on the continuity of the multivariate pade operator abstract continuity of the univariate pade operator was proved in 5 6 we discuss the limitations of a multivariate generalization and prove a multivariate analogon of the continuity property

multivariate pade approximation abstract this paper is a survey on the multivariate pade approximation two types of approximants are considered those which can approximate general meromorphic functions f h g where both h and g are holomorphic and those which are specialized to the approximation of functions of the same form where g is a polynomial algorithms are described together with the different techniques used for proving convergence

multivariate pade approximation multivariate pade approximation is considered in the framework of the theory developed by a cuyt 1982 the denominators are determined from determinants of matrices whose entries are homogeneous polynomials the main difference to the univariate case is a typical shift of the degree of the polynomials singularities atx 0 are analyzed since it is the rule rather than the exception that simultaneous zeros of the numerator and the denominator cannot be removed

some new nonlinear volterra fredholm type discrete inequalities and their applications some new explicit bounds on solutions to a class of new nonlinear volterra fredholm type discrete inequalities are established which can be used as effective tools in the study of certain sum difference equations application examples are also indicated

identification of discontinuous nonlinear systems via a multivariate pade approach we present a nonlinear system identification technique based on multi dimensional rational polynomials a multi dimensional pade legendre approximation is developed to circumvent challenges in dealing with sharp shocks the purpose of this paper is to investigate the accuracy of such approximations for identification of various nonlinear systems particularly systems with a non smooth response surface this identification approach utilizes the generalized form of a pade legendre approximation for studying multivariable functions in the studied problems the nonlinearity is a function of state variables displacement and velocity which requires multi dimensional formulation furthermore a spatial filter is applied to minimize the effects of the singular points in the applicable rational function of the response surface this study presents different types of nonlinearities including smooth irregular and hysteretic functions in order to demonstrate the performance of the approach under different conditions in order to study the robustness of the method in comparison to other identification techniques based on plain polynomial representation a nonlinear system with a sharp discontinuous restoring force surface is considered the performance of both approaches is investigated for different degrees of sharpness in addition the accuracy of the identified models to represent the nonlinear system is verified by comparing the output of the system computed on the basis of the identified model from data sets corresponding to different excitations than those used for identification purposes it is shown that the proposed approach provides a robust identification technique for a broad class of highly nonlinear systems and it is particularly advantageous to use when dealing with systems incorporating discontinuous properties

optimal designs for diallel crosses with specific combining abilities optimal designs for diallel crosses are considered when in addition to the block effects and general combining abilities the model also includes specific combining abilities it is seen that partially balanced incomplete block designs with the triangular association scheme play a key role in this context

on a diagonal pade approximation in two complex variables a special type diagonal pade approximation for a class of hermitian power series in two variables is related to a canonical strong operator topology finite rank approximation of cyclic operators the expected convergence of the process uniform or in measure is derived from operator theory facts

integral inequalities and mild solutions of semilinear neutral evolution equations abstract existence of mild solutions to semilinear neutral evolution equations with nonlocal conditions is proved the result is obtained by using fractional power of operators krasnoselski schaefer type fixed point theorem and by applying a modification of the bihari type inequality to the case of singular integral inequality an application to partial differential equations is given

general order newton pade approximants for multivariate functions pade approximants are a frequently used tool for the solution of mathematical problems one of the main drawbacks of their use for multivariate functions is the calculation of the derivatives off x 1 x p therefore multivariate newton pade approximants are introduced their computation will only use the value off at some points in sect 1 we shall repeat the univariate newton pade approximation problem which is a rational hermite interpolation problem in sect 2 we sketch some problems that can arise when dealing with multivariate interpolation in sect 3 we define multivariate divided differences and prove some lemmas that will be useful tools for the introduction of multivariate newton pade approximants in sect 4 a numerical example is given in sect 5 together with the proof that forp 1 the classical newton pade approximants for a univariate function are obtained

gronwall bellman type nonlinear delay integral inequalities on time scales abstract in this paper some gronwall bellman type nonlinear delay integral inequalities on time scales are established which provide a handy tool in deriving boundedness of solutions of certain delay dynamic equations on time scales our results generalize some of the main results in lipovan 2006 1 pachpatte 2000 2 ferreira and torres 2009 3 zhang and meng 2008 4 cheung and ren 2006 5 kim 2009 6 and some of our results unify continuous and discrete analysis in the literature

on some new inequalities related to certain inequalities in the theory of differential equations in the present paper we establish some new integral inequalities related to a certain inequality arising in the theory of differential equations the discrete analogues of the main results are also given the analysis used in the proofs is elementary and the results established here provide new estimates for these types of inequalities

on the continuity of the pade operator let r m n be the pade approximant of order m n for a given power series f let t m n be the operator that maps f on r m n it is known that t m n satisfies a local lipschitz condition in case r m n is normal but may fail to be continuous if r m n is not normal in this paper we prove that t m n is continuous if and only if r m n has defect zero we also prove a convergence result for pade approximants in the case where the defect is positive

optimal partial diallel crosses even in the absence of blocks each cross in a partial diallel cross design can be formally identified with a block of size two and thus the design itself can be identified with a binary block design we show that unblocked partial diallel crosses so linked with a certain class of group divisible designs are uniquely e optimal in general and also uniquely d and a optimal in the saturated case further results on e optimality applicable even when the number of parental lines does not admit a factorisation are also derived the issue of optimal or efficient blocking of partial diallel crosses is discussed

some new finite difference inequalities abstract in this paper we establish some new finite difference inequalities related to a certain integral inequality arising in the theory of differential equations the inequalities obtained here can be used as handy tools in the theory of some new classes of finite difference and sum difference equations

explicit bounds on some new nonlinear integral inequalities with delay the purpose of the present note is to establish some new delay integral inequalities which provide explicit bounds on unknown functions and generalize some results of li et al some new delay integral inequalities and their applications j comput appl math 180 2005 191 200 the inequalities given here can be used to investigate the qualitative properties of certain delay differential equations and delay integral equations

some new generalized gronwall bellman type discrete fractional inequalities some new gronwall bellman type discrete fractional inequalities are established explicit bounds for unknown functions in fractional inequalities are derived properties of solutions of one certain fractional difference equation are researched in this paper we present some new generalized gronwall bellman type discrete fractional inequalities including fractional sum inequalities and fractional difference inequalities these inequalities are of new forms compared with the existing results so far in the literature and can be used to provide explicit bounds for unknown functions concerned for illustrating the effectiveness of the presented results we apply them to research qualitative and quantitative properties for the solutions of an ivp with respect to a fractional difference equation

on generalized of certain retarded nonlinear integral inequalities and its applications in retarded integro differential equations in this paper some new nonlinear retarded integral inequalities of gronwall bellman pachpatte type are investigated some applications are also presented to illustrate the usefulness of some of our results in estimation of solution of certain retarded integro differential equations with the initial conditions

a direct approach to convergence of multivariate nonhomogeneous pade approximants we present a direct approach for proving convergence in measure product capacity of multivariate nonhomogeneous pade approximants previous approaches have involved projection onto pade type approximation in one variable and only yielded convergence in lebesgue measure

a new approach to an analysis of henry type integral inequalities and their bihari type versions abstract in this paper we propose a new method to solve integral inequalities of henry gronwall type and their bihari nonlinear version nonlinear integral inequalities with weakly singular kernels and with multiple integrals as well as a modification of the ou iang pachpatte inequality are also treated

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

how well can the concept of pade approximant be generalized to the multivariate case what we know about multivariate pade approximation has been developed in the last 25 years in the next sections we compare and discuss many of these results it will become clear that simple properties or requirements such as the uniqueness of the pade approximant and consequently its consistency property can play a crucial role in the development of the multivariate theory a separate section is devoted to a discussion of the convergence properties at the end we include an extensive reference list on the topic

a generalization of retarded integral inequalities in two independent variables and their applications the object of this paper is to establish some nonlinear retarded integral inequalities in two independent variables which can be used as handy tools in the theory of partial differential and integral equations with time delays

pade legendre approximants for uncertainty analysis with discontinuous response surfaces a novel uncertainty propagation method for problems characterized by highly non linear or discontinuous system responses is presented the approach is based on a pade legendre pl formalism which does not require modifications to existing computational tools non intrusive approach and it is a global method the paper presents a novel pl method for problems in multiple dimensions which is non trivial in the pade literature in addition a filtering procedure is developed in order to minimize the errors introduced in the approximation close to the discontinuities the numerical examples include fluid dynamic problems characterized by shock waves a simple dual throat nozzle problem with uncertain initial state and the turbulent transonic flow over a transonic airfoil where the flight conditions are assumed to be uncertain results are presented in terms of statistics of both shock position and strength and are compared to monte carlo simulations

estimates on some power nonlinear volterra fredholm type discrete inequalities and their applications some explicit bounds on solutions to a class of new power nonlinear volterra fredholm type discrete inequalities are established which can be used as effective tools in the study of certain sum difference equations application examples are also given

inequalities applicable in the theory of finite difference equations in the present paper we establish some new nonlinear finite difference inequalities applicable in the theory of certain classes of finite difference equations in various different situations we also present applications of some of the inequalities to show their importance to the literature

birkhoff gustavson normal form and the semiclassical energies of a double pendulum although the double pendulum is a well known system the literature is sparse with regard to the study of its full dynamical behaviour as a simple conservative system that displays both ordered and chaotic motion it poses an interesting problem for the study of classical quantum correspondence in this work we present its birkhoff gustavson normal form and semiclassical energies obtained from the normal form the pade summation technique is used to re sum the normal form series

a generalized retarded gronwall like inequality in two variables and applications to bvp abstract in this paper we establish a generalized retarded integral inequality of gronwall like type in two variables which includes both a nonconstant term outside the integrals and more than one distinct nonlinear integrals without assumption of monotonicity using our result we can solve both the integral inequality in w s cheung some new nonlinear inequalities and applications to boundary value problems nonlinear anal 64 2006 2112 2128 and the one in r p agarwal s deng w zhang generalization of a retarded gronwall like inequality and its applications appl math comput 165 2005 599 612 we apply our result to a boundary value problem of a partial differential equation for boundedness uniqueness and continuous dependence

optimal complete diallel crosses summary optimality of complete diallel crosses in incomplete blocks is investigated optimal complete diallel crosses are characterized and such binary plans are derived using nested balanced incomplete block designs a table of optimal complete diallel crosses for up to 15 lines is also provided

discrete non linear inequalities and applications to boundary value problems in this paper we generalize some existing discrete gronwall bellman ou iang type inequalities to more general situations these are in turn applied to study the boundedness uniqueness and continuous dependence of solutions of certain discrete boundary value problem for difference equations

on some new nonlinear delay integral inequalities abstract some new nonlinear delay integral inequalities of ou iang type are obtained which generalise some results of b g pachpatte 1995 period math hungar 31 229 234 and e h yang 1997 ann differential equations 13 180 188 an application example is also indicated

on some new integral inequalities and their applications the aim of the present paper is to establish some new integral inequalities in two independent variables which provide explicit bounds on unknown functions the inequalities given here can be used as tools in the qualitative theory of certain partial differential equations

on some new integral inequalities of gronwall bellman pachpatte type abstract in this paper we establish new nonlinear integral inequalities of gronwall bellman pachpatte type these inequalities generalize some former famous inequalities and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of some nonlinear ordinary differential and integral equations the purpose of this paper is to extend certain results which proved by pachpatte in inequalities for differential and integral equations academic press new york and london 1998 some applications are also given to illustrate the usefulness of our results

optimal block designs for diallel crosses summary optimal block designs for a type of diallel cross experiment are proposed these incomplete block designs are derived by using triangular partially balanced designs with two associate classes some efficient incomplete block designs for diallel crosses are also reported