillo, D. F., Gerard, L. F., & Linn, M. C. (2020). Impact of graph technologies in K-12 science and mathematics education. Computers & Education, 146. doi:10.1016/j.compedu.2019.103748
Cullen, C. J., Hertel, J. T., & Nickels, M. (2020). The Roles of Technology in Mathematics Education. Educational Forum, 84(2), 166-1
Akkan, Y. (2012). VIRTUAL OR PHYSICAL: In-service and Pre-Service Teacher's Beliefs and Preferences on Manipulatives. Turkish Online Journal of Distance Education (TOJDE), 13(4), 167-192.
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"Random Seed: Definition" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/random-seed-definition/
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DIfferent Mathematical Techniques are being used for regionalization. For example in different references, the authors regionalize the area across the country under different climates.
Nice question
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Is Euclid's Elements still worth studying, or has modern geometry progressed far enough to render the text a historical work and nothing more?
I think it is still an excellent introduction to axiomatic mathematics and to proof.
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I am currently doing a research project on this topic. Any suggestions on academic articles and research papers are welcome.
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I know quantum computers have solved problems that would take an exponential amount of time on classical computers. But have they solved a problem that would take an infinite amount of time on a classical computer?
If this has happened, did it employ quantum indeterminacy?
If this hasn't happened, is there a proof that it can't happen?
The whole field was triggered by Shor's invention of his fameous factoring algorithm for quantum computers. 25 years and billions of \$ later, it is still not possible to factor the number 15 by using this algorithm, and there are no visible reasons to believe that this wonderful breakthrough might happen within the next 25 years. This simple FACT gives us an idea of the perspectives for QC
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I am working on parental beliefs about mathematics and it teaching and learning and want to investigate, in which ways parents support their children with their mathematics education. Therein I am focusing on early secondary school (11-12 year old students).
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In the literature, fractal derivatives provide many physical insights and geometrical interpretations, but I am wondering where we can apply this particular derivative appropriately. Please refer me to references or examples because I am very interested to learn more about new derivatives and their applications!! I greatly appreciate all the brilliant efforts in this discussion!!
They can describe surface roughness of materials Mandelbrot
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I am writing a paper assessing unidimensionality of multiple-choice mathematics test items. The scoring of the test was based on right or wrong answers which imply that the set of data are in nominal scale. Some earlier research studies that have consulted used exploratory factor analysis, but with the little experience in data management, I think factor analysis may not work. This unidimensionality is one of the assumptions of dichotomously scored items in IRT. Please sirs/mas, I need professional guidance, if possible the software and the manual.
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As applied to physics, the source is a mathematically described process and the target is one without a mathematically described process or without a mathematically described process known to the student. Analogy can suggest a mathematical model to a researcher. Analogy assists the student by demonstrating that knowledge already acquired can help in understanding a new subject. Thus analogy can be an investigative tool and a pedagogical tool. John Holland in his book on Emergence from Chaos to Order attributes the source-target characterization to Maxwell (p. 210) but I have not been able thus far to locate Maxwell’s employment of that characterization. Maxwell spoke about analogy as a useful pedagogical tool in an 1870 address to the Mathematical and Physical Sections of the British Association included in his collective works, volume 2, page 215. At page 219: Analogy `is not only convenient for teaching science in a pleasant and easy manner, but the recognition of the formal analogy between the two systems of ideas leads to a knowledge of both, more profound than could be obtained by studying each system separately.’
Do you know the origin of the source-target analogy?
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Dear researchers,
Regarding assumptions of linear regression, can I replace scatter plots with mathematical equations in my article and claim that there is a linear relationship between two variables on the basis of equations. I want to conserve space in my article without presenting scatter plots. Please advise. Thank you.