on a system of klein gordon type equations with acoustic boundary conditions we prove the existence uniqueness and uniform stabilization of global solutions for a generalized system of klein gordon type equations with acoustic boundary conditions on a portion of the boundary and the dirichlet boundary condition on the rest

global smooth solutions and exponential stability for a nonlinear beam in this paper we consider a dynamical system with boundary input and output describing the bending vibrations of a quasi linear beam where the nonlinearity comes from hooke s law first we derive an existence result for short time solutions of the system of equations then we show that the structure of the boundary input and output forces the system to admit global solutions at least when the initial data and the boundary input are small in a certain sense in particular we prove that the norm of the state of the system decays exponentially if the input becomes zero after a finite time the input being zero can be understood as a boundary feedback

on the wave equation with hyperbolic dynamical boundary conditions interior and boundary damping and supercritical sources abstract the aim of this paper is to study the problem u t t u p x u t f x u in 0 u 0 on 0 0 u t t u u q x u t g x u on 0 1 u 0 x u 0 x u t 0 x u 1 x in where is a bounded open subset of r n with c 1 boundary n 2 1 is relatively open on denotes the laplace beltrami operator on is the outward normal to and the terms p and q represent nonlinear damping terms while f and g are nonlinear perturbations in the paper we establish local and global existence uniqueness and hadamard well posedness results when source terms can be supercritical or super supercritical

uniform stabilization of wave equation with localized damping and acoustic boundary condition abstract in this paper we deal with stability of the nonlinear wave equation with acoustic boundary conditions to non locally reacting boundary

some nonlinear wave equations with acoustic boundary conditions abstract we prove the existence and uniqueness of global solutions to the mixed problem for the carrier equation u tt m u 2 dx u u t u t 0 with acoustic boundary conditions

global solutions and blow up solutions for a nonlinear string with boundary input and output abstract in this paper we investigate the global solutions and blow up solutions for a nonlinear string with boundary input and output and prove that under some conditions the system has global solutions and blow up solutions respectively

approximation theorems for the propagators of higher order abstract cauchy problems in this paper we present two quite general approximation theorems for the propagators of higher order in time abstract cauchy problems which extend largely the classical trotter kato type approximation theorems for strongly continuous operator semigroups and cosine operator functions then we apply the approximation theorems to deal with the second order dynamical boundary value problems

an energy preserving nonlinear system modeling a string with input and output on the boundary abstract we study an energy conserving distributed parameter system described by a nonlinear string equation with the input and output at the boundary we prove the existence of global smooth solutions to this quasilinear hyperbolic system if the initial data and the boundary input are small if moreover the input function becomes zero after some finite time then the state trajectories decay exponentially

renormalization group solution of the chutes ladder model abstract we analyze a semi infinite one dimensional random walk process with a biased motion that is incremental in one direction and long range in the other on a network with a fixed hierarchy of long range jumps we find with exact renormalization group calculations that there is a dynamical transition between a localized adsorption phase and an anomalous diffusion phase in which the mean square displacement exponent depends non universally on the bernoulli coin we relate these results to similar findings of unconventional phase behavior in hierarchical networks

stepwise positional orientational order and the multicritical multistructural global phase diagram of the s 3 2 ising model from renormalization group theory the spin frac 3 2 ising model with nearest neighbor interactions only is the prototypical system with two different ordering species with concentrations regulated by a chemical potential its global phase diagram obtained in d 3 by renormalization group theory in the migdal kadanoff approximation or equivalently as an exact solution of a d 3 hierarchical lattice with flows subtended by 40 different fixed points presents a very rich structure containing eight different ordered and disordered phases with more than 14 different types of phase diagrams in temperature and chemical potential it exhibits phases with orientational and or positional order it also exhibits quintuple phase transition reentrances universality of critical exponents is conserved across different renormalization group flow basins via redundant fixed points one of the phase diagrams contains a plastic crystal sequence with positional and orientational ordering encountered consecutively as temperature is lowered the global phase diagram also contains double critical points first order and critical lines between two ordered phases critical end points usual and unusual inverted bicritical points tricritical points multiple tetracritical points and zero temperature criticality and bicriticality the four state potts permutation symmetric subspace is contained in this model

on the wave equation with semilinear porous acoustic boundary conditions the goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary interior sources and a nonlinear boundary interior damping first applying the nonlinear semigroup theory we show the existence and uniqueness of local in time solutions the main difficulty in proving the local existence result is that the neumann boundary conditions experience loss of regularity due to boundary sources using an approximation method involving truncated sources and adapting the ideas in lasiecka and tataru 1993 28 we show that the existence of solutions can still be obtained second we prove that under some restrictions on the source terms then the local solution can be extended to be global in time in addition it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ode and depends on the behavior of the damping terms in several situations the obtained ode can be easily solved and the decay rates can be given explicitly third we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping then the solution ceases to exists and blows up in finite time moreover in either the absence of the interior source or the boundary source then we prove that the solution is unbounded and grows as an exponential function

global existence and asymptotic behavior for a coupled hyperbolic system with localized damping abstract in this paper we investigate the global existence and energy decay rate for the solution of a coupled hyperbolic system the semi explicit energy decay rate is established by using piecewise multiplier techniques and weighted integral inequality we extend the energy decay result in alabau boussouira f alabau boussouira convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems appl math optim 51 2005 61 105 for a single equation to the coupled hyperbolic system

parallel qr decomposition of a rectangular matrix we show that the greedy algorithm introduced in 1 and 5 to perform the parallel qr decomposition of a dense rectangular matrix of sizem n is optimal then we assume thatm n2 tends to zero asm andn go to infinity and prove that the complexity of such a decomposition is asymptotically2n when an unlimited number of processors is available

accurate computation of the product induced singular value decomposition with applications we present a new algorithm for floating point computation of the singular value decomposition svd of the product b tau c where b and c are full row rank matrices the algorithm replaces the pair b c with an equivalent pair b c and then it uses the jacobi svd algorithm to compute the svd of the explicitly computed matrix b tau c in this way each nonzero singular value sigma is approximated with some sigma delta sigma where the relative error delta sigma sigma is up to a factor of the dimensions of order boldmath varepsilon unboldmath min delta in cal d kappa 2 delta b min delta in cal d kappa 2 delta c where cal d denotes the set of diagonal nonsingular matrices kappa 2 cdot denotes the spectral condition number and boldmath varepsilon unboldmath is the roundoff unit of floating point arithmetic the new algorithm is applied to the eigenvalue problem hm x lambda x with symmetric positive definite h and m it is shown that each eigenvalue lambda is computed with high relative accuracy and that the relative error delta lambda lambda of the computed approximation lambda delta lambda is up to a factor of the dimension of order boldmath varepsilon unboldmath min delta in cal d kappa 2 delta h delta min delta in cal d kappa 2 delta m delta the new algorithm can also be used for accurate svd computation of a single matrix g that admits an accurate factorization g b tau c

on nonlinear wave equations of carrier type abstract this paper is concerned with the initial boundary value problem of the n dimensional carrier equation with an internal damping this damping is a fractional power of the velocity of the points of the material the faedo galerkin method tartar approach and compactness arguments provide the global existence of solutions of the above problem with restriction on the size of the initial data the decay of solutions is obtained by the perturbation method

existence and decay of solutions for a viscoelastic wave equation with acoustic boundary conditions abstract in this paper we consider a multi dimensional damped semilinear viscoelastic wave equation with variable coefficient and acoustic boundary conditions first we prove a local existence theorem by using the faedo galerkin approximations combined with a contraction mapping theorem second we show that under suitable conditions on the initial data and the relaxation function the solution exists globally in time and we prove the uniform decay rate of the energy

an alternative givens ordering a new givens ordering is shown empirically and by an approximate theoretical analysis to take appreciably fewer stages than the standard scheme sharper error bounds than gentleman s ensue and the scheme is better suited to parallel computation other schemes less efficient but more easily analysed are discussed the effect of a possible limit in practice on the number of simultaneous computations is considered

communication optimal parallel and sequential qr and lu factorizations we present parallel and sequential dense qr factorization algorithms that are both optimal up to polylogarithmic factors in the amount of communication they perform and just as stable as householder qr we prove optimality by deriving new lower bounds for the number of multiplications done by non strassen like qr and using these in known communication lower bounds that are proportional to the number of multiplications we not only show that our qr algorithms attain these lower bounds up to polylogarithmic factors but that existing lapack and scalapack algorithms perform asymptotically more communication we derive analogous communication lower bounds for lu factorization and point out recent lu algorithms in the literature that attain at least some of these lower bounds the sequential and parallel qr algorithms for tall and skinny matrices lead to significant speedups in practice over some of the existing algorithms including lapack and scalapack for example up to 6 7 times over scalapack a performance model for the parallel algorithm for general rectangular matrices predicts significant speedups over scalapack

decay rate estimates for wave equations of memory type with acoustic boundary conditions abstract a wave equation of memory type u u 0 t g t s u s d s 0 with acoustic boundary conditions is considered this work is devoted to investigating the influence of the kernel function g and proving general rates of decay of solutions when g does not necessarily decay exponentially

uniform stabilization of the wave equation by nonlinear boundary feedback the question of uniformly stabilizing the solution of the wave equation y delta y 0 in omega times 0 infty omega is a bounded domain of bf r n by means of a nonlinear feedback law of the following form is studied partial y partial v k x g y on gamma 0 times 0 infty y 0 on gamma 1 times 0 infty gamma 0 gamma 1 being a suitable partition of the boundary of omega and g a continuous nondecreasing function such that g 0 0 we choose k x in l infty k x geqq 0 such that k x vanishes linearly at the interface points x in bar gamma 0 cap bar gamma 1 then if g s behaves like s p 1 s as s to 0 with p 1 and linearly as s to infty it is proved that the energy of every solution decays like t 2 p 1 as t to infty in the case where p 1 the exponential decay rate is proved

global smooth solutions for the quasilinear wave equation with boundary dissipation abstract we consider the existence of global solutions of the quasilinear wave equation with a boundary dissipation structure of an input output in high dimensions when initial data and boundary inputs are near a given equilibrium of the system our main tool is the geometrical analysis the main interest is to study the effect of the boundary dissipation structure on solutions of the quasilinear system we show that the existence of global solutions depends not only on this dissipation structure but also on a riemannian metric given by the coefficients and the equilibrium of the system some geometrical conditions on this riemannian metric are presented to guarantee the existence of global solutions in particular we prove that the norm of the state of the system decays exponentially if the input stops after a finite time which implies the exponential stabilization of the system by boundary feedback

on a mixed problem with a nonlinear acoustic boundary condition for a non locally reacting boundaries abstract we discuss global solvability to the mixed problem for a nonlinear wave equation in domains with non locally reacting boundaries and nonlinear acoustic boundary condition we prove the existence and uniqueness of solution additionally using the method of nakao we demonstrate the decay of the associated energy stability

from bareiss algorithm to the stable computation of partial correlations abstract this paper presents a new algorithm for the stable computation of sample partial correlation coefficients we start by generalizing bareiss algorithm for the solution of linear systems of equations with non symmetric toeplitz coefficient matrix to matrices that are not toeplitz and show that it computes their lu and ul factorizations for symmetric positive definite matrices b the normalized version of bareiss algorithm is the hyperbolic cholesky algorithm which computes the upper and lower triangular cholesky factors u and l of b by means of 2 2 hyperbolic rotations if b is a convariance matrix certain partial correlation coefficients may be obtained as the geometric means of the multiplier pairs in bareiss algorithm or as the hyperbolic tangents of the hyperbolic rotations the partial correlation coefficients for a given data matrix a may suffer from serious loss of numerical accuracy when computed from the covariance matrix b a t a while the data flow graph of bareiss algorithm suggests a method due to cybenko for computing partial correlation coefficients directly from the columns of a the graph of hyperbolic cholesky suggests an alternative that requires fewer operations nd exhibits a higher degree of parallelism in that method one computes the qr decomposition a qu of the data matrix and applies orthogonal rotations to transform u to l the sines of the rotation angles constitute a set of partial correlation coefficients we extend this approach to determine arbitrary partial correlation coefficients at little extra computational cost

the abstract cauchy problem for dissipative operators with respect to metric like functionals abstract this paper is devoted to a characterization of semigroups of lipschitz operators on a closed subset d of a banach space x and the abstract cauchy problem for an operator a in x satisfying the following condition there exists a proper lower semicontinuous functional from x into 0 such that the effective domain of is d a and such that lim n a x n a x in x for any x d a and any sequence x n in d a satisfying two conditions lim n x n x in x and lim sup n x n x the main result asserts that a semigroup of lipschitz operators on d can be generated by an operator a satisfying the above mentioned condition a dissipative condition with respect to a metric like functional and a subtangential condition the kirchhoff equations with acoustic boundary conditions are solved by the method based on the abstract result with the construction of suitable liapunov functionals and the use of a metric like functional on a suitable set

global existence of classical solutions to the damped vlasov klein gordon equations with small data we study the collective dynamics of an ensemble of relativistic charged particles interacting with a self consistent damped klein gordon field in spatial three dimensions for this we derive a priori pointwise decay estimates for a scalar klein gordon field and its derivatives when the initial data are small and compactly supported these pointwise estimates yield the uniform boundedness of the velocity support which establishes the global existence of classical solutions

quasilinear hyperbolic 2 2 systems with a free damping boundary condition we consider a quasilinear system of equations for two functions u x t v x t and a boundary function s t

an application of semigroups of locally lipschitz operators to carrier equations with acoustic boundary conditions abstract a generation theorem of semigroups of locally lipschitz operators on a subset of a real banach space is given and applied to the problem of the well posedness of the carrier equation u t t u 2 u u t p 1 u t 0 in 0 with acoustic boundary condition where p 2 and is a bounded domain in an arbitrary dimensional space

uniform energy decay of a variable coefficient wave equation with nonlinear acoustic boundary conditions abstract a variable coefficient wave equation with nonlinear damped acoustic boundary conditions is considered the riemannian geometry method is applied to deal with the variable coefficients under some checkable conditions on the coefficients the uniform decay of the energy is achieved without any geometrical conditions on the shape of the dissipative portion of the boundary

polynomial stability for wave equations with acoustic boundary conditions and boundary memory damping we study wave equations with acoustic boundary conditions where only one memory damping acts on the acoustic boundary under some conditions on the memory kernel polynomial energy decay rates are established by using higher order energy estimates among some other techniques

on exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback abstract the uniform stabilization of an originally regarded nondissipative system described by a semilinear wave equation with variable coefficients under the nonlinear boundary feedback is considered the existence of both weak and strong solutions to the system is proven by the galerkin method the exponential stability of the system is obtained by introducing an equivalent energy function and using the energy multiplier method on the riemannian manifold this equivalent energy function shows particularly that the system is essentially a dissipative system this result not only generalizes the result from constant coefficients to variable coefficients for these kinds of semilinear wave equations but also simplifies significantly the proof for constant coefficients case considered in a guesmia a new approach of stabilization of nondissipative distributed systems siam j control optim 42 2003 24 52 where the system is claimed to be nondissipative

a tangent algorithm for computing the generalized singular value decomposition we present two new algorithms for floating point computation of the generalized singular values of a real pair a b of full column rank matrices and for floating point solution of the generalized eigenvalue problem hx lambda mx with symmetric positive definite matrices h and m the pair a b is replaced with an equivalent pair a b and the generalized singular values are computed as the singular values of the explicitly computed matrix f a b 1 the singular values of f are computed using the jacobi method the relative accuracy of the computed singular value approximations does not depend on column scalings of a and b that is the accuracy is nearly the same for all pairs ad 1 bd 2 with d 1 d 2 arbitrary diagonal nonsingular matrices similarly the pencil h lambda m is replaced with an equivalent pencil h lambda m and the eigenvalues of h lambda m are computed as the squares of the singular values of g l h l m 1 where l h l m are the cholesky factors of h m respectively and the matrix g is explicitly computed as the solution of a linear system of equations for the computed approximation lambda delta lambda of any exact eigenvalue lambda the relative error delta lambda lambda is of order p n mbox boldmath varepsilon max min delta in cal d kappa 2 delta h delta min delta in cal d kappa 2 delta m delta where p n is a modestly growing polynomial of the dimension of the problem mbox boldmath varepsilon is the round off unit of floating point arithmetic cal d denotes the set of diagonal nonsingular matrices and kappa 2 cdot is the spectral condition number furthermore floating point computation corresponds to an exact computation with h delta h m delta m where for all i j delta h ij sqrt h ii h jj and delta m ij sqrt m ii m jj are of order of mbox boldmath varepsilon times a modest function of n

well posedness for a variable coefficient wave equation with nonlinear damped acoustic boundary conditions abstract we consider a variable coefficient wave equation with nonlinear damped acoustic boundary conditions well posedness in the hadamard sense for strong and weak solutions is proved by using the theory of nonlinear semigroups

asymptotic stability for a strongly coupled klein gordon system in an inhomogeneous medium with locally distributed damping abstract we consider a strongly coupled klein gordon system posed in an inhomogeneous medium with smooth boundary subject to a local damping distributed around a neighborhood of the boundary according to the geometric control condition we show that the energy of the system goes uniformly and exponentially to zero for all initial data of finite energy taken in bounded sets of finite energy phase space for this purpose refined microlocal analysis arguments are considered by exploiting ideas due to burq and gerard 16 by using sharp l p l q carleman estimates we prove a unique continuation property for coupled systems we also consider a strongly coupled system of wave equations with localized nonlinear damping acting only on one equation considering a compact riemannian manifold we show that the energy of the coupled system goes uniformly to zero

asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions abstract in this paper we consider a multi dimensional wave equation with dynamic boundary conditions related to the kelvin voigt damping global existence and asymptotic stability of solutions starting in a stable set are proved blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained

method for estimating critical exponents in percolation processes with low sampling in phase transition phenomena the estimation of the critical point is crucial for the calculation of the various critical exponents and the determination of the universality class they belong to however this is not an easy task since a large amount of realizations is needed to eliminate the noise in the data in this paper we introduce a novel method for the simultaneous estimation of the critical point p c and the critical exponent applied for the case of explosive bond percolation on two dimensional square lattices and erdos renyi networks the results show that with only a few hundred realizations it is possible to acquire accurate values for these quantities guidelines are given at the end for the applicability of the method to other cases as well

optimal algorithms for parallel givens factorization on a coarse grained pram we study the complexity of the parallel givens factorization of a square matrix of size n on a shared memory architecture composed with p identical processors coarse grained erew pram we show how to construct an asymptotically optimal algorithm we deduce that tje time complexity is equal to formule and that the minimum number of processors in order to compute the givens factorization in asymptotically optimal time 2n o n is equal to p opt n 2 2 o n these results complete previous analysis presented in the case where the number of processors is unlimited

strong stability and uniform decay of solutions to a wave equation with semilinear porous acoustic boundary conditions we consider a wave equation with semilinear porous acoustic boundary conditions this is a coupled system of second and first order in time partial differential equations with possibly semilinear boundary conditions on the interface the results obtained are i strong stability for the linear model ii exponential decay rates for the energy of the linear model and iii local exponential decay rates for the energy of the semilinear model this work builds on a previous result showing generation of a well posed dynamical system the main tools used in the proofs are i the stability theorem of arendt batty ii energy methods used in the study of a wave equation with boundary damping and iii an abstract result of i lasiecka applicable to hyperbolic like systems with nonlinearly perturbed boundary conditions

scaling of clusters near discontinuous percolation transitions in hyperbolic networks we investigate the onset of the discontinuous percolation transition in small world hyperbolic networks by studying the systems size scaling of the typical largest cluster approaching the transition p p c to this end we determine the average size of the largest cluster s max n p in the thermodynamic limit using real space renormalization of cluster generating functions for bond and site percolation in several models of hyperbolic networks that provide exact results we determine that all our models conform to the recently predicted behavior regarding the growth of the largest cluster which found diverging albeit subextensive clusters spanning the system with finite probability well below p c and at most quadratic corrections to unity in p for p p c our study suggests a large universality in the cluster formation on small world hyperbolic networks and the potential for an alternative mechanism in the cluster formation dynamics at the onset of discontinuous percolation transitions

complete second order differential equations in banach spaces with dynamic boundary conditions abstract in this paper we deal with the mixed initial boundary value problem for complete second order in time linear differential equations in banach spaces in which time derivatives occur in the boundary conditions general wellposedness theorems are obtained for the first time which are used to solve the corresponding inhomogeneous problems examples of applications to initial boundary value problems for partial differential equations are also presented

convergence of the wave equation damped on the interior to the one damped on the boundary abstract in this paper we study the convergence of the wave equation with variable internal damping term n x u t to the wave equation with boundary damping x x u t when n x converges to x x in the sense of distributions when the domain in which these equations are defined is an interval in r we show that under natural hypotheses the compact global attractor of the wave equation damped on the interior converges in x h 1 l 2 to the one of the wave equation damped on the boundary and that the dynamics on these attractors are equivalent we also prove in the higher dimensional case that the attractors are lower semicontinuous in x and upper semicontinuous in h 1 e h e

global existence asymptotic stability and uniform attractors for non autonomous thermoelastic systems with constant time delay in this paper we first consider a non autonomous thermoelastic system with a boundary delay and obtain the asymptotic behavior then using the contractive function method and multiplier techniques we establish the asymptotic behavior and the existence of a uniform attractor of the system with a boundary time delay the main advantage of this method is that we only need to verify compactness condition with the type of energy estimates same as those for establishing the absorbing set moreover we investigate an alternative result of solutions to semilinear thermoelastic systems by virtue of the semigroup method

parallel complexity of numerically accurate linear system solvers we prove a number of negative results about practical i e work efficient and numerically accurate algorithms for computing the main matrix factorizations in particular we prove that the popular householder and givens methods for computing the qr decomposition are p complete and hence presumably inherently sequential under both real and floating point number models we also prove that gaussian elimination ge with a weak form of pivoting which aims only at making the resulting algorithm nondegenerate is likely to be inherently sequential as well finally we prove that ge with partial pivoting is p complete over gf 2 or when restricted to symmetric positive definite matrices for which it is known that even standard ge no pivoting does not fail altogether the results of this paper give further formal support to the widespread belief that there is a tradeoff between parallelism and accuracy in numerical algorithms