Mathematics, Pure and Applied Math

• Adrien Brice

  Please i have this differencial equation problem which i find difficult solving

  y = 1=(x²+c) is a one-parameter family of solutions of the first-order Dierential Equation; y+ 2xy² = 0. Find a solution of the first-order Initial Value Problem(IVP) consisting of thisy = 1=(x²+c) is a one-parameter family of solutions of the first-order Dierential Equation; y+ 2xy² = 0. Find a solution of the first-order Initial Value Problem(IVP) consisting of this differential equation and the given initial condition. Give the largest interval I over which the solution is defined. y(2) =1/3

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  • 
    Qassem Al-Hassan replied

    Hi Dr. Lakhdar Thanks, that is exactly what I said.

    8 hours ago
• Ramos Y. Dan

  Mathematics was invented or discovered?

  I could not reach a convincing answer. Could you help me?

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  • 
    Waldemar De Maio replied

    A Matemática é uma linguagem, simbólica que representa as estruturas neurofisiológicas do cérebro humano. São duas as estruturas: a de topologia discreta e a do raciocínio lógico que é um anelA Matemática é uma linguagem, simbólica que representa as estruturas neurofisiológicas do cérebro humano. São duas as estruturas: a de topologia discreta e a do raciocínio lógico que é um anel binário. Vide; "O raciocínio lógico matemáticoa: sua estrutura neurofisiológica. Tese de doutorado disponível na Unesp de Rio claro, ou pela editora Arte e Ciência de São Paulo-SP - Brasil.

    1 day ago
• Rajeswari Kuber

  Hi , I am rajeswari. May i know a book which gives a basic results or informations about Matrix theory.

  Hi , I am rajeswari. May i know a book which gives a basic results or informations about Matrix theory.

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  • 
    Rajesh Mahadevan replied

    The book by Gilbert Strang Linear Algebra and it's applications is a good balance between theory, aplications and calculations. It is found in most libraries

    3 days ago
• Manuel Ortigueira

  Fractional derivatives

  What is really a fractional derivative? When can we affirm it is? Shouldn't we require that they recover the classic when the order becomes integer? The word fractional appears in a lot ofWhat is really a fractional derivative? When can we affirm it is? Shouldn't we require that they recover the classic when the order becomes integer? The word fractional appears in a lot of contexts. It became like a fashion. It is clear that Grunwald-Letnikov, Riemann-Louville, Caputo, or Riesz are fractional derivatives, but it is clear for me that the so called fractional Fourier transform is not really fractional. And like this one there are others. Personally, I believe that the most correct way of going into the fractional derivative is the Grunwald-Letnikov, because all the others can be deduced from it. Besides it is the most suitable for numerical computations.

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  • 
    Yang Xiaojun replied

    The sixth FDA workshop, FDA'2013 (FDA : Fractional differentiation and its Applications) will be held in Grenoble, France, February 4-6, 2013 in the SSSC joint conferences (Track D of thisThe sixth FDA workshop, FDA'2013 (FDA : Fractional differentiation and its Applications) will be held in Grenoble, France, February 4-6, 2013 in the SSSC joint conferences (Track D of this conference). All the important dates of this workshop are in the attached file Papers submission deadline June 15th, 2012) . As for all IFAC events, I remind that all the papers will be peer-reviewed. The reviews will be done on a 6 pages draft (full paper, no abstract). More information also available on the conference web site : http://www.gipsa-lab.fr/SSSC2013/ Invited sessions within the technical scope of the conference are also solicited. These proposals should contain six (6) full papers, or five (5) including a survey paper limited to 12 pages

    6 days ago
• Izac Brandão

  The mathematics can explain everythings in universe, using just numbers and algebra, without gravity, nuclear force, and this like this?

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    Helio Barnabe replied

    A short account on: ‘The Mathematics of Evolution’ Quantum mechanics, a new wing of science born in the first decade of the last century, was only the phenomena of atomicA short account on: ‘The Mathematics of Evolution’ Quantum mechanics, a new wing of science born in the first decade of the last century, was only the phenomena of atomic infrastructure. Someone has said that it is a mathematical formalism that describes the nature of subatomic. Max Planck had discovered that the evolution of matter was given to 'jump' or better said, the transformation was not a continuous phenomenon, that is, he said that the matter in evolution gives and receives 'quantities' compatible with their own 'Nature'. Max Born, on the other hand, said that the waves of the electrons are waves of probability - probable values. After many years of research looking at data from a variety of natural phenomena, the theory "The mathematics of evolution 'has been developed based on the' Theory of Probability '. We have repeated on several occasions that the theory applies not only to physical and chemical phenomena, nor only to quantum physics, but also to all worldly phenomena, ie, serve all phenomena related to the treatment of classical physics, our social, economic and even our politics. The nature contrary to what we thought acts as 'pulses' ('many') in both the micro and macro evolution. Remember, again, "literally", the matrix representing the development of the basic equation Theory: n B ^ i Hn,I = ( ) ----------------- [(C - B) ^ (n - i)] i C ^ i (n - 1) or, as preferred: Hn, k * {[(B ^ i)] * [(C - B) ^ (n - i)] / [C ^ (n - 1)]} So - We represent the matrix: n / i 0 1 2 3. . . 0 C 1 (C-B) B 2 [(C-B)^2]/C 2B(C-B)/C (B^2)/C 3 [(C-B)^3]/(C^2) 3B[(C-B)^2]/(C^2) 3(B^2)(C-B)/(C^2) (B^3)/(C^2) . . . Where Hn, i represents the relative amount of one element of a 'family' i after n periods of evolution. These elements can be referred to the most varied in nature depending on the system being analyzed. C is the 'potential' of the system, B is the characteristic feature of the system and combined with the form (B / C) controls the probability of the development characteristics, i represents the family of progeny developments. k is equal to 'Number Binomial of Newton: n k = ( ) i Whose value is calculated as: n! (n factorial) divided by the product of i! (I factorial) by (n - i)! (Unless i factorial), ie: n! -------------- (n - i)! * I! Important to note that the theory "The mathematics of evolution 'runs fast all natural phenomena without bothering if they were framed in' Quantum Physics', in 'Classical Physics', phenomena in economic, social and even in games of chance by going over of 'chaos theory'. There are many fields of research in the theory, but have not yet had time or technical ability to do so. We quote here an open field in Music. We remember the musician Vincenzo Galilei (father of the famous scientist Galileo Galilei), among other qualities, was a research scientist who wanted to study music from the point of view of mathematics (frequencies). The theory provides an opportunity to study this subject. Finally, we say that the theory "The mathematics of evolution 'has an open field for research. We quote (among others) some subjects studied: - The mathematics of the phenomenon of the Decay of Radioactive Isotopes; - The mathematics of Stem Cell; - Computational Science; - Construction of Periodic Table of Chemical Elements; - Dark Matter Seen By Mathematics'; - The discovery of 'Atom of God'; - The mathematics of evolution; - New Vision Mathematics on Gambling; - Wave of Nuclear Physics; - Interstellar Dust - New Cosmological Vision; - Simplifying the Calculation of the decay of radioactive isotopes; - Realize the Some Interesting Aspects of Values in Energy Levels of the Hydrogen Atom; - Study of Infant Mortality Rate; - Identifying Mathematically System in Transformation; - Overview of the theory "The mathematics of evolution 'on Economic Statistics; - Scale Well Tempered Bach; - Granulometry; - (...) We will be waiting for other researchers to enter the spirit of this new scientific theory and give the deserved breakthrough in our science. We are certain that Nature uses mathematics to regulate the development of all its phenomena. Engineer HélioBarnabé Caramuru São Paulo, 2012, March, 02 e-mail: helio.barnabe@gmail.com / helio_barnabe@hotmail.com / helio.barnabe @ terra.com.br

    10 days ago
• Saravana Priyan

  Which is the most complicated "physical system" available in nature?

  If systems are to be ranked based on systems theory, which would be the most complicated and why?

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  • 
    Henk Smid replied

    And dear Sam Baker, I am glad that I dabble in physics, mathematics, and computer stuff. Strangely enough, I care for people rather than particles and fields and numbers. As far as I can see, yourAnd dear Sam Baker, I am glad that I dabble in physics, mathematics, and computer stuff. Strangely enough, I care for people rather than particles and fields and numbers. As far as I can see, your world-view does not. But best wishes, Henk Smid

    11 days ago
• Dr. Omprakash Sikhwal

  Any one suggest books on domination graph theory?

  Domination graph theory is the most popular topic for research.

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  • 
    Smruti Mane replied

    Fundamentals in domination in graph theory by Teresa Hynes

    11 days ago
• Ayman Arafa

  Evaluating the Lyapunove exponents for time delay dynamical systems

  Does anyone have any recommendations for programs that evaluate the Lyapunove exponents for time delay dynamical systems?

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  • 
    Y. Azizi replied

    If you search for algorithm: http://sprott.physics.wisc.edu/chaos/ddele.htm

    16 days ago
• Juan-Esteban Palomar Tarancon

  Free math software and tools.

  The following list includes free math software and tools together with the corresponding descriptions and download sites. Operating systems: Scientific Linux: A linux distribution put together byThe following list includes free math software and tools together with the corresponding descriptions and download sites. Operating systems: Scientific Linux: A linux distribution put together by Fermilab and CERN. Freely available from http://www.scientificlinux.org/ Ubuntu Linux: A Linux distribution, easy to install and freely available from http://www.ubuntu.com/ Debian: Perhaps the best Linux distribution. http://www.debian.org/ DesktopBSD: A freeBSD distribution easy to use which can be tested through a live DVD. Freely available from http://www.desktopbsd.net/ BSD: Several Unix distributions. http://www.junauza.com/2009/04/5-best-bsd-distributions.html Applications for symbolic calculus. wxMaxima: Calculus with a graphic interface. Freely available from http://sourceforge.net/projects/wxmaxima/ Axiom: Similar to the preceding one. http://axiom-developer.org/ Euler: id. http://euler.sourceforge.net/ Scilab: id. http://www.scilab.org/ octave: id. http://www.gnu.org/software/octave/ Gap: Computational discrete algebra, http://www.gap-system.org/ R: Statistics http://en.wikipedia.org/wiki/R_(programming_language) PSPP: Statistics http://www.gnu.org/software/pspp/ haskell: Pure and lazy functional programming language with an interpreter. http://hackage.haskell.org/platform/ Astronomy: Stellarium: Free astronomy appl. http://www.stellarium.org/ Star charts: Free star charts PDF files. http://www.midnightkite.com/starcharts.html Math graphics: Gnuplot: To build any graphic in 2D or 3D. Freely available from http://www.gnuplot.info/ DISLIN: A graphical library, easy to use. http://www.dislin.de/ Word processors: TexMacs: WYSIWYG editor with a graphical interface, by means of which one can type scientific texts, and export them in PDF, PS, HTML, LaTeX formats. Freely available from http://www.texmacs.org/ Lyx: Similar to the preceding one. http://www.lyx.org/ Miktex: A complete LaTeX distribution for Windows. Freely available from http://miktex.org/ TexMaker: A LaTeX editor: Freely available from http://www.xm1math.net/texmaker/ TeXniccenter: Another powerful LaTeX editor for Windows OS. http://www.texniccenter.org/ Kile: Another LaTeX editor. http://kile.sourceforge.net/ TexShop: A LaTeX distribution and editor for Mac OS X. Freely available from http://pages.uoregon.edu/koch/texshop/ Texlive: A LaTeX distribution for Linux and Unix OS'. http://www.tug.org/texlive/ Open Office: A package similar to Microsoft Office: http://www.openoffice.org/

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  • 
    Kousalya Pappu replied

    Thanks to every one who is contributing valuable information here. can we download an equivalent software for Mathematica from this? http://www.sagemath.org/

    16 days ago
• Gholamreza Soleimani

  The chain Rule

  If we have: z = f (x,y) and z = f (t), could you please answer to my below questions: 1) Can I say: x = f (t) and y = f (t)? 2) How can I analyze dz/ dt? Thanks in advance for your help.If we have: z = f (x,y) and z = f (t), could you please answer to my below questions: 1) Can I say: x = f (t) and y = f (t)? 2) How can I analyze dz/ dt? Thanks in advance for your help. Best Regards Gholamreza Soleiman

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  • 
    Thierry Jecko replied

    It is difficult to help since the letter "f" seems to have two different meanings in your question. Is "f" a function of two variables (x, y) or a function of one variable t. Maybe is yourIt is difficult to help since the letter "f" seems to have two different meanings in your question. Is "f" a function of two variables (x, y) or a function of one variable t. Maybe is your question the following. Let f be a real function of two real variables (x, y) and g be another real function of one real variable t. Now consider the set S of real numbers (x, y, t) such that g(t)=f(x,y). Is it possible to find two real functions X and Y of t such that (x, y, t) belongs to S exactly when x=X(t) and y=Y(t) ? To this question, the answer is most of the time no. Take for instance g(t)=t and f(x, y)=x+y. If the answer to the question was yes, then, for each t, you would have exactly one couple (x, y), namely (X(t), Y(t)), such that x+y=t. But this is not true for instance for t=1 since (x, y)=(1, 0) and (x, y)=(0, 1) are two different couples such that x+y=1. By the way, "the chain rule" means something else in mathematics.

    18 days ago
• Suresh Kannan

  Convergent sequences of real numbers

  Suppose {an}, {bn} are convergent sequences of real numbers such that an > 0 and bn > 0 for all n. Suppose lim an = a and lim bn = b. Let cn = an/bn. n -> oo Then which ofSuppose {an}, {bn} are convergent sequences of real numbers such that an > 0 and bn > 0 for all n. Suppose lim an = a and lim bn = b. Let cn = an/bn. n -> oo Then which of the following is/are correct? 1. {cn} converges if b > 0 2. {cn} converges only if a = 0 3. {cn} converges only if b > 0 4. lim sup cn = infinity if b = 0 I guess (1) is correct. and (2), (3) are not correct. Am I right? and What about option (4)? please explain.

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  • 
    Thierry Jecko replied

    If a and b are finite and b is nonzero, then c_n converge to a/b (this can be proved). If b=0, you may have different behaviors: If a_n= n and b_n=1/n then b=0, a=+infinity and c_n converge to 1.If a and b are finite and b is nonzero, then c_n converge to a/b (this can be proved). If b=0, you may have different behaviors: If a_n= n and b_n=1/n then b=0, a=+infinity and c_n converge to 1. If a_n= n^2 and b_n=1/n then b=0, a=+infinity and c_n diverge to +infinity. If a_n= 2/n and b_n=1/n then b=0, a=0 and c_n converge to 2. If a_n= 2/n^2 and b_n=1/n then b=0, a=0 and c_n converge to 0. If a_n= 2/n and b_n=1/n^2 then b=0, a=0 and c_n diverge to +infinity. If a_n=(2+(-1)^n)/n and b_n=1/n then b=0, a=0 and c_n has no limit. So 1 is true, 2 is false, 3 is false. 4 is also false since for b=0 one can have the convergence of c_n i.e. limsup c_n=lim c_n is finite.

    19 days ago
• Muhammad Saeed Akram

  Applications of matrix factorizations in Computer Science

  Does anybody know some concrete applications of matrix factorizations in Computer Science?

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  • 
    Walner Mendonça Dos Santos replied

    Exist some applications with images processing. For instance, eigenfaces and images compression. You may to search this in Google. You should find some articles.

    19 days ago
• Yang Xiaojun

  Local fractional Fourier analysis, Advances in Mechanical Engineering and its Applications, 1(1) (2012)12-16 Local fractional calculus (LFC) deals with everywhere continuous but nowhereLocal fractional Fourier analysis, Advances in Mechanical Engineering and its Applications, 1(1) (2012)12-16 Local fractional calculus (LFC) deals with everywhere continuous but nowhere differentiable functions in fractal space. In this letter we point out local fractional Fourier analysis in generalized Hilbert space. We first investigate the local fractional calculus and complex number of fractional-order based on the complex Mittag-Leffler function in fractal space. Then we study the local fractional Fourier analysis from the theory of local fractional functional analysis point of view. We finally propose the fractional-order trigonometric and complex Mittag-Leffler functions expressions of local fractional Fourier series. http://www.worldsciencepublisher.org/journals/index.php/AMEA/article/view/264
• Tridib Dutta

  Non negative matrix factorization

  Does anyone know how many different versions of the Non Negative Matrix factorization exist and what they are ? I did a Google search, but couldn't figure out any definitive answer.

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  • 
    Tridib Dutta replied

    Thanks Qassem, I will look into it. It's a famous book in Matrix theory. May contain some pointers at least.

    25 days ago
• Saravana Priyan

  Is the limit of mathematics the limit of science?

  Effect of godel incompleteness theorem on science

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  • 
    Antonio Lucero replied

    We modern humans have to "grow up" and realize that there is no completeness or certainty. Emotionally, we long for such a "well-defined and orderly and predictable" world. But we have to face facts.We modern humans have to "grow up" and realize that there is no completeness or certainty. Emotionally, we long for such a "well-defined and orderly and predictable" world. But we have to face facts. We can employ applicable limited models to help us solve pragmatic problems, but we need to realize that our models are not reality and certainly not universal.

    27 days ago