graphical representation of the partition function of a one dimensional δ function bose gas the one dimensional repulsive function bose system is studied by only using the bethe ansatz equation n particle partition functions are exactly calculated from this expression for the n particle partition function the n particle cluster integral is derived the results completely agree with those of the thermal bethe ansatz tba this directly proves the validity of the tba the theory of partitions and graphs is used to simplify the discussion

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 method for solving stochastic differential equations with poissonian white shot noise we propose a numerical integration scheme to solve stochastic differential equations driven by poissonian white shot noise our formula which is based on an integral equation which is equivalent to the stochastic differential equation utilizes a discrete time approximation with fixed integration time step we show that our integration formula approaches the euler formula if the poissonian noise approaches the gaussian white noise the accuracy and efficiency of the proposed algorithm are examined by studying the dynamics of an overdamped particle driven by poissonian white shot noise in a spatially periodic potential we find that the accuracy of the proposed algorithm only weakly depends on the parameters characterizing the poissonian white shot noise this holds true even if the limit of gaussian white noise is approached

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

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

on the h 1 galerkin method for second order linear two point boundary value problems we discuss several aspects of the h 1 galerkin method for the approximate solution of two point boundary value problems first we present a formulation of the method for second order linear equations subject to general linear separated boundary conditions it is shown that corresponding to such boundary conditions there are adjoint boundary conditions which must be satisfied by elements of the test space optimal error estimates for the new h 1 galerkin method are derived a by product of the analysis being optimal error estimates for the h 1 galerkin method for solving the two point boundary value problem in question when b spline bases are chosen for both the trial approximation and test spaces the linear algebraic systems arising in the h 1 galerkin method have a special almost block diagonal structure which is independent of the form of the boundary conditions results of numerical experiments are presented which demonstrate the efficacy of a new package for solving such

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

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

mean first passage times of processes driven by white shot noise we consider mean first passage times in systems driven by white shot noise with exponentially distributed jump heights simple interpretable results are obtained and the linkage between those results and the steady state probability density function of the process is presented the virtual waiting time or takacs process constant losses and the shot noise process with linear losses are analyzed in depth along with a more complex process with useful implications for the modeling of the soil moisture dynamics in hydrology

on spline basis selection for solving differential equations the suitability of b splines as a basis for piecewise polynomial solution representation for solving differential equations is challenged two alternative local solution representations are considered in the context of collocating ordinary differential equations hermite type and lmonomial both are much easier and shorter to implement and somewhat more efficient than b splines a new condition number estimate for the b splines and hermite type representations is presented one choice of the hermite type representation is experimentally determined to produce roundoff errors at most as large as those for b splines the monomial representation is shown to have a much smaller condition number than the other ones and correspondingly produces smaller roundoff errors especially for extremely nonuniform meshes the operation counts for the two local representations considered are about the same the hermite type representation being slightly cheaper it is concluded that both representations are preferable

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

algorithms for almost block diagonal linear systems codes for solving systems of ordinary differential equations for use in the method of lines for partial differential equations pdes usually provide only a banded system solver in this context a frequently occurring structure is almost block diagonal abd solving abd systems by imposing banded structure introduces fill in and is inefficient though robust efficient abd software has been developed and used in packages for solving boundary value problems with separated boundary conditions for ordinary differential equations bvodes it has not been generally exploited in pde software the situation with bordered almost block diagonal system software for bvodes with nonseparated boundary conditions is less satisfactory this survey draws on material from a variety of sources particularly p amodio et al numer linear algebra appl 7 2000 pp 275 317 and b garrett and i gladwell j comput methods sci engrg 1 2001 pp 75 98 and the references therein

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

higher order chebyshev basis functions for two point boundary value problems cubic basis functions in one dimension for the solution of two point boundary value problems are constructed based on the zeros of chebyshev polynomials of the first kind a general formula is derived for the construction of polynomial basis functions of degree r where 1 r a galerkin finite element method using the constructed basis functions for the cases r 1 2 and 3 is successfully applied to three different types of problem including a singular perturbation problem

a computational study of finite element methods for second order linear two point boundary value problems a computational study of five finite element methods for the solution of a single second order linear ordinary differential equation subject to general linear separated boundary conditions is described in each method the approximate solution is a piecewise polynomial expressed in terms of a b spline basis and is determined by solving a system of linear algebraic equations with an almost block diagonal structure the aim of the investigation is twofold to determine if the theoretical orders of convergence of the methods are realized in practice and to compare the methods on the basis of cost for a given accuracy in this study three parametrized families of test problems containing problems of varying degrees of difficulty are used the conclusions drawn are rather straightforward collocation is the cheapest method for a given accuracy and the easiest to implement also for solving the linear algebraic equations the use of a special purpose solver which takes advantage of the structure of the equations is advisable 1 introduction finite element methods for two point boundary value problems for a single ordinary differential equation may take many forms the simplest type of method is probably collocation 3 where an approximate solution is sought in some finite space subject to the constraint that it satisfy the differential equation at certain specified points this type of method has been applied very successfully in the case of mixed order systems of boundary value problems see for example 1 other methods can be described based on the standard l2 galerkin approximation 9 or on a combination of this and the collocation approach 7 13 25 in addition different weak formulations of the boundary value problem lead to two other techniques the hx and galerkin methods 12 14 15 17 how one would apply these methods to a system of differential equations with the exception of the collocation case is not immediately clear in addition it is not apparent what the relative advantages are of these various methods even when applied to a single equation in this paper we restrict our attention to the case of a single linear differential equation our aim is to investigate numerically five finite element techniques for a second order linear two point boundary value problem with separated boundary conditions of a general nature in particular we consider i the organization of the methods ii the treatment of the boundary conditions

equivalence of tba and qtm the traditional thermodynamic bethe ansatz equations for the xxz model at 1 are derived within the quantum transfer matrix method this provides further evidence of the equivalence of both methods most importantly we derive an integral equation for the free energy formulated for just one unknown function this integral equation differs in physical and mathematical aspects to the established ones the single integral equation is analytically continued to the regime 1

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

a direct calculation of the free energy from the bethe ansatz equation for the heisenberg model thermodynamics of the xxx heisenberg model is studied the trace of the boltzmann weight with respect to the hilbert space is taken in the thermodynamic limit with the number of up spins being fixed the expression of the trace gives an explanation why the correct thermodynamic quantities are derived from the string hypothesis a combination of this with the previous result leads to a conclusion that the free energy can be calculated only from the bethe ansatz equation the method is more direct than other known methods which were used to derive the free energy

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

a study of correlation functions for the delta function bose gas abstract the gel fand levitan equation for the quantum nonlinear schrodinger field theory is used to investigate the correlation functions of the delta function bose gas operator expressions are derived for the field and for nonlocal products of fields in terms of the quantized reflection operators which create and annihilate eigenstates of the hamiltonian for the two point function an explicit series expression is obtained in which the nth term is determined by well defined n body combinatorics in an infinite volume the inductive properties of this series are discussed and used to express the temperature and chemical potential dependence of the correlation functions entirely in terms of previously known thermodynamic functions the zero separation limit of the series for the two point function reproduces the thermodynamics derived by yang and yang while the infinite coupling limit gives the fredholm determinant result of schultz and lenard the latter is related to the painleve v equation by the monodromy arguments of jimbo miwa mori and sato the o 1 c correction to the large coupling limit is calculated from the gel fand levitan series and expressed in terms of solutions to painleve v the asymptotic behavior of the relevant painleve function is discussed and related to the long range behavior of the correlation function

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

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

fractional order theory of thermoelasticity in this work a new theory of thermoelasticity is derived using the methodology of fractional calculus the theories of coupled thermoelasticity and of generalized thermoelasticity with one relaxation time follow as limit cases a uniqueness theorem for this model is proved a variational principle and a reciprocity theorem are derived

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

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

the emerging role of number theory in exactly solvable models in lattice statistical mechanics abstract we review the baxter model the hard hexagon model and their multistate generalizations from a point of view that stresses the connection with modular functions and additive number theory it is shown for example that various physical quantities in the hard hexagon model are all expressible in terms of modular functions the use of rogers ramanujan type identities in solvable models is also reviewed

probabilistic dynamics of some jump diffusion systems some exact solutions to the forward chapman kolmogorov equation are derived for processes driven by both gaussian and compound poisson shot noise the combined action of these two forms of white noise is analyzed in transient and equilibrium conditions for different jump distributions and additive gaussian noise steady state distributions with power law tails are obtained for exponentially distributed jumps and multiplicative linear gaussian noise two applications are discussed namely the virtual waiting time or takacs process including gaussian oscillations and a simplified model of soil moisture dynamics in which rainfall is modeled as a compound poisson process and fluctuations in potential evapotranspiration are gaussian

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

corner transfer matrices and lorentz invariance on a lattice abstract the continuum limit of the baxter eight vertex lattice model is the lorentz invariant massive thirring sine gordon field theory here it is shown that the baxter model exhibits a continuous symmetry which is an exact lattice generalization generalization of lorentz invariance and that the corner transfer matrix recently developed by baxter is a lattice boost operator the role of elliptic function parameters as lattice rapidity variables is discussed

some open problem abstract this conference proceedings covers a variety of topics related by a common theme solitons and coherent structures an objective of this paper is to exhibit some of the relations between topics by identifying some unsolved but well defined problems that either were or might have been discussed during the conference and by suggesting how they might be solved using methods that were discussed here the problems were chosen to identify unifying themes rather than to identify the most important problems in each area for example i will not discuss any of the important work of baxter despite its fundamental role in the development of solvable lattice models the problems discussed come from quantum field theory transonic flow water waves and the two dimensional motion of a perfect fluid

statistical mechanics of an exactly integrable system the equilibrium thermodynamics of the nonlinear schrodinger model at finite temperature is calculated by means of the quantum inverse method working directly in an infinite volume we derive the equation of state and the integral equation which determines the excitation spectrum this integral equation is found to be closely related to the gelfand levitan expression for the charge density operator

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

prescription induced jump distributions in multiplicative poisson processes generalized langevin equations gle with multiplicative white poisson noise pose the usual prescription dilemma leading to different evolution equations master equations for the probability distribution contrary to the case of multiplicative gaussian white noise the stratonovich prescription does not correspond to the well known mid point or any other intermediate prescription by introducing an inertial term in the gle we show that the ito and stratonovich prescriptions naturally arise depending on two time scales the one induced by the inertial term and the other determined by the jump event we also show that when the multiplicative noise is linear in the random variable one prescription can be made equivalent to the other by a suitable transformation in the jump probability distribution we apply these results to a recently proposed stochastic model describing the dynamics of primary soil salinization in which the salt mass balance within the soil root zone requires the analysis of different prescriptions arising from the resulting stochastic differential equation forced by multiplicative white poisson noise whose features are tailored to the characters of the daily precipitation a method is finally suggested to infer the most appropriate prescription from the data

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

intertime jump statistics of state dependent poisson processes a method to obtain the probability distribution of the interarrival times of jump occurrences in systems driven by state dependent poisson noise is proposed such a method uses the survivor function obtained by a modified version of the master equation associated to the stochastic process under analysis a model for the timing of human activities shows the capability of state dependent poisson noise to generate power law distributions the application of the method to a model for neuron dynamics and to a hydrological model accounting for land atmosphere interaction elucidates the origin of characteristic recurrence intervals and possible persistence in state dependent poisson models

staircase matrices and systems difference equations spline approximations and multiperiod linear programs all give rise to linear equation systems that have a characteristic staircase structure a staircase system s variables can be partitioned into a natural sequence of periods in such a way that every equation involves at most the variables of two adjacent periods this paper surveys the numerous properties of staircase systems and of the staircase matrices that comprise their coefficients particular attention is given to reduced and sparse staircase forms and to the varieties of gaussian elimination for solving staircase systems