Science topics: Mathematics
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Mathematics - Science topic

Mathematics, Pure and Applied Math
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Chaos Theory, Chaotic dynamics
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@Shireen Jawad : Period 3 implies chaos.
You can check out Li and Yorke's paper in the link below.
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Right now, in 2022, we can read with perfect understanding mathematical articles and books
written a century ago. It is indeed remarkable how the way we do mathematics has stabilised.
The difference between the mathematics of 1922 and 2022 is small compared to that between the mathematics of 1922 and 1822.
Looking beyond classical ZFC-based mathematics, a tremendous amount of effort has been put
into formalising all areas of mathematics within the framework of program-language implementations (for instance Coq, Agda) of the univalent extension of dependent type theory (homotopy type theory).
But Coq and Agda are complex programs which depend on other programs (OCaml and Haskell) and frameworks (for instance operating systems and C libraries) to function. In the future if we have new CPU architectures then
Coq and Agda would have to be compiled again. OCaml and Haskell would have to be compiled again.
For instance suppose a formal mathematics Agda file started with
{-# OPTIONS --without-K --exact-split #-}
Both software and operating systems are rapidly changing and have always been so. What is here today is deprecated tomorrow.
My question is: what guarantee do we have that the huge libraries of the current formal mathematics projects in Agda, Coq or other languages will still be relevant or even "runnable" (for instance type-checkable) without having to resort to emulators and computer archaeology 10, 20, 50 or 100 years from now ?
10 years from now will Agda be backwards compatible enough to still recognise
current Agda files ?
Have there been any organised efforts to guarantee permanent backward compatibility for all future versions of Agda and Coq ? Or OCaml and Haskell ?
Perhaps the formal mathematics project should be carried out within a meta-programing language, a simpler more abstract framework (with a uniform syntax) comprehensible at once to logicians, mathematicians and programers and which can be converted automatically into the latest version of Agda or Coq ?
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My concern is that building an always-upward-compatible front-end language to either Cog or Agda still has to chase breaking changes in Coq and Agda's languages and is more complicated than achieving that in the lifecycle management of Coq and Agda themselves. It will also fall out of step with additions and extensions to those systems from third parties.
If the Coq/Agda projects are unwilling to address versioning and upward compatibility preservation, I see no practical solution.
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Hello Friends and Colleagues,
Can anyone suggest a mathematical book that helps me to build my own mathematical equations and functions? I want to convert real-life problems(natural sciences) into mathematical formulations.
Note that I have basic knowledge of mathematics.
Thanks in advance,
Hadi
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Many thanks for your recommendation
Best regards,
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Hello everyone,
I would like to know how to locate mathematically a damage on a blade.
Usually a frequency analysis of the blade and a comparison with a similar healthy one helps to determine a default or damage on a blade. However, how could someone locate that damage?
Thank you for your time.
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Hi fellow researcher,
I think the answer depends on what kind of equipment you have on your disposition and what is your purpose. The simpler way is to have a model blade and compare it to the blade you want to determine the integrity using the physical properties of the blade.
For example, if you have an accurate sound sensor and a device that produces an specific sound profile in the model blade you can use this device to produce a similar sound in the test blade. Comparing the Fourier decomposition of frequencies of the sound produced by the test blade will give you information of cracks and non-uniformity in density produced by the forging process or even if the material the blade was made is of quality or not.
You can do a similar approach with thermodynamics. you can heat Specific spots on the test blade. As cracked regions do not conduct heat as well as non-cracked regions you will observe anomalies in the heat map of the blade.
Notice you don't really have to calculate something, but just know what to expect with a model blade data.
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Everybody is eager to see the New winner of the Millenium Prize. Please share all your incomplete works about the Millenium Prize problems of Clay Mathematics Institute in order to collaborate for the solutions.
I am actually using the different nabla operator which I demonstrated mathematically in my published work: " A thesis about Newtonian mechanics rotations and about differential operators ".
This demonstrated differential tool enables to deal differently with the millenium problem about Navier-Stokes equation.
I also suggest that P=NP if the problem can be translated to a differential equation that has a solution. If your lucky friend finds and gives you an easy solution, than that solution leads directly to the general solution of the differential equation.
I will be waiting for your collaborations.
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V. V. Vedenyapin thanks for the article. I hope we will be able to collaborate.
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for different approach
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Famous mathematicians are failing each day to prove the Riemann's Hypothesis even if Clay Mathematics Institute proposes a prize of One Million Dollars for the proof.
The proof of Riemann's Hypothesis would allow us to understand better the distribution of prime numbers between all numbers and would also allow its official application in Quantics. However, many famous scientists still refuse the use of Riemann's Hypothesis in Quantics as I read in an article of Quanta Magazine.
Why is this Hypothesis so difficult to prove? And is the Zeta extension really useful for Physics and especially for Quantics ? Are Quantics scientists using the wrong mathematical tools when applying Riemann's Hypothesis ? Is Riemann's Hypothesis announcing "the schism" between abstract mathematics and Physics ? Can anyone propose a disproof of Riemann's Hypothesis based on Physics facts?
Here is the link to the article of Natalie Wolchover:
The zeros of the Riemann zeta function can also be caused by the use of rearrangements when trying to find an image by the extension since the Lévy–Steinitz theorem can happen when fixing a and b.
Suppositions or axioms should be made before trying to use the extension depending on the scientific field where it is demanded, and we should be sure if all the possible methods (rearrangements of series terms) can give the same image for a known s=a+ib.
You should also know that the Lévy–Steinitz theorem was formulated in 1905 and 1913, whereas, the Riemann's Hypothesis was formulated in 1859. This means that Riemann who died in 1866 and even the famous Euler never knew the Lévy–Steinitz theorem.
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You should also know that the Lévy–Steinitz theorem was formulated in 1905 and 1913, whereas, the Riemann's Hypothesis was formulated in 1859. This means that Riemann who died in 1866 and even the famous Euler never knew the Lévy–Steinitz theorem.
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I'm struggling to understand the method followed in the following analysis. Can someone please explain how the author got the values of Δ_1 and K_1 that justify its analysis?
I have tried to isolate "Δ" and "K" by setting Equation (B8) equal to zero. but I have failed to get similar conditions.
P.S: I'm new to mathematical modelling, so I really need to understand what's going on here. Thanks
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The RHS is a fraction, whose numerator and denominator are quadratic expressions in Δ. Therefore the fraction takes positive values when numerator and denominator are of the same sign...
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why to quantize a Hamilton-Jacobi theory with fractional derivatives?, what are the physical or mathematical advantages?
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Also, Hamilton-Jacobi theory can be applied with not only fractional derivatives but also, definition of fractional derivatives and integrals on time scale Yazen Alawaideh
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didactics of mathematics
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I think a major issue in this regard is designing a balanced curriculum: where a balance is achieved between coverage of the theoretical foundations of the subject and adequate focus on the problem solving/computational aspects.
I believe in modern day context, any course or a set of courses in linear algebra is incomplete without courses aimed at building the basic foundations: analytical and numerical, a course on matrix calculus of real and complex variables, applications of linear algebra in solving problems in Systems theory, Operations Research, Artificial intelligence and Machine learning, Quantum chemistry and other areas of Natural sciences.
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How to people propose a new optimization algorithm. I mean what is the baseline? Is there any intuition or mathematical foundation behind it?
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The question is too general. To generate the basic idea of the algorithm, you need to know the detailed statement of the problem. Typically, the process of developing an algorithm starts with the identification of your problem complexity class. If there is no evidence or clear feeling that the problem is NP-hard, then it is reasonable to try to develop a polynomial algorithm for solving it. Such algorithms are usually based on the use of specific properties of the problem. Sometimes it is possible to construct a polynomial algorithm based on the general scheme of dynamic programming, taking into account the specific properties of the problem.
If the problem is known to be NP-hard, then branch-and-bound methods, dynamic programming, and their modifications often work well for a relatively small problem dimension. Sometimes it is possible to build a successful formulation of the problem in the form of an integer programming model, followed by the use of appropriate methods or ready-made software. For high-dimensional problems, you can either use well-known metaheuristics, or develop your own approximate algorithm. In the latter case, success is usually based on the use of the problem properties. As you can see, in any case, it is useful to start by studying the specific properties of your particular problem.
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When solving mathematical equations or system of equations there are things that are considerable; such as the Universe or domains...
Because, some equations may have no solutions or impossible to solve., at all. If a solution or some solutions exist for an equation or systems of equations, there are regions or intervals containing the solution(s). Such considerations may be important when applying numerical methods.
What are basins of attractions?
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Dear, Tekle Gemechu basins of attraction comes from the dynamical system and chaos theory. It is related with systems behavior. There are several example of basins of attraction. Therefore, definition and examples of basins of attraction are given in scholarpedia. Below scholarpedia's link:
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Does nature understand mathematics?
A connected question is -- How are theory, theorem, and truth related?
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A theory is only ever assumed to be true until proven otherwise. Generally speaking, there is no hard and fast rule to when a theory becomes 'accepted truth' but Kuhn's paradigm idea is a decent fit. Scientific truth is implicitly assumed when an entire field, other than a few fringe scientists, reaches a consensus.
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The constants (G, h, c, e, me, kB), can be considered fundamental only if the SI units they are measured in (kg, m, s ...) are independent. However, if we assign numerical values to the SI units (kg = 15, m = -13, s = -30, A = 3, K = 20), then by matching the unit numbers, we can define (and solve) the least precise (CODATA 2014) constants (G, h, e, me, kB) in terms of the 3 most precise constants (c, μ0, R) ... (diagram #1). Officially this must be just a coincidence, but the precision is difficult to ignore.
We find further anomalies to equal precision when we combine the constants (G, h, c, e, me, kB) in combinations whereby the unit numerical value sums to 0 ... (diagram #2).
The methodology is introduced here
Is a simulation universe the best explanation for these anomalies?
Some general background to the physical constants.
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Hi Hieram, youre welcome! Imho fun should be induced by fruitful scientific research supported by open commenting one other’s ideas (opposed to endless fruitless repeating discussions what presumingly not cannot ever workuntil it does) like iSpace („integer-Space„ or „complex-Space“ when treating the i as the one for a complex number) able to derive and decipher inter-relationships, dependencies and calculate exact arbitrary precision numerical values for most but all constants of nature.
Also recently a new true quantum geometric iSpace-IQ unit system has been developed, able to directly represent native quantum relations of contants while keeping strictly compatible to MKSA/SI system showing a single *time* based conversion factor, effective predicting quantization of time itself.
So - no - being a true long time Apple expert consultant i’d say we do not need to fear to be sued for (at least not in the foreseeable future ;-) ). And please all take the time to read thru the very short yet imho rreally convincing math of both of my newest papers to be found on my RG home.
Here is a link to RG summary of my iSpace project:
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I am aware of the facts that every totally bounded metric space is separable and a metric space is compact iff it is totally bounded and complete but I wanted to know, is every totally bounded metric space is locally compact or not. If not, then give an example of a metric space that is totally bounded but not locally compact.
Follow this question on the given link
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Metric space A is said to be a totally bounded if every Cauchy sequence in A has convergent sub sequence
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What are the areas where mathematics are been applied medically.
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Which type of mathematics? We use statistics in medical and biomedical research. We use artifial intelligance and use mathematical models in public health
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I am trying to model a business scenario mathematically for my research paper but I do not have the required skillset. What is a legitimate way to find and get help. Are there any online sources or paid services. Do I need to add the expert a co-author? What type of solutions exists.
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I have many times served as an applied mathematician on a multi-disciplinary team, including, for instance, biologists, meteorologists, geologists, hydrologists, etc. The other team members possessed essential knowledge to the success of the project but not the math skills. This is good for you to recognize in the study of business because nobody knows everything. A diverse team can solve problems that a single individual cannot. I would have the biologists explain over and over again that part they understood (like fish behavior or metabolic needs) and I would create a model. Then we would run the model and ask, "Is it responding the way you expect it to?" One of these interesting projects considered production of peanut butter crackers and cheese crackers sold in vending machines manufactured on the same assembly line at a factory on the road from my house to the school. Walk over to the Mathematics Department and find a graduate student studying applied mathematics who is looking for a project. You can help each other.
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Why use metaheuristic algorithms when there are so many mathematical optimization tools available, like GAMS?
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Ankur Maheshwari I agree with Ben Cardoen that a heuristic/partial search algorithm may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity where commercial solvers may struggle. But the key issue of heuristics is that they do not guarantee that a globally optimal solution can be found on some class of problems when compared with commercial solvers such as Ipopt, Cplex, Mosek, Gurobi,..., for NLP or LP or MILP or MINLP problems.
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1) What's the difference between SCILAB and MATLAB?
2) Which one would you recommend?
3) Which one is the most friendly user?
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Hello!
Thanks to your question, I heard about SCILAB for the first time. After brief googling, it seems that it is a somewhat alternative for MATLAB. It even says that MATLAB files can be converted to SCILAB files. However, that makes it seem that MATLAB is a primary system and SCILAB is in some way the copying one. I think the code and knowledge base for MATLAB is much wider, for example, there are forum topics considering MATLAB implementations of many things.
There is GNU Octave if you want free access, it runs most MATLAB codes just fine.
Now about real-life problems, what do you mean? Sometimes for them a specific tailored code is better than a general-purpose one.
Sincerely,
Denis
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Dear Colleagues, a recent trend in Fractional Calculus is in introducing more and more new fractional derivatives and integrals and considering classical equations and models with these operators. Thus, we have to think about and to answer questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. These and similar questions have remained mostly unanswered until now. To provide an independent platform for discussion of these trends in the current development of FC, the SI “Fractional Integrals and Derivatives: “True” versus “False””( https://www.mdpi.com/journal/mathematics/special_issues/Fractional_Integrals_Derivatives2021) has been initiated. In this SI, some important papers have been already published. However, you are welcome to share with the scientific community your viewpoint. Contributions to this SI devoted both to the new fractional integrals and derivatives and their justification and those containing constructive criticism of these concepts are welcome.
Best regards
Yuri Luchko
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I like this new thinking. But for me it is difficult to say "true" or "false" since everyone has his own standard. I feel interested in the definition convenient both in the application and mathematical analysis.
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How can we analyze the propagation constant in slab waveguides? Is there a mathematical formula for this parameter?
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If interested you can send different articles from Piaget theory in the learning of mathematics through play.
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I agree that it starts in Piaget's sensory-motor stage of play. Mary Reilly's Systems Explanation of play: Learning through play and the Third form of Information Processing theories mirror and expand on Piaget's Theory of play and learning.
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my article is about the relationship between playing and increasing intelligence via mathematics. this a longitudinal research which has done since 4 years ago until to year. it is a pre-test- post-test research with control group. results are wonderful. assessment tool in this research was Stanford-Binet test. I am following to a journal in grade Q1. I would be grateful if someone could help me.
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Just based on the metrics I would suggest that you might have a look at:
Educational Studies in Mathematics https://www.springer.com/journal/10649 CiteScore 3.6 (SJR Q1 journal), Impact factor 2.853 (JCR Q2 journal)
ZDM – Mathematics Education https://www.springer.com/journal/11858 CiteScore 4.1 (SJR Q1 journal), Impact factor 2.481 (JCR Q2 journal)
Journal of mathematics teacher education https://www.springer.com/journal/10857 CiteScore 3.6 (SJR Q1 journal), Impact factor 1.786 (JCR Q2 journal)
Research in Mathematics Education https://www.tandfonline.com/journals/rrme20 CiteScore 3.4 (SJR Q1 journal), ESCI indexed (so no impact factor and Q ranking (yet))
Best regards.
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Please help me
If any mathematical equations for coupling of pmsm and pmsg in matlab?
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coupling equations available in ODEs and also built-on ode45, ode15, ect code in matlab.
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A study by Po-Shen Loh shows that quadratic equations can be solved using a clever trick that reduces guessing and cramming formula. Kindly follow this link to see examples of quadratic equations solve by Po-Shen Loh https://www.youtube.com/results?search_query=po+shen+loh+quadratic .
Could this idea be applied in class? if so, could it be generalized for other topics in mathematics?
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By practical applications
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Plz share if yes . I want to know how to get patent in vedic maths.
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can anyone suggest or interested to have conversation on AI/ML and PLS based mathematical tool. I need to know more information.
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Explainable ML using OLAP data for verification - that could be an interesting topic.
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Hello? Good evening, I would like to ask if there is a questionnaire aligned to the set of indicators on Mathematical Competence given by Sir Turner?
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Hello Sir? Goodmorning. Thank You for sharing your time and effort in answering my concern. I appreciate your thoughts Sir. I am able to skim the article you've mentioned about Mathematical Literacy and I downloaded it already, I believe this is an edge as I develop my study. Fortunately, a colleague of Sir Ross Turner further give a helping hand. I am beyond grateful for your kindness. Thank You so much!
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Can anyone please confirm whether there exists an explicit mathematical relationship between the gravitational instability growth rate and the corresponding structure (star) formation rate in molecular clouds?
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Thanks a lot, dear Javad Fardaei, for the article
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I have formulated the mathematical equation of the vibration problem. The resulting equation is coupled nonlinear differential equation of 2nd order ODE. Please, anyone, suggest to me how to solve it using MATLAB.
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Dear Sandip,
to answer your question, I agree with Abdelghani: you have 1) to transform the 2nd order equations into 1st order ones and then 2) to use a MATLAB ode solver to numerically solve the resulting 1st order system.
To do step 1), you have to introduce new variables that correspond to first derivatives. For instance, let us say that you have a system of two 2nd order ODEs in x=x(t) and y=y(t), e.g. x''=f(t,x,y,x',y') and y''=g(t,x,y,x',y'). Then you can introduce two dummy variables X=x' and Y=y' (for example) and get a system of four 1st order ODEs: x'=X, X'=x''=f(...), y'=Y, Y'=y''=g(...).
Then, in order to apply step 2), you have to define a variable vector, say v=[x,X,y,Y], and a function, say myFun, that defines the system. In this case:
function vder = myFun(t,v)
vder(1)=v(2); % this equation corresponds to x'=X
vder(2)=f( t, v(1), v(3), v(2), v(4) ); % you should actually write your original equation for x''=X'=...
...etc...
end
Then, choose an ODE solver (for example ode45) and solve the system by using the basic command [t,v] = ode45(@myFun,tspan,v0); where tspan is an interval for the independent variable (e.g. tspan=[0,10]) and v0 is a vector containing the initial values for x, X=x', y, and Y=y'. So please notice that you must provide initial values for the first derivatives!
You can find more details about all this stuff here: https://www.mathworks.com/help/matlab/math/choose-an-ode-solver.html
Hope this helps! :-)
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I am working on RIS aided communication. Whichever paper I go though, they cook up some complicated mathematics specially optimization problem, which seems to be unsolvable at first. But, then I see they are using some techniques which I have never seen anywhere. Can anyone from wireless comm background tell me, how you people proceed and get those sort of maths?
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Optimization is a broad field of mathematics and not some mysterious quackery. I am not surprised that someone from another field entirely (wireless communications) might not be familiar with these topics. This is why I stress the importance of multi-discipline teams. Nobody knows everything. If you get smart people from different fields together in the same room to discuss a problem, you may find some clever solutions that any one person alone would never come up with.
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Hi!
I'm currently working on a Data Science project for optimizing the prices of the products one of the biggest supermarket chains in Mexico.
One of the things that we are working on, is finding the price elasticity of demand of such products. What we usually do, is that, apart from fitting an XGBoost model for predicting sales, we fit a linear regression, and we get the elasticity from the coefficient corresponding to the price (the slope).
However, it is abvious that linear regression is sometimes a poor fit for the data, not to mention that the execution times are way longer since it requires to run separately XGBoost and LR (which is not good considering that there are thousands of products to model).
Because of this, it ocurred to me that we could use numerical differentiation for finding the price elasticity. At last, calculating a numerical derivative is way faster than fitting another model.
However, I'm not sure if this is mathematically correct, since the data does not come from a function.
So the question would be, is this mathematically correct? Does it make sense?
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From my experience, I would not use a linear predictor for elasticity. I know your question is asking about mathematically correct solutions but I don't think that's your issue. I would probably use logistic regression as a first choice.
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Dear colleagues,
I am researching in a topic related to philosophy and teaching methods. Please, could you point out me if are there any sources on dialectics or contradiction in mathematics education?
Thank you for your answers.
Regards
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An activity theory perspective on contradictions in flipped mathematics classrooms at the university level, Helge Fredriksen and Said Hadjerrouit, 520-541, 2019
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Please look at the text of the section on random walk from page 9 to formula 4.7, where you will find mathematical calculations justifying the probabilistic interpretation of the Riemann zeta function.
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If the distribution of the zeros of the Riemann zeta function is implicit in your question, then you may find the following paper exciting:
Regards,
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I will be glad if researchers and professors answer my question with mathematical formulas or explanations. Thank you so much.
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Hi, it should be taken into account that it is actually 'stress' doing the deformation for us. So when you use a roll with a smaller radius, the contact area between the roll and the sheet/foil is also smaller, increasing the stress.
Stress = Force / Area
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I can't understand why each time we divide by the mass of oxidized NH4-N and multiply by the mass of treated NH4-N.
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Look at the attached screenshot search and I think your question is answered if I understand you. Best wishes David Booth
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How can we mathematically calculate the critical thickness of polycrystalline(Sputtering) grown thin?
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Thank you, Dr. Len
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Is multiverse a differential of possibility, a gradient of cross universe space time planes.
Do multiverses branch or all have separate beginnings.
Are multiverses different mathematical constants or is it different potentials.
How can we progress to a mathematical model of multiverse theory.
First we need a mathematical model of the universe and then we need to generalise it for the multiverse. Is this quantum physical, does this take into account the electromagnetic generation of mass and gravity in a recursive relationship?
Does Arc Length calculus change our notion of frequencies and therefor electromagnetism?
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I want to understand the mathematics of fluorescence process in terms of excitation and emission wavelengths. I want to develop a general mathematical model with certain specific parameters and without employing a spectrometer, I want to see the emission spectrum mathematically.
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One can construct simple model (Shifted Harmonic Oscillator model) and derive tractable equations to obtain absorption and emission spectra.
1. Absorption and Emission Lite: Assume ground and excited states are shifted classical Harmonic Oscillator. Ground state |g> energy: Eg(R) = 1/2 ω2R2 & Excited state |e> energy: Ee(R) = 1/2 ω2(R - R0)2 + ΔE. Treating R classically one gets absorption (Ia) and emmision (Ie) spectra as:
Ia(e) = exp[(e-ΔE)2/2σ2] Ie(e) = exp[(E-ΔE + ω2R02)2/2σ2] (Arbitrary Units)
absorption and emission is peaked at different energies and the difference is ω2R02 --- stokes shift, see: https://en.wikipedia.org/wiki/Stokes_shift
σ is the linewidth caused by molecules coupling to environment (Homogeneous Broadening) caused because individual molecules see slightly different environment, e.g. ΔE (Inhomogeneous Broadening) is different for different molecule.
2. Absorption and Emission Pro: Same as 1, but treat R quantum mechanically,
this gives |g>|v0> , |g>|v1> ... |g>|vn> states and |g>|v0'> , |g>|v1'> ... |g>|vn'> where |vn> is nth vibrational state centered around 0 and |vn'> nth vibrational state centered around R0.
  • Energy of |g>|vn> --> <vn|<g| H |g>|vn> = (n + 1/2)ℏω and
  • Energy of |g>|vn> --> <vn'|<e| H |e>|vn'> = (n + 1/2)ℏω + ΔE
With this we write the absorption at T = 0K ( or ℏω >> kT)
Ia(e) = ∑n |<vn'|v0>|2 exp[(e-ΔE - nℏω)2/2σ2]
= ∑n (1/n!) * (ωR02/2)n exp[-(ωR02/2)2] exp[(e-ΔE - nℏω)2/2σ2]
Ie(e) = ∑n |<v0'|vn>|2 exp[(e-ΔE + nℏω)2/2σ2]
= ∑n (1/n!) * (ωR02/2)n exp[-(ωR02/2)2] exp[(e-ΔE + nℏω)2/2σ2]
|<v0'|vn>|2 are Franck-Condon factor,
|<v0'|vn>|2 = |<vn'|v0>|2 = (1/n!) * (ωR02/2)n exp[-(ωR02/2)2].
3. Absorption and Emission Pro Max: Same as 2 but at finite temperature T. Assuming instant thermalization --> states are population according to Bolzmann distribution,
Ia(e) = ∑mn |<vn'|vm>|2 exp[(e-ΔE - nℏω)2/2σ2] * Pm
= mn |<vn'|vm>|2 exp[(e-ΔE - nℏω)2/2σ2] * (exp[-βmℏω] /∑kexp[-βkℏω])
= ∑mn (1/n!) * (ωR02/2)n exp[-(ωR02/2)2] exp[(e-ΔE - nℏω)2/2σ2] * (exp[-βmℏω] /∑kexp[-βkℏω])
Ie(e) = ∑mn (1/n!) * (ωR02/2)n exp[-(ωR02/2)2] exp[(e-ΔE + nℏω)2/2σ2] * (exp[-βmℏω] /∑kexp[-βkℏω])
Pm = (exp[-βmℏω] /∑kexp[-βkℏω])
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Hello, this is my first post on this site. I'm an undergraduate student doing some Raman spectroscopy of CVD-grown graphene strained on silicon dioxide nanospheres. I notice that D and G' peaks show up in some measurements. The transfer process of the graphene to the silicon dioxide nanosphere-coated silicon chips I would think is far from perfect, as in certainly interferes with the structure of the graphene as there are rips and tears across the sample, as well as impurities and other things. You do however have "pristine" regions that only show G and 2D peaks.
On a loosely related tangent, I'm interested in how the molecular symmetry of graphene plays a role in its Raman spectra, and how that can be expressed mathematically. I wonder if perhaps the mathematical description of graphene in terms of group theory can possibly help explain the redshifts that occur in strained graphene versus unstrained graphene. If anyone has some advice or things to read about that, please let me know!
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In perfect graphene, the D-peaks are by symmetry not Raman active. ideal graphene should only show the single G-peak. However, when there is anything disturbing the symmetry and structure, the condition is relaxed and the D-peaks become visible. Hence, their name D for "defect" peaks. Based on the relation of peak intensity or the integrated intensity below the modes, the quality of graphene layers can be quantified.
There are numerous reviews on Raman spectroscopy in graphene, explaining which information can be extracted and how they can be extracted from analyzing the spectra.
Check, for example, this article by Andrea Ferrari:
You should be able to quickly find numerous more articles.
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I have myself tried using the basic method but including incomplete ionization to figure out the depletion width however I failed miserably because of many mathematical roadblocks. I was wondering if this had been done in the literature before and I just missed it.
If anyone can help me in this regard then I would be very grateful. Thanks.
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If you can send me a sample data file, I can have a look at it...
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We are planning to implement matrix based mathematical algorithms on FPGA. Could anyone suggest good book for these topics?
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You mustr try Practical FPGA Programming in C written by "Max" Maxfield.
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please is there any mathematical function that relates the SMD (D32) to the mean diameter (D50)? I actually understand what each of them represent.
thanks
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Thanks for this
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I am primarily interested in 2-player combinatorial games with perfect information. Useful wiki links are below.
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Is there a way to model the influence of pH on the electroosmotic EDL potential and velocity field inside the flat microchannel mathematically?
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Thank you Masuduzzaman.
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How could one increase data values from weekly to daily observations using mathematical algorithm for interpolation?
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Hello Nasiru,
What's the reason for wanting these values? That may have more to do with what sort of approach, if any, might make sense.
At first glance, doing this doesn't sound like a good idea to me. Among the reasons:
Any method for taking adjacent weekly values and inserting some estimate for the 6 six "missing" daily values will only bias the estimates of day-to-day variance in scores/values as well as increase the serial correlation across a lag from 1 to 6 days. As well, the presumption of a (perfectly) predictable day to day change is unlikely to be realized in actual measurements.
Good luck with your work.
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The mathematical representation of both equations is same.
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Please, see the attached file...
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Hi
I'm solving nonlinear second order equation by using finite difference method . finally for calculating value at any desired node, knowing three preceding nodes is required however by knowing boundary condition just one of these nodes becomes obvious and still knowing two other values is necessary. it must be noted there are plenty of guesses for values of these nodes which lead to compatible response.
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please write the ODE, not only the discretization You used.
however, for multi-step methods you need to create the starting values using a single-step method for all required nodes. Use a discretization of the same accuracy.
Note that the second order ODE could be written as system of two first order ODE.
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The 2023 ranking is available through the following link:
QS ranking is relatively familiar in scientific circles. It ranks universities based on the following criteria:
1- Academic Reputation
2- Employer Reputation
3- Citations per Faculty
4- Faculty Student Ratio
5- International Students Ratio
6- International Faculty Ratio
7- International Research Network
8- Employment Outcomes
- Are these parameters enough to measure the superiority of a university?
- What other factors should also be taken into account?
Please share your personal experience with these criteria.
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Cenk Tan; There are, of course, several websites that rank the universities worldwide. However, QS is the most famous of which.
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Here I attached the journal and the mathematical solution of the Rayleigh number. I need to plot graph exactly in Figure 3 from the journal but I didn't know the command. I have tried using this command,
plot(subs(N1 = 0.5, N3 = 2, N5 = 1.5, a1 = 1, a2 = 3, a3 = 1, Q = 10, R), a = 0 .. 10, 11 .. 22);
but the results show only a single line 2D graph. Hopefully anyone could help me with this. Thank you in advanced.
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You have only derived one relationship for R. Each of the graphs in Figure 3 show three relationships [1) linear inverted and parabolic; 2) heating from below and cooling from above; and 3) step function] So you need 3 different equations for R. Then there are the three cases [1) N1=0.1, Q=10; 2) N1=0.1, Q=20; and 3) N1=0.5, Q=10]. Maple is doing exactly what you've told it to do: plot one relationship for R. After Maple solves the equation, you could easily paste it into Excel and plot the results.
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I am currently working on the use of metacognitive abilities to improve teacher proficiency of teaching mathematics in Primary schools. I am looking for international collaborators from Japan, Germany, Singapore, Netherlands, USA, Canada and Australia.
Thank you
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Those with creative thinking skills and intelligence
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topics should be where we can mathematics algorithms
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you can think of in covid 19, Lung cancer, Brain tumor detection using different deep Learning Techniques and possible to use also ML Algorithms.
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I asked people about their knowledge & Interest.
Most had no knowledge but high interest. Now I want to describe this relationship using statistical methods.
I used a likert scale so, the data is ordinal.
Using a Spearman's rank test I get a positive correlation with good significance.
But I don't really understand this result. I expected a negative correlation, since interest and knowledge frequencies have contrary slopes. Does the test look at individual pairs, where those with high knowledge may also have high interest?
PS: How could I form a mathematical equation to describe the relationship (regression)?
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Hello Lukas,
As the software reports, the estimated Spearman correlation is about .34 (Pearson very close, at about .35). Yes, the correlation is positive. That's because the general trend is that, persons having higher self-rating of knowledge tend to have higher self-rated interest, whereas those with lower self-rated knowledge tend to have lower self-rated interest.
Look within any row of your two-way contingency table, and as knowledge rating increases, you'll see a higher relative proportion of high ratings of interest.
Yes, it's true that the correlation is far from perfect. All that tells you is that you'll find exceptions to the general trend described above as you examine knowledge-interest ratings from the same person over your sample.
Mathematical relationship? (Using 0-5 scales for each variables)
Estimated rating of self-interest = 2.62 + 0.35 * rating of knowledge
Good luck with your work.
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I plan to divide my long research article(simulation + mathematical) into two parts, but I am clueless about how to do this. (I can not separate the simulation and mathematical analysis)
I have a few questions regarding the same
1) Do I need to show the common mathematics in both parts?
2) Can the introduction be the same?
3) Can some explanations remain the same in both parts?
Can someone give me the reference of any article divided into two parts?
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Dear Amit Das,
See my comment precede by >>
I plan to divide my long research article(simulation + mathematical) into two parts, but I am clueless about how to do this. (I can not separate the simulation and mathematical analysis)
>> If the mathematical model is highly original and valuable by itself - you can publish it either separately or along with key simulation results. If the model is quite standard, just briefly refer to it and focus on simulation results. Either way, splitting it on two articles hardly makes sense.
I have a few questions regarding the same
1) Do I need to show the common mathematics in both parts?
2) Can the introduction be the same?
3) Can some explanations remain the same in both parts?
Can someone give me the reference of any article divided into two parts?
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Complex systems are becoming one of very useful tools in the description of observed natural phenomena across all scientific disciplines. You are welcomed to share with us hot topics from your own area of research.
Nowadays, no one can encompass all scientific disciplines. Hence, it would be useful to all of us to know hot topics from various scientific fields.
Discussion about various methods and approaches applied to describe emergent behavior, self-organization, self-repair, multiscale phenomena, and other phenomena observed in complex systems are highly encouraged.
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Jiří Kroc: Greetings Prof. Kroc. In neurology the cutting-edge research is on 1) neurodegeneration, 2) neuroprotection, 3) the unification/entanglement between the nervous system and the immune system and 4) disorders of consciousness. thanks, Mustafa.
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In my previous question I suggested using the Research Gate platform to launch large-scale spatio temporal comparative researches.
The following is the description of one of the problems of pressing importance for humanitarian and educational sectors.
For the last several decades there has been a gradual loss in quality of education on all its levels . We can observe that our universities are progressively turning into entertaining institutions, where students parties, musical and sport activities are valued higher than studying in a library or working on painstaking calculations.
In 1998 Vladimir Arnold (1937 – 2010), one of the greatest mathematicians of our times, in his article “Mathematical Innumeracy Scarier Than Inquisition Fires” (newspaper “Izvestia”, Moscow) stated that the power players didn’t need all the people to be able to think and analyze, only “cogs in machines,” serving their interests and business processes. He also wrote that American students didn’t know how to sum up simple fractions. Most of them sum up numerator and denominators of one simple fraction with the ones of the other, i.e. as they did it, 1/2+ 1/3 according to their understand is equal to 2/5 . Vladimir Arnold pointed out that with this kind of education, students can’t think, prove and reason – they are easy to turn into a crowd, to be easily manipulated by cunning politicians because they don’t usually understand causes and effects of political acts. I would add, for myself, that this process is quite understandable and expected because computers, internet and consumer society lifestyle (with its continuous rush for more and newer commodities we are induced to regard as a healthy behavior) have wiped off young people’s skills in elementary logic and eagerness to study hard. And this is exactly what the consumer economics and its bosses, the owners of international businesses and local magnates, need.
I recall a funny incident that happened in Kharkov (Ukraine). One Biology student was asked what “two squared” was. He answered that it was the number 2 inscribed into a square.
The level and the scale of education and intellectual decline described can be easily measured with the help of the Research Gate platform. It could be appropriate to test students’ logic abilities, instead of guess-the-answer tests which have taken over all the universities within the framework of Bologna Process which victorious march on the territories of former Soviet states. Many people can remember the fact that Soviet education system was one of the best in the world. I have therefore suggested the following tests:
1. In a Nikolai Bogdanov-Belsky (1868-1945) painting “Oral accounting at Rachinsky's People's school”(1895) one could see boys in a village school at a mental arithmetic lesson. Their teacher, Sergei Rachinsky (1833-1902), the school headmaster and also a professor at the Moscow University in the 1860s, offered the children the following exercise to do a mental calculation (http://commons.wikimedia.org/wiki/File:BogdanovBelsky_UstnySchet.jpg?uselang=ru):
(10 х 10 + 11 х 11 + 12 х 12 + 13 х 13 + 14 х 14) / 365 = ?
(there is no provision here on Research Gate to write square of the numbers,thats why I have writen through multiplication of the numbers )
19th century peasant children with basted shoes (“lapti”) were able to solve such task mentally. This year, in September, this very exercise was given to the senior high school pupils and the first year students of a university with major in Physics and Technology in Kyiv (the capital of Ukraine) and no one could solve it.
2. Exercise of a famous mathematician Johann Carl Friedrich Gauss (1777–1855): to calculate mentally the sum of the first one hundred positive integers:
1+2+3+4+…+100 = ?
3. Albrecht Dürer’s (1471-1528) magic square (http://en.wikipedia.org/wiki/Magic_square)
The German Renaissance painter was amazed by the mathematical properties of the magic square, which were described in Europe firstly in Spanish (the 1280s) and Italian (14th century) manuscripts. He used the image of the square as a detail for in his Melancholia I painting , which was drawn in 1514, and included the numbers 15 and 14 in his magic square:
16 3 2 13
5 10 11 8
9 6 7 12
4 15 14 1
Ask your students to find regularities in this magic square. In case this exercise seems hard, you can offer them Lo Shu (2200 BC) square, a simpler variant of magic square of the third order (minimal non-trivial case):
4 9 2
3 5 7
8 1 6
4. Summing up of simple fractions.
According to Vladimir Arnold’s popular articles, in the era of computers and Internet, this test becomes an absolute obstacle for more and more students all over the world. Any exercises of the following type will be appropriate at this part:
3/7 + 7/3 = ? and 5/6 + 7/15=?
I think these four tests will be enough. All of them are for logical skills, unlike the tests created under Bologna Process.
Dear colleagues, professors and teachers,
You can offer these tasks to the students at your colleges and universities and share the results here, at the Research Gate platform, so that we all can see the landscape of the wretchedness and misery resulted from neoliberal economics and globalization.
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Mathematics is a language of all science subjects
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"The book of nature is written in the language of mathematics."
Galileo Galilei
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I am looking for papers that provide explanation analytically as well as mathematically
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see the following paper
@article{DBLP:journals/corr/abs-2010-11929, author = {Alexey Dosovitskiy and Lucas Beyer and Alexander Kolesnikov and Dirk Weissenborn and Xiaohua Zhai and Thomas Unterthiner and Mostafa Dehghani and Matthias Minderer and Georg Heigold and Sylvain Gelly and Jakob Uszkoreit and Neil Houlsby}, title = {An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale}, journal = {CoRR}, volume = {abs/2010.11929}, year = {2020}, url = {https://arxiv.org/abs/2010.11929}, eprinttype = {arXiv}, eprint = {2010.11929}, timestamp = {Fri, 20 Nov 2020 14:04:05 +0100}, biburl = {https://dblp.org/rec/journals/corr/abs-2010-11929.bib}, bibsource = {dblp computer science bibliography, https://dblp.org} }
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There are any papers or studies about the Blended Learning in Mathematics, exactly in (Calculus) ?
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The above article is very interesting and it strengthens my conclusions that this problem has been around with up for a long time - at least back to the early 1970''s when I first had experience observing new college students as a TA in grad school. I've taught off and on since the 1960's undergraduate and graduate level courses to both "math majors" and science and engineering majors. My observations were formed originally the early 1970's as the trend of more students taking calculus in high school were less prepared in the mathematical fundamentals and there was a gap in their preparation that showed up at the freshman college level. A teacher in calculus should not have to stop his/her lecture and go over the principle of mathematical induction or the basic analytic geometry of a conic section in freshman calculus. But alas - that was the case. In multidimensional calculus, the students should come in with a firm understanding of linear algebra. However, in my experience that was not always the case. That is the students had holes in their preparations and at some point those holes had to be filled or eventually they would hit a brick wall.
Calculus introduces new and sometimes difficult concepts and the students tend to have little intuition of the concepts of continuity and limits. But without developing a firm understanding and intuition of these and related topological concepts - it is difficult to grasp the calculus. If one does not have the background and facility of understand the fundamental tools of symbolic manipulation (a necessity to do all mathematics), understanding of basic geometry, the basic knowledge of set theory, mathematical induction and logic, it becomes a game of memorization and mechanics. Over time this lack of preparation in the fundamentals has grown more not less prevalent. This lack of preparations is reflected today in that many calculus sequences at the college level include analytic geometry. At one college I have taught specific courses over time, University of South Florida, there is now a required course known as "Bride to Abstract Mathematics." It is a course in logic, construction of proofs, set theory , relations and functions. That is the basic foundations that were once taught in high schools in the US but gave way with the push to present calculus in high school.
I expect we are seeing the same issues arise as subjects like abstract algebra and algebraic geometry become more and more important in applications like computer vision and robotics. It is difficult to apply mathematics to a field when ones understanding of the underlying mathematics has gaps.
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Philosophers of science typically recognize two kinds of values in scientific practice: (1) epistemic (or theoretical, or cognitive) virtues, like accuracy, testability, empirical support, etc, and (2) ethical (or social, or regulative) norms, like justice, egalitarianism, openness, etc. Of course, the strict separation of these categories is open to disagreement.
Are there values or norms (of either kind) that are unique to mathematics? Rigour (or provability) is one possibility; computability is another. Can you think of others? Do values play the same kind of role in math as in the natural sciences?
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Elegance and parsimony are mathematical virtues. They seem to be aesthetic, rather than ethical or straightforwardly epistemic. However, aesthetics can be an aid to cognition.
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Hi all,
There are instructions on the steps of running ‘align’ in a command-line way as shown in the following explanation found online (https://pymol.org/dokuwiki/doku.php?id=command:align). However, I didn’t found the mathematics or details for PyMOL running ‘align’ through the click-button way in GUI interface. Anyone know the mathematics or details behind it? Thanks a lot!
Yaohui
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"In short, “align” is a automated multi-step superposition algorithm based on dynamic programming and iterative refinement. “align” first performs a per-residue global dynamic-programming sequence alignment for the input atom selections using the BLOSUM62 weightings from BLAST. Then, a per-atom correspondance is established between atoms in the selections. Matching side chains atoms will be included if they were provided in the selection arguments. An initial superposition is then performed followed by up to five cycles of iterative refinement wherein atoms with per-atom deviations over two standard deviations from the mean deviation (if any) are thrown out and the fit is repeated. Finally, the number of atoms remaining at the end of this procedure is printed out along with the resulting RMS value for those atoms."
Pymol offers different alignment methods, which are optimised for different levels of sequence similarity:
Basically, "align" https://pymolwiki.org/index.php/Align does a sequence based structural alignment, first doing a sequence alignment to decide which Calpha atoms to perform a 3D alignment on, then iteratively removing very poorly 3D-fitting atoms from the alignment to reduce the influence of structurally variable loops on the alignment.
In contrast "super" https://pymolwiki.org/index.php/Super aligns two selections by a sequence-independent (unlike align) structure-based dynamic programming alignment followed by a series of refinement cycles intended to improve the fit by eliminating pairing with high relative variability (just like align).super is more robust than align for proteins with low sequence similarity.
"cealign" https://pymolwiki.org/index.php/Cealign aligns two proteins using the CE algorithm. It is very robust for proteins with little to no sequence similarity (twilight zone). For proteins with decent structural similarity, the super command is preferred and with decent sequence similarity, the align command is preferred, because these commands are much faster than cealign.
Each of the commands offers a number of parameters to tweak the method, e.g. setting limits to the maximal gap length and specifying the number of iteration cycles
You can also extend the PyMol capabilities using the "TMalign" module https://pymolwiki.org/index.php/TMalign
To do superpositions between exactly defined atom sets (e.g. in ligands), use "fit" https://pymolwiki.org/index.php/Fit or "pair_fit" https://pymolwiki.org/index.php/Pair_fit
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How can you advise on the methods of mathematical prediction of the causes of salinity?
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thank you
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One of my research questions is about the level of democratic practices in the mathematics high school classroom. When examining the normality of the the demoratic practices, it turned out that they are not normal. In normal samples, we use one-sample t-tests with critical values that fit our assumptions of the level of the democratic practice. For example if we want to take into consideration three levels, we divide (5-1)/3=1.33. This enables us to consider what is below the grade 2.33 weak, what is between 2.33 and 3.66 midium, and what is abover 3.66 high. This serves us in doing the one-sample t-test, where the critical value is 2.33 or 3.66 to verify the level of the variable.
My question is: How can we do that in case of non-normal distribution?
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I really thank all of you for your valuable comments. I attach an article in which to find the significance of the level of democratic practices, we used one sample t-test. My question was about what we do if the data does not follow normal distribution.
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I would like to know the effect of temperature and pressure on the density of Fe2O3 nanoparticles, and if there are some tables or equations that describe the change mathematically.
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It is very hard to have a unique mathematical expression that will described changes in density x temperature of treatment. It will strongly depends on your synthetical route of the samples, the crystal structure, porosity, and so on.
Normally, increasing the temperature and pressure you will see the densification of the nanoparticles. However, you can see a phase transition that changes the density of the system, so it is not a straightforward analysis. I recommend you to synthesize several NP at a varied range of temperature, then perform porosity/density measurements employing helium pycnometer.
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Combining more than one higher quality has less quality. So how do we express this mathematically? E.g; Let 2x'2 - 4x'2 +6x'2. If it is noticed, one of them has 1 term and the other has 2 terms. So what do we get from here? it looks like 4x'2 =8x 6x'2=12 x sums will be 20x when the derivative is taken. However, if we take their exponent without the differentiation, it will be 4x'2 =16 6x'2 =36. So when more than one higher attribute comes together, it only has less attributes when deriving. THIS IS ANOTHER DEFINITION OF THE DERIVATIVE. THANK YOU. I didn't actually get this out of the way. THERE WAS A LOT OF STARS IN THE PARIS SAINT GERMAIN FOOTBALL TEAM; HOWEVER, WHEN PLAYING TOGETHER, MANY QUALITIES TURNED INTO FEW QUALITIES. THANKS.
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Maybe you have not captured all of the relevant qualities. Best wishes David Booth
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How can all these discrepancies be explained mathematically?
I am working with a scale that could be considered to have 11 dichotomous (0-1) and polytomous (0-2, 0-3, and 0-5) items OR 20 sub-items (dichotomous and some polytomous). The sample size is sound (> 700 subjects).
A) If I do an exploratory analysis* with 11 items on half of the (randomized) sample, I get 2 factors. The confirmatory analysis** with the other half confirms the two factors, presenting good adequacy indices values. Some authors also obtained 2 factors, either with similar or different methodology (including item-theory analyses).
B) Moreover, I also tested unidimensionality as some found only 1 factor. Again, all indices are adequate (ECVI slightly higher).
C) However, if I do an exploratory analysis* with the 20 sub-items (similarly to other authors), I get 4 factors. Additionally, just out of curiosity, in the total sample, I get 5 factors!
E) There have also been 3, 4, and 5-factor solutions in the literature, either with 11, 20, or 30 sub-items (all dichotomous).
* Unrotated EFA; maximum likelihood extraction; eigenvalues > 1; based on tetrachoric correlation matrix followed by an oblique rotation (promax).
** CFA with the Diagonally Weighted Least Squares method.
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I don't quite understand why the same scale would have 11 or 20 items, but it is not surprising to me that with more items, you could "find" more factors. With more items, there is more room for additional factors (e.g., specific or method factors) to be measured and identified. The more items you use, the more likely it is that some of them will reflect something that is at least slightly different or "unique" relative to the other items. Likewise, with a larger sample size, you have more power to reject models with fewer factors.
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Basically, I am from a Mathematics background. I found interesting to read ANN but I don't have proper knowledge of ANN, especially in the calculation part. Can anyone help me or suggest me a book considering my situation. Thank you.
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If your background is Mathematics the attached "PNN Primer.pdf" may be useful.
For numerical practice download the NNB DEMO software package (only for Windows), unzip and run. It comes with bundled documentation.
In no time you will be handling neural networks numerically.
This is the link to NNB DEMO, which expires on Thursday May 5, 2022.
Please tell if NNB DEMO fits your expectations.
Best regards
Daniel Crespin
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Dear talented researchers,
I want to calculate three solar irradiance components (DNI, DHI, & GHI) from these equations which contain logistics, maximum and minimum, Less than, Greater or equal, terms.
How can I use these equations please? I don not know how to use equations 12 & 13 because they have terms such as max, min.
I am not sure, but it seems to be a Logistic map.
1- just for example, how to solve this part from equation 12?
min (1:88 * 10^-8 CO^4, SOLZEN < 77)
2-how to deal with these mathematical operation such as greater than, less than 77, equal or greater than inside these equations?
Thank you very much for your kind response.
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Dear Zhwan
I have been thinking in your problem and I b elieve that the logistic part that bothers you could have the following explanation:
Logistics refers to a curve normally known as a sigmoid (very similar to the letter S,) but with right horizontal lines at both extremes, instead fo the curls, and very used in many disciplines, most especially in Artificial Intelligence, and normally varies between -x and x. It is defined as tanh and equal to the ratio between sinh and cosh.
In my opinion, for your geographical position, you should compute the ratio solzen and solalt , and then multiply it by CO^2, which meaning I don’t remember.
Because the sigmoid, and think that we can safetly take a value of 0.5, since it is the average of the linear part of the curve.
Multiplying 0.5 by CO^2 this product MUST be < 77.
Just tu represent that in MCDM is my problem
Therefore, I would appreciate it if you can give me the following values:
CO
CO^4
SOLZEN
SOLALT
1/SOLZEN tan^2
I believe that with this data I could be able to solve the problem using SIMUS.
I agree with your efforts to use algebra and trigonometry, but how are you going to express the < relationships?
Anyway, let me know if you agree with my suggestion, and if you do, give me the values I request.
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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 ?
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The Abel prize is a new mathematics prize of the Norwegian Academy of Science and Letters, dedicated to the memory of Niels Henrik Abel (1802-1829) on the occasion of the bicentenary of his birth. It is modeled after the Nobel Prize, and developed from a proposal by the mathematics department at the University of Oslo in fulfillment of a request formulated by the Norwegian mathematician Sophus Lie towards the end of the 19th century.
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AbelPrize.html
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Pls can someone assist me with details on how to calculate effective dose mathematically using exposure parameters such mAs, kV, FFD in x-ray examination
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suppose that A and B are two entities. And arrival of B depends on the state of A. The arrival of A is known and can be expressed in mathematical conditions but B can not be as it depends on A. The arrival of entity depends on when A gets processed (Lets say the process is Process 1 with a triangular func of (5,6,7) mins). Whenever A starts to get processed, B is created. I have been able to create the first creation of B logically which relates to A but, I am not sure how to provide the logic for "Time Between Arrival". 
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I stuck with this kind of problem. However i want to solve this. I have two types of entities, yet rather than use 2 create modules, these two types of entities are created using 1 create module and then I use assign module to ensure they are different entities. How to ensure that a sum of entities are necessary to be processed and dispose from the system before another sum of entities proceed with different process? Both types of entities will be processed using different processes.What condition can be used in decide module to allow this event?