oscillation criteria of yan type for linear hamiltonian systems abstract new oscillation criteria of yan type are established for the linear hamiltonian system x x a t x b t y t t0 y c t x a t y where a t b t and c t are continuous n n matrix valued functions with b t b t 0 c t c t the criteria obtained generalize and improve some previous results for the second order linear matrix differential systems in literature

necessary and sufficient conditions for oscillation of second order neutral differential equations consider the second order nonlinear neutral differential equation with delays e d2 dt2 y t py t q t f y t 0 for t 0 where q t f x are continuous functions q t 0 yf y 0 if y 0 and 0 0 0 when f y satisfies either the superlinear or sublinear conditions which include the special case f y y y 1 of 1 and 0 1 respectively we give necessary and sufficient conditions for the oscillation of all continuable solutions of e when p 0 in e these results reduce to the well known theorems of atkinson and belohorec in the special case when f y y y 1 1

oscillation results for linear hamiltonian systems for linear hamiltonian systems this paper established some new oscillation criteria which improve previous results even for self adjoint second order differential systems the main tool used is a generalized riccati transformation

nonlinear functionals and a theorem of sun we use a recently developed theory of nonlinear functionals in the study of oscillations of second order symmetric vector differential systems to extend a number of theorems of sun new kamenev type theorems for second order linear matrix differential systems appl math lett 2004 in press under a common theme the criteria presented here are of the form the integral of the coefficient matrix is bounded at infinity in a sense to be made explicit in the paper and bounded away from a positive absolute constant implies oscillation at infinity

central limit theorems for permuted regenerative estimators we prove strong laws of large numbers and central limit theorems for some permuted estimators from regenerative simulations these limit theorems provide the basis for constructing asymptotically valid confidence intervals for the permuted estimators

comment on the paper interval criteria for oscillation of second order nonlinear neutral differential equations comput math appl 46 5 6 2003 903 918

new kamenev type oscillation criteria for linear matrix hamiltonian systems some new kamenev type criteria have been obtained for the oscillation of the linear matrix hamiltonian system x a t x b t y y c t x a t y under the hypothesis a t b t b t 0 and c t c t are nxn real continuous matrix functions on the interval t 0 t 0 our results are different from most known ones in the sense that they are given in the form of lim t supg const rather than in the form of lim t sup l 1 where g is a positive linear functional on the linear space of nxn matrices with real entries consequently our results improve some previous results to some extent which can be seen by the examples given at the end of this paper

new oscillation criteria for linear matrix hamiltonian systems abstract some new oscillation criteria are established for the matrix linear hamiltonian system x a t x b t y y c t x a t y under the hypothesis a t b t b t 0 and c t c t are n n real continuous matrix functions on the interval t 0 t 0 these results are sharper than some previous results even for self adjoint second order matrix differential systems

oscillation and nonoscillation criteria for quasilinear differential equations abstract some oscillation and nonoscillation criteria for quasilinear differential equations of second order are obtained these results are extensions of earlier results of huang j math anal appl 210 1997 712 723 and elbert j math anal appl 226 1998 207 219

oscillation of linear second order matrix differential equations in this paper sufficient conditions are obtained for oscillation of all nontrivial prepared symmetric solutions of a class of nonlinear second order matrix differential equations of the form p t y q t f y 0 t geqslant 0 and y q t f y 0 t geqslant 0

oscillation theorems for self adjoint matrix hamiltonian systems involving general means by use of monotone functionals and positive linear functionals a generalized riccati transformation and the general means technique some new oscillation criteria for the following self adjoint hamiltonian matrix system e x t a t x t b t y t y t c t x t a t y t are obtained the results obtained improve and complement that of kumari et al 2000 on kamenev type theorems moreover these results generalize and improve earlier results due to meng 2002 for e erbe et al 1993 meng et al 1998 and wang 2001 for p t x t q t x t 0 or its special cases and wong 2001 for the scalar system x t q t x t 0

new oscillation criteria for linear matrix hamiltonian systems some new criteria have been obtained for the oscillation of the linear matrix hamiltonian system x a t x b t y y c t x a t y under the hypothesis a t b t b t 0 and c t c t are nxn real continuous matrix functions on the interval t 0 t 0 our results are independent of the main results obtained in our recent paper appl math comput 131 2002 357 in the sense that they are given in terms of the positive linear functional on the linear space of nxn matrices with real entries at the same time our results improve some previous results to a great extent which can be seen by the examples given at the end of this paper

interval oscillation criteria for a forced second order nonlinear ordinary differential equations with oscillatory potential new oscillation criteria established in the paper for a forced second order nonlinear equation with oscillatory potential p t y t q t f y t g t are different from the most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are of a high degree of generality and sharper than some previous results and handle the cases which are not covered by known results moreover these results can also be applied to the extreme such as t 0 q s ds

oscillation criteria for second order nonlinear differential equations involving general means consider the second order nonlinear differential equation e y a t f y 0 where a t c 0 f y c1 f y 0 and yf y 0 for y 0 furthermore f y also satisfies either a superlinear or a sublinear condition which covers the nonlinear function f y y y 1 with 1 and 0 1 respectively commonly known as the emden fowler case here the coefficient function a t is allowed to be negative for arbitrarily large values of t kamenev type oscillation criteria involving integral averages for the linear equations l y a t y 0 are extended to the nonlinear equation e by using more general means the results extend similar results on general means by philos for the linear equation l and also results based upon kamenev s integral averaging method concerning the nonlinear equation e

new kamenev type oscillation criteria for second order nonlinear differential equations with damping abstract some new oscillation criteria are established for the nonlinear damped differential equation r t y p t y q t f y 0 that are different from most known ones in the sense that they are based on a class of new functions t s r defined in the sequel our results are sharper than some previous results which can be seen by the examples at the end of this paper

integral inequalities and second order linear oscillation on the interval 0 a u 0 below by a solution we mean a non trivial solution a solution is oscillatory if it has an infinite number of zeros numerous oscillation criteria are known and diversified approaches have proved fruitful among these is the use of the associated riccati equation although the theory of differential and integral inequalities has been used by some investigators see e g hartman 4 71 the authors believe that it has not been fully exploited the non oscillation of 1 1 is equivalent to the existence of a solution of the associated riccati equation on a half line thus one technique of proving oscillation is to show that any solution of the riccati equation diverges to i co at a finite point the theory of differential and integral inequalities comes in handy in the estimation of the growth of such a solution below we describe some known results that are relevant to results established in this paper although these are stated here for the case i co in the rest of the paper we consider both cases a 0 and a 00 it is well known that if q is large in the mean then 1 1 is oscillatory a typical example of such a criterion is due to fite leighton and wintner if

oscillation criteria for linear matrix hamiltonian systems abstract in this paper we present oscillation criteria in terms of the coefficient functions for the matrix linear hamiltonian system u a x u b x v v c x u a x v under the hypothesis h a x b x b x 0 and c x c x are n n matrices of real valued continuous functions on the interval i a a these criteria generalize earlier results due to etgen and pawlowski 1976 erbe qingkai kong and shigui ruan 1993 and fanwei meng jizhong wang and zhaowen zheng 1998 for the system p x u q x u 0 or its special cases

oscillation criteria for second order matrix dynamic equations on a time scale we obtain oscillation criteria for a second order self adjoint matrix differential equation on a measure chain in terms of the eigenvalues of the coefficient matrices and the graininess function we illustrate our results with some nontrivial examples

interval criteria for oscillation of second order linear ordinary differential equations abstract new oscillation criteria are established for the equation py qy 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are more natural according to the sturm separation theorem and sharper than some previous results and can be applied to extreme cases such as t 0 q t dt

weighted means and oscillation conditions for second order matrix differential equations on considere le systeme d equations differentielles d ordre 2 p t y t q t y t 0 pour t 0 ou p et q sont des matrices symetriques n n reelles sur 0 et y un vecteur colonne on suppose que p t est definie positive pour tout t tel que p t 1 on donne des conditions d oscillations

interval oscillation criteria for matrix differential systems with damping abstract this paper concerns the oscillation of solutions to leighton type for the matrix differential system with damping p t y r t y q t y 0 under the hypothesis p t p t 0 q t q t and r t r t are n n matrices of real valued continuous functions on the interval t 0

oscillation theorems for self adjoint matrix hamiltonian systems by using generalized riccati technique linear positive functional and the weighted averages technique some new oscillation criteria for self adjoint hamiltonian matrix system e u x a x u x b x v x v x c x u x a x v x are obtained these results generalize and improve earlier results due to kumari and umamaheswaram 9 for e parhi and praharaj 12 etgen and pawlowski 6 for p x u x q x u x 0 or its special cases and coles 3 for the scalar system y x q x y x 0

oscillation results for matrix differential systems with damping abstract in this paper we establish several new oscillation theorems of leighton type for the matrix differential system with damping p t y r t y q t y 0 under the hypothesis p t p t 0 q t q t and r t r t are n n matrices of real valued continuous functions on the interval t 0 our results are not contained in known results

on the best possible remaining term in the hardy inequality we give a necessary and sufficient condition on a radially symmetric potential v on a bounded domain omega of n that makes it an admissible candidate for an improved hardy inequality of the following type for every element in h 1 0 omega integral omega vector differential u 2 dx n 2 2 2 integral omega u 2 x 2 dx or c integral omega v x u 2 dx a characterization of the best possible constant c v is also given this result yields easily the improved hardy s inequalities of brezis vazquez brezis h vazquez jl 1997 blow up solutions of some nonlinear elliptic problems revista mat univ complutense madrid 10 443 469 adimurthi et al adimurthi chaudhuri n ramaswamy n 2002 an improved hardy sobolev inequality and its applications proc am math soc 130 489 505 and filippas tertikas filippas s tertikas a 2002 optimizing improved hardy inequalities j funct anal 192 186 233 as well as the corresponding best constants our approach clarifies the issue behind the lack of an optimal improvement while yielding the following sharpening of known integrability criteria if a positive radial function v satisfies lim inf r o ln r integral r o sv s ds infinity then there exists rho rho omega 0 such that the above inequality holds for the scaled potential v rho x v x rho on the other hand if lim r 0 ln r integral r o sv s ds infinity then there is no rho 0 for which the inequality holds for v rho

oscillation results for linear second order matrix differential systems with damping in this paper we present some new oscillation criteria in terms of the coefficient functions for the linear second order matrix differential system with damping p t x r t x q t x 0

permuted derivative and importance sampling estimators for regenerative simulations abstract in a previous paper we introduced a new variance reduction technique for regenerative simulations based on permuting regeneration cycles in this paper we apply this idea to new classes of estimators in particular we derive permuted versions of likelihood ratio derivative estimators for steady state performance measures importance sampling estimators of the mean cumulative reward until hitting a set of states and tin estimators for steady state ratio formulas empirical results are presented showing that modest to significant variance reductions can be obtained

oscillation results for selfadjoint differential systems abstract we consider the second order differential system 1 r t y q t y 0 where r q y are n n matrices with r t q t symmetric and r t positive definite for t a r t 0 t a we establish sufficient conditions in order that all prepared solutions y t of 1 are oscillatory that is det y t vanishes infinitely often on a the conditions involve the smallest and largest eigen values n r 1 t and 1 a t q s ds respectively the results obtained can be regarded as generalizing well known results of leighton and others in the scalar case

oscillation of self adjoint linear matrix hamiltonian systems abstract by means of monotone functionals defined on suitable matrix spaces and new methods oscillation criteria for self adjoint linear hamiltonian matrix system of the form x x a x x x b x y x y x c x x x a x y x are obtained there results are sharper than some previous results even for self adjoint second order matrix differential systems in particular our theorems are generalizations and improvements of many existing results including those obtained by sun j math anal appl 279 2003 651 658

oscillation and nonoscillation for second order linear differential equations abstract new oscillation and nonoscillation theorems are obtained for the second order linear differential equation u p t u 0 where p t c 0 and p t 0 conditions only about the integrals of p t on every interval 2 n t 0 2 n 1 t 0 n 1 2 for some fixed t 0 0 are used in the results

oscillation by impulses for a second order delay differential equation we consider a certain second order nonlinear delay differential equation and prove that the all solutions oscillate when proper impulse controls are imposed an example is given

bessel pairs and optimal hardy and hardy rellich inequalities we give necessary and sufficient conditions on a pair of positive radial functions v and w on a ball b of radius r in rn n 1 so that the following inequalities hold for all u in c 0 infty b label one int limits b v x nabla u 2 dx geq int limits b w x u 2dx label two int limits b v x delta u 2 dx geq int limits b w x nabla u 2 dx n 1 int limits b left frac v x x 2 frac v r x x right nabla u 2dx this characterization makes a very useful connection between hardy type inequalities and the oscillatory behaviour of certain ordinary differential equations and helps in the identification of a large number of such couples v w that we call bessel pairs as well as the best constants in the corresponding inequalities this allows us to improve extend and unify many results old and new about hardy and hardy rellich type inequalities such as those obtained by caffarelli et al compos math 53 259 275 1984 brezis and vazquez revista mat univ complutense madrid 10 443 469 1997 wang and willem j funct anal 203 550 568 2003 adimurthi et al proc am math soc 130 489 505 2002 and many others

interval oscillation criteria for second order nonlinear differential equations with damping new oscillation criteria are established for the nonlinear damped differential equation ry py qf y 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are sharper than some previous results and extend and improve the recent interval criteria of kong and huang and can be applied to extreme cases such as t0 q s ds in particular several examples that dwell upon the sharp conditions of our results are also included

oscillation criteria of second order nonlinear matrix differential systems in this paper the second order nonlinear matrix differential systems p t y t f t y t y t 0 t t 0is considered where p t y t and f t y t y t are nxn real continuous matrix functions and p t 0 are positive definite and symmetric one some new oscillation criteria for the systems are established and some known results in the literature are improved and generalized

oscillation for a second order neutral differential equation with impulses we consider a certain type of second order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations called impulses as a matter of fact some particular non impulsive cases of the system are oscillatory already thus we are interested in finding adequate impulse controls under which our system remains oscillatory

note on wong s paper using the method of interval integral average we establish some new oscillation criteria which improve the oscillation criteria due to james s w wong

interval criteria for oscillation of second order nonlinear neutral differential equations some new oscillation criteria are established in this paper for the second order nonlinear neutral delay differential equation r t x t p t x t q t f x t 0 where and are nonnegative constants r p q c t0 r and f c r r these results are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are sharper than some previous results about neutral and delay differential equations in particular several examples that dwell upon the sharp conditions of our results are also included

a note on oscillation criteria of second order nonlinear neutral delay differential equations in recent years many results on oscillation criteria of second order nonlinear neutral delay differential equations have been obtained but some of these criteria are incorrect due to a mistake in a crucial auxiliary result this note examines several of these results provides some counterexamples and points out what causes the problems

a computer program to minimize a function with many variables using computer evaluated exact higher order derivatives this paper describes a computer program for an optimization algorithm using first up to the rth order derivatives to find the optimum of r continuously differentiable functions of many variables the algorithm developed by kalaba and tishler 6 7 obtains the exact values of the derivatives required for the optimization from the table algorithm presented in 4 and 5 the optimization algorithm described here collapses to the well known newton raphson algorithm when only first and second order derivatives are used

oscillation criteria related to integral averaging technique for linear matrix hamiltonian systems by employing a generalized riccati technique and an integral averaging technique new oscillation criteria are established for the linear matrix hamiltonian system u a x u b x v v c x u a x v under the assumption that all a x b x b x 0 and c x c x are n n matrices of real valued continuous functions on the interval i x0 x0 these criteria extend improve and unify a number of existing results and also handle cases not covered by known criteria several interesting examples that illustrate the importance of our results are included

interval oscillation criteria for second order nonlinear perturbed differential equations abstract we present new interval oscillation criteria for certain classes of second order nonlinear perturbed differential equations which are based on the information only on a sequence of subintervals of t o rather than on the whole half line our results are sharper than those known in the literature and deal with the cases which are not covered by the known criteria in particular our results can be applied to extreme cases such as q s ds finally two examples which dwell upon the sharpness of the conditions of our results are also illustrated

interval oscillation criteria related to integral averaging technique for certain nonlinear differential equations abstract we present new interval oscillation criteria related to integral averaging technique for certain classes of second order nonlinear differential equations that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results are sharper than some previous results and handle the cases which are not covered by known criteria in particular several examples that dwell upon the sharp conditions of our results are also included

a finite algorithm for the exact evaluation of higher order partial derivatives of functions of many variables abstract a formal algorithm is given for the systematic exact evaluation of higher order partial derivatives of functions of many variables the algorithm improves upon wengert s method in two key respects applications are envisioned wherever gradients jacobians hessians and power series expansions could be employed

riccati techniques and variational principles in oscillation theory for linear systems on etablit des conditions suffisantes pour que toutes les solutions soient oscillatoires on utilise les techniques de riccati et les principes variationnels

oscillation of two dimensional linear second order differential systems abstract this article is concerned with the oscillatory behavior at infinity of the solution y a r 2 of a system of two second order differential equations y t q t y t 0 t a q is a continuous matrix valued function on a whose values are real symmetric matrices of order 2 it is shown that the solution is oscillatory at infinity if the largest eigenvalue of the matrix at q s ds tends to infinity as t this proves a conjecture of d hinton and r t lewis rocky mountain j math 10 1980 751 766 for the two dimensional case furthermore it is shown that considerably weaker forms of the condition still suffice for oscillatory behavior at infinity

interval oscillation of a general class of second order nonlinear differential equations with nonlinear damping abstract the paper is concerned with the oscillation of a class of general type second order differential equations with nonlinear damping terms several new interval oscillation criteria are established for such a class of differential equations under quite general assumptions examples are also given to illustrate the results in particular it is shown that under some very mild conditions on k 1 k 2 and f the equation k 1 x x cos tk 2 x x x sin tf x 0 is oscillatory which extends the result obtained by kwong and wong j math anal appl 288 2003 15

oscillation theorems for certain second order self adjoint matrix differential systems abstract by means of generalized averaging pair technique and riccati transformation method oscillation criteria for self adjoint differential matrix system of the form r t p t x t p t p t x t q t f x t g x t 0 are obtained this paper generalizes and improves the existing results including those obtained by yang 2002 li and agarwal 2000 and rogovchenko 1999

on the oscillation of differential equations with an oscillatory coefficient we derive lower bounds for the distance between consecutive zeros of solutions of y q t y 0 when q takes both positive and negative values we apply our results to the limit point limit circle classifications of

integral averaging techniques for the oscillation of second order nonlinear differential equations abstract in this paper we enlist some known and establish some new oscillation criteria for the second order nonlinear differential equations of the form if a t x t t su p t t q t f x t 0 where the coefficients p t and q t are not assumed to be nonnegative for all large values of t these criteria are obtained by using integral averaging techniques and can be applied to some special cases where other classical oscillation results are not applicable a systematic study is attempted to extend improve and correlate a number of existing results

philos type oscillation criteria for emden fowler neutral delay differential equations philos type oscillation criteria are established for the emden fowler neutral delay differential equation x t c 1x t q 1 t y email protected a 1y email protected q 2 t y email protected b 1y email protected 0 t t 0 where x t y t p t y email protected the results obtained here essentially improve some known results in the literature in particular two interesting examples that point out the importance of our results are also included

averaging techniques for self adjoint matrix equations on a measure chain abstract we apply averaging techniques to establish oscillation and nonoscillation criteria for the self adjoint matrix dynamic equation lx t p t x t q t x t 0 on a measure chain t these results extend and unify earlier results for the differential and difference equation case

interval oscillation of second order half linear functional differential equations by using an inequality due to hardy littlewood and polya and averaging functions new interval oscillation criteria are established for the half linear functional differential equationr t y t a 1y t q t y t t a 1y t t 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t 0 rather than on the whole half line our results extend and improve some previous oscillation criteria and handle the cases which are not covered by known results and implies that the delay t t t t does not effect the oscillation where t 0 is a constant in particular several examples that dwell upon the sharp conditions of our results are also included

linear transformation and oscillation criteria for hamiltonian systems abstract using a linear transformation similar to the kummer transformation some new oscillation criteria for linear hamiltonian systems are established these results generalize and improve the oscillation criteria due to i s kumari and s umanaheswaram i sowjaya kumari s umanaheswaram oscillation criteria for linear matrix hamiltonian systems j differential equations 165 2000 174 198 q yang et al q yang r mathsen s zhu oscillation theorems for self adjoint matrix hamiltonian systems j differential equations 190 2003 306 329 and s chen and z zheng shaozhu chen zhaowen zheng oscillation criteria of yan type for linear hamiltonian systems comput math appl 46 2003 855 862 these criteria also unify many of known criteria in literature and simplify the proofs

interval criteria for oscillation of certain matrix differential systems by employing a generalized riccati technique and an averaging technique interval oscillation criteria are established for the second order matrix differential system of the form p t y q t y 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of t0 rather than on the whole half line our results are presented in the form of a high degree of generality handle the cases which are not covered by known criteria and can be applied to extreme cases such as limt 1 t0tq s ds in particular several interesting examples that dwell upon the importance of our results are included

oscillation theorems for linear matrix hamiltonian systems using a matrix linear transformation which preserves oscillatory property some new oscillation criteria for the following linear matrix hamiltonian system u a t t i u b t v v c t u t i a t v t t 0 are obtained which improve and generalize some recent results in literature

oscillation of linear hamiltonian systems abstract in this paper sufficient conditions have been obtained for the oscillation of a class of linear hamiltonian systems

riccati techniques and oscillation for self adjoint matrix hamiltonian systems the purpose of this paper is to develop a generalized matrix riccati technique for the self adjoint matrix hamiltonian system u a x u b x v v c x u a x v together with the integral averaging technique and monotone functionals new oscillation and interval oscillation criteria are established for the system these criteria extend improve complement a number of existing results and handle some cases not covered by known criteria in particular two interesting examples are included to illustrate the versatility of our results

sensitivity analysis for simulations via likelihood ratios we present a simple method of estimating the sensitivity of quantities obtained from simulation with respect to a class of parameters here sensitivity means the derivative of an expectation with respect to a parameter the class of parameters includes for example poisson rates discrete probabilities and the mean and variance of a normal distribution the method is extremely well suited to regenerative simulation and can be implemented on extant simulations with little effort increase in running time or memory requirements it is based on some change of measure formulas derived from likelihood ratios in addition to the theorems that underly the technique we present some numerical examples