existence results for dirichlet problems with q p laplacian abstract we prove an existence result for a class of nonlinear systems involving a duality mapping defined on a product spaces as an application we obtained an existence result for a system with q p laplacian

positive solutions of periodic boundary value problems for nonlinear first order impulsive differential equations abstract motivated by liu y liu further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations j math anal appl 327 2007 435 452 li et al x li x lin d jiang x zhang existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects nonlinear anal 62 2005 683 701 and liu and ge y liu w ge stability theorems and existence results for periodic solutions of nonlinear impulsive delay differential equations with variable coefficients nonlinear anal 57 2004 363 399 this paper is concerned with the periodic boundary value problem pbvp for short for the nonlinear impulsive differential equation x t a t x t f t x t a e t 0 t t 1 t p x t k x t k x t k i k x t k k 1 p x t x 0 we obtain new sufficient conditions for the existence of at least one two or three positive solutions of the above pbvp respectively examples are presented to illustrate the main results

asymptotically periodic solutions of n competing species problem with time delays abstract a general nonautonomous lotka volterra system of integro differential equations with infinite delay is considered and sufficient conditions for uniform stability and asymptotic stability of solutions are investigated these limiting equations are used to obtain the existence of asymptotically periodic solutions of the corresponding system of equations where lower limit in the integration is zero

existence and exponential stability of piecewise mean square almost periodic solutions for impulsive stochastic nicholson s blowflies model on time scales the concept of piecewise mean square almost periodic stochastic process is introduced a new impulsive stochastic nicholsons blowflies model is introduced and studied on time scales the first results of the piecewise mean square almost periodic solutions for the model are obtained in this paper a class of impulsive stochastic nicholson s blowflies model with patch structure and nonlinear harvesting terms is introduced and studied on time scales by using contraction mapping principal and gronwall bellman inequality technique some sufficient conditions for the existence and exponential stability of piecewise mean square almost periodic solutions for the model with infinite delays are established on time scales finally an example is given to demonstrate the validity of the conditions of the main theorem

monotonic quantile regression with bernstein polynomials for stochastic simulation quantile regression is an important tool to determine the quality level of service product and operation systems via stochastic simulation it is frequently known that the quantiles of the output distribution are monotonic functions of certain inputs to the simulation model because there is typically high variability in estimation of tail quantiles it can be valuable to incorporate this information in quantile modeling however the existing literature on monotone quantile regression with multiple inputs is sparse in this article we propose a class of monotonic regression models which consists of functional analysis of variance fanova decomposition components modeled with bernstein polynomial bases for estimating quantiles as a function of multiple inputs the polynomial degrees of the bases for the model and the fanova components included in the model are selected by a greedy algorithm real examples demonstrate the advantages of incorporating the monotonicity assumption in quantile regression a

on multivariate lagrange interpolation lagrange interpolation by polynomials in several variables is studied through a finite difference approach we establish an interpolation formula analogous to that of newton and a remainder formula both of them in terms of finite differences we prove that the finite difference admits an integral representation involving simplex spline functions in particular this provides a remainder formula for lagrange interpolation of degree n of a function f which is a sum of integrals of certain n 1 st directional derivatives of f multiplied by simplex spline functions we also provide two algorithms for the computation of lagrange interpolants which use only addition scalar multiplication and point evaluation of polynomials

on delay differential equations with impulses abstract sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of x t ax t j 1 bjx tj t tj t tj and for the existence of a nonoscillatory solution conditions are also obtained for all solutions to be oscillatory the asymptotic behaviour of an impulsively perturbed delay logistic equation is investigated as an extension to a nonlinear equation

analysis of a nonautonomous nicholson blowfly model abstract most dynamic models describing population evolution contain one or more parameters the parameters are treated as fixed constants and qualitative results such as stability of equilibria are calculated using this assumption in reality however the parameters are mathematically evaluated by statistical methods in which the error is decreased over a number of calculations therefore the parameter is a sequence converging to the actual parameter value as time goes to infinity in this article we consider the k th order discrete nicholson blowfly model n n 1 f p n n n n k where and p are parameters for a particular range of parameter values global stability results are well known the general form of the discrete dynamical system is now rewritten as n n 1 f p n n n n n n k where p n and n converge to the parametric values p and we show that when the parameters are replaced by sequences the stability results of the original system still hold this technique may be of general interest to those studying evolutionary systems in which the parameters are not fundamental constants but sequences

existence results for abstract impulsive second order neutral functional differential equations abstract we establish the existence of mild solutions for a class of impulsive second order partial neutral functional differential equations with infinite delay in a banach space

mean square almost periodic solution for impulsive stochastic nicholson s blowflies model with delays in this paper a class of impulsive stochastic nicholson s blowflies model is investigated by applying cauchy matrix under proper conditions the existence and exponential stability of square mean almost periodic solutions for the model with multiple nonlinear harvesting terms and delays moreover an example is provided to illustrate the effectiveness of the results

oscillation of continuous and discrete diffusive delay nicholson s blowflies models in this paper we consider the continuous and the discrete delay diffusive nicholson s blowflies models with different types of boundary conditions our aim is to give some sufficient conditions for oscillation of all positive solutions about the positive steady state we show that these conditions have essentially first order character by reducing the problem of oscillation of the boundary value problem to that of first order delay differential or difference equation

dirichlet problem for the diffusive nicholson s blowflies equation abstract the object of this paper is to consider the asymptotic behavior of solutions of the diffusive nicholson s blowflies equation under dirichlet boundary condition a new approach is developed to study the global attractivity of the positive steady state for a reaction diffusion equation with time delay when monotone or quasi monotone conditions fail to apply this approach should be applicable to other dirichlet problems as well even though our analysis is tailored to the diffusive nicholson s blowflies equation

periodic boundary value problem for first order impulsive functional differential equations this paper discusses the periodic boundary value problem for a class of first order impulsive functional differential equations we establish several existence results under weaker hypotheses by using the leray schauder alternative the lower and upper solution method and the monotone iterative technique the corresponding results in the literature are improved or extended some examples are also given to illustrate the advantage of the results

bayesian prediction of deterministic functions with applications to the design and analysis of computer experiments abstract this article is concerned with prediction of a function y t over a multidimensional domain t given the function values at a set of sites t 1 t 2 t n in t and with the design that is with the selection of those sites the motivating application is the design and analysis of computer experiments where t determines the input to a computer model of a physical or behavioral system and y t is a response that is part of the output or is calculated from it following a bayesian formulation prior uncertainty about the function y is expressed by means of a random function y which is taken here to be a gaussian stochastic process the mean of the posterior process can be used as the prediction function t and the variance can be used as a measure of uncertainty this kind of approach has been used previously in bayesian interpolation and is strongly related to the kriging methods used in geostatistics here emphasis is placed on product linear and product cubic correlation func

dynamics of multi species competition predator system with impulsive perturbations and holling type iii functional responses abstract we investigate the dynamics of a class of multi species predator prey interaction models with holling type iii functional responses based on systems of nonautonomous differential equations with impulsive perturbations sufficient conditions for existence of a positive periodic solution are investigated by using a continuation theorem in coincidence degree theory which have been extensively applied in studying existence problems in differential equations and difference equations in addition sufficient criteria are established for the global stability and the globally exponential stability of the system by using the comparison principle and the lyapunov method

high order collocation methods for differential equations with random inputs recently there has been a growing interest in designing efficient methods for the solution of ordinary partial differential equations with random inputs to this end stochastic galerkin methods appear to be superior to other nonsampling methods and in many cases to several sampling methods however when the governing equations take complicated forms numerical implementations of stochastic galerkin methods can become nontrivial and care is needed to design robust and efficient solvers for the resulting equations on the other hand the traditional sampling methods e g monte carlo methods are straightforward to implement but they do not offer convergence as fast as stochastic galerkin methods in this paper a high order stochastic collocation approach is proposed similar to stochastic galerkin methods the collocation methods take advantage of an assumption of smoothness of the solution in random space to achieve fast convergence however the numerical implementation of stochastic collocation is trivial as it requires only repetitive runs of an existing deterministic solver similar to monte carlo methods the computational cost of the collocation methods depends on the choice of the collocation points and we present several feasible constructions one particular choice based on sparse grids depends weakly on the dimensionality of the random space and is more suitable for highly accurate computations of practical applications with large dimensional random inputs numerical examples are presented to demonstrate the accuracy and efficiency of the stochastic collocation methods

existence and global attractivity of positive periodic solutions for the impulsive delay nicholson s blowflies model in this paper we shall consider the following nonlinear impulsive delay population model 0 1 x t d t x t p t x t m w e a t x t m w a e t 0 t t k x t k 1 b k x t k k 1 2 where m is a positive integer d t a t and p t are positive periodic continuous functions with period w 0 in the nondelay case m 0 we show that 0 1 has a unique positive periodic solution x t which is globally asymptotically stable in the delay case we present sufficient conditions for the global attractivity of x t our results imply that under the appropriate linear periodic impulsive perturbations the impulsive delay equation 0 1 preserves the original periodic property of the nonimpulsive delay equation in particular our work extends and improves some known results

stochastic polynomial interpolation for uncertainty quantification with computer experiments multivariate polynomials are increasingly being used to construct emulators of computer models for uncertainty quantification for deterministic computer codes interpolating polynomial metamodels should be used instead of noninterpolating ones for logical consistency and prediction accuracy however available methods for constructing interpolating polynomials only provide point predictions there is no known method that can provide probabilistic statements about the interpolation error furthermore there are few alternatives to grid designs and sparse grids for constructing multivariate interpolating polynomials a significant disadvantage of these designs is the large gaps between allowable design sizes this article proposes a stochastic interpolating polynomial sip that seeks to overcome the problems discussed above a bayesian approach in which interpolation uncertainty is quantified probabilistically through the posterior distribution of the output is employed this allows assessment of the effe

stochastic collocation methods on unstructured grids in high dimensions via interpolation in this paper we propose a method for conducting stochastic collocation on arbitrary sets of nodes to accomplish this we present the framework of least orthogonal interpolation which allows one to construct interpolation polynomials based on arbitrarily located grids in arbitrary dimensions these interpolation polynomials are constructed as a subspace of the family of orthogonal polynomials corresponding to the probability distribution function on stochastic space this feature enables one to conduct stochastic collocation simulations in practical problems where one cannot adopt some popular node selections such as sparse grids or cubature nodes we present in detail both the mathematical properties of the least orthogonal interpolation and its practical implementation algorithm numerical benchmark problems are also presented to demonstrate the efficacy of the method

data analytic tools for understanding random field regression models random field regression rfr models in which a response is treated as the realization of a random field have been advocated for modeling data from experiments in high signal to noise settings in particular rfr models have proven useful in analyzing data generated from computer simulations of complex processes they offer flexibility for smoothing these data and are able to interpolate the known values for factor settings tested on the simulator however these models lack the easy interpretability of standard regression estimators our purpose in this article is to demonstrate that there is actually much common ground between the rfr models and bayesian regression and to provide some simple data analytic tools that can help expose a regression model associated with an rfr model

on the stability and uniform persistence of a discrete model of nicholson s blowflies abstract consider the delay difference equation n n 1 nn n n pn n k e an n k n 0 1 2 1 which is a discrete analogue of the delay differential equation n t n t pn t e an t t 0 cf 8 we show that when p the zero solution of 1 is uniformly asymptotically stable and every non negative solution of 1 tends to zero as n while for p 1 is uniformly persistent moreover if in addition to p we also have 1 k 1 1 ln p 1 then every positive solution of 1 tends to the positive equilibrium n 1 a ln p

on a stochastic logistic equation with impulsive perturbations a stochastic logistic model with impulsive perturbations is proposed and investigated first we give a new definition of a solution of an impulsive stochastic differential equation isde which is more convenient for use than the existing one using this definition we show that our model has a global and positive solution and obtain its explicit expression then we establish the sufficient conditions for extinction non persistence in the mean weak persistence persistence in the mean and stochastic permanence of the solution the critical value between weak persistence and extinction is obtained in addition the limit of the average in time of the sample path of the solution is estimated by two constants afterwards the lower growth rate and the upper growth rate of the solution are estimated finally sufficient conditions for global attractivity are established

generalised confounding with grobner bases many problems of confounding and identifiability for polynomial and multidimensional polynomial models can be solved using methods of algebraic geometry aided by the fact that modern computational algebra packages such as maple can be used the problem posed here is to give a description of the identifiable models given a particular experimental design the method is to represent the design as a variety v namely the solution of a set of algebraic equations an equivalent description is the corresponding ideal i which is the set of all polynomials which are zero on the design points starting with a class of models m the quotient vector space m i yields a class of identifiable monomial terms of the models the theory of grobner bases is used to characterise the design ideal and the quotient the theory is tested using some simple examples including the popular li8 design

resonance problems for the p laplacian systems abstract two existence theorems of the solutions are obtained for the p laplacian systems at resonance under a landesman lazer type condition by critical point theory

constructing nested nodal sets for multivariate polynomial interpolation we present a robust method for choosing multivariate polynomial interpolation nodes our algorithm is an optimization method to greedily minimize a measure of interpolant sensitivity a variant of a weighted lebesgue function nodes are therefore chosen that tend to control oscillations in the resulting interpolant this method can produce an arbitrary number of nodes and is not constrained by the dimension of a complete polynomial space our method is therefore flexible nested nodal sets are produced in spaces of arbitrary dimensions and the number of nodes added at each stage can be arbitrary the algorithm produces a nodal set given a probability measure on the input space thus parameterizing interpolants with respect to finite measures we present examples to show that the method yields nodal sets that behave well with respect to standard interpolation diagnostics the lebesgue constant the vandermonde determinant and the vandermonde condition number we also show that a nongreedy version of the

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

asymptotic stability of competitive systems with delays and impulsive perturbations abstract a general impulsive nonautonomous lotka volterra system of integro differential equations with infinite delay is considered the impulses are realized at fixed moments of time sufficient conditions for uniform stability and asymptotic stability of solutions are investigated the main results are obtained by using the comparison principle and the lyapunov method

existence of periodic solution of order one of planar impulsive autonomous system based on the situation that all the recent research about state dependent impulsive differential equations is focused on systems which have explicit solutions this paper try to consider those systems with state dependent impulsion which have not explicit solutions we get an existence theorem of periodic solution of order one for a general planar autonomous impulsive system and by applying it to a special state dependent impulsive differential equations we get the concrete conditions of existence of one order periodic solution of that special system

positive almost periodic solution for a class of nicholson s blowflies model with multiple time varying delays in this paper we study the existence and exponential convergence of positive almost periodic solutions for the generalized nicholson s blowflies model with multiple time varying delays under proper conditions we establish some criteria to ensure that the solutions of this model converge locally exponentially to a positive almost periodic solution moreover we give some examples to illustrate our main results

resonance problems for p q laplacian systems abstract some existence results of weak solutions are established for p q laplacian systems which are resonant at an arbitrary eigenvalue by the minimax methods in critical point theory

resonance problems for the p laplacian with a nonlinear boundary condition abstract consider resonance problems at an arbitrary eigenvalue of the elliptic equations p u u p 2 u g 1 u h 1 x in u p 2 u u p 2 u g 2 u h 2 x on some existence theorems are obtained under the landesman lazer type conditions by using variational method

permanence and global stability for nonautonomous n species lotka volterra competitive system with impulses and infinite delays abstract in this paper we consider a class of nonautonomous n species lotka volterra competitive systems with impulses and infinite delays by developing the methods given in teng 2002 25 we give sufficient conditions for permanence and global attractivity of the system

multiplicity of solutions for resonant elliptic systems we establish the existence and multiplicity of solutions for some resonant elliptic systems the results are proved by applying minimax arguments and morse theory

some results on boundary value problems for fuzzy differential equations with functional dependence abstract we calculate the exact solution for a class of boundary value problems for first order linear fuzzy differential equations with impulses under hukuhara differentiability by finding green s function some conclusions can be derived for impulsive fuzzy differential equations including a term with functional dependence for which existence and uniqueness results are proved

lyapunov method for boundedness of solutions of nonlinear impulsive functional differential equations sufficient conditions are investigated for boundedness of solutions of nonlinear impulsive functional differential equations with impulses at fixed moments the main tools are lyapunov functions and gronwall type of inequality

a bayesian approach to the design and analysis of fractionated experiments specifying a prior distribution for the large number of parameters in the statistical model is a critical step in a bayesian approach to the design and analysis of experiments this article shows that the prior distribution can be induced from a functional prior on the underlying transfer function the functional prior requires specification of only a few hyperparameters and thus can be easily implemented in practice the usefulness of the approach is demonstrated through the analysis of some experiments the article also proposes a new class of design criteria and establishes their connections with the minimum aberration criterion

a global selection procedure for polynomial interpolators the drive for efficient methods of testing design ideas and prototypes particularly in engineering has led to a rapid increase in the field of numerical simulation methods using computers such as finite element analysis this increase in popularity has fueled the need for empirical models that interpolate data collected from these simulations we propose a selection algorithm to efficiently explore an appropriate class of polynomial interpolators the storage of polynomial models is made efficient and effective thanks to a special coding finally the last stage of the algorithm returns a model that is no longer an interpolator but having a smaller number of terms is simpler and easier to handle and understand in this way a trade off between accuracy and simplicity of the model is attained

the wiener askey polynomial chaos for stochastic differential equations we present a new method for solving stochastic differential equations based on galerkin projections and extensions of wiener s polynomial chaos specifically we represent the stochastic processes with an optimum trial basis from the askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error several continuous and discrete processes are treated and numerical examples show substantial speed up compared to monte carlo simulations for low dimensional stochastic inputs

global positive periodic solutions of periodic n species competition systems abstract in this paper an easily verifiable necessary and sufficient condition for the existence of positive periodic solutions of generalized n species lotka volterra type and gilpin ayala type competition systems is obtained it improves a series of the well known sufficiency theorems in the literature about the problems mentioned above the method is based on a well known fixed point theorem in a cone of banach space this approach can be applied to more general competition systems

multiplicity of solutions for a noncooperative p laplacian elliptic system in rn in this paper we study a system of p laplacian elliptic equations pu u p 2u fu x u v inrn pv v p 2v fv x u v inrn u v w1 p rn applying principle of symmetric criticality and a limit index theory under some assumptions on fu fv we can obtain the existence of infinitely many radial solutions and nonradial solutions for the above system which extends some results in li nonlinear anal tma 25 1995 1371

probabilistic sensitivity analysis of complex models a bayesian approach summary in many areas of science and technology mathematical models are built to simulate complex real world phenomena such models are typically implemented in large computer programs and are also very complex such that the way that the model responds to changes in its inputs is not transparent sensitivity analysis is concerned with understanding how changes in the model inputs influence the outputs this may be motivated simply by a wish to understand the implications of a complex model but often arises because there is uncertainty about the true values of the inputs that should be used for a particular application a broad range of measures have been advocated in the literature to quantify and describe the sensitivity of a model s output to variation in its inputs in practice the most commonly used measures are those that are based on formulating uncertainty in the model inputs by a joint probability distribution and then analysing the induced uncertainty in outputs an approach which is known as probabilistic sensitivity analysis we present a bayesian framework which unifies the various tools of prob abilistic sensitivity analysis the bayesian approach is computationally highly efficient it allows effective sensitivity analysis to be achieved by using far smaller numbers of model runs than standard monte carlo methods furthermore all measures of interest may be computed from a single set of runs

variational elliptic problems which are nonquadratic at infinity p co if n 1 2 then it is well known that the weak solutions u e h 2 of p are the critical points of the c functional j u ulvul dx jcf x u dx where f x s jif x t dt in this variational setting the literature usually distinguishes between two situations for prob lem p the subquadratic situation where the potential f satisfies lim suplsl f x s s2 i c m and the superquadratic situation where f satisfies limlsl m f x s s2 00 the main goal of this paper is to present a unified approach to both situations by means of a condition of nonquadraticity at infinity on f more precisely our hypotheses are as follows

positive almost periodic solution for a class of lasota wazewska model with infinite delays abstract by utilizing a fixed theorem in cones we study the existence of a unique positive almost periodic solution for a generalized lasota wazewska model with infinite delays some sufficient conditions which ensure the existence of a unique positive almost periodic solution are derived and it cannot be obtained by the contraction mapping principle furthermore under proper conditions we establish some criteria to ensure that all solutions of this model converge exponentially to a positive almost periodic solution an example is provided to illustrate the effectiveness of the proposed result

a domain adaptive stochastic collocation approach for analysis of mems under uncertainties this work proposes a domain adaptive stochastic collocation approach for uncertainty quantification suitable for effective handling of discontinuities or sharp variations in the random domain the basic idea of the proposed methodology is to adaptively decompose the random domain into subdomains within each subdomain a sparse grid interpolant is constructed using the classical smolyak construction s smolyak quadrature and interpolation formulas for tensor products of certain classes of functions soviet math dokl 4 1963 240 243 to approximate the stochastic solution locally the adaptive strategy is governed by the hierarchical surpluses which are computed as part of the interpolation procedure these hierarchical surpluses then serve as an error indicator for each subdomain and lead to subdivision whenever it becomes greater than a threshold value the hierarchical surpluses also provide information about the more important dimensions and accordingly the random elements can be split along those dimensions the proposed adaptive approach is employed to quantify the effect of uncertainty in input parameters on the performance of micro electromechanical systems mems specifically we study the effect of uncertain material properties and geometrical parameters on the pull in behavior and actuation properties of a mems switch using the adaptive approach we resolve the pull in instability in mems switches the results from the proposed approach are verified using monte carlo simulations and it is demonstrated that it computes the required statistics effectively

resonance problems for the p laplacian abstract we consider resonance problems at an arbitrary eigenvalue of the p laplacian and prove the existence of weak solutions assuming a standard landesman lazer condition we use variational arguments to characterize certain eigenvalues and then to establish the solvability of the given boundary value problem

robust design optimization with quadratic loss derived from gaussian process models gaussian process models which include the class of linear models are widely employed for modeling responses as a function of control or noise factors using these models the average loss at control factor settings can be estimated and compared however robust design optimization is often performed based on the expected quadratic loss computed as if the posterior mean were the true response function this can give very misleading results we propose an expected quadratic loss criterion derived by taking expectation with respect to the noise factors and the posterior predictive process approximate but highly accurate credible intervals for the average quadratic loss are constructed via the numerical inversion of the lugannani rice saddlepoint approximation the accuracy of the lugannani rice intervals is compared with intervals constructed via moment matching techniques on real data this article has supplementary materials that are available online

existence and stability of periodic solution of a lotka volterra predator prey model with state dependent impulsive effects according to biological and chemical control strategy for pest we investigate the dynamic behavior of a lotka volterra predator prey state dependent impulsive system by releasing natural enemies and spraying pesticide at different thresholds by using poincare map and the properties of the lambert w function we prove that the sufficient conditions for the existence and stability of semi trivial solution and positive periodic solution numerical simulations are carried out to illustrate the feasibility of our main results

partial persistence and extinction in n dimensional competitive systems abstract in this paper we first consider an n dimensional system slightly more general than the lotka volterra system and give conditions that imply strong persistence of all species using this result we then give computable conditions on the coefficients which imply the ultimate extinction of certain species in an n dimensional lotka volterra system

periodicity on a class of neutral impulsive delay system we present some sufficient conditions for the existence of positive periodic solutions of a class of neutral impulsive delay differential system when our results applied to the differential system without impulse a known result in the literature is corrected moreover one example is given to illustrate the results obtained

global attractivity of the almost periodic solution of a delay logistic population model with impulses in this paper we study the existence of almost periodic solutions of a delay logistic model with fixed moments of impulsive perturbations by using a comparison theorem and constructing a suitable lyapunov functional a set of sufficient conditions for the existence and global attractivity of a unique positive almost periodic solution is obtained as applications some special models are studied our new results improve and generalize former results

global attractivity of the diffusive nicholson blowflies equation with neumann boundary condition a non monotone case abstract in this paper we establish the global attractivity of the positive steady state of the diffusive nicholson s equation with homogeneous neumann boundary value under a condition that makes the equation a non monotone dynamical system to achieve this we develop a novel method combining a dynamical systems argument with maximum principle and some subtle inequalities

bayesian design and analysis of computer experiments use of derivatives in surface prediction this article is concerned with the problem of predicting a deterministic response function yo over a multidimensional domain t given values of yo and all of its first derivatives at a set of design sites points in t the intended application is to computer experiments in which yo is an output from a computer model of a physical system and each point in t represents a particular configuration of the input parameters it is assumed that the first derivatives are already available e g from a sensitivity analysis or can be produced by the code that implements the model a bayesian approach in which the random function that represents prior uncertainty about yo is taken to be a stationary gaussian stochastic process is used the calculations needed to update the prior given observations of yo and its first derivatives at the design sites are given and are illustrated in a small example the issue of experimental design is also discussed in particular the criterion of maximizing the reduction in entropy

second method of lyapunov and existence of integral manifolds for impulsive differential difference equations by means of piecewise continuous functions which are analogues of lyapunov s functions sufficient conditions are obtained for the existence of integral manifolds for impulsive differential difference equations with variable impulsive perturbations

global attractivity and permanence of a sveir epidemic model with pulse vaccination and time delay in this study we propose a new sveir epidemic disease model with time delay and analyze the dynamic behavior of the model under pulse vaccination pulse vaccination is an effective strategy for the elimination of infectious disease using the discrete dynamical system determined by the stroboscopic map we obtain an infection free periodic solution we also show that the infection free periodic solution is globally attractive when some parameters of the model under appropriate conditions the permanence of the model is investigated analytically our results indicate that a large vaccination rate or a short pulse of vaccination or a long latent period is a sufficient condition for the extinction of the disease

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

almost periodic solutions for an impulsive delay nicholson s blowflies model by means of the contraction mapping principle and gronwall bellman s inequality we prove the existence and exponential stability of positive almost periodic solution for an impulsive delay nicholson s blowflies model the main results are illustrated by an example

strong resonance for some quasilinear elliptic equations abstract we study the existence of the weak solutions of the nonlinear boundary value problem p u 1 u p 2 u g u h x in u 0 on where the nonlinearity g is of the landesman lazer type our sufficient conditions generalize all previously published results about the strong resonance at the first eigenvalue

on existence of a globally attractive periodic solution of impulsive delay logarithmic population model in this paper it is shown that a logarithmic population model which is governed by impulsive delay differential equation has a globally attractive periodic solution

existence and stability of positive almost periodic solutions and periodic solutions for a logarithmic population model abstract by means of the cauchy matrix we give sufficient conditions for the existence and exponential stability of almost periodic solutions and periodic solutions for the delay impulsive logarithmic population

on oscillation of a food limited population model with impulse and delay in this paper we consider a food limited population model with impulsive effect several explicit sufficient conditions are established for oscillation and nonoscillation of solutions of the equations

hopf bifurcation analysis in a delayed nicholson blowflies equation abstract the dynamics of a nicholson s blowflies equation with a finite delay are investigated we prove that a sequence of hopf bifurcations occur at the positive equilibrium as the delay increases explicit algorithm for determining the direction of the hopf bifurcations and the stability of the bifurcating periodic solutions are derived using the theory of normal form and center manifold global existence of periodic solutions are established using a global hopf bifurcation result of wu trans amer math soc 350 1998 4799 and a bendixson criterion for higher dimensional ordinary differential equations due to li and muldowney j differential equations 106 1994 27

generalized latin hypercube design for computer experiments space filling designs which satisfy a uniformity property are widely used in computer experiments in the present paper the performance of nonuniform experimental designs which locate more points in a neighborhood of the boundary of the design space is investigated these designs are obtained by a quantile transformation of the one dimensional projections of commonly used space filling designs this transformation is motivated by logarithmic potential theory which yields the arc sine measure as an equilibrium distribution the methodology is illustrated for maximin latin hypercube designs by several examples in particular it is demonstrated that the new designs yield a smaller integrated mean squared error for prediction