weakly damped quasilinear wave equation existence of time periodic solutions among many questions concerning global behaviour of hyperbolic equations the existence of time periodic solutions seems to be of great interest both from the mathematical and physical points of view the aim of the present paper is to add to the vast literature on that subject a result related to the weakly damped quasilinear wave equation see section 1 theorem 1 with a function u u x t of x e 0 1 t e r consider the equation

unique decompositions faces and automorphisms of separable states let sk be the set of separable states on b cm cn admitting a representation as a convex combination of k pure product states or fewer if m 1 n 1 and k max m n we show that sk admits a subset vk such that vk is dense and open in sk and such that each state in vk has a unique decomposition as a convex combination of pure product states and we describe all possible convex decompositions for a set of separable states that properly contains vk in both cases we describe the associated faces of the space of separable states which in the first case are simplexes and in the second case are direct convex sums of faces that are isomorphic to state spaces of full matrix algebras as an application of these results we characterize all affine automorphisms of the convex set of separable states and all automorphisms of the state space of b cm cn that preserve entanglement and separability

quantum measurements and maps preserving strict convex combinations and pure states in this paper a characterization of maps between quantum states that preserve pure states and strict convex combinations is obtained based on this characterization a structure theorem for maps between multipartite quantum states that preserve separable pure states and strict convex combinations is established then these results are applied to characterize injective local quantum measurements and answer some conjectures proposed in hou and liu 2012 j phys a math theor 45 205305

a breakdown free variation of the nonsymmetric lanczos algorithms the nonsymmetric lanczos tridiagonalization algorithm is essentially the gram schmidt biorthogonalization method for generating biorthogonal bases of a pair of krylov subspaces it suffers from breakdown and instability when a pivot at some step is zero or nearly zero which is often the result of mismatch of the two krylov subspaces in this paper we propose to modify one of the two krylov subspaces by introducing a new start vector when a pivot is small this new start vector generates another krylov subspace which we add to the old one in an appropriate way so that the gram schmidt method for the modified subspaces yields a recurrence similar to the lanczos algorithm our method enforces the pivots to be above a certain threshold and can handle both exact breakdown and near breakdown in particular we recover lookahead lanczos algorithms and arnoldi s algorithm as two special cases we also discuss theoretical and practical issues concerning the new start procedure and present a convergence analysis as well as some numerical examples

entropy preserving maps on quantum states abstract in the paper we give a characterization of surjective maps on quantum states preserving quantum entropy of convex combinations let s h be the set of all quantum states positive operators with the unit trace on a complex hilbert space h with dim h n and s the quantum entropy of the quantum state for arbitrary a surjective map s h s h we claim that preserves quantum entropy of convex combinations of quantum states i e satisfies s t 1 t s t 1 t for arbitrary s h and t 0 1 if and only if there exists a unitary or anti unitary operator u on h such that u u for all s h

a characterization of positive linear maps and criteria of entanglement for quantum states let h and k be finite or infinite dimensional complex hilbert spaces a characterization of positive completely bounded normal linear maps from into is given which particularly gives a characterization of positive elementary operators including all positive linear maps between matrix algebras this characterization is then applied to give a representation of quantum channels operations between infinite dimensional systems a necessary and sufficient criterion of separability is given which shows that a state on h k is separable if and only if i 0 for all positive finite rank elementary operators examples of ncp and indecomposable positive linear maps are given and are used to recognize some entangled states that cannot be recognized by the ppt criterion and the realignment criterion

global existence for quasi linear dissipative wave equations with large data and small parameter on considere le probleme aux valeurs initiales pour les equations d onde quasi lineaires eu t u x 0 t u x 0 u x 0 u 0 x x 0 0 x ou e 0 0 t r x r u et sont des fonctions scalaires de x t et est une fonction donnee croissante lisse sur r on etudie le comportement des solutions classiques pour t grand

characterizations of the automorphisms of hilbert space effect algebras in this paper we characterize the automorphisms of hilbert space effect algebras by means of their preserving properties which concern certain relations and quantities appearing in quantum measurement theory

convergence analysis of lanczos type methods for the linear response eigenvalue problem two different lanczos type methods for the linear response eigenvalue problem are analyzed the first one is a natural extension of the classical lanczos method for the symmetric eigenvalue problem while the second one was recently proposed by tsiper specially for the linear response eigenvalue problem our analysis leads to bounds on errors for eigenvalue and eigenvector approximations by the two methods these bounds suggest that the first method can converge significantly faster than tsiper s method numerical examples are presented to support this claim

existence of global smooth solutions to the initial boundary value problem for the quasi linear wave equation with a degenerate dissipative term let c be a bounded domain with smooth boundary dq in the n dimen sional euclidean space rn and let us consider the initial boundary value problem for the classical quasi linear wave equation with a dissipation u v a lvul vu u x u o in qx o ce 4x 0 uo

a look ahead lanczos algorithm for unsymmetric matrices abstract the two sided lanczos algorithm is known to suffer from serious breakdowns these occur when the associated moment matrix does not permit triangular factorization we modify the algorithm slightly so that it corresponds to using a 2 x 2 pivot in triangular factorization whenever a 1 x 1 pivot would be dangerous the incidence of breakdown is greatly reduced the price paid is that the tridiagonal matrix produced by the algorithm now has bumps whenever a 2 x 2 pivot is used author

a convergence analysis for nonsymmetric lanczos algorithms a convergence analysis for the nonsymmetric lanczos algorithm is presented by using a tridiagonal structure of the algorithm some identities concerning ritz values and ritz vectors are established and used to derive approximation bounds in particular the analysis implies the classical results for the symmetric lanczos algorithm

a geometric characterization of invertible quantum measurement maps a geometric characterization is given for invertible quantum measurement maps denote by s h the convex set of all states i e trace 1 positive operators on hilbert space h with dimh and 1 2 the line segment joining two elements 1 2 in s h it is shown that a bijective map s h s h satisfies 1 2 1 2 for any 1 2 s if and only if has one of the following forms m m tr m m or m tm tr m tm where m is an invertible bounded linear operator and t is the transpose of with respect to an arbitrarily fixed orthonormal basis

rayleigh ritz and lanczos methods for symmetric matrix pencils we are concerned with eigenvalue problems for definite and indefinite symmetric matrix pencils first rayleigh ritz methods are formulated and using krylov subspaces a convergence analysis is presented for definite pencils second generalized symmetric lanczos algorithms are introduced as a special rayleigh ritz method in particular an a posteriori convergence criterion is demonstrated by using residuals local convergence to real and nonreal eigenvalues is also discussed numerical examples concerning vibrations of damped cantilever beams are included

the automorphism group of separable states in quantum information theory we show that the linear group of automorphism of hermitian matrices which preserves the set of separable states is generated by natural automorphisms change of an orthonormal basis in each tensor factor partial transpose in each tensor factor and interchanging two tensor factors of the same dimension we apply our results to the preservers of the product numerical range

a novel nonsymmetric k lanczos algorithm for the generalized nonsymmetric k eigenvalue problems in this article we present a novel algorithm named nonsymmetric k lanczos algorithm for computing a few extreme eigenvalues of the generalized eigenvalue problem mx al where the matrices m and l have the so called k structures we demonstrate a k tridiagonalization procedure preserves the k structures an error bound for the extreme k ritz value obtained from this new algorithm is presented when compared with the class nonsymmetric lanczos approach this method has the same order of computational complexity and can be viewed as a special 2 x 2 block nonsymmetric lanczos algorithm numerical experiments with randomly generated k matrices show that our algorithm converges faster and more accurate than the nonsymmetric lanczos algorithm 0 ekevier science inc 1997

the shift inverted j lanczos algorithm for the numerical solutions of large sparse algebraic riccati equations abstract the goal of solving an algebraic riccati equation is to find the stable invariant subspace corresponding to all the eigenvalues lying in the open left half plane the purpose of this paper is to propose a structure preserving lanczos type algorithm incorporated with shift and invert techniques named shift inverted j lanczos algorithm for computing the stable invariant subspace for large sparse hamiltonian matrices the algorithm is based on the j tridiagonalization procedure of a hamiltonian matrix using symplectic similarity transformations we give a detailed analysis on the convergence behavior of the j lanczos algorithm and present error bound analysis and paige type theorem numerical results for the proposed algorithm applied to a practical example arising from the position and velocity control for a string of high speed vehicles are reported

an explicit formula for lanczos polynomials abstract the lanczos algorithm for tridiagonalizing a given matrix a generates a sequence of approximating matrices a p that can naturally be obtained as restrictions to subspaces the eigenvalues of these approximating matrices are well known to be good approximations to the extreme eigenvalues of a in this paper we produce explicit formulas for the characteristics polynomials of the a p in terms of the eigenvalues of a these formulas can be used to explain heuristically why these approximations are often quite good at present we have no concrete analytic argument that explains the quality of the approximation the main result draws on the formal relationship between the lanczos algorithm and pade approximations to the moment generating function of a this result is one of the few analytic results available for the unsymmetric lanczos algorithm

on the damped nonlinear evolution equation wtt σ w xx ywt abstract initial boundary value problems for the damped nonlinear wave equation wtt w xx ywt arise in several areas of applied mathematics and in particular in studies of shearing flow in a nonlinear viscoelastic fluid the problems of global existence and nonexistence of smooth solutions have been extensively studied in the strictly hyperbolic case e 0 r1 as well as in the case where 0 0 and the initial data are chosen so small that w 0 for as long as a smooth solution w x t exists in this paper the global nonexistence problem is studied for the cases 0 0 and 0 0 but