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

oscillation criteria of first order linear difference equations with delay argument abstract this paper presents new sufficient conditions for the oscillation of all proper solutions of the first order linear difference equation with delay argument u k p k u k 0 k n where u k u k 1 u k p n r n n and lim k k examples illustrating the results are given it is to be pointed out that this is the first paper dealing with the oscillatory behaviour of the equation in the case of a general delay argument k

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

upper bounds for the distances between consecutive zeros of solutions of first order delay differential equations abstract by introducing a new class of sequences involving iterates of the delay we are able to derive a sharper estimate on the ratio x t x t based on this we get some new upper bounds for the distance between consecutive zeros of solutions of the first order delay differential equation x t p t x t 0 in particular our results are not covered by previously known results some examples and a table are given to illustrate our results

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

oscillations of delay difference equations with oscillating coefficients abstract in this paper we establish sufficient conditions for the oscillation of all solutions of the delay difference equation y n 1 y n p n y n k 0 n 0 1 2 where pn is a sequence of real numbers and k is a positive integer an open problem in ladas in international conference on differential equations stability and control dekker new york 1990 is solved

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

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

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

an oscillation criterion for a delay difference equation by using the method of yu zhang and qian in j s yu b g zhang x z qian oscillation of delay difference equations with oscillating coefficients j math anal appl 177 1993 432 444 we prove another oscillation criterion for all solutions of the following linear delay difference equation x n 1 x n p nx n k 0 n 0 1 2 where p n is a sequence of real numbers and k is a positive integer

oscillation criteria for delay and difference equations with non monotone arguments consider the first order linear delay differential equation 1 x t p t x t t 0 t t 0 where p email protected c t 0 r t t t 0 and lim t email protected t and the discrete analogue difference equation 1 dx n p n x t n 0 n 0 1 2 where d denotes the forward difference operator dx n x n 1 x n p n is a sequence of nonnegative real numbers and t n is a sequence of integers such that t n 0 and lim n email protected n the state of the art on the oscillation of all solutions to these equations are established especially in the case of non monotone arguments examples illustrating the results are given

new oscillation criteria for delay difference equations abstract this paper is concerned with the oscillation of all solutions of the delay difference equations and where pn and pi n are sequences of nonnegative real numbers an k and ki are positive integers new oscillation criteria of the forms for equation and for equation are obtained where lim infn 1 k n 1i n k pi and c is the the best possible function of in some sense

oscillations of delay difference equations consider the delay difference equation n 1 n pn n k 0 n 0 1 2 where pn is a sequence of real numbers and k is a positive integer new oscillation criteria for this equation are established an extension of the results to difference equations with several delays is also presented

a further result on the oscillation of delay difference equations in this paper we are concerned with the delay difference equations of the form yn 1 yn pnyn k 0 n 0 1 2 where pn 0 and k is a positive integer we prove by using a new technique that n 0 i nn kpi ln i nn k pi 1 sign i nn k pi i n 1n k pi ln i n 1n k pi 1 sign i n 1n k pi guarantees that all solutions of equation oscillate which improves many previous well known results in particular our theorems also fit the case where n 1i n kpi kk 1 k 1 k 1 in addition we present a nonoscillation sufficient condition for equation

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 statistical test for nested radial dea models some problems in economics operations research and engineering may be approached by means of a pair of radial dea models that are nested i e that the set of constraints of one of them is included in that of the other in this paper we have focused on analyzing the marginal role of a given variable called candidate with respect to the efficiency measured by means of a dea model first we have defined a new efficiency contribution measure ecm which finally compares the efficiency scores of the two radial dea models differing in the candidate this can be either one input or one output then based on ecm we have also approached the problem from a statistical point of view to be precise we have developed a statistical test that allows us to evaluate the significance of the observed efficiency contribution of the candidate eventually solving this test may provide some useful insights in order to decide the incorporation or the deletion of a variable into from a given dea model on the basis of the information supplied by the data two procedures for progressive selection of variables were designed by sequentially applying the test a forward selection and a backward elimination these can be very helpful in the initial selection of variables when building a radial dea model

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

oscillation of delay difference equation we introduce some new techniques to analyze generalized characteristic equations to obtain several infinite sum sharp conditions for oscillation of the following delay difference equation xn 1 xn i 1mpi n xn ki 0 n 0 1 2 where pi n 0 and ki are positive integers

on the distribution of zeros of solutions of first order delay differential equations abstract this paper contains new estimates for the distance between adjacent zeros of solutions of the first order delay differential equation x t p t x t 0 where p is a nonnegative continuous function our results are new and improve some known criteria illustrative examples are given to show the strength of some obtained results over the known ones

on the distance between consecutive zeros of solutions of first order delay differential equations this paper is concerned with the distribution of zeros of solutions of first order linear delay differential equations with variable coefficients of the formx t p t x email protected 0 t t where t 0 p t c t 0 by introducing a class of polynomial functions we are able to derive new estimates for the lower and upper bounds of the distance between consecutive zeros of solutions of the above equations we illustrate the obtained results with several examples

regular articlethe distribution of zeros of solutions of differential equations with a variable delay in this paper the distribution of zeros of solutions of the first order differential equation with a variable delayx t ptx t 0is studied the estimate for the distance between adjacent zeros of the oscillatory solution of the above equation is obtained

oscillation of delay difference equations with several delays abstract in this paper we obtain some new oscillation criteria for the difference equation with several delays x n 1 x n i 1 m p i n x n k i 0 n 0 1 2 which improve the existing results in the literature the mistakes in comput math appl 44 2002 817 821 are pointed out

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

estimating the circle closest to a set of points by maximum likelihood using the bhhh algorithm abstract the purpose of this paper is to exploit the idea that in linear models the least squares estimators and the maximum likelihood estimators based on the normality assumption are often identical in particular we wish to add the normality assumption to the problem of finding the best fitting circle the addition of the normality assumption will allow the use of the bhhh algorithm to estimate the model by maximum likelihood although the bhhh algorithm is not especially fast its virtue is that it only requires the first derivatives of the loglikelihood function and is therefore easier to program than the newton raphson algorithm as we will show the likelihood framework also allows for easy testing of several important hypotheses and construction of an r 2 measure from regression analysis

gbsss the generalized big square small square method for planar single facility location abstract big square small square is a geometrical branch and bound algorithm devised by p hansen et al or 33 1251 1265 for the solution of constrained planar minisum single facility location problems with l p norms and continuous non decreasing costfunctions the method basically works by splitting the studied planar region into squares and either rejecting or further processing these squares by the evaluation of a lower bound we present a modified version of this algorithm aimed at correcting a small failure to converge accelerating the calculations minimising the information to be stored and most importantly determining a region of near optimality furthermore the method is applicable to any planar single facility problem with distances measured by mixed norms and as an objective any continuous function of the distances this includes nearly all the models which have been proposed in the literature

new results for oscillation of delay difference equations in this paper we consider the delay difference equation xn 1 xn pnxn k 0 n 0 1 2 where pn is a sequence of nonnegative real numbers and k is a positive integer some new results for the oscillation of this equation are obtained our theorems improve all known results in the literature

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

on oscillation of differential and difference equations with non monotone delays abstract for the delay differential equation x t p t x h t 0 p t 0 h t t t 0 lim t h t we demonstrate that the inequality limsup t h t t p u d u 1 is not sufficient for oscillation moreover for any a 0 the relation limsup t h t t p u d u a generally does not imply oscillation a similar result is obtained for difference equations in terms of the maximal argument new sufficient oscillation conditions are presented for differential and difference equations

the minimax center estimation problem for automated roundness inspection abstract significant advances in computer technology sensing devices pattern recognition and image processing techniques have made the on line inspection of all production parts a feasible option in modern manufacturing systems this study is concerned with the development of efficient algorithms to determine the out of roundness error for automated inspection of circular production parts the out of roundness error is defined as the maximum deviation of a given sey of sample points taken from the boundary of the part from the so called minimax circle

maximum likelihood consistency and data envelopment analysis a statistical foundation this paper provides a formal statistical basis for the efficiency evaluation techniques of data envelopment analysis dea dea estimators of the best practice monotone increasing and concave production function are shown to be also maximum likelihood estimators if the deviation of actual output from the efficient output is regarded as a stochastic variable with a monotone decreasing probability density function while the best practice frontier estimator is biased below the theoretical frontier for a finite sample size the bias approaches zero for large samples the dea estimators exhibit the desirable asymptotic property of consistency and the asymptotic distribution of the dea estimators of inefficiency deviations is identical to the true distribution of these deviations this result is then employed to suggest possible statistical tests of hypotheses based on asymptotic distributions

the distribution of zeros of solutions of first order delay differential equations abstract we give two estimates of the distance between adjacent zeros of the solutions of the first order delay differential equation x t p t x t 0

oscillations of difference equations with several delays abstract consider the first order delay difference equation where lim infn pi n pi 0 ki 0 i 1 2 sufficient conditions for the oscillation of all solutions of the above equation are established in the case when the corresponding limiting equation admits nonoscillatory solutions oscillation criteria for the nonlinear difference equation are also derived as applications

a multivariate statistical approach to reducing the number of variables in data envelopment analysis abstract the usefulness of data envelopment analysis dea depends on its ability to calculate the relative efficiency of decision making units dmus using multiple inputs and outputs unfortunately the greater the number of input and output variables the less discerning the analysis in practice the input and output variables are usually highly correlated with one another often reflecting no more than the relative size of each dmu to counteract the limited distinction provided by a dea with many variables analysts for many years have taken the approach of retaining only some of the variables originally planned for the analysis omitting on an ad hoc basis variables that are highly correlated with those retained in this paper we describe a systematic statistical method for deciding which of the original correlated variables can be omitted with least loss of information and which should be retained results on a number of published datasets reveal that even omitting variables that are highly correlated and thereby contain little additional information on performance can have a major influence on the computed efficiency measures

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 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

sufficient conditions for the oscillation of linear delay difference equations with oscillating coefficients abstract in this paper sufficient conditions for the oscillation of all solutions of the delay difference equation xn 1 xn pnxn k 0 n 0 1 2 are established where the coefficient pn itself may be allowed to be oscillatory we also give an example to demonstrate the advantage of our results

stepwise regression data envelopment analysis for variable reduction in this paper we develop stepwise regression data envelopment model to select important variables we formulate null hypothesis to understand the importance of each variable and use kruskal wallis test for this purpose if the kruskal wallis test does not reject the null hypothesis then we can conclude that all the variables are of equal importance as their presence and on the other hand absence of other variable does not create huge fluctuations in efficiency scores in fact give a complete ranking relative to base model if the kruskal wallis test does reject the null hypothesis this will imply there is significant fluctuation in the efficiency score relative to base model and therefore we have to further check the pair of variables that causes the fluctuation in order to determine its importance using conover inman test the results of the proposed models are compared with the results of previously published models of the same dataset the proposed models helps understand the extent of misclassification decision making units as efficient inefficient when variables are retained or discarded alongside provides useful managerial prescription to make improvement strategies

the distribution of zeros of solutions of neutral differential equations in this paper the distribution of zeros of solutions of the first order neutral differential equation with two variable delays x t p t x g t q t x h t 0is studied the estimate for the distance between adjacent zeros of oscillatory solutions of the above equation is obtained

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

out of roundness problem revisited the properties and computation of the minimum radial separation mrs standard for out of roundness are discussed another standard out of roundness measurement called the minimum area difference mad center is introduced although the two centers have different characteristics the approach to finding both centers shares many commonalities an o n log n k time algorithm which is used to compute the mrs center is presented it also computes the mad center of a simple polygon g where n is the number of vertices of g and k is the number of intersection points of the medial axis and the farthest neighbor voronoi diagram of g the relationship between mrs and mad is discussed

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