estimation for an m g queue with incomplete information summary we consider the estimation of the arrival rate and holding distribution of a discrete time queue using only information about the size of the queue arrivals are not matched to departures so that direct observations of the holding times are not available we study two estimators quickly computed moment estimators and maximum likelihood estimators based on an entropy motivated geometric approximation this approximation lends the problem a markovian structure that permits use of algorithms designed for estimating hidden markov models under the assumed model the resulting maximum likelihood estimators are efficient but the difficulty of their calculation increases exponentially with the number of parameters simulations show that the root mean squared error of maximum likeilihood estimators is about 25 smaller than that of moment estimators simulations also show how the absence of direct observations of holding times reduce the power of tests for detecting deviations from simple models

oscillation of first order neutral differential equations with distributed deviating arguments in this paper we shall consider first order neutral differential equations with distributed deviating arguments some new sufficient conditions are presented for the oscillation of all solutions

oscillatory and asymptotic behavior of certain functional differential equations some new criteria for the oscillatory and asymptotic behavior of odd order functional equations of the form x n t p t x n 1 t q t f x g t are established

oscillations of first order neutral delay differential equations abstract consider the neutral delay differential equation d dt y t py t qy t 0 t t 0 where q and are positive constants while p 1 0 for the case p 1 0 see ladas and sficas oscillations of neutral delay differential equations to appear the following results are then proved theorem 1 assume p and q 1 p 1 e then every solution of eq oscillates theorems 3 assume p 0 then every nonoscillatory solution y t of eq tends to zero as t theorem 4 assume p 0 then a necessary condition for all solutions of eq to oscillate is that theorem 5 assume p 0 and q 1 p 1 e then every solution of eq oscillates extensions of these results to equations with variable coefficients are also obtained

oscillation for first order nonlinear delay differential equations abstract almost sharp oscillation and nonoscillation criteria are obtained for the first order nonlinear delay differential equation x t p t j 1 m x t j j sign x t 1 0 t t 0 where j 1m j 1 some applications are given

non gaussian random walks the authors present an explicit expression for the probability distribution for the position of a continuous time random walker in an arbitrary number of dimensions when the interjump density has a long time tail in contrast to earlier results which require numerical inversion of a fourier integral they replace this numerical procedure by one that relies on the method of steepest descents their results are applied to diffusion on a comb and on a percolation cluster generated on a cayley tree at criticality and are confirmed numerically

oscillations in vector spaces a comparison result for monotone delay differential systems in this paper we will introduce and compare a number of definitions of oscillations for vectorial delay differential equations oscillatory properties of equations have received the most attention in the scalar case for this case there have been a great many contributions without any attempt to be complete we can quote notably 1 3 9 12 14 151 recently a book was devoted to this subject 16 let us also mention a contribution by g seifert 181 for the vector case several generalizations were undertaken notably by j m ferreira and i gyori s we can also mention a recent paper by j wiener and k l cooke 21 for delay equations with piecewise constant arguments however no systematic study of the very notion of oscillation seems to have been done in the vector case despite the fact that we can envision there a number of possible choices our purpose in this paper is to present some of them among which are a weak notion and a strong notion definition 6 a generate will be performed in a restricted class of equations those which generate an order preserving semi flow in such a class we will prove that both notions are equivalent to each other the significance of oscillations in monotone semiflows was recently underlined in 2 it has been shown that oscillatory properties characterize the asymptotic behavior we refer to 3 4 63 for other developments on this subject

asymptotic and oscillatory behavior of solutions of first order nonlinear neutral delay differential equations the authors consider the first order nonlinear neutral delay differential equation e y t p t y t q t y t 0 where p q and are continuous q t 0 0 0 and u u 0 if u 0 they give sufficient conditions for all nonoscillatory solutions of e to converge to zero as t two oscillation theorems for equation e are also proved

oscillations of first order linear retarded differential equations the oscillatory behavior of differential equations with deviating arguments has been studied by many authors in particular several authors have studied the oscillations caused by the deviating arguments the study of such oscillations is a relatively new field and is very interesting in applications for some contributions in this area see the papers by arino gyori and jawhari 11 bowcock and yu 2 gyiiri 4 5 j hunt and yorke 6 kulenovic ladas and meimaridou 7 ladas s ladas sficas and stavroulakis 9 lo ladas and stavroulakis 111 sugie 141 tramov 15 and yan 16 we also refer to the recent book by ladde lakshmikantham and zhang 123 the purpose of this paper is to investigate the oscillatory behavior of the solutions of first order linear retarded differential equations with variable coefftcients and nonconstants delays consider the first order retarded differential equation

some comparison and oscillation results for first order differential equations and inequalities with a deviating argument abstract in this paper we are dealing with first order differential equations and inequalities with a deviating argument and we give some new necessary sufficient and necessary and sufficient conditions concerning a the comparison of oscillatory and asymptotic behavior of solutions of 1 first order vector differential equations and corresponding to them operator and scalar differential equations with a deviating argument and 2 first order differential equations and corresponding to them inequalities with a deviating argument and b the existence of a certain type of nonoscillatory solutions of differential equations and inequalities with a deviating argument what is important in our opinion is the fact that some of the obtained results concern not only the cases of constant sign coefficients but also the cases where the coefficients of equations and inequalities under consideration are of non constant sign

oscillatory and asymptotic behavior of delay differential equations with a nonlinear damping term in this paper we study the oscillatory and asymptotic behavior of the solutions of delay differential equations of the form x n t f t x t x t 0 n even by comparing with certain differential equations of the same or lower order whose behavior is known the obtained criteria can be applied to the delay differential equation x n t q t x t x t sign x t 0 n even where and are positive constants

oscillation criteria for first order differential equations with deviating arguments abstract in this paper we study the oscillatory behavior of first order differential equations with deviating arguments of the general form x t 1 n p i x t i 0 where pi i 1 i n are constants necessary and sufficient conditions have been obtained to guarantee that eq is oscillatory and we also discuss the equivalence of two kinds of oscillation for equation is oscillatory if and only if the characteristic equation 1 n p i e i 0 has no real roots

oscillation of nonlinear delay difference equations in this paper some new oscillation criteria are obtained for all solutions of the nonlinear delay difference equation of the form xn 1 xn pnf xn k 0 n 0 1 2 our results also improve some well known results in the literature even when applying them to the linear delay difference equation

a necessary and sufficient condition for the oscillation of first order linear difference equations with several delay arguments abstract in this article we discuss the oscillation of all solutions of a first order linear delay difference equation with several delay arguments and obtain some new oscillation criteria under more relaxed conditions in particular we establish a necessary and sufficient condition only based on the coefficient functions and delay arguments when the coefficient functions are non negative examples and tables are given to illustrate our results

oscillations caused by several retarded and advanced arguments in this paper we study the oscillatory behavior of equations of the forms y t i 1npiy t i 0 and y t i 1npiy t i 0 where piand i i 1 2 n are positive constants we prove that each one of the following conditions 1 pi i1 e for some i i 1 2 n 2 i 1npi 1 e where min 1 2 n 3 i 1npi 1 n i 1n i 1 e or 4 1 n i 1n pi i 1 2 21 e implies that every solution of and oscillates a generalization in the case where the coefficientspi i 1 2 n are positive and continuous functions is also presented

explicit conditions for the oscillation of difference equations we obtain sufficient conditions for the oscillation of all solutions of the difference equation an 1 an i 1mpian ki 0 n 0 1 2 where the pi s are real numbers and the ki s are integers the conditions are given explicitly in terms of the pi s and the ki s

oscillation and nonoscillation for systems of two first order linear differential equations with delay functional differential equations with delay provide a mathematical model for a physical or biology system in which the rate of change of the system depends upon its past history in the literature there are several papers 14 concerning the study of oscillatory behavior of solutions of first order differential equations with time delay but there are few results s about the oscillation of linear system of first order equation with delay in this paper we study the oscillatory behavior of linear system with delay first in section 2 we consider the case of constant coefficients in details we show that the delay can cause or destroy the oscillations we present constructive procedure to generate or destroy oscillations of a system in section 3 we consider the case of variable coefficients and obtain some results analogous to the result in section 2

multiple integral average conditions for oscillation of delay differential equations we obtain some multiple integral average conditions for oscillation and nonoscillation of the first order nonautonomous delay equations our theorems improve several previous well known results

oscillatory properties of the first order nonlinear advanced and delayed differential inequalities on donne des conditions suffisantes pour que des inegalites differentielles retardees ou avancees aient des solutions oscillatoires

oscillation of certain functional differential equations sufficient conditions are presented for all bounded solutions of the linear system of delay differential equations 1 m 1 frac d m y i t dt m sum limits j 1 n q ij y j t h jj 0 text m geqslant 1 i 1 2 n to be oscillatory where qije hjj 0 i j 1 2 n also we study the oscillatory behavior of all bounded solutions of the linear system of neutral differential equations 1 m 1 frac d m dt m y i t cy i t g sum limits j 1 n q ij y j t h 0 where c g and h are real constants and i 1 2 n

when all solutions of x qi t x t ti t oscillate abstract in this paper the long term behavior of solutions to the equation in the title are examined where q i t and t i t are positive in particular it is shown that if lim inf t i 1 n t i t q i t 1 e all solutions oscillate about 0 infinitely often

necessary and sufficient condition for oscillation of a neutral differential system with several delays abstract in this paper we prove that a general neutral differential system with several delays has a nonoscillatory solution if and only if its characteristic equations has a real root

necessary and sufficient conditions for oscillations of neutral differential equations abstract consider the neutral delay differential equation x t px t qx t 0 t t 0 where q and are positive constants while p is a real parameter then a necessary and sufficient condition for all solutions of to oscillate is that the characteristic equation p e qe 0 of has no real roots

comparison theorems for first order linear delay equations abstract comparison theorems are studied for a delay differential equation of the form x t i 1n qi t x t ti t t 0 the comparisons involve another equation of the same form but with different coefficients and different delays we also define the notion of what we call strong oscillation which turns out to be more restricted than the usual notion of oscillation we consider one situation where the two definitions are equivalent

oscillation of first order delay equations we study the oscillation of first order delay equations using a method that parallels the use of riccati equations in the study of the oscillation of second order ordinary differential equations without delay we give an alternative proof of a comparison theorem first established by kwong and patula obtain some asymptotic behaviors of nonoscillatory solutions prove a new criterion that falls within a gap left open by established results and confirm a conjecture raised by hunt and yorke

oscillation of first order delay differential equations with distributed delay abstract in this paper we obtain some oscillation criteria for the first order delay differential equation with distributed delay x t 0 b t r t s x t s d s 0 by applying these results we also establish some integral conditions for oscillation of the higher order delay differential equations

oscillatory behavior in linear retarded functional differential equations abstract this paper is devoted to the investigation of when all solutions of autonomous and nonautonomous linear retarded functional differential equations are oscillatory