Science topics: Mathematics
Science topic

# Mathematics - Science topic

Mathematics, Pure and Applied Math
Questions related to Mathematics
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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?
Victor Christianto , Nice Topic.
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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?
Following.
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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 M?ssbauer 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?
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.
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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?
Nice Dear Nik Smidt
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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?
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.
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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...
Nice Topic , Following
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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?
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.
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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?
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.
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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?
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
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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.
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).
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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.
I agree with Abdulrahman Dahash
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What is the mathematics behind r.viewshed module in GRASS GIS
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.
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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.
Hi
Please check the following work. It describes the process in details. I believe it will help you.
Regards
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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.
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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 ?
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.
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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.
Manim by Grant Sanderson is the best one out there at the moment.
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Mathematical about the work-related with graphene or any other type of films/coatings.
Lubrication equations in solid films.
Have a look at
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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/ense?anza 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 "dise?o 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?
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.
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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?
The answer to this question can be given in different ways. Suppose the function is a linear function or a quadratic function?
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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
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
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Its a book related to biostatistics.
You can find it in Google Books. D. Booth
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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
Thank you and good luck
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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 ?
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
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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.
Yes, I am working on such modelling for the COVID-19, and I am ready to cooperate with you in this hot topic.
Regards,
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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
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.
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Can someone explain and give me a precise mathematical definition of what "variance" means in terms of principal component analysis (PCA)?
I suggest you check the following link. Hope it may be helpful. https://stats.stackexchange.com/questions/22569/pca-and-proportion-of-variance-explained
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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?
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.
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I need a book, chapter or something like that which discusses PV inverters.
It explains Mathematical relationships and finally Simulates it.
Dear Soroush,
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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?
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
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How can I get an endorsement for my mathematical archive in the arXiv website?
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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.
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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
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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.
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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
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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
Dear all,
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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.
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
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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.
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.
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It is required in the designing of instrument.
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..
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It is the requirement of one project of location of the dams and rivers in the country.
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
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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.
Dear Sanjay Kumar,
Convert the original and enhanced images to HSV color space first, and then, use MSE & PSNR to the V-component only.
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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
Mental capabilities are different from one person to another and this must be taken into account by the subject teacher
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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.
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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.
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
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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.
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.
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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?
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)
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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.
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)?
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List of journals pure and applied mathematics
Impact factor in Scopus or Thomson. Only journals requesting author reviewers
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.
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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 ?
The change of the imaginary part with concentration is essentially Beer's law:
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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?
If you search in Google, for " throughput equation"
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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?
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
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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:
It is not x^s = e^sin(x).
It is x^s = e^sln(x).
the power is (s)(ln(x)).
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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.
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.
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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
Thank you so much! Paul Louangrath David Morse
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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.
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."
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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.
very nice question as you i wait to see the answer
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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?
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.
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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".
certainly
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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!!
Thank you Dr. Mila Ilieva !!
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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!!!
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
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How to find the URL to know about the Call for papers & Book Chapter in Elsevier, Springer & IEEE?
(Specially for mathematics and applied mathematics)
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Any mathematical study for sickle cell disease?
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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 Schr?dinger 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 Schr?dinger 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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doing simulation analysis by using a three-construct model and converting it into maths equation and formulas. any resources can help??
Hello Ibrahim,
Here's a resource that gives multiple examples and the implicit equations for most of them: https://www.lexjansen.com/wuss/2006/tutorials/TUT-Suhr.pdf
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Recently years, we noticed more and more that the mathematics field is surely recommended to apply in all other fields of study to get accurate and undisputed results. with my good background in mathematics and computer programming, I'm looking for a good project to work with to use it in administration and/or economic fields. any suggestions?
I"m suggest that a research about the design of a mathematics model to measure the credit capacity of the borrower in the Iraqi environment.
It also suggested that a financial program design associate with commercial credit, accounting and and mobile payment companies
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Is it correct in assuming that any number (x) added to another number (y) will result in a number (Z) that will be less than the sum (Z) of the same numbers (x,y) MULTIPLIED together? In other words:
will x + y = ? always be less than (x) x (y) = ?
With a simple example, to show that (x + y) will not always be less than x.y; You can look at the example x = 0 and y = 1. Good luck
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Consider the linearized Euler equation (valid for the acoustic process of small amplitude in a quiescent medium),
\rho_0 \frac{\partial u}{\partial t} = \nablaP
Taking curl on both sides implies
$$\nabla\times \vec{u} = 0$$ instead of $$\frac{\partial (\nabla \times \vec{u})}{\partial t} = 0$$
But how? What is the mathematical reasoning behind this?
First of all, the 1D linearized Euler equation is not what you wrote. It is
that reduces to your equation is the background constant velocity is zero.
Then, the curl applied to the equation can be commuted with the time derivative and you get that the vorticity vector field is constant in time (not in space). Of course a zero vorticity field is a banal solution.
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About two years ago, I have submitted a manuscript to a reputed journal. After a couple of months of the peer review process, the response was “major revision has been requested”. I made the necessary adjustments and resubmitted it again. The Journal's editor responded that my manuscript requires minor revision. Well, the decision was <<"Revise for Editor Only'' he claimed that revision should be quick and it will not undergo the entire review process>>. Again, I made the required edits in order to make the manuscript acceptable for publication. Afterward, I resubmitted it. It is the day 120 and the status is "With Editor". In fact, I did send two emails to the editorial team to update the status. Their response to both emails was the same, saying that they contacted the editor to accelerate the process.
Dear readers, I need to have a piece of advice: what to do as a next step?
Bassam
My wild guess:
1. Editor is either on long leave or has resigned.
2. The paper has been referred again to original reviewers for their comments and they have slept over it.
3. The revised manuscript is lost in transit.
4. In the unfortunate case of death of either the Editor or Reviewer, the manuscript is being left unattended. It happened with one of my colleagues. He received a paper for review and took it to 顺心彩票 for reading. Unfortunately he died the next day. His wife was a Scientist and she recognised the importance of the Reviewer work. She returned the manuscript to the Editor.
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What is the best way to teach mathematics?
I used to do lot of exercises for practice..For one topic in maths I used to follow so many textbooks and guides..
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A lot of studies were devoted to find a rigorous mathematical convergence proof for GAs. In fact analytical techniques could have been used to derive the convergence. However, no concrete answer is there to this query.
I should think that a very small portion of the instances of the small problems you can think of might be solved quite correctly - but for the vast majority of problem instances it will fail.
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how can i contact sir wayne w. Welch? I want to ask permission if i can use and guide how to use the Mathematics attitude inventory?
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Dear colleagues, I am contacting you because I am organizing a special issue about “Application of Mathematical Analysis and Models to Financial Economics” of the open access journal, Mathematics (http://www.mdpi.com/journal/mathematics), which provides an advanced forum for studies related to mathematics. Mathematics is published by MDPI online monthly. The journal has been indexed in the SCIE, Scopus and Zentralblatt MATH. The First impact factor is 1.105 (Q1, JCR 2018, Mathematics). The submission deadline of this special issue has been extend to 20 December 2020, and the main purpose is to collect articles including mathematical applications on economics and finance issues, such as interest rates, volatility modelling, factor models, risk management, derivatives, portfolio management and uncertainty, in a Quantitative Finance context. Thus, if you are interested in contributing to this special issue, please, send me an email with information about your potential proposal; in concrete, name of authors, affiliation, email address and topic or title of your potential contribution. I would need this information as soon as possible, in order to give you a potential 50% discount on the article proccessing charges (50% x 1,200 CHF = 600CHF), because I will send it to the editorial office for approval. Kind regards, Prof. F. Jare?o Guest Editor Keywords: Derivatives; Factor Models; Financial Mathematics; Interest Rates; Portfolio Management; Quantitative Finance; Risk Management; Uncertainty; Volatility Modelling
If you give a potential 100% discount (free of charge) on the article processing charges, it will be OK for researcher from development countries.
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Hello,
I am working on a 3 variable system that has an oscillatory behaviour (Hopf).
I would like to seek for the region for oscillation parameter space.
I found a link draw some figures like the ones I wish to construct.
What are the mathematics behind these figure or what should I do to be able to find these region and plot them.
Your suggestions in this regards are highly appreciated.
Thank you
I hope following paper are in the direction
Structure of the control parameter space for a nonautonomous piecewise linear oscillator
E. P. Seleznev, A. M. ZakharevichJournal:Technical Physics
A structure of the oscillation frequencies parameter space for the system of dissipatively coupled oscillators
Emelianova, Yulia P., Kuznetsov, Alexander P., Turukina, Ludmila V., Sataev, Igor R., Chernyshov, Nikolai Yu.Journal:Communications in Nonlinear Science and Numerical Simulation
Structure of the parameter space for the van der Pol oscillator
E. J. Ding
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Any difference in their basic mathematical formula ? Like p= Cov (X,Y)/ ((var X * var Y)^1/2)?
Seyed Mahdi Amir Jahanshahi Unfortunately you are incorrect. A correlation coefficient measures correlation between two ordinary variables say x, y. A cross correlation coefficient usually measures the correlation between two time series say x(t), y(t). full details at https://www.google.com/search?q=correlation&rlz=1C1CHBF_enUS874US874&oq=correlation&aqs=chrome..69i57.8275j0j1&sourceid=chrome&ie=UTF-8
and
Please notice that t can be more general than time as we think of it in most time series applications. Best, David Booth
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What is the mathematical expression to represent channel of a multi-core fiber? (Including Inter-core crosstalk (XT), noise and other impairments)
In Y=H.X+N, how can we find the channel coefficients in 'H' matrix? What are the other parameters to be considered along with XT for calculating h(i,j) in H?
Furthermore, any suggestion on considering 'N' other than AWGN?
I propose, If we consider the a single-core in MCF as a SMF that affected by the same phenomena( linear and nonlinear), herein we can use Schordinger eqaution for each cores and we need to add a development to describe the XT between cores.
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I want to demonstrate mathematically that there is no even harmonic in normal condition and there are in the transient of fault
Hi dear colleague,
your question is a general one, so I would like to offer you to analyze evenness of non-sinusoidal current or voltage under consideration (if possible). If your function is an odd one it will surely mean absence of all the even harmonics in the Fourier expansion.
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What is the application of the mathematics in architecture?
Application of mathematics in architecture is similar to application of chemistry in medicine...
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If we integrate STEM in learning, do all aspects of Science, Technology, Engineering and Mathematics have to be present in every activity? Or may only 2 or 3 aspects appear?
The biggest problem with this thinking is that all of those terms are far too broad to design detailed and specific learning outcomes. You might argue that all of those disciplines will influence how we shape the requirements of the teaching method, but ultimately applied are often driven 'bottom up'. Such that we start at the problem and design a teaching framework around the measures we can place on how well the problem is solved.
For example: If I am attempting to teach somebody a practical skill such as welding, my metrics are going to be a lot more specific and goal-driven (I.E. has it penetrated correctly, is the surface reasonably 'clean') than trying to start at the abstract end of STEM and work out what mathematics / technology I want to teach in the process. Eventually, under a QA / teaching review I might decide that the welder should undertake some kind of arithmetic assessment to hit the "M" part, or perhaps understand some of the metallurgical process for the "T" component etc... but that is more than likely secondary to ensuring that they are welding correctly and at a sufficient rate / quality point.
For modern education activities that are perhaps a bit more abstract (such as classroom staples of mathematics and essential sciences) then you could certainly use all four components to enrich the lesson. For example: take a lesson on organic chemistry (such as Alkene reactions) which covers "S" - we could add information about catalysts for "T", applications of chemicals or reaction rates / equilibria for "E" and some basic equation balancing or empirical calculus (such as exponential cooling or thermal model) for "M". However, you only have a certain amount of time to teach somebody and they can only retain a certain volume of information, so we are back with the earlier philosophy that the teaching method is usually more specific and drive by what the outcome needs are, rather than using STEM vernacular to guide teaching.
Personally, I think you should strive to attain something from all 4, but that is only a very basic high level assessment of general education. There are so many skill areas that you'll be unaware of until you spend time working with / or become an expert(s) in the given problem space.
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Simplex method in linear programming.
The Simplex algorithm is a mathematical tool primarily. Some statistical fitting problems can be cast as a linear program, but I consider this incidental.
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I want to publish my paper very fast for my PG project.
Thank you sir
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I am working on Mathematical Modelling project and looking to using some mathematical tools that they are widely used in cancer models.
Just to back up Matija's response, have a look at the 'History Matching' papers from Vernon, Goldstein and Williamson (2010 onwards is a good date, although there is a seminal paper from 1997 by Craig et. al.). That stream of work is currently being applied to just about everything going. Also consider work on 'Bayesian Calibration' for good examples of general techniques (although beware this is now being shunned in high-dimensional / large input spaces)
Those search terms in Google Scholar (or look at the researchers I follow on my page + who they follow / co-author with etc...), will give you a great overview of applying mathematical models to general problems.
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Mathematics is the queen of Sciences. It deals with the scientific approach of getting useful solutions in multifarious fields. It is the back bone of modern science. Ever since its inception it is going into manifold directions. Now in these days of advanced development, it is interlinked with every important branch of technical and modern science. Pure mathematics and Applied mathematics are two eyes of Mathematics. Both are having and playing an equal and significant role in the field of research.
Mathematics is a backbone of all branches of knowledge.
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How to mathematically interpret the formula Kb=Kf (1?Rw)
I think reading through this article would be helpful. It is a research on the MUSLE model,this is a Modified version of the Universal Soil Loss Equation.
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How tolerance factor in ABO3 ceramics is related to spontaneous polarization? Is there any mathematical relation between them?
Spontaneous polarization happens in non-centro-symmetric crystal structures, which are not cubic. Take, for instance, barium titanate which has 3 ferroelectric phases, none of which are cubic. The tolerance factor, however, demonstrates how much crystal structure is close to the "ideal" cubic structure. Therefore, its being deviated from unity is desirable for spontaneous polarization.
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In the python library Scipy, the optimization.minimize() API has several algorithms which we can use to optimize our objective functions. But in my case, when I use this API with those algorithms it doesn't give me an expected optimal value. I just want to know whether that API has the ability to converge into a global minimum.
Indeed I recognize the names from my previous work as a bachelor and PhD student. These functions will, in general, not give you optimal solutions, but perhaps a near-stationary point.
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I wish to understand the mathematical relationship between the land surface temperature and air temperature.
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I wanted to know if it is possible to generate random numbers using GAN and what mathematical background is necessary.
If a GAN can accept Non-Parallel data then it has the ability to generate random numbers.
1. They may have a sequence in past to predict new numbers. OR
2. Just a random sequence .
I worked with non parallel voice data using GAN and it worked, then this has also the ability to work for random numbers as well. But this method may not be the best choice as there are other models SVM,LSTM(for exmple). But your question is "whether we can ?" Then you can give it a try.
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One remembers, first, that all matter used in anything is constructed of atoms, where atoms are made of particles, where quantum mechanics (QM) physically works.
Any physics, chemistry, engineering, computer science, even mathematics -- where the electrons, light, wave, and number behaviors are determining these fields by Nature -- will obey quantum rules, such as NO "law of the excluded middle" and NO "axiom of choice", and where QM principles play main roles.
One reads, for example, at Stanford U. that: the concepts and techniques of quantum mechanics are essential in many areas of engineering and science such as materials science, nanotechnology, electronic devices, and photonics.
Nominations by participants here (in order of appearance) include:
Superfluidity, superconductivity, HVDC with QM rectification by a thyristor (semiconductor), incandescence, laser, quantum decoherence, entanglement, P-type or N-type semiconductors, transistor radio, and the entire known universe for 13.8 billion years so far.
What is your reasoned opinion? What is your best example of QM having visible effects on microscopic and macroscopic scales?
One thing that comes to mind in regards to your primary question is hydrodynamic quantum analogs. These experiments were done at MIT in July of 2013 published in Physical Review Letters E. Dr. Daniel M. Harris displayed that "a coherent wavelike statistical behavior emerges from the complex underlying dynamics and that the probability distribution is prescribed by the Faraday wave mode of the corral." I hope this helps!
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Interested in looking at aviation-centred training and use of latest ideas in neuroscience and maths/science education for improving learning outcomes.
Thanks - I'll folow up later in the week.
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It all started with the Normalized Difference Vegetation Index (NDVI). I am curious to know how a researcher gets to derive or modify such mathematical (sometimes complicated equations) equations by making use of two bands (absorbing and reflecting bands)? Is it by trial and error method?
For example, NDVI seems to be a simple normalization of NIR and RED bands. MSAVI has NIR and red bands along with mathematical operations both in numerator and denominator. How do we come to such a relatively complex formula?
Thank you very much in advance.
The modified vegetation indices (such as EVI and MSAVI) are generally aimed to reduce the effects of atmosheric attenuation and soil background. The form of these complex formula can be determined or inspired by radiative transfer theory and also soil line theory. The coefficients are determined empirically or based on training datasets.
Trial and error method can be used to develop new indices, but the new indices should in most cases be supported by physical principles. Even for the machine learning method, those important independent variables (related to the dependent variable) are generally selected for learning.
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Dear All,
Greetings. I am looking for reader-friendly books that explain tensors analysis for Fluid Mechanics. The objective to be comfortable dealing with tensors.
Dear All,
Thanka a lot for the suggestions.
Much appreciated.
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As The First Generation of Infinite Set Theory is based on present classical infinite theory system, contradictory concepts of "potential infinite” and “actual infinite" make people unable to understand at all what the mathematical things being quantitative cognized in set theory are-------- are they "potential infinite things” or “actual infinite things " or the mixtures of both or none of both? People have been unable to understand at all what kind of relationship between the quantitative cognizing theory and the unavoidable concepts of "potential infinite, actual infinite" in set theory: If the mathematical things being quantitative cognized are "potential infinite”, what kind of "potential infinite” cognizing idea, operations and results should people have; if the mathematical things being quantitative cognized are "actual infinite”, what kind of "actual infinite” cognizing idea, operations and results should people have; if the mathematical things being quantitative cognized are the mixtures of both or none of both "potential infinite” and "actual infinite”, what kind of mixing cognizing idea, operations and results should people have? Are there "one to one correspondence" theories and operations for "potential infinite elements” or “actual infinite elements" or the mixtures of both or none of both? Why?
Therefore, it is very free and arbitrary for people to conduct quantitative cognitions to any infinite related mathematical things in The First Generation of Infinite Set Theory: It can either be proved that there are as many elements in Rational Number Set as there are in Natural Number Set or that there are more elements in Rational Number Set than that in Natural Number Set; the T = {x|x??x}theory can either be used to create Russell’s Paradox or to create "Power Set Theorem", make up the story of “the Hilbert Hotel forever with available rooms” ------- strictly make all the family members of the Russell's Paradox mathematicization and turn all the family members of Russell's Paradox into all kinds of Russell's Theorems; ...
However, because it has a little to do with applied mathematics; it is impossible to verify the scientificity of many practical quantitative cognitive operations and results in set theory. So, there are far more unscientific contents (more arbitrary quantitative cognizing behaviors) in the quantitative cognitive process of present classical infinite set theory than in present classical mathematical analysis.
You have raised many simultaneous questions about the (finite) and (infinite) concepts. Indeed the latest (infinite) is full of paradoxes in mathematics.
One can observe that :
(*) the part may include the whole,
(*) many infinite sums rearranged to obtain different answers,
(*) ambiguity of Cantor sets,
(*) infinity is not real,
All terms: inf - inf, 0xinf, inf/inf, inf^inf, inf^0 1^inf all are undefined!!
So one can stay with such paradoxes years without any clear answer.
And this doesn't mean that we can't use infinity. It is useful to find particular answers for a given mathematical problem. Also, we can construct new definitions that should be consistent with the axioms of the set theory and all other branches of current modern mathematics. All are considered valid based on the added axiom. This is very similar to change the fifth postulate of Euclid's to construct hundreds of non-euclidean geometries; all are consistent and accepted.
So, you can say that the sum of the angles of the triangle is 180 degrees or > 180degree, or < 180 degrees all are correct but in different geometries.
All agree with the initial axioms, but they differ by one axiom.
We can do the same for the set theory.
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Does it make sense to discuss this?
Learning through and with art?
Can an imaginative teaching model be the solution to multiple forms of learning and divergent production?
In my doctoral thesis, I assigned students the task of imagining a text math assignment and trying to draw it or present and solve it using instruments / sounds. Mathematical musical and visual representation of mathematical textual tasks and vice versa ..
From sound to image / icon / symbol.
The results are impressive ... What do you think about it ..
We are discussing the Mozart effect in our review:
The influence of music on the surgical task performance: A systematic review
• November 2019
• International Journal of Surgery (London, England)
• DOI:
• 10.1016/j.ijsu.2019.11.012