eigenvalue theorems for discrete multipoint conjugate boundary value problems abstract we consider the following boundary value problem n y k p k y y n 1 y k 0 m j y k i 0 j 0 n i 1 i 1 r where r 2 ni 1 for i 1 r i 1 r n i n and 0 k1

scalar wave equation by the boundary element method a d bem approach with constant time weighting functions a d bem approach based on time weighting residuals is developed for the solution of two dimensional scalar wave propagation problems the modified basic equation of the d bem formulation is generated by weighting with respect to time the basic d bem equation under the assumption of linear and cubic time variation for the potential and for the flux a constant time weighting function is adopted the time integration reduces the order of the time derivative that appears in the domain integral as a consequence the initial conditions are directly taken into account an assessment of the potentialities of the proposed formulation is provided by the examples included at the end of the work copyright 2009 john wiley sons ltd

a comparative study of three boundary element approaches to calculate the transient response of viscoelastic solids with unbounded domains abstract as an alternative to domain discretization methods the boundary element method bem provides a powerful tool for the calculation of dynamic structural response in frequency and time domain field equations of motion and boundary conditions are cast into boundary integral equations bie which are discretized only on the boundary fundamental solutions are used as weighting functions in the bie which fulfil the sommerfeld radiation condition i e the energy radiation into a surrounding medium is modelled correctly therefore infinite and semi infinite domains can be effectively treated by the method the soil represents such a semi infinite domain in soil structure interaction problems the response to vibratory loads superimposed to static pre loads can often be calculated by linear viscoelastic constitutive equations conventional viscoelastic constitutive equations can be generalized by taking fractional order time derivatives into account in the present paper two time domain bem approaches including generalized viscoelastic behaviour are compared with the laplace domain bem approach and subsequent numerical inverse transformation one of the presented time domain approaches uses an analytical integration of the elastodynamic bie in a time step viscoelastic constitutive properties are introduced after laplace transformation by means of an elastic viscoelastic correspondence principle the transient response is obtained by inverse transformation in each time step the other time domain approach is based on the so called convolution quadrature method in this formulation the convolution integral in the bie is numerically approximated by a quadrature formula whose weights are determined by the same laplace transformed fundamental solutions used in the first method and a linear multistep method a numerical study of wave propagation problems in 3 d viscoelastic continuum is performed for comparing the three bem formulations

a lower bound for parallel string matching this paper presents an omega log log m lower bound on the number of rounds necessary for finding occurrences of a pattern string p 1 m in a text string t 1 2m in parallel using m comparisons in each round the bound is within a constant factor of the fastest algorithm for this problem d breslauer and z galil siam j comput 19 1990 pp 1051 1058 and also holds for an m processor crcw pram in the case of a general alphabet consequently the paper derives the parallel complexity of the string matching problem using p processors for general alphabets which is theta frac m p if p leq frac m log log m theta log log m if frac m log log m leq p leq m theta log log 2p m p if m leq p leq m 2 theta 1 if p geq m 2 or in short theta lceil frac m p rceil log log lceil 1 p m rceil 2p

fast numerical solution of weakly singular volterra integral equations abstract we give a fortran program for the numerical solution of abel volterra convolution equations of the second and first kind we use a fractional linear multistep method bdf4 1 2 and use fast fourier transform techniques to exploit the convolution structure a detailed description of the computation of the quadrature weights using fft is given numerical examples are included

optimal bounds for decision problems on the crcw pram optimal o log n log log n lower bounds on the time for crcw prams with polynomially bounded numbers of processors or memory cells to compute parity and a number of related problems are proven a strict time hierarchy of explicit boolean functions of n bits on such machines that holds up to o log n log log n time is also exhibited that is for every time bound t within this range a function is exhibited that can be easily computed using polynomial resources in time t but requires more than polynomial resources to be computed in time t 1 finally it is shown that almost all boolean functions of n bits require log n log log n o 1 time when the number of processors is at most polynomial in n the bounds do not place restrictions on the uniformity of the algorithms nor on the instruction sets of the machines

an optimal o log n time parallel string matching algorithm an optimal o log log n time parallel algorithm for string matching on crow pram is presented it improves previous results of galil inform and control 67 1985 pp 144 157 and vishkin inform and control 67 1985 pp 91 113

optimal off line detection of repetitions in a string an algorithm is presented to detect within optimal time o n log n and space o n off line on a ram all of the distinct repetitions in a given textstring on a finite alphabet the proposed strategy is self contained as it depends more heavily on algorithmic design considerations than on the combinatorial properties of the output it is based on a new data structure the leaf tree which is particularly suited to exploit simple properties of the suffix tree associated with the string to be analyzed

a multiplicity result for second order impulsive differential equations via the leggett williams fixed point theorem using the leggett williams fixed point theorem we present in this paper criteria which guarantee the existence of three nonnegative solutions to second order impulsive equations

a numerical method for a partial integro differential equation a method is considered for the integration in time of a partial integro differential equation the discretization technique employed is patterned after an idea of ch lubich error bounds are derived for both smooth and nonsmooth initial data

initial conditions contribution in a bem formulation based on the convolution quadrature method this work presents a two dimensional boundary element method bem formulation for the analysis of scalar wave propagation problems the formulation is based on the so called convolution quadrature method cqm by means of which the convolution integral presented in time domain bem formulations is numerically substituted by a quadrature formula whose weights are computed using the laplace transform of the fundamental solution and a linear multistep method this bem formulation was initially developed for scalar wave propagation problems with null initial conditions in order to overcome this limitation this work presents a general procedure that enables one to take into account non homogeneous initial conditions after replacing the initial conditions by equivalent pseudo forces the numerical results included in this work show the accuracy of the proposed bem formulation and its applicability to such kind of analysis copyright 2006 john wiley sons ltd

stabilization of solutions of a degenerate nonlinear diffusion problem i 4 u f u in l l x r u tl t o in r u x 0 uo x in l l where m 1 is a parameter f is locally lipschitz continuous f 0 0 and u is bounded problems of this form arise in a number of areas of science for instance in models for gas or fluid flow in porous media 2 and for the spread of certain biological populations 13 161 this paper is divided into two parts in part i we consider what may be called the motivating example problem i which consists of problem i with the special choice f u u 1 u u a 1 for suitably restricted parameters a we begin by describing in detail the set l of nonnegative equilibrium solutions of problem i clearly 8 l contains the trivial solution u 0 for all l 0 write 8 l e l o in the description of z l there are two critical parameter values lo and l1 with 0 lo l1 j we show that i g l 4 for 0 l lo

the existence of multiple positive solutions to boundary value problems of nonlinear delay differential equations with countably many singularities on infinite interval in this paper we consider the existence of countably many positive solutions to a boundary value problem of a nonlinear delay differential equation with countably many singularities on infinite interval f x t a t f t x t x t 0 0 x t 0 where f r r is an increasing homeomorphism and a positive homomorphism with f 0 0 x t is a function in c r 0 r defined by x t s x t s for r s 0 and x c r 0 r by using the fixed point index theory and a new fixed point theorem in a cone we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem the conclusions in this paper essentially extend and improve the known results

eigenvalues and eigenfunctions of discrete conjugate boundary value problems abstract we consider the following boundary value problem 1 n p n y f k y y n 1 y n 2 0 k m i y 0 0 0 i p 1 i y m n i 0 0 i n p 1 where 1 p n 1 is fixed and 0 a characterization of the values of is carried out so that the boundary value problem has a positive solution next for 1 criteria are developed for the existence of two positive solutions of the boundary value problem in addition for particular cases we also offer upper and lower bounds for these positive solutions several examples are included to dwell upon the importance of the results obtained

an algorithm for approximate solutions to weakly filtered synchronous control systems and nonlinear renewal processes a multi time perturbation algorithm is derived to study certain synchronous control systems and nonlinear renewal processes the new methods presented here study singular perturbation problems for nonlinear volterra integro differential equations whose kernels are close to the dirac delta function the algorithm provides useful approximate solutions to weakly filtered phase locked loop circuits and to nonlinear renewal equations describing certain population dynamics

transducers and repetitions the factor transducer of a word associates to each of its factors or subwords their first occurrence optimal bounds on the size of minimal factor transducers together with an algorithm for building them are given analogue results and a simple algorithm are given for the case of subsequential suffix transducers algorithms are applied to repetition searching in words le transducteur des facteurs d un mot associe a chacun de ses facteurs leur premiere occurrence on donne des bornes optimales sur la taille du transducteur minimal d un most ainsi qu un algorithme pour sa construction on donne des resultats analogues et un algorithme simple dans le cas du transducteur sous sequentiel des suffixes d un mot on donne une application a la detection de repetitions dans les mots

the solution of elastostatic and dynamic problems using the boundary element method based on spherical hankel element framework summary in this paper new spherical hankel shape functions are utilized to reformulate boundary element method for two dimensional 2d elastostatic and elastodynamic problems to this end the dual reciprocity dr boundary element method bem is reconsidered by employing new spherical hankel shape functions to approximate the state variables displacements and tractions of navier s differential equation using enrichment of a class of radial basis functions rbfs called spherical hankel rbfs hereafter the interpolation functions of a hankel boundary element framework has been derived for this purpose polynomial terms are added to the functional expansion that only uses spherical hankel rbf in the approximation in addition to polynomial function fields the participation of spherical bessel function fields has also increased robustness and efficiency in the interpolation it is very interesting that there is no runge phenomenon in equispaced hankel macroelements unlike equispaced classic lagrange ones several numerical examples are provided to demonstrate the effectiveness robustness and accuracy of the proposed hankel shape functions and in comparison with the classic lagrange ones they show much more accurate and stable results

approximate periods of strings the study of approximately periodic strings is relevant to diverse applications such as molecular biology data compression and computer assisted music analysis here we study different forms of approximate periodicity under a variety of distance functions we consider three related problems for two of which we derive polynomial time algorithms we then show that the third problem is np complete

convolution quadrature and discretized operational calculus ii operational quadrature rules are applied to problems in numerical integration and the numerical solution of integral equations singular integrals power and logarithmic singularities finite part integrals multiple timescale convolution volterra integral equations wiener hopf integral equations frequency domain conditions which determine the stability of such equations can be carried over to the discretization

fibonacci arrays and their two dimensional repetitions abstract notions related to repetitive substructures in two dimensional arrays are introduced and studied in an attempt to parallel some of the analogous developments already known for strings in particular sequences of fibonacci arrays are defined capable of exhibiting extremal properties in terms of certain repetitive subpatterns called tandems two types of tandems are considered for one type it is shown that the number of occurrences in an m n fibonacci array attains the general upper bound of o m 2 n log n

dynamic analyses of plane frames by integral equations for bars and timoshenko beams abstract since especially for higher frequencies timoshenko s theory gives more reliable results than euler bernoulli s theory systems of beams like frames under arbitrary dynamic excitations should be analyzed on the basis of this refined theory in this paper after deriving the basic fundamental solutions of a lateral unit point force and of a unit single moment the deflection and the rotation of the beam cross section are given as integral equation forms of the governing second order differential equation system in the laplace and the frequency domain since in frameworks axial displacements also occur the well known integral equations for bars under tension or compression are added to complete the modelling of plane frame structures from these the unknown boundary values may be exactly determined via point collocation at the beam ends and solution of the resulting algebraic system with these boundary values the exact deflection and rotation can also be found at arbitrary interior points finally the convolution quadrature method is applied to the laplace domain integral equation formulation in order to analyze the time dependent wave propagation process two examples are presented to demonstrate the method s exactness compared with conventional finite element results a single beam where the shift of the resonance frequencies when using the timoshenko theory instead of euler bernoulli s theory is shown and a two storey framework where in addition to the frequence response the causality of the propagating wave is studied

an energy approach to space time galerkin bem for wave propagation problems in this paper we consider dirichlet or neumann wave propagation problems reformulated in terms of boundary integral equations with retarded potential starting from a natural energy identity a space time weak formulation for 1d integral problems is briefly introduced and continuity and coerciveness properties of the related bilinear form are proved then a theoretical analysis of an extension of the introduced formulation for 2d problems is proposed pointing out the novelty with respect to existing literature results at last various numerical simulations will be presented and discussed showing unconditional stability of the space time galerkin boundary element method applied to the energetic weak problem copyright 2009 john wiley sons ltd

an optimal o log log n time parallel algorithm for detecting all squares in a string an optimal o log log n time concurrent read concurrent write parallel algorithm for detecting all squares in a string is presented a tight lower bound shows that over general alphabets this is the fastest possible optimal algorithm when p processors are available the bounds become theta lceil n log n p rceil log log lceil 1 p n rceil 2p the algorithm uses an optimal parallel string matching algorithm together with periodicity properties to locate the squares within the input string

compression of time generated matrices in two dimensional time domain elastodynamic bem analysis this paper describes a new scheme to improve the efficiency of time domain bem algorithms the discussion is focused on the two dimensional elastodynamic formulation however the ideas presented apply equally to any step by step convolution based algorithm whose kernels decay with time increase the algorithm presented interpolates the time domain matrices generated along the time stepping process for time steps sufficiently far from the current time two interpolation procedures are considered here a large number of alternative approaches is possible chebyshev lagrange polynomials and linear a criterion to indicate the discrete time at which interpolation should start is proposed two numerical examples and conclusions are presented at the end of the paper

uniform error estimates of galerkin methods for monotone abel volterra integral equations on the half line we consider galerkin methods for monotone abel volterra integral equations of the second kind on the half line the l2 theory follows from kolodner s theory of monotone hammerstein equations we derive the loo theory from the l2 theory by relating the l2and loo spectra of operators of the form x b ax to one another here denotes convolution and b e l1 and a e loo as an extra condition we need b t o t a 1 with a 0 we also prove the discrete analogue in particular we verify that the galerkin matrix satisfies the discrete conditions

an analysis of the modified l1 scheme for time fractional partial differential equations with nonsmooth data we introduce a modified l1 scheme for solving time fractional partial differential equations and obtain error estimates for smooth and nonsmooth initial data in both homogeneous and inhomogeneous c

three symmetric solutions of lidstone boundary value problems for difference and partial difference equations we consider the boundary value problem 2my k m f y k 2y k 1 2iy k 1 2 m 1 y k m 1 k a 1 b 1 2iy a 1 m 2iy b 1 m 2i 0 0 i m 1 where m 1 and 1 m f rm 0 is continuous by using amann and leggett williams fixed point theorems we develop growth conditions on f so that the boundary value problem has triple positive symmetric solutions the results obtained are then applied in the investigation of radial solutions for certain partial difference equation subject to lidstone type conditions

usefulness of the karp miller rosenberg algorithm in parallel computations on strings and arrays abstract the karp miller rosenberg 1972 algorithm was one of the first efficient almost linear sequential algorithms for finding repeated patterns and for string matching in the area of efficient sequential computations on strings it was soon superseded by more efficient and more sophisticated algorithms we show that the karp miller rosenberg algorithm kmr must be considered as a basic technique in parallel computations for many problems variations of kmr give the known most efficient parallel algorithms the representation of the set of basic factors subarrays of a string array produced by the algorithm is an extremely useful data structure in parallel algorithms on strings and arrays this gives also a general unifying framework for a large variety of problems we show that the following problems for strings and arrays can be solved by almost optimal parallel algorithms pattern matching longest repeated factor subarray longest common factor subarray maximal symmetric factor subarray also the following problems for strings can be solved within the same complexity bounds finding squares testing even palstars and compositions of k palindromes for k 2 3 4 computing lyndon factorization and building minimal pattern matching automata in the model without concurrent writes the parallel time is o log n 2 with n processors and in the model with concurrent writes the time for most of the problems is o log n with n processors for two problems related to the one dimensional case longest repeated factor and longest common factor there were designed parallel algorithms using suffix trees apostolico et al 1988 however our data structure is simpler and furthermore for the two dimensional case suffix trees do not work the complexity of our algorithms does not depend on the size of the alphabet except for the computation of pattern matching automata

detecting regularities on grammar compressed strings we address the problems of detecting and counting various forms of regularities in a string represented as a straight line program slp which is essentially a context free grammar in the chomsky normal form given an slp of size n that represents a string s of length n our algorithm computes all runs and squares in s in o n 3 h time and o n 2 space where h is the height of the derivation tree of the slp we also show an algorithm to compute all gapped palindromes in o n 3 h g n h log n time and o n 2 space where g is the length of the gap as one of the main components of the above solution we propose a new technique called approximate doubling which seems to be a useful tool for a wide range of algorithms on slps indeed we show that the technique can be used to compute the periods and covers of the string in o n 2 h time and o n h n log 2 n time respectively

fractional linear multistep methods for abel volterra integral equations of the second kind fractional powers of linear multistep methods are suggested for the numerical solution of weakly singular volterra integral equations the proposed methods are convergent of the order of the underlying multistep method also in the generic case of solutions which are not smooth at the origin the stability properties stability region a stability a a stability are closely related to those of the underlying linear multistep method