Science topics: Mathematics
Science topic

# Mathematics - Science topic

Mathematics, Pure and Applied Math
Questions related to Mathematics
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Mathematical concepts, being abstract in nature, could be simplify if one can find concrete substitute. Hence there is need to define mental prototype of shapes and their possible impact on Students' performance in geometry or mathematics in general.
Dr. Juan Weisz, that's very useful. Could you elaborate more on the game. The psychological aspect of it to be specific. Thank you.
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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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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.
I am not in this area. Please remove me from you 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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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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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"
It seem like, only few studies are talking about problem-solving skills, especially in Africa. Busy trying to find more articles but its hectic.
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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?
@Anton: Thanks for sharing your comment with me. To round e using exp to say 3 digits we would type round(exp(1),3). Instead if e is defined in MATLAB by en, say, then we would type round(en,3). The former requires two function calls while the latter would require only one call. In terms of speed, the latter is reasonably faster.
@Colin: Good point. That’s why I suggest to define e as a constant instead. In most common floating-point systems, one typically use double-precision floating point representations; thus working with about 16 significant digits—with the last digit being a random junk digit in certain computations. So, defining e by this finite range of digits is very practical.
@Emad: Salam Alaikom my deer friend, colleague, and one of my favorite teachers who ever taught me. I feel so delighted that you shared your comment here in this forum. You have a point indeed that this would be a kind of redundancy. But it remains important to ask: why should we evaluate exp at x=1 when e is a very known value? In almost all algorithms I developed in my career so far, I frequently use constant parameter inputs defined as double-precision numbers, i.e. are represented by 16 significant digits. In double-precision floating-point systems, this is typically the case. So why should we ask MATLAB to compute exp at x=1 when we can use its 16 significant digits representation instead. This would be faster and computationally more efficient. How about other important constants like the golden ratio which does not occur redundant with other functions? Why should we calculate them when their values are very known values? One of the reasons MATLAB Developers are proud of is that they have a huge library of functions that can help programmers and users to do certain tasks with minimal programming efforts, but they fail to have even a decent library for important mathematical constants. If they define these constants, we could use them directly in our works without having to calculate them using other functions or formulas. To calculate an expression like sin(exp(1)*x)+3*exp(1), why should we ask MATLAB to calculate the exponential function twice at x=1, when we could easily define exp(1) as a constant, say en, and type sin(en*x)+3*en; this would be faster and computationally cost effective indeed. Of course, if one needs more accuracy than 15 or 16 significant digits, we can then ask MATLAB to evaluate the exp function at x=1. But I, as a computational mathematician, never used more than 16 significant digits in all my previous works except when I wanted to compare my approximations with the exact values of the solution—I typically prefer to use MATHEMATICA in this case. Once again I thank you for sharing your smart comment with us. Stay safe my dear teacher.
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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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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?
Many thanks for engaging with my question and for the links. John Mendy raises an uninteresting idea about contextualising COVID-19 reports so that they tie the science and mathematics to a much more human level of reporting that might help the public connect with the stories rather than switching off from too much technical reporting that doesn't seem to involve real people.
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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.
Question
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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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 Question 68 answers 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). Relevant answer Please see this paper: Question 91 answers 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 Relevant answer This link talked about the importance of Math: Question 952 answers 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!! Relevant answer Answer They can describe surface roughness of materials Mandelbrot Question 28 answers 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. Relevant answer Answer "factor analysis" is the phrase often used when both the observed and latent variables are assumed interval (or metric). It is part of the general latent variable model, and when the observed variables are binary this is usually called item response theory (IRT) or latent trait modeling. So it you are wanting latent variable models with binary observed data see the package I suggested above, mirt. Question 8 answers 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? Relevant answer Answer Please see this useful link: Question 96 answers 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. Relevant answer Answer I'm not sure why there's any discussion here. The equation of a straight line is y = mx + c. This is an inviolate mathematical formula. The equation itself justifies nothing - it's perfect. Data sets are fitted with an appropriate model which in the case of a linear fit is usually a least squares procedure. The equation itself tells you nothing about the data going into that best fitting procedure. The 'goodness' of the model is assessed by deviations from that model. Here correlation coefficients (e.g. R2) can be employed. So, the equation on its own tells you nothing about whether that model is appropriate or not. How close theory and practice are, however, tells you something about the appropriateness of the model. Be careful with 2 things: • Inappropriate correlations. This is where an understanding of the basis of the model is so important. I've shown a couple above • Over-complicating the situation. n points on a p;lot can be fitted perfectly by an equation of (n - 1)th degree. This definitely does not mean that the more complicated model explains more. On the contrary, it's basically an empirical fitting... Question 51 answers I want to construct a model for the world COVID-19 data Relevant answer Answer I think, systems dynamics and regression models. Question 68 answers Dear Colleagues, I have written a paper but when I checked the plagiarism I found most of the equations are plagiarised. Please tell me the way how to remove these plagiarism from equations. Thank you in advance. Regards, Ramashis Banerjee. Relevant answer Answer I agree with Hamed Majidian : Results that are textbook knowledge do not necessarily require a reference. And in most cases a reference to the original source would be useless unless you really used that original. Typically, I'd cite rather a comprehensive textbook. Please be aware: Citations serve two purposes: 1. Give credit to whom it deserves - in case of the gravitation law, nobody would guess you found it, even in case there is no reference at all. And good old Newton also don't need a push of his H-index. 2. Give readers the chance to find and check your sources. Again, for textbook knowledge the reader may find it on his own. In practice, you may still give a suitable reference, in particular for less common established results. Question 20 answers Review Article in spoecific, Research area Potential Theory Relevant answer Answer I don’t think Scopus advertises the magazines in its database. I have another question Is the list of journals covering the math direction to the scopus database for 2020 approved? Question 10 answers As a founder of making dialectical logic mathematically, author has constructed a mathematical expression for dialectical logic, and proofed the formal logic is only a special case in dialectical logic, see preprint titiled "mathematical foundation for dialectical logic" in my profile, then do you admit author's viewpoints in this field? Relevant answer Answer To Salah Mehdi Salih, Thanks for reply! Question 18 answers PhotoMath is a new application for solving math problems by capturing their images. Do you think it will be also useful for solving math proofs? What do you think? Relevant answer Answer Victor Christianto , Nice Topic. Question 8 answers Generally QSR is considered as the parameter for location based service. End-to-end delay, number of hops etc. are the parameters for routing. Why combination of routing and location service enhances the performances of the parameters? Relevant answer Answer Following. Question 35 answers There is a contradiction between the natural width of the energy transition, which is determined by the lifetime at the corresponding energy level and the spectral line width of the radiation line, which is determined by the duration of the wave train. For example: For the Mössbauer transition, whose lifetime is of the order of 2 years, while the interaction time at the receiving end is about 10^(-10) sec. Mathematically, this interaction is expressed by the Feynman diagram of the electron - electron interaction, which integrates over the internal photon line, which, together with the delta functions of the vertex parts, limits the photon spectrum. By the way, the same paradox applies to any other type of collision. So, is exist (really) the electromagnetic field? Relevant answer Answer Paradox is in the contradiction between narrow energetic widths of transmitter and receiver, because of long decay times, and wide spectral width of wave packet, because of short interaction time. As a possible explanation it can be the consideration the process as a virtual, which expressed the Feynman diagram. Question 16 answers Hi everyone! Greetings from Munich! It appears in my mediation analysis, that X is negatively related to M, and M is positively related to Y. Also, i find a significant negative effect of X on Y through M. But since M is determined as a perceived benefit, i am currently struggling with the interpretation of this indirect effect. Mathematically, of course, this indirect effect result makes sense since "- x + = -", but can i interpret this by saying the benefit is overridden or is it rather that the benefit "backfires" on Y and thus a negative indirect is found? Many thanks in advance! Relevant answer Answer Nice Dear Nik Smidt Question 15 answers a transport model (e.g logit model or ...) is based on statistical data and field works or merely based on mathematical theories or both of them? If I want to define a model ( e.g. a new model in freight transportation ), what actions should I do? what kinds of data should I gather? Relevant answer Answer Obviously you need to define in detail which parts of the enormous system, that we may call "the logistics network." What do you want to capture with your model? Also: before you start something new, do you know what parts of this enormous system you would like to provide a model for? You will definitely need to scale down from the global chains of transport and logistics - so what parts are you interested in? What is the purpose of this exercise? Could you, for example, start by reading the recent years of logistics networks papers, so that you can see what the models need, in terms of data, for example? Do you want to collaborate with a logistics partner, in order to obtain real data? There are lots of questions to be answered, as what model you end up with will determine what questions will be possible to answer. This is not a five-minute exercise, but a PhD project, perhaps with actual partners from logistics. Question 20 answers I am trying to justify the use of AT instead of UTAUT for my paper on teacher challenges faced when using technology to teach mathematics... Relevant answer Answer Nice Topic , Following Question 225 answers While many modern causal models do not seem to adhere to Laplace's demon (strict determinism) which treated error factors as merely unknown causes, they do not also always address the issue of freedom and responsibility sufficiently. While it is acknowledged that the human element (as far as intervention) is concerned might involve an exogenous factor (perhaps, "transcendent cause" in neoplatonic terms), posing problem to the equilibrium of an otherwise deterministic system, the models themselves might seem relevant for systems that are independent of human intervention, e.g. artificial intelligence. But, that evokes ethical questions, especially regarding whether formalism of such models can totally ignore the question of responsibility or should they really be resolving them. In more practical terms, can such a machine be constructed based on a causal model that can correctly predict and make right moral decisions for humans? Relevant answer Answer Mathematical models will never simulate human behavior precisely. Different models show different results. So, if some model provides some precise conclusions about some community, it is not necessarily the same for the others. People's insights, morals, freedom, and responsibility are very complicated to be captured and recorded in exact equations or tables. Some approximated partial results are accepted for making decisions about some phenomenon. Question 60 answers To me it is mostly a story. There is, at the outset, a puzzle about some natural phenomena, perhaps encountered by inadvertence. Then some other process exhibits a similar pattern. The question becomes is there some reason, perhaps based on the thermodynamics of the two systems, that connects them? This takes the curious inquirer into a conceptual forest, or overgrown garden, path obscured, looking for a common principle. When a principle is discerned, there are more questions. Does the pattern appear elsewhere? Is there a more fundamental principle underlying the first principle discerned? Does a principle, even more fundamental, connect all the different phenomena sharing a kind of pattern? Does the same pattern appear but in subtle ways in other phenomena? Can the phenomena be modeled? What assumptions are extraneous to arriving a model in common? What is the set of minimal assumptions? Many more paths and tangles appear. Can the winding path so obscure at the outset be reduced to a set of logical statements that resemble in their appearance mathematical deduction? Never finally, but at least provisionally? But first, there is a story. How do you regard physics? Relevant answer Answer Robert Shour, No truer words were ever spoken. I am somewhat reminded me of the "Two Cultures of Mathematics" discussions that went on in the wee hours between mathematics graduate students. That is the "problem solvers" vs. the "theory builders." Some subjects lend themselves to problem solvers, say analytic number theory which requires everything including the kitchen sink to be thrown at it and on the other hand algebraic number theory which has volumes theory laid as foundations. Paul Endros was maybe the King of the Problem Solvers and Michael Atiyah the King of the Theory Builders. Of course most mathematicians are somewhere between and broad theories all start out addressing a problem - often with long historical roots. Which category a mathematician falls in is more a matter of temperament and personality than a choice and most mathematicians most likely move between the two. There are those that focus on a problem and during that focus understand what assumptions can be loosen so that the solution is not just of a specific problem but a theory for a much larger category of problems. Often times one sets out to develop a theory - hoping to apply it to a larger category of problems just to find the assumptions required in the theory are not satisfied by the candidate problems one is trying to address. This happened in the 1960's in what was termed global analysis where problems in the calculus of variations were to be viewed as critical points of functions on infinite dimensional manifolds - with a broad robust calculus developed to apply to this critical point theory similar to Morse theory for function on finite dimensional space to variational prolems. Smale's condition C, now know as the Palais- Smale compactness condition was required for the functional calculus. After this beautiful theory was developed, it turns out that most of the classic problems in calculus of variations do not satisfy condition C. The utility envisioned for this theory - did not fully materialize. While those that focus on expanding the tools of theoretical physics often find that they make progress by starting with examples (specific problems) and exploring the commonality. For me the solution of the problem (or a category of similar problems) is the key and I lose interest in working to expand the conditions under which the results still hold. As Gauss says once a problem has been wrestled to the ground and tamed, time to move on the the next challenge. But as you say that is a matter of temperament. As far the theoretical physicists it is often - their vision needs quite a bit of help wrapping mathematical rigor around it. For example without Maurice Grossman, Einstein would not have able to present his theory of general relativity in a coherent and simple mathematical way. Without Roger Penrose, Steven Hawkins would have suffered in his understanding and explaining of black holes, singularities, big bang, etc., in a robust way. In fact on Hawkins' thesis defense, Penrose noted Hawkins' sloppy mathematics. After that the two started working together. It took Stone and von Neumann and later Segal and Bargmann to put quantum mechanics and quantum field theory as envisioned by Dirac, Pauli, Feynman, etc. on a firm robust mathematical footing that it enjoys today. So in reality I think theoretical physicists are more of the story tellers who often depend on others to fill in the details to make the story meaningful and to be able to stand up to experimental validation/falsification. Question 6 answers In the litterature about quantization schemes, people tend to use Weyl ordering a lot. Altough it enjoys some desirable properties like sending real functions into self-adjoint operators or sending Schwarz functions into trace class operators, we know that these features are not unique of Weyl ordering. Is there any deep reason (being mathematical of physical) to prefer Weyl ordered quantizers? Relevant answer Answer From a physical point of view, Weyl ordering provides a consistent procedure for quantizing polynomial Hamiltonians, but of course this is not enough to be preferred as a quantization method. From a mathematical point of view, its importance lies in the subsequent developments of Weyl's idea by Wigner and Moyal which, ultimately, led to the idea of star products and deformation quantization. It was proved by Kontsevich in the late 90s (in a work that gave him the Fields medal) that any Poisson manifold can be quantized following these ideas. You can see a somewhat cursory description of this line of reasoning in the introduction to a paper of mine: https://arxiv.org/pdf/1110.5700.pdf Question 30 answers Hi, I'm attempting to create nonlinear metamaterial structures in comsol and I don't know how to measure second harmonic generation. How do I measure that frequency x goes into structure and generates frequency 2x ? Thanks for any help. Relevant answer Answer Does this work? One fundamental problem I am facing how to see the frequency components (in ewfd physics, frequency-domain study) in COMSOL other than the excited one( mean by the mode at other frequencies). A very simple experiment if I take one 500nm width by 30 nm height Si waveguide (2d simulation), and excite it with 193.42 THz at port 1 end, now if I want to see the frequency components at 300 or 200 THz it should appear null or no field components. But how to observe it in COMSOL (the modes or the field components can be seen at 193.42 THz since it's the excited one). Question 24 answers Why many scientists use the term mathematical model ? If you have a certain phenomenon and you want to model it, you will describe its, more or less, approximate behaviour by applying to it laws which can be physical, chemical, economical, geometrical and so on, depending on the phenomenon. Mathematics is only a tool to describe these laws, so you should speak of physical, chemical, economical, geometrical ... models and not of mathematical ones. Most of the models I encounter in my research are physical models because, to build them up, the laws of physics are used. Each time I hear the term mathematical model, my nose gets wrinkled. What is your opinion ? Relevant answer Answer I agree with Abdulrahman Dahash Question 18 answers What is the mathematics behind r.viewshed module in GRASS GIS Relevant answer Answer Dear Mr.Thaisa Jawhly I sent you a guide that can help you, also this software is open as Mr Som Pal Singh said. Good luck. Question 40 answers I want to conduct a qualitative research about math teaching and learning at pandemic Covid-19 in several specific area in my country. But i don't have any idea to start because i'm not good in qualitative research. It's kindly opened for join research. Saya ingin melakukan penelitian kualitatif ttg KBM Matematika selama wabah Covid-19 di beberapa daerah di Indonesia. Tapi saya bingung dalam merancangnya krn minim pengalaman dalam penelitian kualitatif. Sangat terbuka untuk penelitian bersama. Relevant answer Answer Hi Please check the following work. It describes the process in details. I believe it will help you. Regards Question 36 answers Dear sir/madam! I'm a final semester student in BS Mathematics and my research interest is in Mathematical Biology. Would you like to provide me the best SEIQR ODEs model for stability and optimal control? I want to do stability and optimal control for our province's real data. So, please recommend the paper. Thank you so much. Relevant answer Question 36 answers Is there any alternative topic/theory/mathematical foundation to compressed sensing (CS) theory? successive to Nyquist Criterion is CS theory, is there any theory that surpasses the CS theory ? Relevant answer Answer Dear Vishwaraj B Manur, First of all, we should separate the concept of Sampling against the concept of Sensing. These two are not interchangeable! 1. Compressed Sensing theory states that it could recover a set of coefficients (which represents in a specific transform domain the useful information from the analyzed signal) from less samples than Nyquist sampling criteria in order to be able to reconstruct a signal (of course as it could be reconstructed from uniform samples by classical Shannon theory). 2. Compressive Sampling theory states that a signal can be sampled by a protocol (non-uniform sampling, random sampling, modulation and sampling, etc.) which will allow later to be reconstructed by means of a Compressed Sensing algorithm which knows about the used sampling protocol. 3. There are at least 4 sampling ways (according to Figure 2 from https://core.ac.uk/download/pdf/34645298.pdf ) to acquire the information from a signal. Take into account that practical CS is a lossy compression, and this is due to the non-ideal process which happens when the sampling process take place. Question 28 answers I want to create an animation to insert it in my math presentation (e.g. a ball hitting the wall, deforming and bouncing back: just an example). Is there any free and easy to use software (preferably, for Mac OS X) to do that? Which one is the best? I know how to create some animations in Matlab and Mathematica, but this is different: I don't want to code the whole scene as functions. Relevant answer Answer Manim by Grant Sanderson is the best one out there at the moment. Question 9 answers Mathematical about the work-related with graphene or any other type of films/coatings. Lubrication equations in solid films. Relevant answer Answer Have a look at Question 90 answers STEM fue el tema principal de la conferencia internacional ASTE 2019, con al menos 8 pósteres, 27 presentaciones orales y 3 talleres que promovieron las aulas STEM, la instrucción/enseñanza STEM, las lecciones STEM, los campamentos de verano STEM, los clubes STEM y las escuelas STEM sin proporcionar una conceptualización o definición operativa de lo que es STEM. Algunas presentaciones defendían la integración de las disciplinas, pero el ejemplo proporcionado fue principalmente prácticas "indagatorias" y de "diseño de ingeniería" que de hecho no diferían del tipo de actividades en el aula hands-on/minds-off mal conceptualizadas y epistemológicamente incongruentes. Por lo tanto, vale la pena considerar: (1) ¿Por qué lo llamamos STEM si no difiere de las prácticas aplicadas durante décadas (por ejemplo, indagación, actividades hands-on)? (2) ¿Qué beneficios (si los hubiere) puede aportar esta mentalidad/tendencia de STEMinificación a la educación científica y su investigación? Relevant answer Answer Radu Bogdan Toma, posiblemente lo decimos/dicen porque se ha convertido en un término "mainstream" que permite "vender el producto" con mucha mayor facilidad. Sospecho (y es más que una sospecha, de hecho) que este tipo de situaciones se dan con otros muchos otros constructos que se vuelven populares y son utilizados de una forma más o menos gratuíta para justificar algunos trabajos a pesar de que, realmente, no se haga uso esencial de ello. Question 6 answers I wish to shift multiple lines or curves (up to 25 lines/curves) so that they are superimposed on one another. This is to enable me see clearly the points or regions where any one of the curves deviate from the others. In this procedure I also want to be able to vary or determine the region or range of superimposition or overlay of the curves. What mathematical function or formulae can enable me do that? Relevant answer Answer The answer to this question can be given in different ways. Suppose the function is a linear function or a quadratic function? Question 64 answers I couldn't see any options to show complete axes of 3D plot in MATLAB software ? There is option to tick Box. But it doesn't covers top axes in Relevant answer Answer the best answer is set(gca,'box','on') but in this situation the you add axis. if you want to change the thickness of axis, therefore set(gca,'linewidth', 2) 2 can be change to an arbitrary thickness Question 9 answers Its a book related to biostatistics. Relevant answer Answer You can find it in Google Books. D. Booth Question 72 answers Call for Papers & Submissions The 9th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2020) will be held on August 25-28, 2020 in Skopje, North Macedonia. IECMSA-2020 will be organized in cooperation with International Balkan University. The annual International Eurasian Conference on Mathematical Sciences and Applications (IECMSA) series aim to promote, encourage, and bring together researchers in the different fields of Mathematics by providing a forum for the academic exchange of ideas and recent research works, The previous conferences were held as follows: IECMSA-2012, Prishtine, Kosovo, IECMSA-2013, Sarajevo, Bosnia and Herzegovina, IECMSA-2014, Vienna, Austria, IECMSA-2015, Athens, Greece, IECMSA-2016, Belgrade, Serbia, IECMSA-2017, Budapest, Hungary, IECMSA-2018, Kyiv, Ukraine, and IECMSA-2019, Baku, Azerbaijan. Website: www.iecmsa.org IMPORTANT DATES Deadline for Early Registration: May 22, 2020 Deadline for Hotel Reservation: May 22, 2020 Deadline for Registration: July 17, 2020 Deadline for Abstract Submission: July 17, 2020 Relevant answer Answer Thank you and good luck Question 182 answers The Riemann zeta function or Euler–Riemann zeta hypothesis is the more challenging and unsolved problem in mathematics. What's the applications in physics and science engineering ? Some research advances to solve it ? Relevant answer Answer The Zeta function is a very important function in mathematics. While it was not created by Riemann, it is named after him because he was able to prove an important relationship between its zeros and the distribution of the prime numbers. His result is critical to the proof of the prime number theorem. For more details see Question 735 answers I am interested in collaborating with any researcher working on modelling corona virus using fractional derivatives. If you are a researcher or you have a related project, please feel free to let me know if you need someone to collaborate with you on this research study. If you know someone else working on this research project, please share my collaboration interest with him.her. I would be very happy to collaborate on this research project with other researchers worldwide. Relevant answer Answer Yes, I am working on such modelling for the COVID-19, and I am ready to cooperate with you in this hot topic. Regards, Emad Question 45 answers 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? Relevant answer Answer Most HEIs will have Language test and an associated test i.e. ELTs. But what is needed is a portfolio of evidence or entrance exam or written and oral tests or a combination of all three. I also know of "bridging weeks" where all tests, up skilling etc are completed as part of a pre-registration induction week Question 50 answers Hi everyone, I currently use MCS method to analyze effect of some uncertain parameters on electrical power system and run 10,000 simulations to calculate the output which approximately takes around 1 hour. I recently read some methods which can reduce the MCS scenarios thus, resulting in low computational time. So, can our fellow researchers elaborate more on this topic or suggest me any other techniques which has the potential to significantly reduce the computational time of MCS (say around 5 minutes for my work) with reasonable accuracy? Cheers Sam Relevant answer Answer It depends on what is your application of Monte Carlo simulation. You could have different computational time reduction strategy. But generally speaking, to have a good sampling technique will make your Monte Carlo simulation much easier and more efficient. I would suggest the Latin hypercube sampling (LHS) sampling technique, which I used quite often. It will make the distribution of your samples very close to the expected distribution with small number of sample generation. Question 24 answers Can someone explain and give me a precise mathematical definition of what "variance" means in terms of principal component analysis (PCA)? Relevant answer Answer I suggest you check the following link. Hope it may be helpful. https://stats.stackexchange.com/questions/22569/pca-and-proportion-of-variance-explained Question 54 answers I have been looking at different types of inductive teaching for mathematics. These include inquiry-based, discovery, problem-based, project-based, case-based, just-in-time, and a hybrid of project and problem-based. Is there an inductive teaching approach or curriculum that uses everyday topics and students learn the mathematics needed to understand different pieces of it? For example, a class is discussing gardening. So the students learn how to calculate area of their garden. Then they look at mixture problems (fertilizer and soil). Then they see how Fibonacci plays into petals and seed patterns. It doesn't quite fit one of the inductive teachings exactly. I think it is a combination of several. Who has done research on this? Who/what should I be looking for? Relevant answer Answer Views differed on induction, so there are those who place it within the direct approach, and there are those who place it within the types of discovery, according to the role of both the teacher and the learner. For you, you can look for a discovery-based induction or a combination of several types of discovery. Question 20 answers I need a book, chapter or something like that which discusses PV inverters. It explains Mathematical relationships and finally Simulates it. Relevant answer Answer Dear Soroush, Refer the following link and files that helpful for you about PV systems using PSCAD. Question 15 answers When we derive the formula for length contraction, we use the direct Lorentz transformation. But for solving the formula for time dilation, we use the inverse transformation. Why is that so? Relevant answer Answer SRT is completely erroneous since it is based on the wrong kind of transformations: they have lost the scale factor characterizing the Doppler effect. First, Lorentz considered a more general form of transformations (with a scale factor), but then he, and also Poincare and Einstein equated it 1 without proper grounds. Their form was artificially narrowed, the formulas became incorrect. This led to a logical contradiction of the theory, to unsolvable paradoxes. Accordingly, GRT is also incorrect. For more details, see my brochure "Memoir on the Theory of Relativity and Unified Field Theory" (2000): http://vixra.org/abs/1802.0136 Question 12 answers How can I get an endorsement for my mathematical archive in the arXiv website? Relevant answer Answer Question 25 answers I am currently for maths project creating a card game that focusses to improve subitizing for students' age between 6-9 years old. I now want to create the 'best' colors for the game but I am looking for research that shows the effect of colors toward children. If you could help me or link me to research I'd highly appreciate it. Relevant answer Answer make them happy or sad Question 18 answers Hello, I'm currently working on a Structural Health monitoring approach for the foundations of an offshore wind turbine based on its resonance frequencies. On the basis of a large dataset that recovers measurements of several independent variables , I have already established a linear model in order to predict the target (here, the resonance frequency). I performed a Dominance analysis, Regressions, Features selection etc., in order to evaluate which features influences my target the most. However, I would like to improve the accuracy of my linear model by adding more features to my dataset (and then select the best features to build the most suitable model.), i.e. identify underlying mathematical expression (non-linear) between the independent variables and the target. I already performed Genetic Programming (GP) with symbolic regression (SymbolicRegressor) but didn't get consistent results. Is there a method by which I could get these underlying (non-linear) mathematical relationships ? Thanks a lot, Lolo_jr Relevant answer Answer Question 15 answers Can you help me interpret the result of of the ATMI different factors..how can i interpret it as how low, moderate, or very high the result is of the factors. Relevant answer Answer Question 9 answers I need this article : Chen-Ricci inequality for submanifolds of contact metric manifolds because I am interest in inequality of Sasakian manifold. Author: Mukut Mani Tripathi Date: Annual 2008 From: Journal of Advanced Mathematical Studies(Vol. 1, Issue 1-2) Publisher: Fair Partners Team for the Promotion of Science Relevant answer Answer Here is the paper, download from above link: Question 30 answers Dear ResaerchGate Members, I would like to check the observability and controlability of a system that has 200 states. When I use the conventional method ofobservability based rank, the Matrix of A^(n-1) (A^199 , where A has 200x200 arrays) will have the array of infinity. I would be thankful to have your recommendations? Best regards, Reza #Observability ; #Controlability ; #Control Relevant answer Answer Dear all, thank you very much for your answers and help. Question 6 answers My institution(where I work), Accra Institute of Technology(AIT) is switching to Open-Book Exams Questions for our mid-sem exams. A little challenge is with the applied mathematics courses and how the students will submit their responses in MS Word format. Hence this inquiry. Attached is a sample question. Relevant answer Answer I would suggest to your administration that this is a poor idea for mathematical and chemical courses at least. In these one size does not fit all. Best, D. Booth Question 30 answers Movement in musical scores does not have an equation of motion or a calculus of variations. Is there any other kind of harmonic motion that does not obey Newtonian law? Of course, frequency is velocity-like but I do not see this in the literature. I understand that the force field may be uniform so dF = 0, but is it not true there must be a force if movement occurs. Relevant answer Answer Mechanics. Newton's first axiom says that, in the absence of an external force, a body either is at rest or moves with constant velocity. In fact, this is a statement opposing Aristotle's view that a force is needed to keep a body in motion at any non-zero velocity. Other than that trivial movment in the absence of a force, one might argue that quantum mechanical zero-point motion is movement without a force. So there are several places outside music where movement appears without a force. In fact, I doubt the applicability of the same notion of movement as in physics to the "flow of notes". Movement in music is a different concept from that of movement in physics. The same word has different connotations in different fields. I believe, it would be easy to argue that with a similar change of meaning to the word force, you would find that the "flow of notes" does not happen without a force. There is a tendency of confusing and therefore (often unintentionally) abusing notions having the same name but meaning different things in different contexts. For example, when people speak about energy they gain by meditation, this has nothing to do with an energy that might be describable by a hamiltonian or be subjected to energy conservation. Question 18 answers It is required in the designing of instrument. Relevant answer Answer Quoting " A CT scan takes pictures of the inside of the body using x-rays taken from many angles. A computer combines these pictures into a detailed, 3-dimensional image. This image will show abnormal areas and any tumors." See the details and visit Computed Tomography (CT) Scan | Cancer.Net www.cancer.net › diagnosing-cancer › tests-and-procedures › comput.. Question 9 answers It is the requirement of one project of location of the dams and rivers in the country. Relevant answer Answer The following some useful papers in the topic Study of techniques of identifying the earthquake precursory anomalies in terms of mathematical modeling Zun-guo Yan, Jia-dong Qian, Jun-hua Chen, Sheng-le LiJournal:Earthquake ScienceYear:2000 Earthquakes in quasistatic models of fractures in elastic media: formalism and numerical techniques Chen, Kan, Bhagavatula, Ravi, Jayaprakash, CJournal:Journal of Physics A: Mathematical and General PhysicsYear:1997 Question 36 answers when using this [peaksnr,snr]=psnr(watermarked_rgb,host); value is 44.13 and 38.39 but when using MSE=mse(watermarked_rgb,host); value is 0.2456,0.2146 and 0.2691 respectively. If you use the mathematical equation PSNR = 10log10(255*255/MSE) values came 54.So which one is correct. Relevant answer Answer Dear Sanjay Kumar, Convert the original and enhanced images to HSV color space first, and then, use MSE & PSNR to the V-component only. Question 15 answers 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 Relevant answer Answer Mental capabilities are different from one person to another and this must be taken into account by the subject teacher Question 44 answers I have used the code in this repository linked below and implemented a lane segmentation system: Then I found this demo which is Tesla Vision Path Prediction To See Around Blind Corners. i was kind of thinking that if I could be able to estimate slopes of the detected lanes and draw their tails in the image till they meet each other on intersection. anyway, I wonder if anyone can help me to find any algorithm, paper or code that can use the detected lanes and output the predictions? Thanks. Question 18 answers I am looking for simple text book references to understand the mathematics used by Ashtekar in papers like Asymptotic with positive cosmological constant. I understands GTR so far as Einstein equation and its solution like Schwartzchild solution, kerr etc. There is a great bandgap in mathematics used by these two scenarios. Relevant answer Answer I advise you the following papers Existence and structure of past asymptotically simple solutions of Einstein's field equations with positive cosmological constant Helmut FriedrichJournal:Journal of Geometry and PhysicsYear:1986 Asymptotics of Solutions of the Einstein Equations with Positive Cosmological Constant Alan D. RendallJournal:Annales Henri PoincaréYear:2004 and the books The Role of Neutrinos, Strings, Gravity, and Variable Cosmological Constant in Particle Physics KluwerKursunoglu B., et al. (eds.)Year:2002 Theory of the cosmological constant Coleman.Categories:Physics\\Astronomy: AstrophysicsYear:1988 Good Luck Question 24 answers basically scholar is having maths and statistics background but he is doing research in fluid mechanics. he is interested but difficulty is finding problem and doing paper publications. so we need some suggestions. how to develop knowledge on this research area being a mathematics scholar. Relevant answer Answer If a person is good in mathematics and has command over it, that means he has good logic aptitude and grasping ability. If now he want to do research in Fluid mechanics of course he can. He should start with reading the basic physics books and gradually increase the level to engineering fluid mechanics. Which, at this stage, should be a matter of not more than 6 focused months. after that he will be able to do like masters. Do not run behind paper publication from the start it will a by product of your focused learning and problem solving. Question 24 answers Study the history of mathematics. Likely, it will start at Mesopotamia 3000 BC. Now, it is undisputed H. sapiens trace back to Africa, perhaps earlier than 200 millennia ago. So, didn’t the early humans think about themselves and the environment around them? Of course they did. And they used tools of mathematics. Nearly 60 years ago, that mathematics was discovered in Ishango, the border between Uganda and the DRC. So, why does mathematics ignore Ishango? Relevant answer Answer The most interesting, of a large number of tools discovered in 1960 at Ishango, is a bone tool handle called the Ishango Bone (now located on the 19th floor of the Royal Institute for Natural Sciences of Belgium in Brussels, and can only be seen on special demand) Question 24 answers Would you like to read (look through) this book? By the way, book publishing shy away from such a proposal, so along the way I wanted to ask our community for advice. Relevant answer Answer Jack Sarfatti, Everything is wonderful, but I do not perceive it well by ear. Could you write a few words about what is relevant now that excites you and prevents you from thinking about the philosophical question of the origin of nature (the nature of things)? Question 25 answers List of journals pure and applied mathematics Impact factor in Scopus or Thomson. Only journals requesting author reviewers Relevant answer Answer You want to know the journals that one can talk to regarding which referee will be selected? Normally that is never a concern for the scientist, as the journal typically has a long list of available referees, and also a database that tells them how quick and good they are, and what special topics they would rather be in service for. Typically the journal will NOT pick anyone of the ones that you suggest, as they might think that they may be your friends. As an editor myself, I would hesitate picking anyone among the suggested reviewers, unless I know them, and know that they are conscientious. Question 4 answers How the imaginary part of the refractive index or the extinction co-efficient glycerol or ethanol changes with the glycerol or ethanol concentration in an aqueous solution? Is there any mathematical expression to calculate the change in the imaginary part of the refractive index of glycerol or ethanol with its concentration ? Relevant answer Answer The change of the imaginary part with concentration is essentially Beer's law: Question 6 answers The Throughput is the amount of data received by the user in a unit of time. How can I write this in a mathematical equation? Relevant answer Answer If you search in Google, for " throughput equation" you will receive the following sit that tells you all about this equation. Question 110 answers Hi, Is there a mathematical equation or formula to find the extinction coefficient or absorption coefficient of a thin layer based on transmittance or from the refractive index of the material? Relevant answer Answer The relationship between the absorption coefficient alpha and the extinction coefficient k can be expressed by the relation: alpha= 4 pi f k/ c f the frequency of the incident wave, and c is the speed of light. Best wishes Question 10 answers The paper titled by "Closed-form formula of Riemann zeta function and eta function for all non-zero given complex numbers via sums of powers of complex functions to disprove Riemann hypothesis" disproves the well known unsolved mathematics problem, Riemann hypothesis. Thank you for your time and consideration. The full paper is available here: Relevant answer Answer You are misreading the relation. It is not x^s = e^sin(x). It is x^s = e^sln(x). the power is (s)(ln(x)). Question 20 answers The substrate is in a rectangular shape, the length is 7,6 cm and width is 2.86 cm. The particle density is 1.2, the volume of the particles is 50nm and the PH value is 2 and the amount of the particles in volume used to coat is 1000 microliters. Relevant answer Answer Mostafa Gamal Emam Hussein Your question 'How to calculate mathematically SiO2 nano particles of 50 nm size thickness on glass substrate?' does not make grammatical sense in English. Using 'Sio2' (which I have corrected in my italics above and PH (should be pH) and a density of 1.2 (no units specified; indeed g/l is a very strange - and low - density) plus a 'volume' of 50nm (50 nm) - 50 nm is a length, not a volume - shows a marked scientific confusion. What do you want to calculate mathematically? Only useful comment I can make is that 1000 microliters is about 50 drops. Question 15 answers Hello dear friends For my thesis work, I need to first grade students in mathematics achievement test. Please, any of you can help with this. Thank you forever for your kindness Relevant answer Answer Thank you so much! Paul Louangrath David Morse Question 216 answers 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 … Relevant answer Answer Stay at home. :-) Question 21 answers How to validate mathematical equations which govern a process/ phenomenon? I have few mathematical models which govern a mechanical phenomenon..Experimentation is not possible..hence I want to do the validation. Relevant answer Answer First and foremost mathematical expressions do not " govern a mechanical phenomenon." The equations describe a relationship between the variables in the equations and how they evolve over time. For utility in the sciences, it is hoped the equations actually are an accurate representation of the physics in this case. The equations are a theory of how the physics behaves. Predictions can be derived from the equations. However, the final piece of the scientific method is to verify or falsify the theory through comparing the prediction to experimental data. Or to quote Richard Feynman: "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong." Question 8 answers I got a laser source with the following parameters, 800 nm with pulse duration 110 fs. I intend to perform an SHG (Second Harmonic Generation) in order to produce a field of 400 nm wavelength. What should be my BBO crystal length to achieve, and what mathematical expression can I use to get it. Relevant answer Answer very nice question as you i wait to see the answer Question 91 answers 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? Relevant answer Answer According to an appendix of Matter and Mind of the late Mario Bunge, there are two kinds of truth: Formal truths of logic and mathematics and Factual truths of ordinary knowledge science and technology. Confusion between the two kinds of truth is a source of more confusion if possible. While the first kind of truth is easy to assess, even if some theoretical facts are undecidable the second lacks a well-structured formalism. Possibly you are taking of the second class of truths, so this might be associated to a perhaps neverending debate... Question 4 answers Hello, we all know entropy from physics and complexity of information, so my question is about the possiblity to reorder information zu a certain more ordered state of the past by human and digital technologies. The factors I see in conguence to physics are (direction, entropy, time ...), in information science (information capability, and modal situational logic) and in maths (combination as sort of differentiation functionality to gain avarage information content towards a cause) So to think is one example of such neg-entropy Are there others? Relevant answer Answer Although there is no direct answer to your question, it might be of interest to reconsider Maxwell's demon and Quantum Biology research. I do recall that Prof. Capek's research--from our mutual discussions--from Charles University in Prague as he was working on a quantum model of Maxwell's demon. There is ongoing a lot of research on Quantum Biology. It has a very bright future despite it is not, to the surprise of all, working at the absolute zero temperature as novel quantum computers. We researchers are becoming more and more aware of the fact that QM approaches can shed light on many so far unsolvable scientific problems including the very foundations of biological functioning. Question 39 answers In mathematics, there is a kind of number carriers with cognizable quantitative properties (such as imaginary number, fuzzy number, infinitesimal variables and monads … in present mathematics)"; these “mathematical carriers of abstract concepts and laws” can join any quantitative calculation process with finite number forms (number forms with Archimedean Property) but their exact values are unknown. They are defined as “number forms with Half Archimedean Property". The history of our mathematics has proved that people need to carry out various necessary qualitative and quantitative cognitions and studies on those “mathematical carriers of abstract concepts and laws with “Archimedean Property” or “Half Archimedean Property". Relevant answer Answer certainly Question 270 answers There are many existing publishers that publish high quality books in mathematics, but my question here is: I want some suggestions about publishers who most likely publish books in the field of fractional calculus and fractional differential equations because I am interested in submitting a book proposal for a suggested publisher. Could you please share you information/knowledge about such recommended publishers in this specific field of research in mathematics? I would greatly appreciate your brilliant efforts and time!! Relevant answer Answer Thank you Dr. Mila Ilieva !! Question 9 answers To me, Distance, Space and Time are the ever-most important ingredients for mathematical based sciences and mathematics itself at the most. Every human being know and understand mathematics according to their needs and careers. There may be fundamental keys for other areas for example Machine learning is based on discriminant analysis or finding roots of the linear/nonlinear equations or finding first derivative of the model/function, equating it to zero and finding roots or optimal points at the given domain. Dear RG members on individual specificity bases may you describe the fundamental keys/pillars of your research areas? (For similar example, as I described above for mathematics and machine learning. You may explain your answers more explicitly please!!! Relevant answer Answer It is a very general question. Distance, space and time, etc. is equivalent to define the suitable manifold structure and atlas charts that are the best to describe the environment (Universe) of your mathematical model. Concerning the question about the set of the fundamentals, say {F} that are needed to study the field or topic P. In general, the essential tools of mathematics like calculus, linear algebra, differential equations, and the undergraduate elementary mathematics are strongly needed in almost all branches of sciences. But for some specific topics, special preliminaries are needed too. Examples: (1) General topology is a prerequisite of Algebraic or differential topology. (2) Multivariable calculus is a prerequisite for optimization theory. (3) Advanced Matrix theory is strongly recommended as a prerequisite to study the dynamical systems and control theory. (4) Group theory is needed to understand Galois theory. (5) Probability theory is a must for decision making. Etc. Best regards Question 15 answers Any mathematical study for sickle cell disease? Relevant answer Question 10 answers I approach this issue constructively. I'll give you my example, and you can point me to other examples of physical interpretation of arithmetic functions. My example in the attached paper "On the winding of a sphere" in which are the conclusion: "Thus, our abstract mathematical constructions have some similarities with the mathematical formalism of quantum mechanics, and therefore the questions of the substantiation of quantum mechanics could possibly get an answer within the framework of the mathematical formalism developed here. At least, bearing in mind that the Jacobi theta function$\theta(z, \tau)\$ satisfies the Schrodinger equation with complex variables, we could interpret it as `quantum'' oscillations of the mathematical pendulum of the sphere winding, and Hurwitz zeta function satisfying the generalized Schrodinger equation, interpreted as a function of the oscillations of a mathematical pendulum with an evolving (for example, decaying) complex angle of deflection of the winding. On the other hand, the metaphysical method of random walks around winding a sphere that we have developed will probably find application in the substantiation of the Hilbert-Polya conjecture on the connection of nontrivial zeros of the Riemann zeta function with the eigenvalues of a certain differential operator."
and the abstract:
"First, we bring the reader to one remarkable result of the action of a modular group on a sphere, proving that of all closed torus windings wound around a sphere, single-wound windings that are indexed by a set of primes stand out. Further, we show that the rotation of the torus windings on a sphere, together with the measurement of the complex value of the angular coordinates of a discrete set of their points, gives us all the necessary data for the formation of the Riemann zeta function. Then, considering the dynamics of the windings, we notice that in the problem of random walk along the broken lines of the winding of a sphere, the concept of complex probability amplitude arises quite naturally, and the dynamics of the probability amplitude of the stray particle obeys a differential equation generalizing the Schrodinger equation."
I will only add that, perhaps, we can find a technological application of this equation.
Indeed, if the generalized Schrödinger equation works in nature, then the interaction time should be included as an additional factor in the nuclear reaction. In other words, due to the exponentially time-dependent coefficient of the generalized Schrödinger equation, the longer the nuclei come closer, the higher the probability of a nuclear reaction.
Muhammad Ali, I am glad that I met a like-minded person here, but I would like to note that mathematical models describe reality (nature) in some cases, and fantasy (invented nature) in others. My goal is to describe moving matter.
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