Mathematics

Follow this topic

Answer added to:
20 Are there sources that show the relation between linguistics and linear algebra, and other hand, linguistics and matrices?
By George Dueñas · National University of Colombia

Carlos Restrepo ·

Hola George Hace algunos años, cuando yo era estudiante de física de la UN, tuve la oportunidad de conocer algunos trabajos de Noam Chomsky que tra... [more]

Hola George Hace algunos años, cuando yo era estudiante de física de la UN, tuve la oportunidad de conocer algunos trabajos de Noam Chomsky que trataban de Gramática generativa transformacional, entre ellos "Estructuras sintácticas", donde se me hizo evidente la relación íntima entre lenguaje y transformaciones matemáticas. Una buena exposición del tema la pude leer en "La revolución de Chomsky en lingüística" de John Rogers Searle. Para detalles matemáticos ya le han dado muchas orientaciones, pero podemos comunicarnos si le interesa más la cuestión. Mucha suerte.

Following
Answer added to:
62 Mathematics and literature – do you know examples of mathematical structure or concepts leading to great, enduring literary works?
By Frederic Briand · CIESM - The Mediterranean Science Commission

Leonardo Riccardi · Politecnico di Bari

Another option which comes to my mind is the "Divina Commedia" (The divine Comedy) from Dante Alighieri. In this work (of course, is not a novel) the ... [more]

Another option which comes to my mind is the "Divina Commedia" (The divine Comedy) from Dante Alighieri. In this work (of course, is not a novel) the author puts a lot of the mathematical/theological ideas of that time to build a "divine" world which is run by rules and that has a precise (i would say) "geometrical" structure.

Following
Question:
New International Conference on Mathematical Techniques in Engineering Applications (ICMTEA 2013) October 24-25, 2013, GEU, Dehradun, India
International Conference on Mathematical Techniques in Engineering Applications (ICMTEA 2013) October 24-25, 2013, Graphic Era University, Dehradun, I... [more]

International Conference on Mathematical Techniques in Engineering Applications (ICMTEA 2013) October 24-25, 2013, Graphic Era University, Dehradun, India

ICMTEA 2013-brochure.pdf ×

By Mangey Ram · Graphic Era University

Following
Answer added to:
26 Continuity?
By Avinash Kumar · Rayat Institute of Engineering and Information Technology

Banibrata Mondal · Visva Bharati University

Of course, the function is discontinous at x=0.

Of course, the function is discontinous at x=0.

Following
Answer added to:
9 Does a 3-D chaotic system (flow) with only a curve equilibria or with only a surface equilibria exist? Is that possible?
By Sajad Jafari · Amirkabir University of Technology

John Pearson · Los Alamos National Laboratory

Sajad, that is interesting. I didn't think of that (obviously)!

Sajad, that is interesting. I didn't think of that (obviously)!

Following
Answer added to:
21 Do we need the concept of Infinity in Mathematics and Physics?
By Ulrich Mutze · Ludwig-Maximilian-University of Munich

Ulrich Mutze · Ludwig-Maximilian-University of Munich

@Simen. I think presently there is enough 'messing with the foundations of mathematics' going on from the side of mathematicians that applied scienti... [more]

@Simen. I think presently there is enough 'messing with the foundations of mathematics' going on from the side of mathematicians that applied scientists should find what they need if they are willing to dig. For instance, a constructive definition of natural numbers N (and Z, Q), is well established, although the much inferior predicative axiomatic definitions, e.g. Peano arithmetic, or Peano axioms (requiring second order logic) are more widely known and and applied. More general, constructive mathematics combined with the syntactic inovations which emerged from Object Oriented Programming could provide an adequate framework for natural sciences. I found your remark concerning spectra of quantum mechanical observables interesting. Approached from a natural point of view, the problem does not exist: Of course, if the configuration space (on which the wave functions are complex-valued functions) is a finite lattice of points, the Hilbert space of such wavefunctions is finite-dimensional and any symmetric operator is self-adjoint and the spectrum of such an operator is discrete. What in the infinite dimensional case is a continuous spectrum, in our finite-dimensional approximation is a discrete spectrum with closely packed points. The spacing of spectral points may vary over many orders of magnitude and may change with the position. The operator thus may show a very interesting 'spectral behavior'. An example for 'finite quantum mechanics' is given in the work in the following link.

http://www.ma.utexas.edu/mp_arc/c/06/06-356.pdf ×

Following
Answer added to:
15 What is the best method to investigate the existence of chaos in a 3D conservative continues system (flow)?
By Sajad Jafari · Amirkabir University of Technology

Oreste Piro · University of the Balearic Islands

The term conservative is often used with some ambiguity leaving rigor in the hands of context. It might refer to those that preserve energy, in mechan... [more]

The term conservative is often used with some ambiguity leaving rigor in the hands of context. It might refer to those that preserve energy, in mechanics, but it might also refer to those that preserve a given measure in the space state of more general dynamical systems. In 3D it is common to speak conservative systems to refer to those that preserve the three-dimensional volume. A common source of 3D volume preserving dynamical systems comes from hydrodynamics: the Lagrangian description of the flow of incompressible fluids. Please note that while in 2D this problem can be easily asociated with a Hamiltonian system (the stream function place the role of H) in 3D this is not the case. While the dynamics of 3D volume preserving flows with or without periodic time-dependence shares many qualitative features with Hamiltonian systems, they cannot rigorously associated to this class. Therefore, strictly symplectic methods do not apply to this case. Nevertheless, there are generalizations of the symplectic methods that can be applied to ensure volume-preservation in odd-dimensional systems.

Following
Answer added to:
5 What objective function is better for non linear optimization algorithm in EXCEL?
By Vassilis Aschonitis · Universita degli studi di Ferrara

Samuel Arba Mosquera · Independent Researcher

similar to MengChang, it seems to me that the least squares approach you apply is rather general and does not depend on linear or non-linear behaviour... [more]

similar to MengChang, it seems to me that the least squares approach you apply is rather general and does not depend on linear or non-linear behaviour behind. Anyway, you may want to add or refine you model (e.g. by adequate weighting or selection of sampled values) to avoid biasing your results towards a specific region or response model. I mean, since you have your simulated values, you already have a model for the response and you know how linear or non-linear (i.e. which other pattern) it is. Being this the case you can select also non-linear sampling, or weight differently (lower weights) for the sampled regions leading to similar responses. Ultimately, you may also linearize your problem, and check for consistency on your solver results (which I also use quite often).

Following
Answer added to:
18 What is the purpose of dimensionless equations?
By Alfredo Hernández Rodríguez · National Polytechnic Institute

Joseph Uphoff · The Institute Of Martial Arts, Journal Of Regional Criticism

The machine is very slow today.

The machine is very slow today.

Following
Answer added to:
204 Are differential equations the proper tool to describe reality?
By Marek Gutowski · Instytut Fizyki PAN

Antonio Quintana · Center for Research and Advanced Studies of the National Polytechnic Institute

As we always say, Physics is just a (very well) approximation of reality. Sometimes we abuse of these approximations, and that differentiates a good p... [more]

As we always say, Physics is just a (very well) approximation of reality. Sometimes we abuse of these approximations, and that differentiates a good physicist from a bad one. I have some examples in which I think the approximations are good enough. We have much of them in Statistical Mechanics. I remember when a teacher was applying the Equipartition Theorem for a discrete variable, when the demonstration is clearly valid only for continuous variables (is made in terms of Riemman's integrals) and I inmediatly asked why he did that, and he made me remember that an integral is the limit of a infinite sum, and those concepts are of course approximations of reality, so we can "abuse" of the notation in certain cases (when the number of particles is "big enough" or the integral is approximate to the discrete sum).

Following
Answer added to:
13 How can I solve a nonlinear differential equation in matlab software?
By Kazem reza kashyzadeh · Sharif University of Technology

Francesco Ferrante · Laboratoire d’Analyse et d’Architecture des Systèmes (LAAS)

Clearly, I supposed that y=y(x)

Clearly, I supposed that y=y(x)

Following
Answer added to:
21 Is a triangular waveform a sinusoidal function or not?
By Gagan Meena · Indian Institute of Technology Delhi

Stevan Hilarius

So, it is possible and we can call it a bipolar input, am I right? And what will we call it? DC or AC? (Still a bit confused for the DC/AC). So, what... [more]

So, it is possible and we can call it a bipolar input, am I right? And what will we call it? DC or AC? (Still a bit confused for the DC/AC). So, what is the main difference between AC and DC? Their value/polarity (- or +) or frequency (as I know the frequency for DC is 0, CMIIW). Thanks.

Following
Answer added to:
1 Mathematical proofs-
By Maximiliano Vides · National University of Cordoba, Argentina

Following
Answer added to:
5 When did n! become popular for "n factorial"? How was it made popular?
By D. Kreher · Michigan Technological University

Samuel Arba Mosquera · Independent Researcher

Pascal may have know factorial, but not necessarily the n! notation. The linked website also shows: "History, biographies Multiple scientists worked ... [more]

Pascal may have know factorial, but not necessarily the n! notation. The linked website also shows: "History, biographies Multiple scientists worked on this subject, but the principal inventors are J. Stirling in 1730 who gives the asymptotic formula after some work in collaboration with De Moivre, then Euler in 1751 and finally C. Kramp and Arbogast who introduces between 1808 and 1816 the actual notation: n!. Of course other scientists such as Taylor also worked a lot with this notation."

Following
Answer added to:
47 Free math software and tools.
By Juan-Esteban Palomar Tarancon · I am retired

Juan-Esteban Palomar Tarancon · I am retired

An interesting software is http://cocoa.dima.unige.it/users.html Do not confuse with cocoa programming language. It is a computation system in commuta... [more]

An interesting software is http://cocoa.dima.unige.it/users.html Do not confuse with cocoa programming language. It is a computation system in commutative algebra.

Following
Answer added to:
23 How can we recognize the pattern of a high dispersion dataset?
By Vahid Nouri · Islamic Azad University Mashhad Branch

Vahid Nouri · Islamic Azad University Mashhad Branch

Do you think frcatal distance measurment can solve this problem? Do you have any idea about fractal clustering to predict this dataset?

Do you think frcatal distance measurment can solve this problem? Do you have any idea about fractal clustering to predict this dataset?

Following
Answer added to:
40 What is the best introductory book on Functional Analysis?
By Enrique Mallada · Cornell University

A. Breev · Tomsk State University

In my opinion, the good detailed book devoted to the functional analysis, is K. Moren, Methods of Hilbert Space (1959 Varshava). And Rudin Functional ... [more]

In my opinion, the good detailed book devoted to the functional analysis, is K. Moren, Methods of Hilbert Space (1959 Varshava). And Rudin Functional Analysis (1991).

Following
Answer added to:
35 Does anyone know any approximate analytic solution for the root of the equation a*x^b-c*x^d-e=0?
By Henrique Giacomini · University of Toronto

Following
Answer added to:
27 Can anybody suggest me some open problems in mathematics involving matrix theory
By Uma M. S · JIT, Bangalore , India

Herbert Homeier · Universität Regensburg

As regards the square root of a symmetric positive matrix with real entries, this is well-defined over the field of the real numbers. Such a symmetric... [more]

As regards the square root of a symmetric positive matrix with real entries, this is well-defined over the field of the real numbers. Such a symmetric strictly positive matrix M has only positive real eigenvalues. If P(lambda) is the orthogonal projector to the eigenspace for eigenvalue lambda >0, i.e., if M = sum lambda P(lambda), then sqrt(M) = sum sqrt(lambda) P(lambda) where the sum. is over all eigenvalues in both cases. This definition is meaningful because sqrt is one-to-one and onto the reak halfline (0,infinity). For nxn matrices of the form that Donald described it is easy to show that they are completely symmetric under the permutation group of n objects whence one may give all the eigenvectors explicitly. Then, all the eigenvalues follow easily, and it turns out that the vector of n ones is the only eigenvector (not normalized) with a non-degenerate eigenvalue e1, while all the other eigenvectors belong to an (n-1)-fold degenerate eigenvalue e2. The orthogonal projector for e1 is the easily found, and the projector for e2 is P(e2) = I - P(e1) where I is the nxn unit matrix. The latter is seen to hold since the n eigenvectors form a complete orthonormal basis in the relevant vector space. Since the entries mentioned by Donald are positive integers it could be that he is talking about some vector space over a finite field instead of that of the real numbers. Then, Christophers comment may be relevant that one has to define the meaning of the square root of a matrix differently. It could well be that a redefinition of the square root of a number for such fields could suffice for this end.

Following
Answer added to:
4 Can anyone tell me how to check the convergence and divergence of the function like integral(1/{Sqrt(x^4-1)}), with lower limit 2 and upper limit infinity?
By Tauqeer Hussain Shah · Linnaeus University

Victor Shestopal · Institute for Theoretical and Experimental Physics

P>-1

P>-1

Following
Answer added to:
4 What is the percolation threshold in case of polymer matrix composite and what is its significance?
By Unmesh Vibhute · College of Engineering, Pune

Unmesh Vibhute · College of Engineering, Pune

Thanks Nadia Saidi & John Texter

Thanks Nadia Saidi & John Texter

Following
Answer added to:
11 Transforms versus convolution?
By Avinash Kumar · Rayat Institute of Engineering and Information Technology

Yumnam Kirani · Centre for Development of Advanced Computing

@Imran Shafi, To my view egg came earlier thann hen. The logic is simple, egg has only one cell and hen have many cells. 2 cannot come before 1 be... [more]

@Imran Shafi, To my view egg came earlier thann hen. The logic is simple, egg has only one cell and hen have many cells. 2 cannot come before 1 because to make 2 we need two 1's. Regarding convolution and transformation, I would rather say that transformation is any operation or a set of operations you on something to change the original form to someother form. The operation may also be a convolution operation or some simple addition or subtraction operation. For example, you have an image matrix (say gray image) and you subtract every pixel of the image from 255. Then you will get another image, called negative image which is a simple example of transfromation. Transformation may also be done using convolution operation, for example, you have an image matrix, and you perform convolution operation of it with a Fourier kernel of appropriate size, then you will get Fourier transform. The comvolution operation may also be combined with some other operations in a some other kind of transforms, for example, wavelet transform in which you perform convolution of the signal with wavelet transform kernel (popularly called wavelet filter coefficients) then you perform downsampling operations. About convolution, it is nothing but a polynomial multiplication. Why we see convolution operation as simple multiplication in Z tranforms is becuase in Z tranforms, the signals are in polynomial form in Z. In Fourier domain, the signals are represneted in the form of polynomial in exponential. So, in the Fourier domain also, we convolution means multiplication. More about convolution and multiplication can be obtained from the following link www.oocities.org/kiranisingh/multi.html . Hope it may help you. Y. K. Singh

Following
Answer added to:
25 How to publish a paper in Mathematics online? Anyone please give me some clear guidelines.
By Rakesh Pk · iact Computer Education

Prasanth G. Narasimha-Shenoi · Government College, Chittur, Palakkad, Kerala, India - 678104

You may use Arxive, for publishing these journals online. Its easy and good

You may use Arxive, for publishing these journals online. Its easy and good

Following
Answer added to:
1 Up to isomorphism how many groups are possible of order n(>0),for any n?
By Vinay Pandey · Indian Institute of Technology Bombay

Amin Saéidi · Kharazmi University

In general, no formula is known for the number of groups of order n. The number is sometimes incredibly huge. For example, there exist about 50 billi... [more]

In general, no formula is known for the number of groups of order n. The number is sometimes incredibly huge. For example, there exist about 50 billion groups of order 1024. If |G|=pq where p,q are prime numbers and p < q, then there exists one or two groups of order pq, according to whether or not p divides q-1.

Following
Answer added to:
89 What is your favourite algorithm?
By Daniel Page · University of Manitoba

Mario Buntic · University of Zagreb

I vote for Ant Colony Optimization metaheuristic. It was defined by Dorigo, Di Caro and Gambardella.

I vote for Ant Colony Optimization metaheuristic. It was defined by Dorigo, Di Caro and Gambardella.

Following
Answer added to:
2 Convergence of an infinite series, each term of which is a product of two infinite cgt series. Product taken needs not be of consecutive terms.
By Arghya Bandyopadhyay · Khalisani College, Chandannagar

Arghya Bandyopadhyay · Khalisani College, Chandannagar

I should have posed the question differently, to make my point clear. Let sigma{an} and sigma{bn} be two given series, we can always form the double s... [more]

I should have posed the question differently, to make my point clear. Let sigma{an} and sigma{bn} be two given series, we can always form the double series sigmaf(m, n), where f(m, n) = ambn. For every arrangement g of f into a sequence G, we are led to a further series sigmaG(n) The convergence and sum of the series sigmaG(n) will depend on the arrangement of g. Different choices of g may yield different values of the product. But there is one very important case in which the terms f(m, n) are arranged diagonally to produce the Cauchy product and as @ Patrick_Sole has said the absolute convergence of series sigma(an) and sigma(bn) [ not the squared one, I think] implies convergence of the Cauchy product [ In fact Cauchy product arises quite naturally when we multiply two power series]. My point was about the other possible arrangement and their relation with convergence. I have simply no idea.... I would love no know on this.

Following
Answer added to:
34 Any body can tell me.. How to find the root of any number or digit without using the calculator.. I need formula for that...
By Deepak Sah · ncet college bangalore(vtu)

Nimmagadda Venkata Nagendram · Lakireddy Bali Reddy College of Engineering

use synthetic division method or finding similar numbers or digits as factors for finding roots of examples herewith 4 = 2 X 2 consider 2 square r... [more]

use synthetic division method or finding similar numbers or digits as factors for finding roots of examples herewith 4 = 2 X 2 consider 2 square root of 9 = 3 X 3 is 3 so on.

Following
Answer added to:
6 Regarding Prime numbers.
By Tridib Dutta · University of Pittsburgh

Tridib Dutta · University of Pittsburgh

Well..I just found out that these are called Per-mutable primes...and there aren't very many. In fact, there is a wikipedia entry regarding prime numb... [more]

Well..I just found out that these are called Per-mutable primes...and there aren't very many. In fact, there is a wikipedia entry regarding prime numbers. Here is the link http://en.wikipedia.org/wiki/Permutable_prime

Following

About Mathematics

Mathematics, Pure and Applied Math

Topic Followers (43388) See all

Sergey Gubarenko

University of Toronto
Mehrzad Mohareri

Isfahan University of Technology
Venkata siva rama raju Sagiraju

Maharaj Vijayaram Gajapati Raj College of Engineering
Mattia Manica

Università degli Studi di Trento
Javier Eduardo Contreras Doria

Metropolitan Autonomous University
Thomas Sonar

Technische Universität Braunschweig
J. P. Vila

Institut National des Sciences Appliquées de Toulouse
Stefan Moller

University of South Africa
Hector Bonilla

Pontificia Universidad Javeriana - Cali
Jens Kaad

Paris Diderot University

Mathematics

About Mathematics

Topic Followers (43388) See all

Log in