random number generators for parallel processors abstract the fundamental requirements for the sequence of numbers produced by a random number generator in a computer program are that 1 the sequence be indistinguishable from that produced by an iid sequence of standard uniformly distributed random variables 2 the sequence be identically reproduced on a subsequent execution of the same computer program for computers with multiple processors it is sensible to add the additional requirement that 3 the sequences used by each of the several processors be indistinguishable from independent sequences if one uses a standard random number generator developed for a uniprocessor in an environment with multiple processors then each one of these requirements may be violated this paper contains a review of previous attempts to satisfy the three requirements for a multiprocessor and concludes that none are really successful

the cauchy problem and a generalization of the hille yosida theorem on demontre une generalisation du theoreme de hille yosida en caracterisant les generateurs d une certaine classe de semi groupes d operateurs non bornes sur un espace de banach on resout le probleme de cauchy abstrait

a statistical evaluation of multiplicative congruential random number generators with modulus 231 1 abstract this article presents the results of empirically testing 16 alternative multipliers for a multiplicative congruential random number generator with modulus 231 1 two of the multipliers are in common use six are the best of 50 candidate multipliers according to the theoretical spectral and lattice tests and eight are the worst with regard to 2 tuples among the 50 the test results raise serious doubts about several of the multipliers including one in common use the tests were also applied to a well known theoretically poor generator randu and gave strong empirical evidence of its inadequacy since comparison of the results of the first eight multipliers with those for the eight worst multipliers failed to show any apparent gross differences one may want to relax the currently employed stringent criteria for acceptable performance on the lattice and spectral tests

abstract cauchy problems for quasi linear evolution equations in the sense of hadamard this paper is devoted to the well posedness of abstract cauchy problems for quasi linear evolution equations the notion of hadamard well posedness is considered and a new type of stability condition is introduced from the viewpoint of the theory of finite difference approximations the result obtained here generalizes not only some results on abstract cauchy problems closely related with the theory of integrated semigroups or regularized semigroups but also the kato theorem on quasi linear evolution equations an application to some quasi linear partial differential equation of weakly hyperbolic type is also given

determining the appropriate sample size for nonparametric tests for location shift for the case in which two independent samples arc to be compared using a nonparametric test for location shift we propose a bootstrap technique for estimating the sample sizes required to achieve a specified power the estimator called boot uses information from a small pilot experiment for the special case of the wilcoxon test a simulation study is conducted to compare boot to two other sample size estimators one method called anpv is based on the assumption that the underlying distribution is normal with a variance estimated from the pilot data the other method called noether adapts the sample size formula of noether for use with a location shift alternative the boot and noether sample size estimators are particularly appropriate for this nonparametric setting because they do not require assumptions about the shape of the underlying continuous probability distribution the simulation study shows that a sample size estimates can have large uncertainty b boot is at least as accurate as an

initializing generalized feedback shift register pseudorandom number generators the generalized feedback shift register pseudorandom number generators proposed by lewis and payne provide a very attractive method of random number generation unfortunately the published initialization procedure can be extremely time consuming this paper considers an alternative method of initialization based on a natural polynomial representation for the terms of a feedback shift register sequence that results in substantial improvements in the initialization process

estimating the power of the two sample wilcoxon test for location shift summary traditional methods for calculating the power of a statistical test for location shift require knowledge of the shape of the underlying probability distribution the distribution shape however may be unknown this paper describes a bootstrap method for using observed data or pilot data to approximate the power no assumptions need be made about the shape of the underlying continuous probability distribution simulation evidence shows that when applied to the wilcoxon two sample test for location shift the suggested method is reliable the evidence also shows that it is more accurate than a benchmark traditional approach the bootstrap method is applied to a real data example the analysis demonstrates how the method can be used to determine sample sizes and how to choose the more powerful of two alternative tests for location shift

compound random number generators abstract recently marsaglia 1984 proceedings of the sixteenth symposium on the interface noted a trend toward increasingly more demanding use of random number generators after observing that for current uses generators must pass increasingly more sophisticated tests for randomness in order to provide acceptable results marsaglia described a class of combination generators and recommended two specific combination generators that passed an extensive battery of stringent tests for randomness the present article describes an alternative class of generators which produce random values by compounding or intermixing several different sequences of random values these compound generators are easier to implement especially on smaller computers than are marsaglia s recommended generators five specific compound generators two standard generators and marsaglia s two combination generators were subjected to several tests for randomness including marsaglia s stringent tests the standard generator

the serial test for pseudo random numbers generated by the linear congruential method we consider the linear congruential method for pseudo random number generation and establish effective criteria for the choice of parameters in this method which guarantee statistical almost independence of successive pseudo random numbers applications to numerical integration are also discussed

statistical independence of a new class of inversive congruential pseudorandom numbers linear congruential pseudorandom numbers show several undesirable regularities which can render them useless for certain stochastic simulations this was the motiviation for important recent developments in nonlinear congruential methods for generating uniform pseudorandom numbers it is particularly promising to achieve nonlinearity by employing the operation of multiplicative inversion with respect to a prime modulus in the present paper a new class of such inversive congruential generators is introduced and analyzed it is shown that they have excellent statistical independence properties and model true random numbers very closely the methods of proof rely heavily on weil stepanov bounds for rational exponential sums 39 refs

on a nonlinear congruential pseudorandom number generator a nonlinear congruential pseudorandom number generator with modulus m 2 w is proposed which may be viewed to comprise both linear as well as inversive congruential generators the condition for it to generate sequences of maximal period length is obtained it is akin to the inversive one and bears a remarkable resemblance to the latter

pseudorandom vector generation by the multiple recursive matrix method pseudorandom vectors are of importance for parallelized simulation methods in this paper we carry out an in depth analysis of the multiple recursive matrix method for the generation of uniform pseudorandom vectors which was introduced in an earlier paper of the author we study in particular the periodicity properties the lattice structure and the behavior under the serial test for sequences of pseudorandom vectors generated by this method

toda lattice mass transport in lagrangian mechanics and in a two dimensional system abstract this paper explores the connection between the hydrodynamic mass transport description and the thermodynamic description for a nonlinear range of the toda lattices particular attention is paid to the broken isotropy in the kdv and burgers equations the flow variable representation is established from the lagrangian mechanics for hydrodynamic mass transport based on the inverse scattering transform the gel fand levitan marchenko glm equation is formulated from the kdv equation expressed by the flow variable representation we found that a kernel of the glm equation is given by the concentration variable q x t a lagrangian is formulated for the kdv equation in state space q x t k x t next an extension of the flow variable representation is sought in a two dimensional system the lhs of the kadomtsev petviashvili kp equation takes the same form as in the second formalism of the kdv equation by setting up the flow variable representation of the kp equation the burgers equation in two dimensions is formulated these results contribute to an understanding of the broken isotropy for the nonlinear mass transport equations these results provide physical insight into various consequences of the generalized form of the kawasaki ohta equation from the viewpoint of mass transport

statistical independence properties of pseudorandom vectors produced by matrix generators abstract the uniformity test and the serial test are standard statistical tests for equidistribution and statistical independence respectively in sequences of uniform pseudorandom numbers we introduce analogues of these tests for sequences of uniform pseudorandom vectors and we apply these tests to matrix generators for uniform pseudorandom vector generation the results show that these generators behave well under these tests provided that the matrix in the generation algorithm is chosen carefully the essential condition is that a certain figure of merit attached to the matrix be large we also prove a general theorem which guarantees the existence of matrices with large figure of merit

lax pair backlund transformation and n soliton like solution for a variable coefficient gardner equation from nonlinear lattice plasma physics and ocean dynamics with symbolic computation abstract in this paper a generalized variable coefficient gardner equation arising in nonlinear lattice plasma physics and ocean dynamics is investigated with symbolic computation the lax pair and backlund transformation are explicitly obtained when the coefficient functions obey the painleve integrable conditions meanwhile under the constraint conditions two transformations from such an equation either to the constant coefficient gardner or modified korteweg de vries mkdv equation are proposed via the two transformations the investigations on the variable coefficient gardner equation can be based on the constant coefficient ones the n soliton like solution is presented and discussed through the figures for some sample solutions it is shown in the discussions that the variable coefficient gardner equation possesses the right and left travelling soliton like waves which involve abundant temporally inhomogeneous features

mass transport theory for the toda lattices dispersive and dissipative abstract to establish mass transport theory on nonlinear lattices we formulate the korteweg devries kdv equation and the burgers equation using the flow variable representation so as to facilitate comparison with the boltzmann equation and with the cahn hilliard equation in classical statistical mechanics we also study toda lattice microdynamics using the flaschka representation and compare with the liouville equation like the linear diffusion equation the boltzmann equation and the liouville equation are to be solved for a distribution function which is intrinsically probabilistic transport theory in linear systems is governed by the isotropic motions of the kinetic equations in contrast the kdv perturbation equation derived from the toda lattice microdynamics expresses hydrodynamic mass transport the kdv equation in hydrodynamics and the burgers equation in thermodynamics do not involve a probability distribution function the nonlinear lattices do not retain isotropy of the mass transport equations in consequence it is proposed that in the presence of hydrodynamic flows to the left kdv wave propagation proceeds to the right this basic property of the kdv system is extended to thermodynamics in the burgers system these features arise because linear systems are driven towards an equilibrium by molecular collisions whereas the inhomogeneities of the nonlinear lattices are generated by the potential energy of interaction diffusion as expressed by the burgers equation is governed not only by a chemical potential but also by the toda lattice potential energy

inversive congruential pseudorandom numbers avoid the planes nonlinear congruential pseudorandom number generators based on inversions have recently been introduced and analyzed these generators do not show the lattice structure of the widely used linear congruential method in the present paper it is proved that the points formed by d consecutive pseudorandom numbers of an inversive congruential generator with prime modulus possess an even stronger property any hyperplane in space contains at most d of these points that is to say the hyperplane spanned by d arbitrary points of an inversive congruential generator contains no further points this feature makes the inversive congruential method particularly attractive for simulation problems where linear structures within the generated points should be avoided

a chemical response theory of the toda lattice in an external mechanical perturbation abstract in the preceding paper using the so called flow variable representation we reported the formulation of the korteweg devries kdv and the burgers equations to express mass transports the transport theories were constructed by pertaining to correspondence with the toda lattices our present purpose is to understand a connection between these nonlinear wave equations formulated independently from the generalized form of the kawasaki ohta equation for this purpose we formulate the burgers equation from the kdv in correspondence to a transition from the dispersive toda lattice to a dissipative model for this formulation we employ an external mechanical perturbation method the paper is concerned with a variation method as to how to prepare a perturbation lax bracket for the burgers formulation variations in one of the lax operators are assumed to be 1 as an obstruction operator against the convection flows expressed by in the repulsive potential field we conclude that the obstruction is caused by attractive interactions the main point is that the burgers equation is transformed to a nonlinear diffusion equation by the hopf cole transform the variation method and the argumentation for the burgers formulation are proved by this transformation

testing for heterogeneity of evoked potential signals using an approximation to an exact permutation test in brain evoked potential research and various other fields a signal embedded in noise is observed in each of many repeated trials we propose a new test of the null hypothesis that the signal is the same in every trial the test has power against the alternative hypothesis that the signal is changing slowly from trial to trial the test statistic is the distance between the average of the trials and a parametric or nonparametric estimate of a slowly changing signal we derive the exact mean and variance of the test statistic under permutation of the trials and use these moments to approximate the exact permutation test we use simulated evoked potential data to evaluate the proposed test and to compare it to three previous tests

equidistribution properties of quadratic congruential pseudorandom numbers this paper deals with the quadratic congruential method for generating uniform pseudorandom numbers equidistribution properties of the generated pseudorandom number sequences over parts of the period are considered based on the discrepancy of corresponding point sets an upper bound for the average value of these discrepancies is established

some nonlinear degenerate wave equations on etudie la resolubilite locale du probleme aux valeurs limites et initiales suivant 2 u t 2 m gradu x t 2 dx u 0 dans 0 u 0 sur w 0 u 0 0 u t 0 dans ou m r est une fonction c 1 non negative sur 0 un domaine borne de r n a frontiere lisse w

matrices and the structure of random number sequences abstract this note provides a short self contained treatment using linear algebra and matrix theory for establishing maximal periods underlying structure and choice of starting values for shift register and lagged fibonacci random number generators

on a new class of pseudorandom numbers for simulation methods abstract the deficiencies of classical methods for uniform pseudorandom number generation have recently led to the development of alternative methods such as nonlinear congruential methods a particularly attractive nonlinear congruential method is the explicit inversive congruential method recently introduced by eichenauer herrmann we establish several new results on the structural and statistical properties of pseudorandom numbers generated by this method these results demonstrate that this method is eminently suitable for the generation of parallel streams of pseudorandom numbers with desirable properties

l p maximal regularity for second order cauchy problems we introduce the concept of l p maximal regularity for second order cauchy problems we prove l p maximal regularity for an abstract model problem and we apply the abstract results to prove existence uniqueness and regularity of solutions for nonlinear wave equations

are there hyperbolas in the scatter plots of inversive congruential pseudorandom numbers abstract given a scatter plot of overlapping pairs xn xn 1 of pseudorandom numbers and the information that it stems from either a linear congruential or an inversive congruential generator with small modulus it is usually no problem to guess the type of the generator the points of a linear generator form a grid or lattice whereas inversive and explicit inversive congruential pseudorandom numbers exhibit hyperbola like structures we give an analytical description of this most eye catching structural element of inversive congruential generators

factorization of polynomials and some linear algebra problems over finite fields abstract the recently developed algorithm of niederreiter for the factorization of polynomials over finite fields provides a linearization of the factorization problem via differential equations in rational function fields we show that the range of applicability of this algorithm can be extended by various techniques such as the application of normal bases and the use of hasse teichmuller derivatives we also discuss topics from pseudorandom vector generation and combinatorial linear algebra that lead to interesting linear algebra problems over finite fields

perturbation of local c semigroups abstract let c be a bounded linear injective operator and a be the generator of a local c semigroup s t 0 t t on a banach space x it is proved that if b is a bounded operator such that r b r c and bcx cbx for all x d a then a b also generates a local c semigroup

the lattice structure of pseudo random vectors generated by matrix generators abstract in many areas of science the problems treated by monte carlo simulations become more and more complex and more extensive because of that generators like linear congruential matrix generators are needed which produce enormously many pseudo random numbers in order to assess stochastical properties of the generated pseudo random vectors the lattice structure of these matrix generators is studied here

random number generations generators on vector supercomputers and other advanced architectures this paper is divided into three parts the first part surveys the more common techniques for generating and testing uniformly distributed random numbers the second part considers the efficient ge