performance comparison of numerical inversion methods for laplace and hankel integral transforms in engineering problems abstract different methods for the numerical evaluations of the inverse laplace and inverse of joint laplace hankel integral transforms are applied to solve a wide range of initial boundary value problems often arising in engineering and applied mathematics the aim of the paper is to present a performance comparison among different numerical methods when they are applied to transformed functions related to actual engineering problems found in the literature most of our selected test functions have been found in the solution of boundary value problems of applied mechanics such as those related to transient responses of isotropic and transversely isotropic half space to concentrated impulse or those related to viscoelastic wave motion in layered media these classes of test functions are frequently encountered in similar problems such as those in boundary element or boundary integral equations theoretical seismology soil structure interaction in time domain and so on therefore their behavior with different numerical inversion algorithms could make a useful guide to a precise choice of more suitable inversion method to be used in similar problems some different methods are also investigated in detail and compared for the inversion of the joint hankel laplace transforms where more sophisticated integrand functions are encountered it is shown that durbin crump d amore fixed talbot gaver whyn rho gwr and direct integration methods have excellent performance and produce good results when applied to the same problems on the contrary gaver stehfest and piessens methods furnish results not very reliable for almost all classes of transformed functions and they seem good only for simple transformed functions particularly the performance of gwr algorithm is very good even for transformed functions with infinite number of singularities where the other methods fail in addition in case of double integral transforms only the fixed talbot durbin and weeks methods are recommended

numerical simulation for non linear thermal wave the present work applies the hybrid method of the laplace transform technique and a modified discretization scheme to analyze the non linear hyperbolic heat conduction problems in a semi infinite domain with either linearly or exponentially temperature dependent thermal conductivity the laplace transform method is used to remove the time dependent terms in the governing differential equation and the boundary conditions and then the transformed equations are discretized by a modified discretization scheme to show the rationality and reliability of the present results a comparison between the present numerical results and those in the literature is made results show the behavior of hyperbolic heat conduction is sensitive to the function form of thermal conductivity the speed of heat propagation changes for the variation of thermal conductivity

disturbance due to mechanical sources in micropolar elastic medium with voids the dynamic response of a homogeneous isotropic micropolar half space with voids subjected to a set of normal point sources is investigated the integral transforms have been inverted by using a numerical technique to obtain the normal force stress normal displacement tangential force stress tangential couple stress and volume fraction field in the physical domain for the two different sources the results of these quantities for a magnesium crystal like material are given and illustrated

periodically varying heat source response in a functionally graded microelongated medium abstract the present paper deals with the response due to periodically varying heat sources in the neighborhood of the origin of a functionally graded isotropic unbounded microelongated medium in the context of generalized thermoelastic theory the expressions for displacement microelongation and temperature fields have been obtained in laplace fourier transformed domain after computing the inverse fourier transforms by contour integration technique the inversion of laplace transforms has been obtained numerically the changes of displacement microelongation and normal strain have been shown graphically for different types of heat source

study of non fickian diffusion problems with the potential field in the cylindrical co ordinate system the present study applies a hybrid numerical scheme of the laplace transform technique and the control volume method in conjunction with the hyperbolic shape functions to investigate the effect of a potential field on the one dimensional non fickian diffusion problems in the cylindrical co ordinate system the laplace transform method is used to remove the time dependent terms in the governing differential equation and the boundary conditions and then the resulting equations are discretized by the control volume scheme the primary difficulty in dealing with the present problem is the suppression of numerical oscillations in the vicinity of sharp discontinuities results show that the present numerical results do not exhibit numerical oscillations and the potential field plays an important role in the present problem the strength of the jump discontinuity can be reduced by increasing the value of the potential gradient the propagation speed of mass wave is independent of the potential gradient and the boundary condition copyright 2003 john wiley sons ltd

on 2 generator subgroups of so 3 we classify all subgroups of so 3 that are generated by two elements each a rotation of finite order about axes separated by an angle that is a rational multiple of 7r in all cases we give a presentation of the subgroup in most cases the subgroup is the free product or the amalgamated free product of cyclic groups or dihedral groups the relations between the generators are all simple consequences of standard facts about rotations by 7r and 7r 2 embedded in the subgroups are explicit free groups on 2 generators as used in the banach tarski paradox

do we need hundreds of classifiers to solve real world classification problems we evaluate 179 classifiers arising from 17 families discriminant analysis bayesian neural networks support vector machines decision trees rule based classifiers boosting bagging stacking random forests and other ensembles generalized linear models nearest neighbors partial least squares and principal component regression logistic and multinomial regression multiple adaptive regression splines and other methods implemented in weka r with and without the caret package c and matlab including all the relevant classifiers available today we use 121 data sets which represent the whole uci data base excluding the large scale problems and other own real problems in order to achieve significant conclusions about the classifier behavior not dependent on the data set collection the classifiers most likely to be the bests are the random forest rf versions the best of which implemented in r and accessed via caret achieves 94 1 of the maximum accuracy overcoming 90 in the 84 3 of the data sets however the difference is not statistically significant with the second best the svm with gaussian kernel implemented in c using libsvm which achieves 92 3 of the maximum accuracy a few models are clearly better than the remaining ones random forest svm with gaussian and polynomial kernels extreme learning machine with gaussian kernel c5 0 and avnnet a committee of multi layer perceptrons implemented in r with the caret package the random forest is clearly the best family of classifiers 3 out of 5 bests classifiers are rf followed by svm 4 classifiers in the top 10 neural networks and boosting ensembles 5 and 3 members in the top 20 respectively

behavior of micropolar cubic crystal due to various sources the response of a micropolar cubic crystal due to various sources acting at the free surface has been studied the eigenvalue approach using integral transforms has been employed and the transforms have been inverted by using a numerical technique the displacement stress and microrotation components in the physical domain are obtained numerically the results of displacement and stresses have been compared for micropolar cubic crystal and micropolar isotropic solid the numerical results are illustrated graphically for a particular model

improvement of accuracy in numerical methods for inverting laplace transforms based on the post widder formula abstract the paper proposes a new computational version for numerical inversion of laplace transforms at a point and on an interval based on the post widder formula in this version the original sequence of post widder approximants is calculated using operations on series and the approximate value of the sought function is constructed as a limit of this sequence using polynomial and rational extrapolation to the limit some procedures are proposed for improvement of accuracy in the problem of inversion at equidistant points of an interval without computing additional approximants an extension of the method to the two dimensional case is discussed the one dimensional version is illustrated with some probabilistic examples involving both explicit and implicit functions the accuracy achieved in these examples with using the standard double precision arithmetic evaluated in terms of relative errors is about 10 10 10 14 even in case of out of scale parameters computational aspects are discussed in comparison with previously known realizations of the post widder method

magnetothermoelasticity with two relaxation times in conducting medium with variable electrical and thermal conductivity the equations of magneto thermoelasticity with two relaxation times and with variable electrical and thermal conductivity for one dimensional problems including heat sources are cast into matrix form using the state space and laplace transform techniques the resulting formulation is applied to a problem for the whole conducting space with a plane distribution of heat sources it also is applied to a semispace problem with a traction free surface and plane distribution of heat sources located inside the conducting medium the inversion of the laplace transforms is carried out using a numerical approach numerical results for the temperature displacement and stress distributions are given and illustrated graphically for both problems a comparison is made with the results obtained in the following cases a the electrical and thermal conductivities have constant values b the absence of magnetic field and c the coupled theory in magneto thermoelasticity

a subgroup of so 3 r generated by rotations of orders 4 and 8 abstract we prove that a subgroup of the real 3 dimensional special orthogonal group generated by a pair of rotations of respective orders 4 and 8 belonging to a family of such groups considered by radin and sadun in c radin l sadun on 2 generator subgroups of so 3 trans amer math soc 351 1999 114469 114480 has an epimorphic image which is one of psl 2 p psl 2 p 2 pgl 2 p or pgl 2 p 2 depending on the congruence of p mod 16 for all odd primes p by considering its reduction mod p as a linear group

evaluation of inverse fourier transforms through romberg integration this study deals with evaluation of inverse integral transforms through numerical integration arguments are presented to explain that such a numerical evaluation is mathematically incorrect in recent years a sudden increase has been noticed in the number of research publications in which romberg integration is said to have used in evaluating the inverse fourier transforms in this regard even the references cited in these papers do not support such an evaluation but suggest contrary an immediate concern is to caution the researchers studying the source problems in the field of solid mechanics over the use and approval of an erroneous numerical technique

interactions due to mechanical thermal sources in a micropolar thermoelastic medium possessing cubic symmetry abstract the present problem is the deformation of micropolar thermoelastic solids with cubic symmetry under the influence of various sources acting on the plane surface analytic expressions for displacement components microrotation force stress couple stress and temperature distribution are obtained in the physical domain for lord shulman l s and green lindsay g l theories of thermoelasticity by applying integral transforms a numerical inversion technique has been applied to obtain the solution in the physical domain the numerical results are presented graphically for a particular model

a laplace transorm potential theoretic method for acoustic propagation in subsonic flows this paper introduces a competitive computational approach for determining time dependent far field sound generated by subsonic flows around lifting airfoils the procedure assumes the linearity of the sound field away from a bounded region surrounding the airfoil it is assumed that the sound pressure on the boundary of this enclosed region referred to as the kirchhoff surface is specified possibly by another procedure such as solving the full euler equations away from the kirchhoff surface the euler equations are linearized about a uniform mean flow it is well known that linearized euler equations can be uncoupled into a scalar convective wave equation however due to the anisotropy present in the convective wave equation it is difficult to compute solutions in this context direct numerical simulation of the convective wave equation requires proper numerical descriptions of far field boundary conditions which is a non trivial task moreover if accurate far field conditions can be formulated the computational cost of direct simulation can be prohibitive even in a modest computational domain in this paper we present an alternate solution procedure first the problem is transformed via the laplace transform with appropriate initial conditions into a reduced wave equation the convective term in the reduced wave equation is removed using a dependent variable transformation then we use gothert s rule to obtain a helmholtz like equation with complex wave number which is subsequently solved using double layer potential theory finally upon application of numerical inverse laplace transform techniques far field acoustic pressure is obtained as a function of space and time

exponential solution of a problem of two dimensional motion of micropolar fluid in a half plane in this paper we generalize the results of the homogenous equation in fluid mechanics in the half plane for the type of micropolar fluid when the shear stresses spin micro rotation and one component of the velocity are given on the boundary we use laplace fourier transforms and then we convert laplace transform to find the solution in laplace domain then the numerical solution is applied to obtain the real solution in the physical domain graphically

a method for the numerical inversion of laplace transforms abstract in this paper a numerical inversion method for laplace transforms based on a fourier series expansion developed by durbin 5 is presented the disadvantage of the inversion methods of that type the encountered dependence of discretization and truncation error on the free parameters is removed by the simultaneous application of a procedure for the reduction of the discretization error a method for accelerating the convergence of the fourier series and a procedure that computes approximately the best choice of the free parameters suitable for a given problem the inversion method allows the adequate application of these procedures therefore in a big range of applications a high accuracy can be achieved with only a few function evaluations of the laplace transform the inversion method is implemented as a fortran subroutine

hybrid laplace transform finite difference method for transient heat conduction problems the new method involving the combined use of the laplace transform and the finite difference method is applicable to the problem of time dependent heat flow systems the present method removes the time derivatives from the governing differential equation using the laplace transform and then solves the associated equation with the finite difference method the transformed temperature is inverted numerically by the method of honig and hirdes to obtain the result in the physical quantities the present results are compared in tables with exact solutions and those obtained from the combined use of the laplace transform and the finite element method it is found that the present method is reliable and efficient

mechanical and thermal sources in a micropolar generalized thermoelastic medium abstract the disturbance due to mechanical and thermal sources in a homogeneous isotropic micropolar generalized thermoelastic half space is investigated by the use of laplace fourier transform technique the analytical expressions of displacement components normal force stress tangential force stress and temperature field so obtained have been inverted by using a numerical technique numerical results are presented graphically for a magnesium crystal like material

transient wave analysis of a cantilever timoshenko beam subjected to impact loading by laplace transform and normal mode methods abstract this study applies two analytical approaches laplace transform and normal mode methods to investigate the dynamic transient response of a cantilever timoshenko beam subjected to impact forces explicit solutions for the normal mode method and the laplace transform method are presented the durbin method is used to perform the laplace inverse transformation and numerical results based on these two approaches are compared the comparison indicates that the normal mode method is more efficient than the laplace transform method in the transient response analysis of a cantilever timoshenko beam whereas the laplace transform method is more appropriate than the normal mode method when analyzing the complicated multi span timoshenko beam furthermore a three dimensional finite element cantilever beam model is implemented the results are compared with the transient responses for displacement normal stress shear stress and the resonant frequencies of a timoshenko beam and bernoulli euler beam theories the transient displacement response for a cantilever beam can be appropriately evaluated using the timoshenko beam theory if the slender ratio is greater than 10 or using the bernoulli euler beam theory if the slender ratio is greater than 100 moreover the resonant frequency of a cantilever beam can be accurately determined by the timoshenko beam theory if the slender ratio is greater than 100 or by the bernoulli euler beam theory if the slender ratio is greater than 400

a numerical treatment to the solution of quasiparabolic partial differential equations this paper presents results obtained by the implementation of a hybrid laplace transform finite element method to the solution of quasiparabolic problem the present method removes the time derivatives from the quasiparabolic partial differential equation using the laplace transform and then solves the associated equation with the finite element method the numerical inverse of the laplace transform is realized by solving linear overdetermined systems and a polynomial equation of the kth order test examples are used to show that the numerical solution is comparable to the exact solution of the initial boundary value problem at the given grid points

magnetohydrodynamic unsteady free convection flow of a couple stress fluid with one relaxation time through a porous medium the method of the matric exponential which constitutes the basis of the state space approach of modern control theory is applied to the non dimensional equations of a magnetohydrodynamic unsteady free convection flow of a couple stress fluid through a porous medium with one relaxation time the resulting formulation together with laplace transform technique is applied to a thermal shock problem also a problem with distribution of heat sources is considered numerical results for the velocity induced magnetic field angular velocity and temperature distributions are given and illustrated graphically for each problem

numerical solutions for the hyperbolic heat conduction problems in a layered solid cylinder with radiation surface the numerical scheme based on the hybrid application of the laplace transform method and a control volume formulation in conjunction with the hyperbolic shape functions is applied to investigate the hyperbolic heat conduction problems in an infinitely long layered solid cylinder with the nonlinear boundary conditions in order to perform the laplace transform method the nonlinear boundary conditions are linearized with taylor s series expansion results show that the present numerical scheme can overcome the mathematical difficulties induced by the nonlinear boundary conditions the geometry the composite interface and the singular point and has stability and reliability for such problems effects of the thermal properties of two dissimilar materials on heat transfer are also discussed

numerical analysis for the hyperbolic heat conduction problem under a pulsed surface disturbance a hybrid application of the laplace transform method and a control volume formulation in conjunction with the hyperbolic shape functions is applied to investigate the hyperbolic diffusion problems with the pulsed boundary conditions in various coordinate systems the laplace transform method is used to remove the time dependent terms in the governing differential equations and the boundary conditions and then the transformed equations are discretized by the control volume scheme the primary difficulty in dealing with the present problem is the suppression of numerical oscillations in the vicinity of sharp discontinuities the results show that the numerical results agree well with the analytic solution and do not exhibit numerical oscillations in the vicinity of the jump discontinuity the present method also can solve the problems with the singular point

state space approach of two temperature generalized thermoelasticity of one dimensional problem abstract in this paper we will consider a half space filled with an elastic material which has constant elastic parameters the governing equations are taken in the context of the two temperature generalized thermoelasticity theory youssef h 2005a the dependence of the modulus of elasticity and the thermal conductivity on the reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity j appl math mech 26 4 4827 youssef h 2005b theory of two temperature generalized thermoelasticity ima j appl math 1 8 the medium is assumed initially quiescent laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions the general solution obtained is applied to a specific problem of a half space subjected to thermal shock and traction free the inverse laplace transforms are computed numerically using a method based on fourier expansion techniques some comparisons have been shown in figures to estimate the effect of the two temperature parameter

elastodynamics of an axisymmetric problem in an anisotropic liquid saturated porous medium the laplace and hankel transforms have been employed to find the general solution to the field equations in an anisotropic liquid saturated porous medium for plain axisymmetric problem in the transformed form an application of an infinite space with impulsive force at the origin has been considered to show the utility of the solution obtained the results of the corresponding problem in isotropic liquid saturated porous medium can be derived as a special case to get the solutions in the physical form a numerical inversion technique has been applied the results in the form of displacement and stress components have been obtained numerically and discussed graphically for a particular model

passage times of asymmetric anomalous walks with multiple paths we investigate the transient and the long time behaviour of asymmetric anomalous walks in heterogeneous media two types of disorder are worked out explicitly weak and strong disorder in addition the occurrence of disordered multiple paths is considered we calculate the first passage time distribution of the associated stochastic transport process we discuss the occurrence of the crossover from a power law to an exponential decay for the long time behaviour of the distribution of the first passage times of disordered biased walks

on a numerical technique regarding inversion of the laplace transform abstract we have discussed a method to convert the laplace transform into an integral equation of the first kind of convolution type which is an ill posed problem and used a regularization method to solve it we investigated the behavior of the optimal regularization parameter the optimal choice of parameter in the regularization of ill posed inverse problems depends on several features of a given problem we have compared our results with varah s 1979 1983 results and they are shown in respective diagrams for comparison purposes

numerical methods for nonlinear second order hyperbolic partial differential equations i time linearized finite difference methods for 1 d problems abstract a three parameter family of finite difference methods for one dimensional hyperbolic equations with damping and nonlinearities based on the introduction of a new dependent variable and three implicitness parameters for the time discretization and the diffusion and reaction terms is presented and shown to result in two time level semi discrete equations second order accurate spatial discretizations and time linearization of the nonlinear source terms are shown to result in three time level linear finite difference equations which are second order accurate in time whenever the reaction and diffusion terms are allocated in the proportion 1 2 1 to the past current and future time levels second order accurate in time time linearized three point compact operator methods for the spatial derivatives which only involve three time levels and three grid points and are fourth order accurate in space are also presented and their linear stability analyzed an exhaustive comparison between analytical and numerical results indicates that the accuracy of time linearized methods increases as the time step and grid spacing are decreased and is nearly independent of the order of the spatial discretization when there is a sufficient number of grid points to resolve the wave structure and the best accuracy is achieved when the three implicitness parameters are equal to 1 2 it is also shown that the accuracy of time linearized methods is a strong function of the wave speed as the wave speed is increased and the wave equation tends to a parabolic one the methods are still three time level techniques which may not preserve the positivity of the solution whereas a crank nicolson discretization of the corresponding parabolic equation does preserve this property provided that there are no mathematical incompatibilities between the initial and the boundary conditions it is also shown that for one dimensional wave equations with monotonic kinetics and time dependent forcing there are very few differences between second and first order time accurate discretizations of the diffusion terms provided that the time step and grid size are sufficiently small and the discretization of the reaction terms plays a less important rule than that of the diffusion terms

subgroup families controlling p local finite groups a p local finite group consists of a finite p group s together with a pair of categories which encode conjugacy relations among subgroups of s and which are modelled on the fusion in a sylow p subgroup of a finite group it contains enough information to define a classifying space which has many of the same properties as p completed classifying spaces of finite groups in this paper we examine which subgroups control this structure more precisely we prove that the question of whether an abstract fusion system mathcal f over a finite p group s is saturated can be determined by just looking at smaller classes of subgroups of s we also prove that the homotopy type of the classifying space of a given p local finite group is independent of the family of subgroups used to define it in the sense that it remains unchanged when that family ranges from the set of mathcal f centric mathcal f radical subgroups at a minimum to the set of mathcal f quasicentric subgroups at a maximum finally we look at constrained fusion systems analogous to p constrained finite groups and prove that they in fact all arise from groups

solving the multiple instance problem with axis parallel rectangles the multiple instance problem arises in tasks where the training examples are ambiguous a single example object may have many alternative feature vectors instances that describe it and yet only one of those feature vectors may be responsible for the observed classification of the object this paper describes and compares three kinds of algorithms that learn axis parallel rectangles to solve the multiple instance problem algorithms that ignore the multiple instance problem perform very poorly an algorithm that directly confronts the multiple instance problem by attempting to identify which feature vectors are responsible for the observed classifications performs best giving 89 correct predictions on a musk odor prediction task the paper also illustrates the use of artificial data to debug and compare these algorithms

an application of the ltdrm to transient diffusion problems with nonlinear material properties and nonlinear boundary conditions in this paper we shall present an application of the laplace transform dual reciprocity method ltdrm to the solution of transient diffusion problems with nonlinear material properties and nonlinear boundary conditions two methods with and without utilizing the kirchhoff transformation will be discussed the nonlinear terms in both governing equation and boundary conditions are linearized first followed by the removal of the time variable from the linearized differential system with the laplace transformation and then the problem is solved by the dual reciprocity method as a result a solution at any specific time can be obtained without step by step calculations in time domain and computations of domain integrals to show the efficiency and accuracy of the present method several problems are analyzed and their solutions are compared with those obtained either analytically or numerically

the extended durbin method and its application for piezoelectric wave propagation problems abstract based on the well known durbin method an efficient numerical method was developed for the inversion of the two sided laplace transform the accuracy of the method was verified using examples as an application of the method transient elastic waves propagating in a two layered piezoelectric medium subjected to anti plane concentrated loading and in plane electric displacement loading were investigated one sided and two sided laplace transforms were applied to determine the shear stresses and electric displacements in the double laplace transform domain subsequently the durbin method for one sided laplace transform inversion and the extended durbin method for two sided laplace transform inversion were used to implement the numerical inversions additionally the numerical results of the transient stresses and electric displacements were evaluated and discussed it showed that the arrival time of transient waves satisfies physical phenomena and the transient solution oscillates near the static solution and rapidly approximates the static solution

a half space problem in the theory of generalized thermoelastic diffusion abstract in this work we consider the problem of a thermoelastic half space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time the bounding surface of the half space is taken to be traction free and subjected to a time dependent thermal shock the chemical potential is also assumed to be a known function of time on the bounding plane laplace transform techniques are used the solution is obtained in the laplace transform domain by using a direct approach the solution of the problem in the physical domain is obtained numerically using a numerical method for the inversion of the laplace transform based on fourier expansion techniques the temperature displacement stress and concentration as well as the chemical potential are obtained numerical computations are carried out and represented graphically

effect of body forces on a 2d generalized thermoelastic long cylinder in this work we consider a two dimensional problem for an infinitely long solid cylinder the lateral surface of the cylinder is taken to be traction free and is subjected to a known temperature distribution under the action of solenoidal body forces laplace transform techniques are used the solution in the transformed domain is obtained by using a direct approach in the form of an infinite series the inverse laplace transforms are obtained by using a numerical method based on fourier expansion techniques numerical results are computed for the temperature displacement and stress distributions and shown graphically

numerical inversion of the laplace transform from the real axis a numerical method for inversion of the laplace transform f p given for p 0 only is proposed recommendations for the choice of the abscissa of convergence and parameters of numerical integration are given the results of the numerical tests are discussed

amalgams blocks weights fusion systems and finite simple groups abstract we associate an iterated amalgam of finite groups to a certain class of fusion systems on finite p groups p a prime in such a way that the p group of the fusion system is a maximal finite p subgroup of the resulting group unique up to conjugacy and furthermore the conjugation action of the resulting usually infinite group on p subgroups induces the original fusion system on the p group 1 in view of earlier work of puig and of broto castellana grodal levi and oliver c broto n castellana j grodal r levi r oliver subgroup families controlling p local finite groups proc london math soc 3 91 2005 325 354 the fusion systems we deal with include all saturated fusion systems the resulting amalgam has free normal subgroups of finite index and we examine the images of the group by its maximal free normal subgroups of finite index these images all contain isomorphic copies of the original p group and are generated by the images of the finite groups used in the amalgamation if there is no non trivial normal p subgroup of the fusion system equivalently if the iterated amalgam constructed has no non trivial normal p subgroup then the generalised fitting subgroup of each of these homomorphic images is a direct product of non abelian simple groups each of order divisible by p and if there is no proper non trivial strongly closed p subgroup in the fusion system then the generalised fitting subgroup of any of these finite groups is characteristically simple we note that the finite dimensional representation theory of this amalgam is almost by construction p locally determined in the case of the fusion system associated to a p block of a finite group we suggest strong links between block theoretic invariants of the above finite epimorphic images of the associated amalgam and of the original block we believe that the results of this paper offer the prospect of at least the beginnings of a structural explanation for some of the current numerical conjectures in block theory e g j l alperin weights for finite groups in proc sympos pure math vol 47 amer math soc providence 1987 pp 369 379 e c dade counting characters in blocks i invent math 109 1 1992 187 210

state space approach to generalized thermoelastic problem with thermomechanical shock in this work the state space formulation for one dimensional problem of generalized thermoelasticity with one relaxation time is introduced the resulting formulation together with the laplace transform technique is applied to a thermomechanical shock half space problem the solution in the transformed domain is obtained the inverse laplace transforms is evaluated numerically the results are obtained and represented graphically

a simple and efficient algorithm to compute tail probabilities from transforms we present an algorithm to approximately compute the tail probability that a random variable exceeds a specified number given only an expression for its transform we also show that the problem is p hard more difficult than np hard suggesting that no efficient procedure can solve it exactly our method consists essentially of summing a power series and thus is easy to perform and requires little memory furthermore its computational effort is nearly linear in the reciprocal of a prespecified worst case error bound

restricted set classification who is there abstract we consider a problem where a set x of n objects instances coming from c classes have to be classified simultaneously a restriction is imposed on x in that the maximum possible number of objects from each class is known hence we dubbed the problem who is there we compare three approaches to this problem 1 independent classification whereby each object is labelled in the class with the largest posterior probability 2 a greedy approach which enforces the restriction and 3 a theoretical approach which in addition maximises the likelihood of the label assignment implemented through the hungarian assignment algorithm our experimental study consists of two parts the first part includes a custom made chess data set where the pieces on the chess board must be recognised together from an image of the board in the second part we simulate the restricted set classification scenario using 96 datasets from a recently collated repository university of santiago de compostela usc our results show that the proposed approach 3 outperforms approaches 1 and 2

a problem of numerical inversion of implicitly defined laplace transforms abstract a procedure is proposed for numerical inversion of laplace transforms x s implicitly defined from the functional equation x s g a s cx s where a and g are known functions c is a known constant this equation is encountered in queueing inventory and insurance problems the procedure constructs coefficients of the laguerre series for the original in the laguerre series inversion method and a sequence of approximants in the post widder inversion method scalar and matrix cases are treated in the same fashion the numerical results are compared with those attainable with the fourier series method

a modified euler method for dynamic analyses a modified version of the well known euler method for numerical integration is presented and its application in analyses of the dynamic response of structures is discussed this modified method was first introduced in 1981 and it has been reported that it was discovered by accident when first introduced however valuable information related to the accuracy stability and merits of the method were not provided it is shown that the modified euler method has features that make it an attractive approach for applications in dynamic analyses of structures accuracy and stability analyses are made for the method by considering free vibrational responses of linear undamped single degree of freedom systems the method is explicit and extremely easy to use however it is conditionally stable applications of the method are also made which illustrate its usefulness and inherent simplicity furthermore comparisons of the modified euler method and the newmark beta method are reported which elucidate the relative merits of these methods

hybrid method for transient response of circular pins the combined application of the laplace transform and the finite element method is used to analyse the transient response of circular pins the present method removes the time dependence terms from the governing differential equations and boundary conditions using the laplace transform and then the eigenfunction expansion method is applied to reduce the two dimensional boundary value problem to that of one dimension accordingly the final transformed equation can easily be solved by the finite element method the transformed temperature is inverted to the physical quantity numerically the present results agree well with analytical solutions in addition it is seen that the results of axisymmetric transient heat conduction problems with the central node at r 0 can accurately be obtained using the present method