Science topics: Mathematics
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Mathematics - Science topic

Mathematics, Pure and Applied Math
Questions related to Mathematics
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I have the x,y data of two curves (solid red and blue in the attached image) and I want to find out the envelope function of the two (dashed magenta curve in the attached image). Is there a way to do it in Origin or Igor? Or in any other mathematical software for instance?
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Arani Biswas Deconvolution of a composite peak into its individual peaks plays an important role in the interpretation of many types of graphs including XRD, XPS, FTIR, and PL etc. In this video, I have discussed how to deconvolute simple combined peaks, composite peaks and how to correct missing data in a given peak with the help of deconvolution. In the case you want to further ask about it, please do comment on the specific video, I'll respond to it shortly. I have provided the practice files (OriginLab) here. Thanks
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I want to integrate two carbon fiber materials together and want to model it mathematically considering the processes of joining the materials and the possible stress around the joints due to external loads.
I will appreciate if someone can recommend and the numerical methods which one is better suited for this purpose.
Thank you all in advance
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Assuming you have a strong join (no delamination issues etc.) then you have continuity of the displacement and the stresses across the join. However, strains will *not* be continuous across the join. The weak form of the elasticity equations will still hold, and energy minimization (for static problems) also holds. Using FEM, make the element boundaries conform with the join to avoid the problems of trying to approximate discontinuous functions (e.g., strains) with the discontinuity inside an element.
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In the recent paper which has been exhibited in the 51th Annual Iranian Mathematics Conference entitled "Notes on maximal subrings of rings of continuous functions" we give some
properties of maximal subrings of some classes of subrings of C(X). However, we could not answer the following two important questions in this context.
1. Is every maximal subring of C(X) unit-free (i.e., whenever R is a maximal subring of C(X) and
f is an element of R with empty zero-set, then f is a unit of R)?
2. Is every maximal subring of C(X) uniformly closed (i.e., closed under uniform topology on C(X))?
I would be very delighted if you could let me your opinion about any ideas towards approaching the answers of these questions.
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It is not hard to see that for each real number t which is not algebraic over integers, C(X) has a maximal subring R_t which contains t but not t^-1, which immediately implies that the first question is not correct
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I recently saw a question regarding the relationship between language and mathematical learning, but am interested in learning more about the opposite.
Can anyone recommend relevant readings that explore the relationship between mathematical ability/maths learning and language acquisition. I am primarily interested in second/foreign language acquisition, but also interest in first language acquisition and the relation to mathematics.
(This question was prompted by something I read in one of Georgette Yakman's papers on STEAM learning (2008, I believe), which suggested something along the lines that understanding of mathematics was integral to understanding language, and am interested in learning more about the topic).
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I recommend for you to read: "Situated Learning: A Legitimate Peripheral Participation in Learning Mathematics in Public Schools"; Author: Zoncita D. Norman
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Can you just assume a situation with no figures or data to back it ? Is it reasonable?
#Logic #mathematics #data
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Kwadwo Boakye RE: "Can you just assume a situation with no figures or data to back it ? Is it reasonable?"
Yes to both questions. If you are giving a reductio ad absurdum argument, your assumption is formulated solely for the purpose showing that it is untenable because it entails a logical contradiction or absurdity.
A reductio ad absurdum argument that the square root of two is not rational has been attributed to Aristotle.
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As it is well known, Linked Opend Data (LOD) and computational ontologies have great success in the fields of Life Sciences (Biology, Medicine, etc). See e.g. the big LS-cluster at <https://lod-cloud.net/>.
However, I wonder why mathematics are – in comparison – covered only sparsely by ontologies or LOD.
Indicators (to the best of my current knowledge):
Probably there is some (machine-processable) formalization of mathematical knowledge but it seems almost disconnected from the "semantic web" and LOD-bubble.
Questions:
  1. Why is this?
  2. Should this be changed?
  3. If 2., how?
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Dear Carsten Knoll. I developed ThingFO two y. ago, so I'm not aware so far that other researchers used it for abstract mathematical concepts like polynomial or complex number as you are looking for. My interest in ontologies started in early 2000. At that moment, we developed a process ontology, and an ontology for metrics and indicators. In the last years we have harmonized semantically those ontologies with ThingFO in the context of the four-layered ontological architecture. Obviously that for indirect metrics and elementary and derived indicators, we use mathematical constructs (formulas, aggregation models), but that is all. These ontologies are specified at the low-domain level.
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I shared the picture of three parameters 1.Change in Temperature, 2. Change in Relative Humidity, 3. Change in Pressure and respective error value for that.
From the attached data(picture and excel file attached), I need to find the Error value for different input parameter.
If
1.Change in Temperature = 1°C
2. Change in Relative Humidity = 1%
3. Change in Pressure = 1mbar
What is the error value?
If
1.Change in Temperature = 2°C
2. Change in Relative Humidity = 2%
3. Change in Pressure = 2mbar
What is the error value?
If
1.Change in Temperature = 4°C
2. Change in Relative Humidity = 3%
3. Change in Pressure = 2mbar
What is the error value?
Is it possible to find the error value by mathematics. Please tell the way to calculate using calculator or python programming.
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if you don’t have the original model that this error term come from then you can’t get the exact answer you’re after. Though you could approximate it by fitting a regression model. E.g. fit a least-squares model to find the best set of parameters a,b,c,d to the equation error = a*temp + b*humid + c*pressure +d.
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I need to write a MATLAB code that has the ability to process a GIS image in order to extract the coordinates of the grid points within the red region (R) and that are at least distance "d" from its boundary. Each point in the R is given a weight w1 (attached figure). The same procedure is to be made for the green region (G) but w2 is the weight of any point in G. The gathered data are saved in a matrix formed of three rows: row 1 contains the abscissa, row 2 contains the ordinate, and row 3 the weight.
I am looking forward to getting your suggestions...thanks in advance.
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im=imread('GIS.jpg');
%imshow(im);
BW = im2single(im);
numclust=5;
[L,Centers] = imsegkmeans(BW,numclust); % matlab inbuilt
temp_mask = L==1;
figure,imshow(temp_mask);
might help:)
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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?
Many thanks in advance!
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We have the same dilemma. how did you interpret your research? Nik Smidt
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Suppose we have a matrix relation as
A=Bn
where A and B are square matrices and n is a positive integer.
If A is know, how to calculate B? The can be easily calculated by MATLAB. We can get it as B=A(1/n). How to calculate it mathematically?
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Does anybody know about an mathematical optimization model which combines vendor managed inventory with fixed lot-sizes for production? That is, a model that performs a simultaneous production and delivery (transportation) planning with respect to production and transportation lot sizes.
So the keyfigures should be fixed lot-sizes for production, transportation assets, capacities and costs from vendor to VMI-stock, known demand on customer (retailer) side and inventory restrictions for the VMI-stock.
It will be also helpful if you just know about any paper or similiar which has recognized this problem.
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We know many largest numbers as googol number(=10^100), googolplex number(=10^googol), and other unimaginable large numbers.
What is the largest known number that is the result of solving a problem in physics or mathematics?
Are they really practical or just based on conjecture?
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The largest such numbers I know of come from combinatorial problems, e.g., Ramsey Theory
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using BTE how do we get mobilities and conductivity ,more calculation(mathematics) oriented answers would be helpful.
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You can check the equation 2.11 and 2.12 in the paper attach
Regards,
K
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Question about the loss of hyperbolicity in nonlinear PDE: when complex eigenvalues appear, what is the effect on flow? I understand that we do not have general results on existence in this case, but is it only the mathematical tools that are lacking where can we show physical phenomena of instability?
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Filippo Maria Denaro The reference is Bulletin of the American Mathematical Society, volume 45, p. 135-152 (2008); the quote appears on page 143.
I don't know why you say "I am used to approach differently the issue". This is precisely what I described and where I start. However, In the case of the discrete equations, it is not necessary to proceed to the limit, which is ill-posed. That is one of the advantages of the discrete formulation. Much of this is discussed in my paper "Finite scale theory: The role of the observer in classical fluid flow" (2014). In any case, it is mathematical nonsense to say "as dx --> 0". dx is a length scale, and so can only be described as being small with respect to some other length scale.
I believe the CFL limit is well defined. But operationally, for a given problem just start to increase the explicit time step. The simulation will tell you where instability begins; since the CFL (advective) instability grows exponentially, there is little ambiguity.
As for hyperbolicity, I have had several discussion with my young colleague @Ilya Peshkov who convinced me that hyperbolicity has been given several definitions, none of which seem to apply to the discrete equations. Perhaps Ilya will comment.
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Why CPW square slot antenna gives a wide impedance bandwidth?
Is any mathematical derivation/equation is available for it?
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as long as you need only information, yes.
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Why is it necessary to study the History of Mathematics?
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Borrowing from Mathematical Association of America (MAA) Homepage: There are many excellent reasons to study the history of mathematics. It helps students develop a deeper understanding of the mathematics they have already studied by seeing how it was developed over time and in various places. It encourages creative and flexible thinking by allowing students to see historical evidence that there are different and perfectly valid ways to view concepts and to carry out computations.
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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 would suggest that you skim through conference proceedings papers from ICME (International Congress on Mathematical Education) topic study group number 39 and CERME (Congress of European Research in Mathematics Education) thematic working group number 9 and then search for more journal articles with authors from these two groups. Also, I highly recommend the book "Speaking mathematically: communication in mathematics classrooms" by David Pimm and the series of papers published in "for the learning of mathematics" by Dave Hewitt called "Arbitrary and Necessary" Part 1, 2 and 3 (accessible online)
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Most plagiarism checkers don’t work because they cannot check equations and theorems which are the fundamental core of a mathematics article.
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Dear Colleagues and Authors,
plenty of problems in mathematics, economics, physics, biology, chemistry, and engineering, e.g., optics, radar, acoustics, communication theory, signal processing, medical imaging, computer vision, geophysics, oceanography, astronomy, remote sensing, natural language processing, machine learning, non-destructive testing, and other disciplines, can be reduced to solving an inverse problem in an abstract space, e.g., in Hilbert and Banach spaces. Inverse problems are called that because they start with the results and then calculate the causes. Solving inverse problems is a non-trivial task that involves many areas of Mathematics and Techniques. In cases where the problem is ill-posed, small errors in the data are greatly amplified in the solution, and therefore, regularization techniques using parameter choice rules with optimal convergence rates are necessary.
Currently, I am editing a special issue on "Numerical Analysis: Inverse Problems – Theory and Applications 2021" with a Switzerland-based "Mathematics" MDPI Journal.
I would like to draw your attention to this possibility of submitting research articles:
Please let me know if you need any help.
Thank you for your kind consideration,
Christine Böckmann
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How much time does it take to accept or publish a paper in special issue?
Thank you
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It is known in a input / output feedback linearization control that in a closed loop the physical state of the system is transformed into a linear mathematical state, which we have to stabilize by a linear auxiliary control, this linear mathematical state must be obtained, either by successive derivations of its outputs which is not recommended in case of implementation, or by a Luenberger observer.
In this question we want to know how demonstrate that this stabilizing linear control of the closed loop system can be developed via the physical state estimated by a nonlinear Thau observer.
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While calculating channel capacity, I wish to know how path loss directly or indirectly affects the Bandwidth. Is there any mathematical relationship in this regard?
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See the attached paper which is useful
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A large number of learners do not wish to study mathematics and have negative attitudes towards mathematics, including students in mathematics departments. In your opinion, what are the reasons?
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Conversely, what attributes of the physical universe do attributes of the natural logarithm model?
For example, the exponential function based on the natural logarithm has itself as its derivative. That seems to model aspects of the physical universe.
What are other math-physics correspondences for the natural logarithm?
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Borrowing from Stefanie Reichert: The constant e appears practically everywhere in science: popping up in the definition of the standard normal distribution; allowing us to decompose a time-dependent signal into its frequencies via Fourier transformation; telling us how to calculate the half-life of radioactive elements; playing a crucial role in the growth of bacteria; and governing temperature-activated chemical reactions.
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If anyone could help me. It is my dissertation work. Thank you. I am looking for the matlab code to solve PDE using RBF.
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I am interested in broadening my understanding of the physical assumptions needed to simplify its mathematical description. From these assumptions i will to choose a suitable turbulence model to run the simulation in Ansys.
The problem is fairly basic;
Inlet flow conditions: Velocity in= 44.2 m/s, Mach number inlet = 0.128, atmospheric total pressure and temperature. Turbulent boundary layer thickness @ 4H upstream of the step is 1.9 cm.
Outlet flow conditions: Fully developed flow.
Any advice would be much appreciated
Kind regards
Anton
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If you want to use the RANS formulation you should assume your flow field is totally developed. That means you can set the inflow profile according to a statistically mean velocity in a channel
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As a beginner, how can one start research on Machine Learning in Mathematics. Please suggest some research papers.
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see the following papers
An Empirical Study of Machine Learning Algorithms for Stock Daily Trading Strategy
Lv, Dongdong, Yuan, Shuhan, Li, Meizi, Xiang, YangJournal:Mathematical Problems in EngineeringYear:2019
A Proposal on Machine Learning via Dynamical Systems
E, WeinanJournal:Communications in Mathematics and StatisticsYear:2017
A machine learning approach to ornamentation modeling and synthesis in jazz guitar
Giraldo, Sergio, Ramírez, RafaelJournal:Journal of Mathematics and MusicYear:2016
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I need this software to be interactive: allowing to enter a signal on real time of simulation. Maybe SimuLinks can do this, I could not say. I would appreciate all the information you can apport.
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I am developer of Uyamak. Please look at Uyamak. You can use it to simulate a mathematical model in real time. However, communication with a data acquisition card is not yet available.
No need to install and it is free to use.
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I have a query that
How the flatten layer in deep learning model transform pooled feature matrix into a vector??
What is the mathematical equation for flattened layer?
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simply 1xQ; where Q is product of dimensions of tensor at the input. Further help can be taken at https://deeplizard.com/learn/video/fCVuiW9AFzY
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How can I find out the dependency of two variables from one or multiple equations.
Example:
Set 1 -
x1,a
f(x1,a)=z1
Set 2 -
x2,a
f(x2,a)=y2
f(y2)=z2
How highly ( zand x1 ) and ( z2 and x2 ) are related among themselves and can we quantify it?
Which Set's relation/dependency of the variables are stronger in comparison with the other Set ?
How easy will it be to get back x from z from both the Sets ? Which one will be harder and how to express that ?
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You need to work under a set of hypotheses allowing you to apply the
Inverse function theorem for f ( ⋅ , ⋅ ) in the first case, and for the composition ff ( ⋅ , ⋅ ) in the latter case.
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Creep is a time dependent process whereas MD simulation is restrictive in terms of the time scale. Hence to get appreciable strain in fs/ps time range we have to use a stress of GPa magnitude. Can we correlate this data with real-life service condition where only 10-200 MPa stress is observed. Is there any mathematical way of proving that?
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Perhaps only near the peak of stress-concentration tips and Grain boundary/precipitates or near-dislocation regions. If one tries to correlate Creep relaxation and strain, one might fit the data (usually viscoelastic time-dependent+instantaneous deformation) with standard viscoelastic models (Kelvin, Voigt, Maxwell) and/or creep models (Nabarro-Herring, Coble, Harper-Dorn) to find out the parameters, and do some dimensional analysis to represent the data in reduced-dimensional form (Common in Fluid Mechanics, Heat and Mass transfer, CIvil Engg.) using standard method (like Rayleigh, Buckingham-Pi), then even significantly different data may be compared.
To see the strength of scaling laws, see it!
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How does blood perfusion change during hyperthermia and hypothermia? What mathematical expressions exist for these phenomena? I would like indications of research about the subject. Thank you!
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@Alisson Figueiredo.
The viscocty of blood varies with temperature invivo or invitro. In low Ts, the viscocity increases and in accordance with Hagen-poiseillue equation on flow, as flow is inversely proportional to viscocity , this suggests a reduced blood flow. In addition, physiologically, in low temperatures, peripheral blood vessels constrict redirecting flow to vital organs. If you apply the same equation where flow is proportional to the radius of a vessel( which is reduced when vasoconstricted), still the flow should reduce. Vive versa, in hyperthermia.
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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?
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As a follow up to the above discussion, a MATLAB file that can give the numerical value of Euler's number accurate to 10,000 significant digits is now available via https://www.mathworks.com/matlabcentral/fileexchange/77046-euler-s-number. You can download the file and add it to MATLAB path. To call the function just type en in the Command Window. To show Euler's number for 2 <= d <=10,000 digits, type vpa(en,d).
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Recently I face some problems with the mathematical ( calculation) on the reference governor and command governor, so I need some help from you all to get which platform or journal can let me understanding the calculation. Thx
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انا لا أعلم اي مجلة من التي تبحث عنها
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  • How was the importance of the zeta function discovered ?
  • why do zeta function contain so much information ?
  • What other areas of mathematics does it relate to ?
  • Are there any books on the RH ?
  • I've heard something about a connection with quantum physics – what's that about?
  • Isn't there a connection with cryptography? Would a proof compromise the security of Internet communications and financial transactions?
  • What are the Extended Riemann Hypothesis, Generalised RH?
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The Zeta function is a very important function in mathematics. Because he was able to prove an important relationship between its zeros and the distribution of the prime numbers. hi.zeta(s=a+ib)=0
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I have a symmetric airfoil with known equation. Now a sine function passes along the airfoil equation like following figure. I want to find the sine function in (x,y) coordinate system.
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PS. The LaTeX file from my previous post after processing
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Dear colleagues,
I invite you to send your articles to the special issue that I edit, together with Dr. Martín Cervantes:
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Terry Tao blogged about this unfortunate event. Kindly share among Mathematical community and increase awareness.
Thanks.
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Oke ... Thank
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Any decision-making problem when precisely formulated within the framework of mathematics is posed as an optimization problem. There are so many ways, in fact, I think infinitely many ways one can partition the set of all possible optimization problems into classes of problems.
1. I often hear people label meta-heuristic and heuristic algorithms as general algorithms (I understand what they mean) but I'm thinking about some things, can we apply these algorithms to any arbitrary optimization problems from any class or more precisely can we adjust/re-model any optimization problem in a way that permits us to attack those problems by the algorithms in question?
2. Then I thought well if we assumed that the answer to 1 is yes then by extending the argument I think also we can re-formulate any given problem to be attacked by any algorithm we desire (of-course with a cost) then it is just a useless tautology.
I'm looking foe different insights :)
Thanks.
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rez-ord.docx
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Teaching Mathematics at school to all students is commonly justified by the opinion that it improves their problem-solving skills and "makes them smarter" (whichever measure is implied by this). I wonder a few things about this:
1) If there is a clear empirical support for this opinion. Does that evidence answer the question of the causality direction between learning maths and cognitive ability? Recommendations on good literature about this would be appreciated too.
2) Do the abilities students develop improve performance for solving problems that are non explicitly mathematical. For example - learning volumes of 3D shapes could improve spatial navigation.
3) And importantly, are these improvements particularly due to teaching maths? E.g. for the previous example - wouldn't learning world maps in a geography class or spatial maze tasks develop spatial navigation more efficiently than learning calculation of volumes?
Thank you!
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Mathematics usually helps to develop better thinking among different subjects, including mathematical issues of a creative nature
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I came across a term pseudo inverse laplacian/generalized inverse laplacian. What is the impact of pseudo inverse laplacian on the graph, both in directed and undirected graph.
Part II
What is the procedure for calculating the orthonormal basis for a matrix which is equivalent to requiring that [(1/sqrt (N)*[N*1 matrix] transpose of orthonormal basis) ] is an orthogonal matrix.
In the reference paper pseudo inverse is calculated for bipartite graph while my case involves directed and undirected graphs both.
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You can use google or bing.com to search "how to get the pseudo inverse laplacian/generalized inverse laplacian" or just some words
This is also interesting. However difficult if the graph is not specified.
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Our knowledge of the world begins not with matter, but with perception. There are no physical quantities independent of the observer. All physical quantities used to describe Nature refer to the observer. Moreover, different observers can take into account the same sequence of events in different ways. Consequently, each observer assumes a “stay” in his physical world, which is determined by the context of his own observations.
If mathematics and physics, which describe the surrounding reality, are effective human creations, then we must consider the relationship between human consciousness and reality. Undoubtedly, the existing unprecedented scientific and technological progress will continue. However, if there is a limit to this progress, the rate of discovery will slow down. This remark is especially important for artificial intelligence, which seeks to create a truly super intelligent machine.
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Dear Boris Menin ,
Golden ratio is a geometric mean or average . it could be apply to every aspect of life even in which amount we have to inhale and exhale to getting the perfectness that also explain by the meditation. The perfectness can achieve by the meditation that reflects in many Indian temples architecture those follow the Fibonacci series pattern in the temple architecture without knowledge of the series but due the devotion towards the god temple construction they constructed temple with meditation. There are also the statue of Gautam Buddha in which we found the golden ratio without knowledge of golden ration . So some where you can see the golden ration and meditation and devotion are the synonyms .
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My dissertation thesis is Perceptions of mathematical ceonceptions depending on MBTI personalities. It can includes methods of solving, understanding, imaginations of math issues, etc. I would like to know if there is any research connects MBTI with solving university mathematics for example methods of solving depending on MBTI, because I was struggling to find something similar.
EDIT: instead of MBTI I should use BIG FIVE TYPOLOGY!
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By personality style
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I am interested in the practical uses of mathematical minimal surfaces in engineering design (such as gyroids, Schwarz surfaces, etc.). Can anyone provide good examples, particularly in art and design (or nature-based design)? I am particularly interested in examples that have been physically created and used for some practical purpose or as art. However, I am having a hard time finding published work on this topic that is not purely computational.
If anyone has published work in this area, please consider sharing it in this thread so we can get a good discussion going.
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On the construction of minimal surfaces from geodesics
By: panelJ.Sánchez-Reyes
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I wish to develop a peer mentoring model based on the content knowledge and pedagogical content knowledge knowledge in Mathematics and technological skills. Unfortunately I cant find a standardized test/ assessment tool to determine their competence level on each domain. Hopefully some of you can help me find a link or way to find an assessment tool ? Thank you in advance
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Hello Ana-Lyn,
You could try:
1. Using released items from NAEP for the high school level (https://nces.ed.gov/NationsReportCard/nqt/help/NQT_Help/!SSL!/WebHelp_Pro/NQT_Help.htm);
2. Using previous versions of PISA items (https://www.oecd.org/pisa/pisaproducts/pisa-test-questions.htm)
3. Using previous versions of TIMMS items (https://nces.ed.gov/timss/released-questions.asp), though these are generally only for as high as grade 8.
Some combination of these sources would likely serve to give you a good starting point for assessing teachers' command of a specific discipline, at least at a level commensurate with that of high school training. Of course, if the teachers you assess are very strong in the discipline (and good at test-taking!), then you may end up with a lot of very high scores (so-called "ceiling effect").
Short of that, you could obviously assemble a group of subject-matter experts, a test-development expert, and attempt to: (a) define the relevant domain of skills that you believe a teacher should possess; and (b) develop and try out items designed to measure whether a given examinee sufficiently possesses each given skill.
Good luck with your work.
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HI Everyone!
I am asking to know by you, expert in cybersecurity and mathematics, if Computer virology (the one of Cohen and Andler) is still an active field of research. That research made in France at Inria at 2000-2010 . I do not see any prosecutor and I do not understand if this is a dead branch or not. I am interested in it in order to understand malware and detect behavior.
Thank you very much for your precious help!
Bye
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I have written two articles about a generalization of Multiple zeta values and Multiple zeta star values. I also presented applications for this generalization including partition identities, polynomial identities, a generalization of the Faulhaber formula, as well as MZV identities. If you are intrested check them out on my profile and give me your opinion.
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If anyone read my articles and has recommendations or comment, please inform me of these comments. Any comments or suggestions would be very helpful.
Also if anyone knows someone that would be interested in my articles please do recommend it to them.
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Math relates numbers to other numbers. But this is insufficient for physics. Physics models which include a cause-and-effect are more useful and result in bettter human understanding. For example, current models are time reversable. If cause-and-effect is part of the calculation, the model would not be time reversable without another equation showing how energy (entropy) is expended. Further, any proposed model that was only mathematical manupliation would not be considered physics.
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You are correct. Causality and the arrow of time are being consistently ignored as both Quantum probabilities and General relativity seem to develop math models at the expense of little regard for causality. Then there are the many complex papers on how to determine causality after the models have made liberal use of probability and shifting parameters from one side to the other of equations with only the number relations of math as a justification. This is the reason for the question.
The FQXi site seems to be devoting more to causality, sometimes called correlation.
Thanks for your insight. Perhaps, the comment should extend to fundamental principles.
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The parameters are:
1. Stator phase resistance (Rs).
2. Inductances (Ld & Lq).
3. Flux linkage established by magnets (V.s)
4. Inertia (j)
5. Viscous damping coefficient (F).
6. No. of pole pairs
7. Generator speed (wm)
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@ Subir Datta Sir did you got the answers, if yes then please share the designing with me I knew many equations regarding this but I am confused how to calculate these parameters.
Thanking you sir.
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In this link shifted functions are defined as r*(x-o)/100 (where r is the original range)to keep the range between 100. But for optimizing the functions should I generate the values of X between [-100,100] or between [o-100,o+100]? If the function is shifted by o vector then the respective ranges should also change. Because if for 0<-100 or o>100, the global optimum won't fall in the range. And even if I generate the o values between [-100,100] then the function would be shifted in the range rather than being in the range where it is well defined.
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Yes, you must shift all the conditions. All the problem has to be changed: The bounds, the conditions. Finally, you must come back the first problem: the first condition and the first bounds. To interpret the results, you need to return.
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  • An understanding of theories about how people learn, and the ability to apply these theories in teaching mathematics; It is one of the primary requirements for effective teaching of mathematics, and a large number of scientists have studied mental development and the nature of learning in different ways, and this resulted in various theories of learning.
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There are many theories, but most popular one is (Behavioral theory).
Please refer to the link below:
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Dear Colleagues,
I would like to invite you to submit both original research and review articles to the Special Issue on "Modern Applications of Numerical Linear Algebra" organised by Mathematics (IF=1.747) ISSN 2227-7390. For more details see https://mdpi.com/si/74727.
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I hope the review process would be fast and how many weeks will it take to index accepted paper in web of science?
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This is my very first encounter with functional equation of this kind, and methods of series solution and differential equations are of not much help. The solution to this problem, or at least the mathematical prerequisites to understand solution to this problem is asked.
This function is asymptotically zero at both +_ infinity, positive otherwise, and has a peak near zero.
If I am correct, then this is the frequency distribution of numbers fed to the sequence xn+1=a ln (xn2) as long as the sequence generated is chaotic and sufficiently large in number (value of a is usually limited to 0.2 to 1.3, Positive and negative signs of a are essentially immaterial except for the sequence is negated after first term) .The sequence is initiated or seeded with number roughly as the same order of magnitude of 1 in both positive and negative side, except for the values that eventually lead to zero or infinity in the sequence. The sequence is allowed to proceed, and frequency distribution of numbers in the sequence are noted, from which a continuous probability distribution may be numerically guessed but not analytically found. The expression to find out formula of the continuous probability distribution comes to me from the following reasoning
  • Suppose, the probability distribution is given by y=f(x). Now, if I consider a "dx" (infinitesimally) thin strip around x, then I come up with f(x) dx fraction of all points required to construct the probability distribution. When this fraction of all points are passed through yet another sequence of transformation through the recurrence xn+1 =a ln (xn)2 , the fraction of points involved must be unchanged. That is, when x is substituted with a ln x2 , the infinitesimal strip area, which changes to f( a ln x^2) d (a ln x^2), must be numerically equal to f(x) dx, thus the functional equation is postulated
  • I am not entirely sure about this reasoning, and experts are welcome to point out my fault of reasoning and show the correct equation , if I am mistaken.
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The operator f{*} is defined as follows
f{g(x)}=1/g(x)\ (the reciprocal of the derivative)
f{x}=1/1
f{x2}=1/2x
f{sinx}=1/cosx
etc,..
We find that this operator works as a solution for the given equation.
You can see
f(a ln x2)/f(x)= (1/2a(1/x))/(1)= x/2a.
You can also replace x with any other function, and the relationship works.
Here f is considered as an operator.
Best wishes
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Considering the majority of the population, as if, they do not know as to what is their strength. This perhaps is due to their considerably lesser exposure to various possibilities, as a result under exploitation of visible potential indicators being observed perceivably reflective. This is somewhat mathematically to be calculated based on the following generic formula which could further be deepened by incorporating a finer level of referrals and parameters as per the identified essentials during the study.
Average calculated potential vs actual harvested potential vs differential potential = under or over harnessed potential
Over harnessed potential to be analyzed in terms of negative or positive impact in achieving socioeconomic equilibrium, so should be recommended to calculate in case of under harvested potential as well.
The above study should reflect socioeconomic loss vs gain due to under or overutilization of the human resource.
I would highly appreciate your view on the above.
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Bitte erklären Sie das Problem klar. Gruß
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For a function, usually sign of second derivative (and if it is zero, even/odd index of higher order derivative whose numerical value is zero) is enough to detect whether the extreme point is maximum/minimum/saddle point, if first derivative is zero. For a functional (NOT A FUNCTION), Euler-Lagrange equation plays the role of first "derivative" of Functional. However, it the RHS of Euler-Lagrange equation is set to zero and the resultant differential equation is solved, then how to find whether this function (as solution to differential equation) corresponds to minimum, maximum or saddle "point" of functional?
Unfortunately, the nature of extremum of a functional is usually declared to be "beyond the scope" of most preliminary/introductory functional analysis resources (I have not checked all). How difficult is that mathematics and what are the prerequisites to understand the mathematics involved in finding the nature of functional extremum?
Please note my knowledge on variational calculus, integral equations and transformations as well as group theory and advanced differential geometry is rudimentary.
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Actually, the idea in the case of a functional is the same as in the ordinary calculus: you have to resort to the second variation of the functional, and then to study several conditions depending on the weak or strong character of the critical point (Jacobi condition for weak extrema, Weierstrass condition for strong ones). You can find a readable treatment in the classic book "Calculus of Variations", by Gelfand and Fomin (Dover's edition is very affordable), chapters 5 and 6.
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Let T denote the circle group, that is, the multiplicative group of all complex numbers with absolute value 1. Let f : T → T be a (sequentially) continuous map, and such that f(z2 ) = f2 (z) for all z ∈ T. Then there is an integer k such that f(z) = zk for all z ∈ T.
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I agree with Mehdi Mesrizadeh
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Let a ∈ ℝ and b > 0 be fixed. Find all functions f : [0, ∞) → ℝ satisfying the differential equation f'(x) = -a + b/f(x) for x > 0 and f(0) = 0.
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You are correct Omran, as usual. Thank you!
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How to predict remaining useful life (RUL) on used aeroengine and its components level?
(or)
Any standard mathematical relations for RUL?
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THENNAVARAJAN SUBRAMANIAN you may want to employ LSTM. Attached is the paper with the concept of Hochreiter and Schmidhuber (1977).
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I am on a quest to solve how a cell repairs itself through encoding-decoding of proteins. Is there any link to genetic algorithms to solve age old questions such as aging and how we heal?
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Hi,
I suggest you to see this link i hope it's in the topic.
Best regards
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I have calculated EVI2 using landsat 7 surface reflectance images and I am getting values above 1.25 (mathematical maximum for EVI2 based on the formula) in my study area (heavily vegetated). I get a range between 0.2 and 1.8. Many publications stipulate -1 to 1, especially based on MODIS data. I also did a check with Landsat 7 TOA images, and I get ranges from -1 to 1, as the publications say. Does this mean something is wrong with the Landsat 7 surface reflectance images, or should values above 1.25 still be okay?
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It is absolutely fine and fair to get values above 1.25 as you are using a surface reflectance imagery and sine you mentioned that the area is heavily vegetated, the values reflect the colour composite and type of strata so the number and the work is acceptable.
Best wishes and good luck !
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Computer Aided Design (Cad) subject deals with the backend mathematical calculation that happens in a 3D design.
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Elements of Parametric Design Book by Robert Francis Woodbury can be useful especially in parametric modelling.
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I want to ask if I can get good resources that can explain the mathematical approach behind the Adaptive Model Predictive Control AMPC MATLAB toolbox?
am not be able to find the mathematical analysis behind this toolbox even on the MathWorks webpage.
thank you
Mohamed
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Mathematical programming is the best optimization tool with many years of strong theoretical background. Also, it is demonstrated that it can solve complex optimization problems on the scale of one million design variables, efficiently. Also, the methods are so reliable! Besides, there is mathematical proof for the existence of the solution and the globality of the optimum.
However, in some cases in which there are discontinuities in the objective function, there would be some problems due to non-differentiable problem. Some methods such as sub-gradients are proposed to solve such problems. However, I cannot find many papers in the state-of-the-art of engineering optimization of discontinuous optimization using mathematical programming. Engineers mostly use metaheuristics for such cases.
Can all problems with discontinuities be solved with mathematical programming? Is it easy to implement sub-gradients for large scale industrial problems? Do they work in non-convex problems?
A simple simple example of such a function is attached here.
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It may be useful to make a distinction between 'global' optimisation (where one is given an explicit, non-convex objective function) and 'black-box' optimisation (where the function is not given explicitly). The methods for them are very different.
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Problem: 5 minutes of play are worth more than an hour of study
Knowing that: G = Game S = Gtudy 1 hour = 60 min
The mathematical formula that defines the statement is: 5 x G> 60 x S The quantitative ratio of the minutes expressed in the mathematical formula can be simplified: 60: 5 = 12, therefore the simplified mathematical formula is: G> 12 x S
So, 1 minute of play is worth more than 12 minutes of study Or it can be said that: game G is worth more than 12 times than study S.
Therefore, the quantitative value of physical objects (or of spatial and / or temporal quantities) must be calculated differently from the qualitative value of human life experiences.
Explain why it is possible___________________________________________________________________
___________________________________________________________________________
(Exercise based on Fausto Presutti's Model of PsychoMathematics).
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We're all faced throughout our lives with decisions and choices, some on a grand scale, most of them on lesser points. We define ourselves by the total sum of decisions and choices we have made.
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I only have one sample size. I want to find if there is a significance difference between BSED-Math Students' Perceptions on Face-to-Face and Online Mathematics Learning.
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Yes, your assumption is right. I am using a Likert- Scale. The same participants rated the same statements for both learning context. The number of respondents of my study is more than 30. Well, thank you for responding my question Anna-Gesina Hülemeier .
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I have some complicated hints and clues, but I think their solutions should be much simpler.
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Long and boring solutions are attached. If anyone can provide a nicer argument, please share.
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If it makes easier, assume that f is continuous on [0,∞).
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A not too complicated solution, please see attached.
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Specifically, I know that there are discontinuous everywhere solutions f of the given equation. I also know how to prove that, if f is continuous at 0, then f(x)=0 for all x∈ℝ. I don't know what gives the assumption of continuity of f at a non-zero point?
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Excellent Omran, your construction solves my inquest, with the minimal continuity set for f.
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In several discussions, I have often come across a question on the 'mathematical meaning of the various signal processing techniques' such as Fourier transform, short-term fourier transform, stockwell transform, wavelet transform, etc. - as to what is the real reason for choosing one technique over the other for certain applications.
Apparently, the ability of these techniques to overcome the shortcomings of each other in terms of time-frequency resolution, noise immunity, etc. is not the perfect answer.
I would like to know the opinion of experts in this field.
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Utkarsh Singh There is an esthetic reason in why a mathematical method is of interest in signal processing:
-a beautiful algorithm is well articulated, says what it does in few instructions, and does it in a stable and reliable manner
-this hints to the underlying algebra
With powerful and minimal computation, we go deep into algebra structures: group, rings, fields (see references on Evariste Galois as the inventor of "group" as we know it)
-Fourier transform is an interesting invention: it allows to decompose a signal into resonating modes (as for piano music: you produce a sound at frequency F, but also its harmonic NxF...). Naturally there is the aliasing question and the Nyquist theorem for reconstruction
There are many more time-frequency representations: Fourier, Laplace, discrete or continuous, cosine transform, wavelet transform, etc.
The interesting feature of discrete algorithms for those transforms is that you can implement a butterfly structure.
The key idea is to replace a very large number of multiplications (in brute force "non-esthetic" programming) by a smaller number of additions.
This idea worked for me for developing a codec system using underlying GF(n) properties.
See this patent:
The regularity in the processing and the efficiency of the representation go hand in hand.
Let me go back to a very basic mathematical method: the Gram-Schmidt decomposition: take a sequence of n vectors v(1),..., v(n), and the matrix of cross-products m(i,j)=<v((i),v(j)>. The Gram-Schmidt method diagonalises this matrix. It extracts eigenvalues, and eigen vectors. In frequency terms, it extracts modes (resonating modes present in the signal).
This algorithm highlights the efficiency side of the representation: it's projecting the signal onto something found "in itself", call it principal components if you want.
There are only two reasons for choosing a technique in engineering:
-(i) it addresses the problem completely
-(ii)it's economically implementable.
Both criteria are equally important and a good way to find these is to look for elegant, esthetic solutions (minimal and complete at the same time).
Does it help?
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In recent years, many new heuristic algorithms are proposed in the community. However, it seems that they are already following a similar concept and they have similar benefits and drawbacks. Also, for large scale problems, with higher computational cost (real-world problems), it would be inefficient to use an evolutionary algorithm. These algorithms present different designs in single runs. So they look to be unreliable. Besides, heuristics have no mathematical background.
I think that the hybridization of mathematical algorithms and heuristics will help to handle real-world problems. They may be effective in cases in which the analytical gradient is unavailable and the finite difference is the only way to take the gradients (the gradient information may contain noise due to simulation error). So we can benefit from gradient information, while having a global search in the design domain.
There are some hybrid papers in the state-of-the-art. However, some people think that hybridization is the loss of the benefits of both methods. What do you think? Can it be beneficial? Should we improve heuristics with mathematics?
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I am surprised that a known scholar with a long experience in the transportation domain maintains such a hard stance on heuristic search. Obviously, we live in a world where extreme opinions are those which are the most echoed. Truth is, assuming that all practical optimization problems can be solved to optimality (or with approximation guarantees) is essentially wishful thinking. Given this state of art, better integration of exact and heuristic algorithms can largely benefit the research community. At the risk of repeating myself, here are some important remarks to consider:
• CPLEX and Gurobi (the current state of the art solvers for mixed integer programming optimization) rely on an army of internal heuristics for cut selection, branching, diving, polishing, etc... Without these heuristic components, optimal solutions could not be found for many problems of interest. CPLEX has even recently made a new release permitting a stronger heuristic emphasis (https://community.ibm.com/community/user/datascience/blogs/xavier-nodet1/2020/11/23/better-solutions-earlier-with-cplex-201). MIP solvers also heavily depend on the availability of good (heuristic) initial solutions to perform well. For many problems, cut separation is also done with heuristics. In the vehicle routing domain, we have a saying: heuristics are the methods that find the solutions, exact methods are those that finally permit to confirm that the heuristics were right (sometimes many decades later, and only for relatively small problems with a few hundred nodes despite over 60 years of research on mathematical models)...
• The machine learning domain is quickly taking over many applications that were previously done with optimization. Among the most popular methods, deep learning applies a form of stochastic gradient descent and does not guarantee convergence to optimal parameters. Neural networks currently face the same scrutiny and issues as the heuristic community, but progress in this area has still brought many notable breakthroughs. Decision-tree construction and random forests are also largely based on greedy algorithms, same for K-means (local improvement method) and many other popular learning algorithms.
• Even parameter tuning by the way is heuristic... I'm sorry to say that, but most design choices, even in the scientific domain, are heuristic and only qualify as good options through experimentation.
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Hi
I would really appreciate if someone helps me out with this MATLAB problem. I have uploaded both MATLAB file (which is not working properly) and the question.
Thank you very much in advance
#MATLAB
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Hi, you can directly use the following MATLAB function : fminsearch that uses the Nelder-Mead simplex (direct search) method instead of trying to implement your own version. Best
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In the lands with ancient plain sediments, the courses of rivers change dramatically over time for easy movement and the arrival of rivers to an advanced geomorphic stage.
Are there mathematical arrays that achieve digital processing such as spectral or spatial improvements or special filters to detect buried historical rivers?
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Ruqayah Al-Ani The digital elevation model (DEM) is a good component in the field of remote sensing and GIS. The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM). The ASTER GDEM needs further error-mitigating improvements to meet the expected accuracy specification. The RMSE values can be used to represent the DEM errors, in addition to mean error and standard deviation (stddev).
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The mathematical relations how it comes.
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Vinayak - this is just a preprint, the authors are allowed to write whatever they like and how they like it; I would follow the printed version (in a journal, conference proceedings etc) - usually it gets better when reviewed & printed.
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List of unsolved problems in mathematics, engineering, industry, science, etc.
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An Euler brick is a cuboid that possesses integer edges a>b>c and face diagonals. If the space diagonal is also an integer, the Euler brick is called a perfect cuboid, although no examples of perfect cuboids are currently known.
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In the definition of a group, several authors include the Closure Axiom but several others drop it. What is the real picture? Does the Closure Axiom still have importance once it is given that 'o' is a binary operation on the set G?
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What actually happens is that, closure property is a common one to almost all structures (systems). Therefore, authors who drop it in their texts assume that it is automatically embedded in the structure. Others who include it want to be vivid in their texts for clarity sake.
So, those who drop this important property do not truncate it entirely or cancel it.
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I am considering to send my research about Sophie Germain primes and it´s relation with primes of the form prime(a)+prime(b)+1= prime(c) and prime(b)-prime(a)-1= prime(c)
Mainly you have to send a mathematic research but others science researchs are accepted too. I don´t know the level of the contest but my chance is that my research i´ts have a deep relation with the work of Sophie Germain.
Do you have any recomendation of the form to present my work and the form of write to the responsables of the prize?
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I don´t understand you. It´s no trivial to find two prime numbers whose sum +1 will be other prime number. In fact my formula have a success of the 80%
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For any given function f : [a, b] → R, there exists a sequence of polynomial functions converging to f at each point where f is continuous. (Note that we did not ask the convergence to be uniform).
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Please see attached my take on this problem.
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FYI: "Is mathematics an effective way to describe the world?",
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As a mathematician & statistician, I can say that, when modeling reality, we make compromises; and, when validating the models, we have lots of surprises.
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Let 0 < xn ↗ ∞ such that xn+1 - xn → 0 as n → ∞ . Then, for every 0 < c < 1, there exists a subsequence k(n) such that xk(n) - xn → c as n → ∞ .
Is the problem true if c ≥ 1?
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I was thinking of defining k(n) := sup { k ≥ n : xk - xn < c }. Then
xk(n) - xn < c ≤ xk(n)+1 - xn , and the length of the interval containing c is xk(n)+1 - xn , which → 0 as n → ∞ by hypothesis.
Is this OK for all c > 0?
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Hi, Prof and Dr. the following is my thesis title. Any comment, please.
"the study of predicted factors of teachers' intention in teaching Mathematics Problem Solving through online"
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Design optimization, fabrication, and performance evaluation of solar parabolic trough collector for domestic applications
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I am working on a research and i am looking for someone who can help with a mathematics matters.
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Attached for your kind perusal@Miss. A.M
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Abstract
This paper studies the proof of Collatz conjecture for some set of sequence of odd numbers with infinite number of elements. These set generalized to the set which contains all positive odd integers. This extension assumed to be the proof of the full conjecture, using the concept of mathematical induction.
You can find the paper here: (PDF) Collatz Theorem. Available from: https://www.researchgate.net/publication/330358533_Collatz_Theorem [accessed Dec 21 2020].
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The first 11 theorems in your article provide a limit family of numbers that obey the Collatz conjecture and the number of steps needed to reach 1.
Unfortunately, in theorem (12), you have assumed that Collatz conjecture is true!!
In fact, your assumptions of the existence of b1 , b2 , ....bk-1 where k is finite
is exactly the Collatz conjecture, and the rest is an elementary computation of the number of steps to reach 1.
Can you prove that k is finite?
Obviously, if one assumes k is finite, then he assumes that Collatz conjecture is true.
Anyway, you have determined a nice family of numbers that satisfy the Collatz conjecture.
I wish you good luck to show k is finite.
Best regards
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How i can extract mathematical function by the given data set
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Ajit - if you are not interested in statistical analyses (regressions etc), a polynomial interpolation will do just fine.
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Some Mathematical expressions will be helpful.
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No
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I am looking for a research paper about the mathematical or computational modelling of protein oxidation (caused by reactive oxygen species).. I would really appreciate that if someone helps me with this.
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Would prefer a book for learners.
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see
Anh C.T., Hung P.Q., Ke T.D., Phong T.T.: Global attractor for a semilinear parabolic equation involving Grushin operatot. Electron. J. Differ. Equ. 32, 1–11 (2008)
D’Ambrosio L.: Hardy inequalities related to Grushin type operators. Proc. Am. Math. Soc. 132, 725–734 (2004)
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I am looking for any book/article reference about the mathematical description of zero normal flux boundary condition for shallow water equations. My concern is that for a near-shore case how it is obvious to have zero normal flux. Physically, it does make sense that we have a near-shore case and on the boundary, there is no flow in the normal direction. How to mathematical explain it using the continuity equation in the case when there is a steady flow? The continuity equation suggests that $\partial h / \partial t + u. \partial h/ partial x = 0$. If we take steady flow then it is clear to me to get zero normal flux condition. But what if the first term is not zero? or do we say that at the boundary the flow is always steady?
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Shallow Water Hydrodynamics: Mathematical Theory and Numerical Solution for a Two-dimensional System of Shallow Water Equations
ElsevierTan Weiyan (Eds.)Year:1992
Lattice Boltzmann Methods for Shallow Water Flows
Springer-Verlag Berlin HeidelbergDr. Jian Guo Zhou (auth.)Year:2004
Numerical Methods for Shallow-Water Flow
Springer NetherlandsC. B. Vreugdenhil (auth.)Year:1994
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