swapping labeled tokens on graphs consider a puzzle consisting of n tokens on an n vertex graph where each token has a distinct starting vertex and a distinct target vertex it wants to reach and the only allowed transformation is to swap the tokens on adjacent vertices we prove that every such puzzle is solvable in o n 2 token swaps and thus focus on the problem of minimizing the number of token swaps to reach the target token placement we give a polynomial time 2 approximation algorithm for trees and using this obtain a polynomial time 2 approximation algorithm for graphs whose tree spanners can be computed in polynomial time finally we show that the problem can be solved exactly in polynomial time on complete bipartite graphs

uniform convergence of the free energy of the classical heisenberg model to that of the gaussian model we show that the free energy of the classical heisenberg model converges to the free energy of the gaussian in the low temperature limit the limit is uniform as the field is taken to zero

approximating minimum max stretch spanning trees on unweighted graphs given a graph g and a spanning tree t of g we say that t is a tree t spanner of g if the distance between every pair of vertices in t is at most t times their distance in g the problem of finding a tree t spanner minimizing t is referred to as the minimum max stretch spanning tree mmst problem this paper concerns the mmst problem on unweighted graphs the problem is known to be np hard and the paper presents an o log n approximation algorithm for it furthermore it is established that unless mathrm p mathrm np the problem cannot be approximated additively by any o n term

diameters and eigenvalues we derive a new upper bound for the diameter of a k regular graph g as a function of the eigenvalues of the adjacency matrix namely suppose the adjacency matrix of g has eigenvalues ai a2 a with ia i i vi21 ia i where ai k a ia21 then the diameter d g must satisfy d g we will consider families of graphs whose eigenvalues can be explicitly de termined these graphs are determined by sums or differences of vertex labels namely the pair i j being an edge depends only on the value i j or i j for directed graphs we will show that these graphs are expander graphs with small diameters by using an inequality on character sums which was recently proved by n m katz bell communications research 445 south street morristown new jersey 07960 this content downloaded from 207 46 13 111 on sat 21 may 2016 07 00 04 utc all use subject to http about jstor org terms

global smooth solutions for a class of quasilinear hyperbolic systems with dissipative terms in this paper we prove an existence theorem of global smooth solutions for the cauchy problem of a class of quasilinear hyperbolic systems with nonlinear dissipative terms under the assumption that only the c 0 norm of the initial data is sufficiently small while the c 1 norm of the initial data can be large the analysis is based on a priori estimates which are obtained by a generalised lax transformation

association schemes and coding theory this paper contains a survey of association scheme theory with its algebraic and analytical aspects and of its applications to coding theory in a wide sense it is mainly concerned with a class of subjects that involve the central notion of the distance distribution of a code special emphasis is put on the linear programming method inspired by the macwilliams transform this produces upper bounds for the size of a code with a given minimum distance and lower bounds for the size of a design with a given strength the most specific results are obtained in the case where the underlying association scheme satisfies certain well defined polynomial properties this leads one into the realm of orthogonal polynomial theory in particular some universal bounds are derived for codes and designs in polynomial type association schemes throughout the paper the main concepts methods and results are illustrated by two examples that are of major significance in classical coding theory namely the hamming scheme and the johnson scheme other topics that receive special attention are spherical codes and designs and additive codes in translation schemes including z sub 4 additive binary codes

time domain finite difference and finite element methods for maxwell equations in complex media extensions of finite difference time domain fdtd and finite element time domain fetd algorithms are reviewed for solving transient maxwell equations in complex media also provided are a few representative examples to illustrate the modeling capabilities of fdtd and fetd for complex media the term complex media refers here to media with dispersive bi anisotropic inhomogeneous and or nonlinear properties present in the constitutive tensors

solving boundary value problems on networks using equilibrium measures abstract the purpose of this paper is to construct solutions of self adjoint boundary value problems on finite networks to this end we obtain explicit expressions of the green functions for all different boundary value problems the method consists of reducing each boundary value problem either to a dirichlet problem or to a poisson equation on a new network closely related with the former boundary value problem in this process we also get an explicit expression of the poisson kernel for the dirichlet problem in all cases we express the green function in terms of equilibrium measures solely which can be obtained as the unique solution of linear programming problems in particular we get analytic expressions of the green function for the following problems the poisson equation on a distance regular graph the dirichlet problem on an infinite distance regular graph and the neumann problem on a ball of an homogeneous tree

laplacian eigenvalues and distances between subsets of a manifold in this paper we give a new method to convert results dealing with graph theoretic or markov chain laplacians into results concerning laplacians in analysis such as on riemannian manifolds we illustrate this method by using the results of cgy97 to prove 1 1 dist x y cosh 1 xc y c x y 2 for 1 the first positive neumann eigenvalue on a connected compact riemannian manifold and x y any two disjoint sets and where xc is the complement of x this inequality has a version for the k th positive eigenvalue involving k 1 disjoint sets and holds more generally for all analytic laplacians described in cgy97 we show that this inequality is optimal to first order in that it is impossible to obtain an inequality of this form with the right hand side divided by 1 for any fixed constant 0

three dimensional modeling of ip effects in time domain electromagnetic data understanding the effects of induced polarization ip effects on time domain electromagnetic data requires the ability to simulate common survey techniques when taking chargeability into account most existing techniques preform this modeling in the frequency domain prior to transforming their results to the time domain even though this technique can allow for chargeable material to be easily incorporated its application for some problems can be computationally limiting we developed a new technique for forward modeling the time domain electromagnetic response of chargeable materials in three dimensions the frequency dependence of ohms law translates to an ordinary differential equation when considered in the time domain the system of ordinary partial differential equations was then discretized using an implicit time stepping algorithm that yielded absolute stability this approach allowed us to operate directly in the time domain and avoid frequency to time domain transformations although this approach can be applied directly to materials exhibiting debye dispersions other cole cole dispersions resulted in fractional derivatives in time to overcome this difficulty pade approximations were used to represent the frequency dependence as a rational series of integer order terms the resulting method was then simplified to generate a reduced time domain model that can be used to forward model the ip decay curves in the absence of any electromagnetic coupling we found numerical examples in which the method produced accurate results the potential application of the method was demonstrated by modeling the full time domain electromagnetic response of a gradient array ip survey and the occurrence of negative transients in airborne time domain electromagnetic data

globally smooth solutions of quasilinear hyperbolic systems in diagonal form abstract we prove the existence of a large class of globally smooth solutions of the cauchy problem for the system of n equations u t x t u u x 0 where is a diagonal matrix we show that under certain monotonicity conditions on both and the initial data u 0 the solution u will be locally lipschitz continuous at positive times since u 0 is a function of locally bounded variation our result thus provides both for the smoothing of discontinuities in u 0 as well as for the global preservation of smoothness the global existence results from an a priori estimate of u x which we obtain by a device which enables us to effectively uncouple the system of equations for u x finally we prove a partial converse which demonstrates that our hypotheses are not overly restrictive

some new results on eigenvectors via dimension diameter and ricci curvature abstract we generalise for a general symmetric elliptic operator the different notions of dimension diameter and ricci curvature which coincide with the usual notions in the case of the laplace beltrami operators on riemannian manifolds if 1 denotes the spectral gap that is the first nonzero eigenvalue we investigate in this paper the best lower bound on 1 one can obtain under an upper bound on the dimension an upper bound on the diameter and a lower bound of the ricci curvature two cases are known namely if the ricci curvature is bounded below by a constant r 0 then 1 nr n 1 and this estimate is sharp for the n dimensional spheres lichnerowicz s bound if the ricci curvature is bounded below by zero then zhong yang s estimate asserts that 1 2 d 2 where d is an upper bound on the diameter this estimate is sharp for the 1 dimensional torus in the general case many interesting estimates have been obtained this paper provides a general optimal comparison result for 1 which unifies and sharpens lichnerowicz and zhong yang s estimates together with other comparison results concerning the range of the associated eigenfunctions and their derivatives

a general method for fdtd modeling of wave propagation in arbitrary frequency dispersive media a general formulation is presented for finite difference time domain fdtd modeling of wave propagation in arbitrary frequency dispersive media two algorithmic approaches are outlined for incorporating dispersion into the fdtd time stepping equations the first employs a frequency dependent complex permittivity denoted form 1 and the second employs a frequency dependent complex conductivity denoted form 2 a pade representation is used in z transform space to represent the frequency dependent permittivity form 1 or conductivity form 2 this is a generalization over several previous methods employing either debye lorentz or drude models the coefficients of the pade model may be obtained through an optimization process leading directly to a finite difference representation of the dispersion relation without introducing discretization error stability criteria for the dispersive fdtd algorithms are given we show that several previously developed dispersive fdtd algorithms can be cast as special cases of our more general framework simulation results are presented for a one dimensional 1 d air muscle example considered previously in the literature and a three dimensional 3 d radiation problem in dispersive lossy soil using measured soil data

conservative modeling of 3 d electromagnetic fields part i properties and error analysis conservation of electric current and magnetic flux can be explicitly enforced by modeling maxwell s equations on a staggered grid where the different field components are sampled at points offset relative to each other a staggered finite difference sfd approximation gives divergence free magnetic fields and electric currents ensuring good behavior at all periods comparisons of sfd solutions with 2 d quasi analytic solutions are very good 1 rms error when a modeled region can be subdivided into uniform subdomains comparison of analytic solutions and sfd approximations show that the greatest differences occur near the nyquist wavenumbers the sfd solutions do not attenuate in space as rapidly as the analytic solutions the accuracy of a computed sfd solution can be estimated from its wavenumber content for test cases the accuracy estimates are surprisingly close to the actual accuracies grid requirements for modeling short horizontal wavelength components of a solution seem more demanding than

fast linear algebra is stable in demmel et al numer math 106 2 199 224 2007 we showed that a large class of fast recursive matrix multiplication algorithms is stable in a normwise sense and that in fact if multiplication of n by n matrices can be done by any algorithm in o n operations for any 0 then it can be done stably in o n operations for any 0 here we extend this result to show that essentially all standard linear algebra operations including lu decomposition qr decomposition linear equation solving matrix inversion solving least squares problems generalized eigenvalue problems and the singular value decomposition can also be done stably in a normwise sense in o n operations

convergence to strong nonlinear diffusion waves for solutions to p system with damping on quadrant in this paper we consider the so called p system with linear damping on quadrant we show that for a certain class of given large initial data v0 x u0 x the corresponding initial boundary value problem admits a unique global smooth solution v x t u x t and such a solution tends time asymptotically at the lp 2 p optimal decay rates to the corresponding nonlinear diffusion wave v x t u x t which satisfies 1 9 provided the corresponding prescribed initial error function v0 x u0 x lies in h3 r l1 r h2 r l1 r

on the parabolic kernel of the schrodinger operator etude des equations paraboliques du type q x t t u x t 0 sur une variete riemannienne generale introduction estimations de gradients inegalites de harnack majorations et minorations des solutions fondamentales equation de la chaleur et noyau de green operateur de schrodinger

davies gaffney grigor yan lemma on simplicial complexes we prove davies gaffney grigor yan lemma for heat kernels of bounded discrete hodge laplacians on simplicial complexes

asymptotic behaviors of solutions of quasilinear hyperbolic equations with linear damping ii this paper as a follow up to the recent work of k nishihara 1997 j differential equations133 384 395 is concerned with the asymptotic behaviors of the solution of quasilinear hyperbolic equation with linear damping vtt a vx x vt 0 a v 0forallv r which satisfies the following prescribed initial condition v t x vt t x t 0 v0 x v1 x x r compared with the results obtained by k nishihara the main novelties of our present paper lie in the following first we recover all the results obtained by k nishihara under some other smallness assumptions on the initial data v0 x v1 x which are much weaker than those needed in k nishihara s arguments second under some additional assumptions on the nonlinear function a v and on the initial data v0 x v1 x when 0 0 1 0 we succeed in proving that t x is still an asymptotic profile of v t x and this answers partially the open problem left by k nishihara

the dual cheeger constant and spectra of infinite graphs abstract in this article we study the top of the spectrum of the normalized laplace operator on infinite graphs we introduce the dual cheeger constant and show that it controls the top of the spectrum from above and below in a similar way as the cheeger constant controls the bottom of the spectrum moreover we show that the dual cheeger constant at infinity can be used to characterize that the essential spectrum of the normalized laplace operator shrinks to one point

a low temperature expansion for classical n vector models iii a complete inductive description fluctuation integrals we give a complete inductive description of the effective densities generated by applications of the renormalization transformations to the densities of the classical n vector models described in the paper 1 and we formulate the main theorems of this sequence of papers this description includes now all the large field domains which we ve excluded from the discussions of 1 4 we apply the renormalization transformation to a density satisfying the inductive hypotheses we introduce large field small field partitions and we determine and analyze the fluctuation integrals in the general setting

spectral gap and logarithmic sobolev inequality for kawasaki and glauber dynamics we prove that the spectral gap of the kawasaki dynamics shrink at the rate of 1 l2 for cubes of sizel provided that some mixing conditions are satisfied we also prove that the logarithmic sobolev inequality for the glauber dynamics in standard cubes holds uniformly in the size of the cube if the dobrushin shlosman mixing condition holds for standard cubes

eigenvalue interlacing and weight parameters of graphs eigenvalue interlacing is a versatile technique for deriving results in algebraic combinatorics in particular it has been successfully used for proving a number of results about the relation between the adjacency matrix or laplacian spectrum of a graph and some of its properties for instance some characterizations of regular partitions and bounds for some parameters such as the independence and chromatic numbers the diameter the bandwidth etc have been obtained for each parameter of a graph involving the cardinality of some vertex sets we can define its corresponding weight parameter by giving some weights that is the entries of the positive eigenvector to the vertices and replacing cardinalities by square norms the key point is that such weights regularize the graph and hence allow us to define a kind of regular partition called pseudo regular intended for general graphs here we s aow how to use interlacing for proving results about some weight parameters and pseudo regular partitions of a graph for instance generalizing a well known result of lovfisz it is shown that the weight shannon capacity 6 of a connected graph f with n vertices and adjacency matrix eigenvalues 2j 2 2 satisfies

fast finite volume simulation of 3d electromagnetic problems with highly discontinuous coefficients we consider solving three dimensional electromagnetic problems in parameter regimes where the quasi static approximation applies and the permeability permittivity and conductivity may vary significantly the difficulties encountered include handling solution discontinuities across interfaces and accelerating convergence of traditional iterative methods for the solution of the linear systems of algebraic equations that arise when discretizing maxwell s equations in the frequency domain the present article extends methods we proposed earlier for constant permeability e haber u ascher d aruliah and d oldenburg j comput phys 163 2000 pp 150 171 d aruliah u ascher e haber and d oldenburg math models methods appl sci to appear to handle also problems in which the permeability is variable and may contain significant jump discontinuities in order to address the problem of slow convergence we reformulate maxwell s equations in terms of potentials applying a helmholtz decomposition to either the electric field or the magnetic field the null space of the curl operators can then be annihilated by adding a stabilizing term using a gauge condition and thus obtaining a strongly elliptic differential operator a staggered grid finite volume discretization is subsequently applied to the reformulated pde system this scheme works well for sources of various types even in the presence of strong material discontinuities in both conductivity and permeability the resulting discrete system is amenable to fast convergence of ilu preconditioned krylov methods we test our method using several numerical examples and demonstrate its robust efficiency we also compare it to the classical yee method using similar iterative techniques for the resulting algebraic system and we show that our method is significantly faster especially for electric sources

solution of time convolutionary maxwell s equations using parameter dependent krylov subspace reduction we suggest a new algorithm for the solution of the time domain maxwell equations in dispersive media after spacial discretization we obtain a large system of time convolution equations then this system is projected onto a small subspace consisting of the laplace domain solutions for a preselected set of laplace parameters this approach is a generalization of the rational krylov subspace approach for the solution of non dispersive maxwell s systems we show that the projected system preserves such properties of the initial system as stability and passivity as an example we consider the 3d quasistationary induced polarization problem with the cole cole conductivity model important for geophysical oil exploration our numerical experiments show that the introduction of the induced polarization does not have significant effect on convergence

a finite difference time domain solution for three dimensional electromagnetic modeling we have developed a finite difference solution for three dimensional 3 d transient electromagnetic problems the solution steps maxwell s equations in time using a staggered grid technique the time stepping uses a modified version of the du fort frankel method which is explicit and always stable both conductivity and magnetic permeability can be functions of space and the model geometry can be arbitrarily complicated the solution provides both electric and magnetic field responses throughout the earth because it solves the coupled first order maxwell s equations the solution avoids approximating spatial derivatives of physical properties and thus overcomes many related numerical difficulties moreover since the divergence free condition for the magnetic field is incorporated explicitly the solution provides accurate results for the magnetic field at late times an inhomogeneous dirichlet boundary condition is imposed at the surface of the earth while a homogeneous dirichlet condition is employed along the subsurface boundaries numerical dispersion is alleviated by using an adaptive algorithm that uses a fourth order difference method at early times and a second order method at other times numerical checks against analytical integral equation and spectral differential difference solutions show that the solution provides accurate results execution time for a typical model is about 3 5 hours on an ibm 3090 600s computer for computing the field to 10 ms that model contains 100 x 100 x 50 grid points representing about three million unknowns and possesses one vertical plane of symmetry with the smallest grid spacing at 10 m and the highest resistivity at 100 omega m the execution time indicates that the solution is computer intensive but it is valuable in providing much needed insight about tem responses in complicated 3 d situations

fast simulation of 3d electromagnetic problems using potentials we consider solving three dimensional electromagnetic problems in parameter regimes where the quasi static approximation applies the permeability is constant the conductivity may vary significantly and the range of frequencies is moderate the difficulties encountered include handling solution discontinuities across interfaces and accelerating convergence of traditional iterative methods for the solution of the linear systems of algebraic equations that arise when discretizing maxwell s equations in the frequency domain we use a potential current formulation a with a coulomb gauge the potentials a and decompose the electric field e into components in the active and null spaces of the operator we develop a finite volume discretization on a staggered grid that naturally employs harmonic averages for the conductivity at cell faces after discretization we eliminate the current and the resulting large sparse linear system of equations has a block structure that is diagonally dominant allowing an efficient solution with preconditioned krylov space methods a particularly efficient algorithm results from the combination of bicgstab and an incomplete lu decomposition we demonstrate the efficacy of our method in several numerical experiments

lattice systems with a continuous symmetry iii low temperature asymptotic expansion for the plane rotator model we prove that the expansion in powers of the temperature t of the correlation functions and the free energy of the plane rotator model on a d dimensional lattice is asymptotic to all orders in t the leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series we also prove the inverse power decay of the pair correlation at low temperatures for d 3

an auxiliary differential equation method for fdtd modeling of wave propagation in cole cole dispersive media a method for modeling time domain wave propagation in dispersive cole cole media is presented the cole cole model can describe the frequency dependence of the electromagnetic properties of various biological tissues with great accuracy over a wide frequency range and plays a key role in microwave medical imaging the main difficulty in the time domain modeling of cole cole media is the appearance of fractional time derivatives in the proposed method a pade approximation is employed resulting in auxiliary differential equations of integer order a finite difference time domain method is developed to solve the differential equations obtained the comparison of analytical and calculated relative complex permittivity values over wideband frequency domain proves the validity of the method

convergence to strong nonlinear diffusion waves for solutions of p system with damping this paper is concerned with the p system with frictional damping and our main purpose is two fold first we show that for a certain class of given large initial data nu 0 x u 0 x the cauchy problem 1 1 1 2 admits a unique global smooth solution nu t x u t x and such a solution tends time asymptotically at the optimal l p 2 less than or equal to p less than or equal to infinity decay rates to the corresponding nonlinear diffusion wave over bar t x u over bar t x governed by the classical darcy s law provided that the corresponding prescribed initial error function v 0 x u 0 x ties in h 3 x h 2 r boolean and l 1 x l 1 r compared with former results in this direction obtained by l hsiao and t p liu 1992 comm math phys 143 599 605 k nishihara 1996 j differential equations 131 171 188 and k nishihara w k wang and t yang 2000 j differential equations 161 191 218 our main novelty lies in the facts that the nonlinear diffusion wave over bar t x u over bar t x need not to be weak and v 0 x u 0 x can be chosen arbitrarily large secondly we show that the nonlinear diffusion waves over bar t x u over bar t x are nonlinear stable provided that the strength or the nonlinear diffusion waves is weak and that the initial disturbance v 0 x u 0 x satisfies the assumption that parallel tov 0xx x parallel to l infinity parallel tou 0x x parallel to l infinity is sufficiently small we also show that the smallness assumption imposed oil the strength of the diffusion waves is a necessary condition to guarantee the nonlinear stability result and compared with the corresponding results obtained by l hsiao and t p liu 1992 comm math phys 143 599 605 the smallness conditions we imposed on the initial disturbance are much more weaker c 2001 academic press

validity of the spin wave approximation for the free energy of the heisenberg ferromagnet we consider the quantum ferromagnetic heisenberg model in three dimensions for all spins s 1 2 we rigorously prove the validity of the spin wave approximation for the excitation spectrum at the level of the first non trivial contribution to the free energy at low temperatures our proof comes with explicit constructive upper and lower bounds on the error term it uses in an essential way the bosonic formulation of the model in terms of the holstein primakoff representation in this language the model describes interacting bosons with a hard core on site repulsion and a nearest neighbor attraction this attractive interaction makes the lower bound on the free energy particularly tricky the key idea there is to prove a differential inequality for the two particle density which is thereby shown to be smaller than the probability density of a suitably weighted two particle random process on the lattice

commutators spectral trace identities and universal estimates for eigenvalues using simple commutator relations we obtain several trace identities involving eigenvalues and eigenfunctions of an abstract self adjoint operator acting in a hilbert space applications involve abstract universal estimates for the eigenvalue gaps as particular examples we present simple proofs of the classical universal estimates for eigenvalues of the dirichlet laplacian as well as of some known and new results for other differential operators and systems we also suggest an extension of the methods to the case of non self adjoint operators

3d finite difference frequency domain modeling of controlled source electromagnetic data direct solution and optimization for high accuracy three dimensional modeling of marine controlled source electromagnetic csem data is vital to improve the understanding of electromagnetic em responses collected in increasingly complex geologic settings a modeling tool for simulating 3d marine csem surveys based on a finite difference discretization of the helmholtz equation for the electric fields has been developed optimizations for csem simulations include the use of a frequency domain technique a staggering scheme that reduces inaccuracies especially for horizontal electric dipole sources located near the seafloor and a new interpolation technique that provides highly accurate em field values for receivers located in the immediate vicinity of the seafloor source singularities are eliminated through a secondary field approach in which the primary fields are computed analytically for a homogeneous or a 1d layered background the secondary fields are computed using the finite difference technique exploiting recent advances in computer technology and algorithmic developments the system of finite difference equations is solved using the mumps direct matrix solver in combination with the other optimizations this allows accurate em field computations for moderately sized models on small computer clusters the explicit availability of matrix factorizations is advantageous for multisource modeling and makes the algorithm well suited for future use within an inversion scheme comparisons of simulated data for 1 1d models to data generated using a 1d reflectivity technique and 2 3d models to published 3d data demonstrate the accuracy and benefits of the approach

lattice systems with a continuous symmetry we prove that the expansion in powers of the temperature t of the correlation functions and the free energy of the plane rotator model on a d dimensional lattice is asymptotic to all orders in t the leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series we also prove the inverse power decay of the pair correlation at low temperatures for d 3

upper bounds for eigenvalues of the discrete and continuous laplace operators in this paper we are concerned with upper bounds of eigenvalues of laplace operator on compact riemannian manifolds and finite graphs while on the former the laplace operator is generated by the riemannian metric on the latter it reflects combinatorial structure of a graph respectively eigenvalues have many applications in geometry as well as in combinatorics and in other fields of mathematics we develop a universal approach to upper bounds on both continuous and discrete structures based upon certain properties of the corresponding heat kernel this approach is perhaps much more general than its realization here basically we start with the following entries 1 an underlying space m with a finite measure 2 a well defined laplace operator on functions on m so that is a self adjoint operator in l m with a discrete spectrum 3 if m has a boundary then the boundary condition should be chosen so that it does not disrupt self adjointness of and is of dissipative nature 4 a distance function dist x y on m so that dist 1 for an appropriate notion of gradient

global solutions with shock waves to the generalized riemann problem for a system of hyperbolic conservation laws with linear damping abstract it is proven that a class of the generalized riemann problem for quasilinear hyperbolic systems of conservation laws with the uniform damping term admits a unique global piecewise c 1 solution u u t x containing only n shock waves with small amplitude on t 0 and this solution possesses a global structure similar to that of the similarity solution u u x t of the corresponding homogeneous riemann problem as an application of our result we prove the existence of global shock solutions piecewise continuous and piecewise smooth solution with shock discontinuities of the flow equations of a model class of fluids with viscosity induced by fading memory with a single jump initial data we also give an example to show that the uniform damping mechanism is not strong enough to prevent the formation of shock waves

solution of 3d time domain electromagnetic problems using optimal subspace projection abstracttime domain problems for controlled source electromagnetic exploration require accurate discretization of the solution for multiple spacial and temporal scales therefore forward simulation using conventional computational methods becomes computationally expensive even without accounting for induced polarization ip effects these effects create another complication caused by the presence of a convolution integral in the time domain maxwell system we suggested a novel fast and robust algorithm to solve the 3d time domain electromagnetic em problems that can be considered as a generalization of the spectral lanczos decomposition method the new method also allowed us to incorporate the ip effects without significant cost increase the discretized large scale maxwell system was projected onto a small subspace consisting of the laplace domain solutions the so called parameter dependent krylov subspace for an optimally chosen set of laplace parameters the projected system preserved stabilit

transient electromagnetic response of a three dimensional body in a layered earth the three dimensional 3 d electromagnetic scattering problem is first formulated in the frequency domain in terms of an electric field volume integral equation three dimensional responses are then fourier transformed with sine and cosine digital filters or with the decay spectrum the digital filter technique is applied to a sparsely sampled frequency sounding which is replaced by a cubic spline interpolating function prior to convolution with the digital filters typically 20 to 40 frequencies at five to eight points per decade are required for an accurate solution a calculated transient is usually in error after it has decayed more than six orders in magnitude from early to late time the decay spectrum usually requires ten frequencies for a satisfactory solution however the solution using the decay spectrum appears to be less accurate than the solution using the digital filters particularly after early times checks on the 3 d solution include reciprocity and convergence checks in the frequenc

from fixed energy localization analysis to dynamical localization an elementary path we review several techniques initiated by a remarkable work written by spencer j stat phys 51 1009 1019 1988 a quarter of century ago used and further developed in numerous subsequent researches we also describe a fairly general elementary derivation of spectral and strong dynamical anderson localization from the fixed energy analysis of the green s functions on locally finite graphs of polynomial growth obtained either by the multi scale analysis or by the fractional moment method this derivation goes in the same direction as the simon wolf method commun pure appl math 39 75 90 1986 but provides more quantitative estimates can be adapted to multi particle models and combined with a simplified variant of the germinet klein argument commun math phys 222 415 448 2001 results in an elementary proof of strong dynamical localization on arbitrary graphs of polynomial growth

permutation invariant qudit codes from polynomials abstract a permutation invariant quantum code on n qudits is any subspace stabilized by the matrix representation of the symmetric group s n as permutation matrices that permute the underlying n subsystems when each subsystem is a complex euclidean space of dimension q 2 any permutation invariant code is a subspace of the symmetric subspace of c q n we give an algebraic construction of new families of d dimensional permutation invariant codes on at least 2 t 1 2 d 1 qudits that can also correct t errors for d 2 the construction of our codes relies on a real polynomial with multiple roots at the roots of unity and a sequence of q 1 real polynomials that satisfy some combinatorial constraints when n 2 t 1 2 d 1 we prove constructively that an uncountable number of such codes exist

permutationally invariant codes for quantum error correction abstract a permutationally invariant n bit code for quantum error correction can be realized as a subspace stabilized by the non abelian group sn the code is spanned by bases for the trivial representation and all other irreducible representations both those of higher dimension and orthogonal bases for the trivial representation are available for error correction a number of new non additive binary codes are obtained including two new 7 bit codes and a large family of new 9 bit codes it is shown that the degeneracy arising from permutational symmetry facilitates the correction of certain types of two bit errors the correction of two bit errors of the same type is considered in detail but is shown not to be compatible with single bit error correction using 9 bit codes

the mixed initial boundary value problem for quasilinear hyperbolic systems with linearly degenerate characteristics abstract in this paper we investigate the mixed initial boundary value problem with small bv data for linearly degenerate quasilinear hyperbolic systems with general nonlinear boundary conditions in the half space t x t 0 x 0 as the result in a bressan contractive metrics for nonlinear hyperbolic systems indiana univ math j 37 1988 409 421 suggests that one may achieve global smoothness even if the c 1 norm of the initial data is large we prove that if the c 1 norm of the initial and boundary data is bounded but possibly large and the bv norm of the initial and boundary data is sufficiently small then the solution remains c 1 globally in time applications to quasilinear hyperbolic systems arising in physics and mechanics particularly to the system describing the motion of the relativistic string in the minkowski space time r 1 n are also given

computing spectral bounds of the heisenberg ferromagnet from geometric considerations we give a polynomial time algorithm for computing upper bounds on some of the smaller energy eigenvalues in a spin 1 2 ferromagnetic heisenberg model with any graph g for the underlying interactions an important ingredient is the connection between heisenberg models and the symmetric products of g our algorithms for computing upper bounds are based on generalized diameters of graphs computing the upper bounds amounts to solving the minimum assignment problem on g which has well known polynomial time algorithms from the field of combinatorial optimization we also study the possibility of computing the lower bounds on some of the smaller energy eigenvalues of heisenberg models this amounts to estimating the isoperimetric inequalities of the symmetric product of graphs by using connections with discrete sobolev inequalities we show that this can be performed by considering just the vertex induced subgraphs of g if our conjecture for a polynomial time approximation algorithm to solve the edge isoperimetric problem holds then our proposed method of estimating the energy eigenvalues via approximating the edge isoperimetric properties of vertex induced subgraphs will yield a polynomial time algorithm for estimating the smaller energy eigenvalues of the heisenberg ferromagnet we give a polynomial time algorithm for computing upper bounds on some of the smaller energy eigenvalues in a spin 1 2 ferromagnetic heisenberg model with any graph g for the underlying interactions an important ingredient is the connection between heisenberg models and the symmetric products of g our algorithms for computing upper bounds are based on generalized diameters of graphs computing the upper bounds amounts to solving the minimum assignment problem on g which has well known polynomial time algorithms from the field of combinatorial optimization we also study the possibility of computing the lower bounds on some of the smaller energy eigenvalues of heisenberg models this amounts to estimating the isoperimetric inequalities of the symmetric product of graphs by using connections with discrete sobolev inequalities we show that this can be performed by considering just the vertex induced subgraphs of g if our conjecture for a polynomial time approximation algorithm to solve the edge isoperi

on asymptotic limits for the quantum heisenberg model the authors discuss various asymptotic limits of the classical and quantum heisenberg model they give a new proof that the thermodynamic free energy of the quantum model converges to the free energy of the classical model in the limit of large spins they also obtain gaussian and free bose gas limits for the classical and quantum models respectively

proof of aldous spectral gap conjecture aldous spectral gap conjecture asserts that on any graph the random walk process and the random transposition or interchange process have the same spectral gap we prove the conjecture using a recursive strategy the approach is a natural extension of the method already used to prove the validity of the conjecture on trees the novelty is an idea based on electric network reduction which reduces the problem to the proof of an explicit inequality for a random transposition operator involving both positive and negative rates the proof of the latter inequality uses suitable coset decompositions of the associated matrices with rows and columns indexed by permutations

existence of global smooth solution to the initial boundary value problem for p system with damping abstract this paper is concerned with the initial boundary value problem for the p system with damping we prove the existence of the global smooth solution under the assumption that only the c 0 norm of the derivative of the initial data is sufficiently small while the c 0 norm of the initial data is not necessarily small the proof is based on several key a priori estimates the maximum principle and the characteristic method

random walk representations of the heisenberg model we develop random walk representations for the spin s heisenberg ferromagnet with nearest neighbor interactions we show that the spin s heisenberg model is a diffusion with local times controlled by the spin s ising model as a consequence expectations for the heisenberg model conditioned on zero diffusion are shown to be ising expectations

a low temperature expansion for classical n vector models ii renormalization group equations this paper continues the analysis of the low temperature expansions for classicaln vector models started in 1 a main part of it is a derivation of renormalization group equations and a construction of their solutions to do this we have to introduce a fluctuation integral connected with a next renormalization transformation and to make its preliminary analysis the results of the paper are summarized in theorems stating that the renormalization transformation preserves the space of densitites or actions described inductively in 1

mimetic discretizations for maxwell s equations we have constructed reliable finite difference methods for approximating the solution to maxwell s equations using accurate discrete analogs of differential operators that satisfy the identities and theorems of vector and tensor calculus in discrete form the numerical approximation does not have spurious modes and mimics many fundamental properties of the underlying physical problem including conservation laws symmetries in the solution and the nondivergence of particular vector fields numerical examples demonstrate the high quality of the method when the medium is strongly discontinuous and for nonorthogonal nonsmooth computational grids

multi way dual cheeger constants and spectral bounds of graphs we introduce a set of multi way dual cheeger constants and prove universal higher order dual cheeger inequalities for eigenvalues of normalized laplace operators on weighted finite graphs our proof proposes a new spectral clustering phenomenon deduced from metrics on real projective spaces we further extend those results to a general reversible markov operator and find applications in characterizing its essential spectrum