The Experts below are selected from a list of 13596 Experts worldwide ranked by ideXlab platform

Martin Ziegler - One of the best experts on this subject based on the ideXlab platform.

  • real computation with least discrete advice a complexity theory of nonuniform computability
    6th International Conference on Computability and Complexity in Analysis (CCA'09), 2008
    Co-Authors: Martin Ziegler
    Abstract:

    It is folklore particularly in numerical and computer sciences that, instead of solving some general problem $f:A\to B$, additional structural information about the input $x\in A$ (that is any kind of promise that $x$ belongs to a certain subset $A'\subseteq A$) should be taken advantage of. Some examples from real number computation show that such discrete advice can even make the difference between computability and uncomputability. We turn this into a both topological and combinatorial complexity theory of information, investigating for several practical problem show much advice is necessary and sufficient to render them computable. Specifically, finding a nontrivial solution to a Homogeneous Linear Equation $A\cdot\vec x=0$ for a given singular real $n\times n$-matrix $A$ is possible when knowing $\rank(A)\in\{0,1,\ldots,n-1\}$; and we show this to be best possible. Similarly, diagonalizing (i.e. finding a basis of eigenvectors of) a given real symmetric $n\times n$-matrix $A$ is possible when knowing the number of distinct eigenvalues: an integer between $1$ and $n$ (the latter corresponding to the nondegenerate case). And again we show that $n$--fold (i.e. roughly $\log n$ bits of) additional information is indeed necessary in order to render this problem (continuous and) computable; whereas finding \emph{some single} eigenvector of $A$ requires and suffices with $\Theta(\log n)$--fold advice.

  • real computation with least discrete advice a complexity theory of nonuniform computability
    arXiv: Computational Complexity, 2008
    Co-Authors: Martin Ziegler
    Abstract:

    It is folklore particularly in numerical and computer sciences that, instead of solving some general problem f:A->B, additional structural information about the input x in A (that is any kind of promise that x belongs to a certain subset A' of A) should be taken advantage of. Some examples from real number computation show that such discrete advice can even make the difference between computability and uncomputability. We turn this into a both topological and combinatorial complexity theory of information, investigating for several practical problems how much advice is necessary and sufficient to render them computable. Specifically, finding a nontrivial solution to a Homogeneous Linear Equation A*x=0 for a given singular real NxN-matrix A is possible when knowing rank(A)=0,1,...,N-1; and we show this to be best possible. Similarly, diagonalizing (i.e. finding a BASIS of eigenvectors of) a given real symmetric NxN-matrix is possible when knowing the number of distinct eigenvalues: an integer between 1 and N (the latter corresponding to the nondegenerate case). And again we show that N-fold (i.e. roughly log N bits of) additional information is indeed necessary in order to render this problem (continuous and) computable; whereas for finding SOME SINGLE eigenvector of A, providing the truncated binary logarithm of the least-dimensional eigenspace of A--i.e. Theta(log N)-fold advice--is sufficient and optimal.

Wang Xiao-feng - One of the best experts on this subject based on the ideXlab platform.

  • One-time Password Authentication Protocol Based on Non-Homogeneous Linear Equations
    Computer Engineering, 2010
    Co-Authors: Wang Xiao-feng
    Abstract:

    An identity authentication protocol and a message authentication protocol based on non-Homogeneous Linear Equation proposed by Liu Li and two other co-authors(Journal of Academy of Armored Force Engineering,2005,No.2) uses a single authentication protocol which can not resist the pseudo-sever attack,and can be only applied in computer network communication system of fixed terminal.To solve the problem,this paper proposes an improved scheme: a mutual authentication protocol by using RSA arithmetic at the convenience of user authentication and security.The new scheme can conquer the security problem of the original scheme and hold higher security and operability.

Joséricardo Figueiredo - One of the best experts on this subject based on the ideXlab platform.

  • Performance of five-point differencing schemes for two-dimensional fluid transport Equations
    Journal of Computational Physics, 1992
    Co-Authors: Joséricardo Figueiredo
    Abstract:

    Abstract Sample exact solutions sweeping the Fourier spectrum of the steady-state, two-dimensional, constant coefficients, Homogeneous Linear Equation for the convective and diffusive transport of a conserved property in fluid media are used as test cases for a comparative study of four numerical discretization schemes: central differencing, upwind scheme, and the exponential schemes due to Allen and Southwell and Dennis and Hudson. The generality provided by this method allows a discussion on the concept of numerical diffusion in multi-dimensional problems, which identifies the upwind and other schemes' errors with the angle between the flow and the grid.

Frank E. Harris - One of the best experts on this subject based on the ideXlab platform.

  • Vectors and Matrices
    Mathematics for Physical Science and Engineering, 2014
    Co-Authors: Frank E. Harris
    Abstract:

    This chapter introduces the basic concepts of vector algebra and shows how to work with vectors in Maple and Mathematica. The basic properties of matrices and symbolic computations of them are presented. The determinant is defined and its role in the solution of Linear Equation systems is discussed. The solution of Homogeneous Linear Equation systems is examined in detail.

Samir Fatajou - One of the best experts on this subject based on the ideXlab platform.

  • Exponential dichotomy and pseudo-almost automorphy for partial neutral functional differential Equations
    Nonlinear Analysis: Theory Methods & Applications, 2009
    Co-Authors: Mohamed Alia, Khalil Ezzinbi, Samir Fatajou
    Abstract:

    Abstract In this work, we study the existence and uniqueness of a pseudo-almost automorphic solution for some partial functional differential Equations of neutral type. We assume that the undelayed part is not necessarily densely defined and satisfies the Hille–Yosida condition. The delay part is assumed to be pseudo-almost automrophic in time. We prove if the Homogeneous Linear Equation has an exponential dichotomy, then the nonHomogeneous Linear Equation has a unique pseudo-almost automorphic solution. An application is given for some nonLinear Equations. We present also a new concept of generalized pseudo-almost automorphy.

  • C n -almost automorphic solutions for partial neutral functional differential Equations
    Applicable Analysis, 2007
    Co-Authors: Khalil Ezzinbi, Samir Fatajou, Gaston M. N’guérékata
    Abstract:

    In this work, we study the existence of C n -almost periodic solutions and C n -almost automorphic solutions (n ≥ 1), for partial neutral functional differential Equations. We prove that the existence of a bounded integral solution on ℝ+ implies the existence of C n -almost periodic and C n -almost automorphic strict solutions. When the exponential dichotomy holds for the Homogeneous Linear Equation, we show the uniqueness of C n -almost periodic and C n -almost automorphic strict solutions.