on oscillation of nonlinear second order differential equation with damping term we present new oscillation criteria for the second order nonlinear differential equation with damping our theorems are stated in general form they complement and extend related results known in the literature the relevance of our results is illustrated with a number of examples to facilitate computations in these examples we use mathematica r a symbolic computer language

new kamenev type oscillation criteria for second order neutral nonlinear differential equations abstract in this paper some new oscillation criteria for second order neutral nonlinear differential equation r t y t p t y t i 1 n q i t f i y i t 0 t t 0 are established new oscillation criteria are different from most known ones in the sense that they are based on a class of new functions t s l defined in the sequel our results are sharper than some previous results which can be seen by the example at the end of this paper

oscillation criteria for even order half linear distributed delay differential equations with damping by using the generalized riccati technique and an inequality due to hardy littlewood and polya several new oscillation criteria are established for a class of even order half linear distributed for a differential equation with damping the results obtained extend and improve earlier results in existing literature

interval criteria for oscillation of second order half linear differential equations by employing a generalized riccati technique and an integral averaging method interval oscillation criteria are established for the second order half linear differential equation r t x t 1x t q t x t 1x t 0 these criteria are different from most known ones in the sense that they are based on information only on a sequence of subintervals of t0 rather than on the whole half line they also extend improve and complement a number of existing results and can be applied to extreme cases such as t0 q s ds in particular several interesting examples that illustrate the importance of our results are included

oscillation criteria for second order nonlinear delay dynamic equations on time scales by employing the generalized riccati transformation we establish some new oscillation criteria for second order delay dynamic equations on time scales the obtained results essentially improve the well know oscillation results for half linear dynamic equations such as kamenev type and philos type oscillation criteria some interesting examples are given to illustrate the versatility of our results

asymptotic behavior of solutions of second order nonlinear delay differential equations with impulses this paper is concerned with second order nonlinear delay differential equations with impulses of the form r t x t p t x t f t x email protected 0 t t k x t k i k x t k x t k j k x t k t t k k 1 2 t t 0 by impulsive differential inequality and riccati transformation sufficient conditions of asymptotic behavior of all solutions of second order nonlinear delay differential equations with impulses are obtained some examples are also inserted to illustrate the impulsive effect

the distance between zeros of an oscillatory solution to a half linear differential equation consider the oscillatory equation u t 1u t q t u t 1u t 0 where q t a r is locally integrable for some a 0 we prove some results on the distance between consecutive zeros of a solution of we apply also the results to the following equations r t u t 1u t q t u t 1u t 0 and i 1ndi du n 2diu c x u n 2u 0 a where i r c 0 0 and ar t 1 ii di xi d d1 dn a x rn x a is an exterior domain and c c a 0 iii 0 n 1 and n 2

oscillation criteria for second order quasi linear neutral delay differential equations abstract in this paper some new oscillation criteria for second order neutral nonlinear differential equation r t x t p t x t m 1 x t p t x t q t f x t 0 are established new oscillation criteria are different from most known ones in the sense that they are based on a class of new functions t s l defined in the sequel

generalized inverse eigenvalue problem for matrices whose graph is a path abstract in this paper we analyse a special generalized inverse eigenvalue problem a n x b n x for the pair a n b n of matrices each of whose graph is a path on n vertices by investigating the leading principal minors of the matrix a n b n from the given data consisting of b n a matrix a k k n whose graph is a path on k vertices two column vectors x 2 y 2 r n k and distinct real numbers and we construct a n and two column vectors x 1 y 1 r k such that a k is the leading principal sub matrix of a n and x y are the eigenpairs of a n b n where x x 1 t x 2 t t and y y 1 t y 2 t t further numerical examples are also given to demonstrate the applicability of the results developed here

sturmian comparison theorem for half linear second order differential equations let be defined by s s p 2 s with p 1 a fixed number we extend sturm comparison theorem of the linear differential equation to the nonlinear differential equation by using the wirtinger inequality a lyapunov inequality and some oscillation criteria of e are also given

oscillation theorems for certain nonlinear differential equations of second order abstract we present new oscillation criteria for the second order nonlinear differential equations these criteria involve the use of averaging functions our theorems are stated in general form they complement and extend related results known in the literature also the relevance of our results is to show that some of manojlovic s results contain the superfluous condition

asymptotic behavior of solutions of second order nonlinear impulsive differential equations in this work the asymptotic behavior of all solutions of second order nonlinear ordinary differential equations with impulses is investigated by impulsive differential inequality and riccati transformation sufficient conditions of asymptotic behavior of all solutions of second order nonlinear ordinary differential equations with impulses are obtained an example is also inserted to illustrate the impulsive effect

interval criteria for oscillation of second order functional differential equations by using averaging functions new interval oscillation criteria are established for the second order functional differential equation r t x t a 1x t f t x t x t t x t x t t 0 t t 0that are different from most known ones in the sense that they are based on information only on a sequence of subintervals of t 0 rather than on the whole half line our results can be applied to three cases ordinary delay and advance differential equations in the case of half linear functional differential equations our criteria implies that the t t t delay and gt t t advance cases do not affect the oscillation in particular several examples are given to illustrate the importance of our results

oscillation criteria for second order nonlinear neutral variable delay dynamic equations abstract this paper is concerned with oscillation of second order nonlinear neutral dynamic equations on time scales with a variable delay by using the generalized riccati technique and integral averaging technique new oscillation criteria are obtained for all solutions of the equation some results extend known results for difference equations when the time scale is the set z of positive integers and for differential equations when the time scale is r several examples are given to illustrate the results of the paper

interval oscillation criteria for second order neutral nonlinear differential equations some oscillation criteria for the second order neutral nonlinear differential equation y t p t y s t email protected i 1 nq i t f i y t i t 0 t t 0are established new oscillation criteria 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

generalized inverse eigenvalue problem with mixed eigendata abstract in this paper we consider a generalized inverse eigenvalue problem j n x c n x where j n is a jacobi matrix and c n is a nonsingular diagonal matrix that may be indefinite let j k be k k leading principal submatrix of j n given c n two vectors x 2 x k 1 x k 2 x n t y 2 y k 1 y k 2 y n t r n k two distinct real numbers we construct a jacobi matrix j n and two vectors x 1 x 1 x 2 x k t y 1 y 1 y 2 y k t r k such that j n x c n x and j n y c n y where x x 1 t x 2 t t and y y 1 t y 2 t t we find necessary and sufficient conditions for solvability of this problem and we give an example

oscillation theorems for nonlinear differential equations of second order abstract in this paper we present some new criteria for the oscillation of the differential equation a t x t x t p t x t q t f x t 0 the obtained results extend improve and correlate a number of existing criteria

integral averages and oscillation criteria for half linear partial differential equation the technique of weighted integral averages known in the oscillation theory of ordinary differential equations is extended to the half linear partial differential equation e div email protected email protected p email protected u c x u p 2u 0 p 1 this technique is used to obtain new oscillation criteria for e on the unbounded domains

oscillation of even order half linear functional differential equations with damping in this paper a class of even order half linear functional differential equations with damping are studied by using the generalized riccati transformation and the integral averaging technique the new oscillation criteria which generalize and improve some known results are obtained for all solutions of the equations

security analysis and improvement of a double trapdoor encryption scheme at asia crypt 03 bresson et al proposed a probabilistic public key encryption scheme with a double trapdoor decryption mechanism in this paper we provide security analysis of it and point out three insecurities of the encryption scheme it suffers from adaptive chosen ciphertext attacks cca and can be broken in three different ways by constructing proper ciphertexts the adversary can calculate the user s private key or factorize the modulus after getting the decrypted plaintexts so she can decrypt all the plaintexts encrypted under this encryption scheme to overcome these insecurities we suggest a simple method to improve the encryption scheme against active attacks and prevent the adversary from getting important or private information and strengthen its security

oscillation criteria for second order sublinear differential equation abstract the basic purpose of this paper is to present a new oscillation criteria for second order sublinear differential equation a t x t x t q t t 0 t t 0 0 where a a c 1 t 0 is positive function q c t 0 has no restriction on its sign c 1 r are such that x 0 x x 0 for x 0

oscillation criteria for second order nonlinear perturbed differential equations abstract we present new oscillation criteria for the second order nonlinear perturbed differential equations these criteria are of a high degree of generality and they extend and unify a number of existing results

oscillation criteria for half linear dynamic equations on time scales this paper is concerned with oscillation of the second order half linear delay dynamic equation r t x p t x t 0 on a time scale t where 1 is the quotient of odd positive integers p t and t t are positive rd continuous functions on t r t is positive and delta differentiable t t and limt t we establish some new sufficient conditions which ensure that every solution oscillates or converges to zero our results in the special cases when t r and t n involve and improve some oscillation results for second order differential and difference equations and when t hn t q n 0 and t n 2 our oscillation results are essentially new some examples illustrating the importance of our results are also included

oscillation and asymptotics for second order half linear differential equations this paper discusses a class of second order half linear differential equations by using the generalized riccati technique and the averaging technique new oscillation criteria are obtained for all solutions of the equations to be oscillatory asymptotic behavior for forced equations is also discussed

kamenev type oscillation criteria for second order nonlinear dynamic equations on time scales the purpose of this paper to establish oscillation criteria for second order nonlinear dynamic equation r t x t f t x g t 0 on an arbitrary time scale t where is a quotient of odd positive integers and r is a positive rd continuous function on t the function g t t satisfies g t t and limt g t and f c t r r we establish some new sufficient conditions such that the above equation is oscillatory by using generalized riccati transformation our results in the special cases when t r and t n involve and improve some oscillation results for second order differential and difference equations and when t hn t qn0 and t n2 our oscillation results are essentially new some examples illustrating the importance of our results are included

ordinary differential equations in the oscillation theory of partial half linear differential equation abstract in the paper we study the damped half linear partial differential equation div a x u p 2 u b x u p 2 u c x u p 2 u 0 using radialization method we derive general oscillation results which allow to deduce new oscillation criteria for this equation from oscillation criteria for ordinary differential equations using careful radialization we improve several known oscillation criteria

oscillation and asymptotics for nonlinear second order differential equations this paper discusses a class of second order nonlinear differential equations by using the generalized riccati technique and the averaging technique new oscillation criteria are obtained for all solutions of the equation to be oscillatory asymptotic behavior for forced equations is also discussed

oscillation criteria for second order nonlinear perturbed differential equations abstract some criteria are obtained which guarantee that all solutions of the second order nonlinear perturbed differential equations r t y t p t y t q t y t h t y t y t are oscillatory

an inverse extreme eigenpair problem and its parallel iterative solution for symmetric tridiagonal matrices this article concerns computing the largest or smallest eigenvalue and corresponding eigenvector of a large irreducible symmetric tridiagonal matrix we divide the original extreme eigenpair problem into p subproblems when the matrix is partitioned in p block form an inverse extreme eigenpair problem associated with the divide method is considered find a p 1 dimensional vector a such that the largest eigenvalue lambda of a given symmetric tridiagonal matrix t is the common largest eigenvalues of p small matrices t i a which are updated matrices of the diagonal blocks t i of t with rank one two corrections we prove that the inverse problem is solvable and has a unique positive solution and that the corresponding eigenvector of t i a with the positive solution a forms a section of the eigenvector of t corresponding to its largest eigenvalue an algorithm is proposed for solving the inverse problem iteratively on which a system of nonlinear equations should be solved for each of it

two methods of directly constructing probabilistic public key encryption primitives based on third order lfsr sequences linear feedback shift registers are a commonly used method of producing pseudo random sequences with large period this paper investigated another applications of the third order linear feedback shift register sequence 3 lfsr it proposed two methods for directly constructing probabilistic public key encryption primitives the proposed probabilistic encryption schemes have properties of one wayness and semantic security

oscillation criteria for second order linear differential equations abstract some oscillation criteria are given for the second order linear differential equation r t u t c t u t 0 where r t c 1 t 0 0 and c t c t 0 r these results improve oscillation criteria of wintner hartman kamenev yan and philos by using a generalized riccati transformation t a t r t u t u t f t where f c 1 is a given function on t 0 and a t exp 2 t f s ds

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

on the construction of a jacobi matrix from its mixed type eigenpairs in this paper an inverse eigenvalue problem of constructing a jacobi matrix from its mixedtype eigenpairs is considered the necessary and sufficient conditions for the existence and uniqueness of the solutions are derived one numerical algorithm and two numerical examples are given

public key cryptosystems based on cubic finite field extensions the cryptographic properties of third order linear feedback shift register lfsr sequences over gf p are investigated a fast computational algorithm for evaluating the kth term of a characteristic sequence of order 3 is presented based on these properties a new public key distribution scheme and an rsa type encryption algorithm are proposed their security implementation information rate and computational cost for the new schemes are discussed

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

oscillatory behavior of solutions of certain second order nonlinear differential equations abstract in this paper some simple inequalities are used to offer sufficient conditions for the oscillation of all solutions of the differential equation formula where 0 p q with p q odd integers or p even and q odd integers several examples which dwell upon the importance of our results are also included

averaging technique and nonlinear second order elliptic oscillation abstract by using the refinement of the standard integral averaging technique we obtain new oscillation criteria for certain nonlinear second order damped elliptic differential equations we do not impose any additional conditions on the damping terms except for the continuity in particular when n 1 our results extend those of rogovchenko and tuncay yu v rogovchenko f tuncay oscillation criteria for second order nonlinear differential equations with damping nonlinear analysis 69 2008 208 221 for second order nonlinear differential equations with damping to damped elliptic differential equations when n 2 our results improve the oscillation criteria of xu jia ma z xu b jia d ma oscillation theorems for elliptic equations with damping appl math comput 156 2004 93 106 for second order elliptic equations with damping four examples are provided to illustrate the relevance of the main results