rectifiable and unrectifiable oscillations for a class of second order linear differential equations of euler type the main purpose of the paper is to pay attention to a new kind of oscillations so called rectifiable and unrectifiable oscillations which occur in a class of linear second order differential equations including the famous linear euler differential equation it will be shown that this kind of oscillations only depends on a positive real parameter which appears in a singular term of the main equation as well as in a suitable boundary layer condition

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

tripled fuzzy metric spaces and fixed point theorem abstract one of the most important topics of research in fuzzy sets is to get an appropriate notion of fuzzy metric space fms in the paper we propose a new fms tripled fuzzy metric space tfms which is a new generalization of george and veeramani s fms then we present some related examples topological properties convergence of sequences cauchy sequence cs and completeness of the tfms moreover we introduce two kinds of notions of generalized fuzzy contractive f c mappings and derive a fixed point theorem fpt on the mappings in the space

a bernstein von mises theorem in the nonparametric right censoring model in the recent bayesian nonparametric literature many examples have been reported in which bayesian estimators and posterior distributions do not achieve the optimal convergence rate indicating that the bernstein von mises theorem does not hold in this article we give a positive result in this direction by showing that the bernstein von mises theorem holds in survival models for a large class of prior processes neutral to the right we also show that for an arbitrarily given convergence rate n with 0 1 2 a prior process neutral to the right can be chosen so that its posterior distribution achieves the convergence rate n

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

a functional approach to the stationary waiting time and idle period distributions of the gi g 1 queue the gi g 1 queueing model is regarded as a functional which maps the service and interarrival time distributions onto output quantities of interest such as the stationary waiting time distribution for the case where the input distributions have densities techniques from infinite dimensional analysis are used to obtain derivatives and taylor series expansions for the functionals these yield approximations to the output distributions which can be viewed as nonparametric alternatives to parametric approximations such as those provided by infinitesimal perturbation analysis or the phase method

some asymptotic theory for the bootstrap efron s bootstrap method of distribution approximation is shown to be asymptotically valid in a large number of situations including t statistics the empirical and quantile processes and von mises functionals some counter examples are also given to show that the approximation does not always succeed

a donsker theorem for levy measures abstract given n equidistant realisations of a levy process l t t 0 a natural estimator n n for the distribution function n of the levy measure is constructed under a polynomial decay restriction on the characteristic function a donsker type theorem is proved that is a functional central limit theorem for the process n n n n in the space of bounded functions away from zero the limit distribution is a generalised brownian bridge process with bounded and continuous sample paths whose covariance structure depends on the fourier integral operator f 1 1 the class of levy processes covered includes several relevant examples such as compound poisson gamma and self decomposable processes main ideas in the proof include establishing pseudo locality of the fourier integral operator and recent techniques from smoothed empirical processes

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

decompounding an estimation problem for poisson random sums given a sample from a compound poisson distribution we consider estimation of the corresponding rate parameter and base distribution this has applications in insurance mathematics and queueing theory we propose a plug in type estimator that is based on a suitable inversion of the compounding operation asymptotic results for this estimator are obtained via a local analysis of the decompounding functional

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

on harmonic renewal measures let be a probability and nu h sum limits n 1 infty frac 1 n mu n the corresponding harmonic renewal measure complementing earlier results where is concentrated on a halfline we investigate the behaviour ofvh x x 1 and the harmonic renewal functiong x vh x asx ifm1 x dx 0 we also consider the casem1 0

fuzzy differential game of guarding a movable territory in most earlier works of differential game problems which are based solely on crisp mathematics it is generally assumed that all information obtained by each player is perfect thus the games are treated with full information in many practical situations the information obtained by any player may contain some sort of uncertainties which are usually difficult to characterize either deterministically or stochastically we treat such uncertain information as fuzzy information and consider a differential game problem with fuzzy information as a fuzzy differential game problem in this paper we consider the fuzzy differential game of guarding a movable territory in a general problem of guarding a territory key concepts are the favorable region of the invader and the boundary curve for simplicity the movable territory is assumed to be a circle in this paper we will show that when the center of the territory is located outside the favorable region of the invader the value of the game exists otherwise the value does not exist a fuzzy control strategy is proposed and some computer simulations are provided in this paper

nonoscillation and oscillation of second order half linear differential equations abstract we study the oscillation problems for the second order half linear differential equation p t x q t x 0 where u u r 1 u with r 0 1 p and q are locally integrable on r p 0 q 0 a e on r and 0 p 1 r t d t we establish new criteria for this equation to be nonoscillatory and oscillatory respectively when p 1 our results are complete extensions of work by huang c huang oscillation and nonoscillation for second order linear differential equations j math anal appl 210 1997 712 723 and by wong j s w wong remarks on a paper of c huang j math anal appl 291 2004 180 188 on linear equations to the half linear case for all r 0 these results provide corrections to the wrongly established results in j jiang oscillation and nonoscillation for second order quasilinear differential equations math sci res hot line 4 6 2000 39 47 on nonoscillation when 0 r 1 and on oscillation when r 1 the approach in this paper can also be used to fully extend elbert s criteria on linear equations to half linear equations which will cover and improve a partial extension by yang x yang oscillation nonoscillation criteria for quasilinear differential equations j math anal appl 298 2004 363 373

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

fuzzy controller theory limit theorems for linear fuzzy control rules abstract for a general fuzzy controller employing linear fuzzy control rules it is shown that as the number of rules grow the defuzzified output becomes a linear function of the input in particular for a sufficiently large number of rules the defuzzified output is approximately the same as the pi pid controller

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

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

a note on recovering the distributions from exponential moments the problem of recovering a cumulative distribution function of a positive random variable via the scaled laplace transform inversion is studied the uniform upper bound of proposed approximation is derived the approximation of a compound poisson distribution as well as the estimation of a distribution function of the summands given the sample from a compound poisson distribution are investigated applying the simulation study the question of selecting the optimal scaling parameter of the proposed laplace transform inversion is considered the behavior of the approximants are demonstrated via plots and table

a reliable data based bandwidth selection method for kernel density estimation we present a new method for data based selection of the bandwidth in kernel density estimation which has excellent properties it improves on a recent procedure of park and marron which itself is a good method in various ways first the new method has superior theoretical performance second it also has a computational advantage third the new method has reliably good performance for smooth densities in simulations performance that is second to none in the existing literature these methods are based on choosing the bandwidth to approximately minimize good quality estimates of the mean integrated squared error the key to the success of the current procedure is the reintroduction of a non stochastic term which was previously omitted together with use of the bandwidth to reduce bias in estimation without inflating variance

nonparametric estimation of the stationary waiting time distribution function for the gi g 1 queue the gi g 1 queueing model is regarded as a functional that maps the service and interarrival time distribution functions onto the stationary waiting time distribution function by considering the output of the functional when it is applied to nonparametric estimators of the input distribution functions we obtain a nonparametric estimator of the stationary waiting time distribution function using appropriate continuity and differentiability properties of the functional we show that statistical properties of the input estimators carry over to corresponding properties for the stationary waiting time distribution function estimator

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

efficient nonparametric inference for discretely observed compound poisson processes a compound poisson process whose parameters are all unknown is observed at finitely many equispaced times nonparametric estimators of the jump and levy distributions are proposed and functional central limit theorems using the uniform norm are proved for both under mild conditions the limiting gaussian processes are identified and efficiency of the estimators is established kernel estimators for the mass function the intensity and the drift are also proposed their asymptotic properties including efficiency are analysed and joint asymptotic normality is shown inference tools such as confidence regions and tests are briefly discussed

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case

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

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

nonparametric estimation of the probability of a long delay in the m g 1 queue abstract an m g 1 queue is approached by stationary poisson traffic with known arrival rate observations of service times are all that is known about the service distribution nonparametric estimates of the probability of a long customer delay are given the estimates include the solution of an equation involving the empirical transform of the service times asymptotic properties of the estimates are derived simulation studies of the small sample behavior of the estimates are reported the jackknife is used to provide error assessment of the estimates and to construct confidence intervals in the simulation studies of small sample behavior keywords asymptotic normality

synthesis of positive real multivariable feedback systems this is a tutorial paper describing the application of infinity norm optimal control theory to the synthesis of sector bounded and positive real multivariable feedback systems the paper gives a concise treatment of the practical aspects of the theory describing how it has been implemented via state space oriented computer algorithms included is a concise summary of the state space approach to infinity norm control developed by doyle and by safonov and verma based on the hankel model reduction theory and incorporating the multivariable hankel results of glover

a strategy for a payoff switching differential game based on fuzzy reasoning in this paper a new concept of a payoff switching differential game is introduced in this new game any one player at any time may have several choices of payoffs for the future moreover the payoff switching process including the time of payoff switching and the outcome payoff of any one player is unknown to the other indeed the overall payoff which is a sequence of several payoffs is unknown until the game ends an algorithm for determining a reasoning strategy based on fuzzy reasoning is proposed in this algorithm the fuzzy theory is used to estimate the behavior of one player during a past time interval by deriving two fuzzy matrices gsm game similarity matrix and vgsm variation of gsm the behavior of the player can be quantified two weighting vectors are selected to weight the relative importance of the player s behavior at each past time instant finally a simple fuzzy inference rule is adopted to generate a linear reasoning strategy the advantage of this algorithm is that it provides a flexible way for differential game specialists to convert their knowledge into a reasonable strategy a practical example of guarding three territories is given to illustrate our main ideas

a dynamic games approach to controller design disturbance rejection in discrete time it is shown that the discrete time disturbance rejection problem formulated in finite and infinite horizons and under perfect state measurements can be solved by making direct use of some results on linear quadratic zero sum dynamic games for the finite horizon problem an optimal minimax controller exists and can be expressed in terms of a generalized time varying discrete time riccati equation the existence of an optimum also holds in the infinite horizon case under an appropriate observability condition with the optimal control given in terms of a generalized algebraic riccati equation also being stabilizing in both cases the corresponding worst case disturbances turn out to be correlated random sequences with discrete distributions which means that the problem viewed as a dynamic game between the controller and the disturbance does not admit a pure strategy saddle point results for the delayed state measurement and the nonzero initial state cases are presented

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

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

nonparametric inference about service time distribution from indirect measurements in studies of properties of queues for example in relation to internet traffic a subject that is of particular interest is the shape of service time distribution for example we might wish to know whether the service time density is unimodal suggesting that service time distribution is possibly homogeneous or whether it is multimodal indicating that there are two or more distinct customer populations however even in relatively controlled experiments we may not have access to explicit service time data our only information might be the durations of service time clusters i e of busy periods we wish to deconvolve these concatenations and to construct empirical approximations to the distribution and particularly the density function of service time explicit solutions of these problems will be suggested in particular a kernel based deconvolution estimator of service time density will be introduced admitting conventional approaches to the choice of bandwidth

oscillation and nonoscillation for second order linear impulsive differential equations abstract we study the oscillation and nonoscillation for the second order linear impulsive differential equation u p t u where p t is an impulsive function defined by p t n 1 a n t t n and we establish a necessary and sufficient condition for oscillation or nonoscillation of the equation u p t u we give some sufficient conditions for the oscillation and nonoscillation in two particular cases

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

the length of the shorth soit n 0 1 la longueur de l fraction la plus courte de l echantillon ordonne x 1 n x 2 n x n n on utilise le concept de derivees compactes des fonctionnelles statistiques pour etudier le comportement asymptotique de n lorsque n

decompounding on compact lie groups noncommutative harmonic analysis is used to solve a nonparametric estimation problem stated in terms of compound poisson processes on compact lie groups this problem of decompounding is a generalization of a similar classical problem the proposed solution is based on a characteristic function method the treated problem is important to recent models of the physical inverse problem of multiple scattering

large sample bayesian analysis for rm geo g 1 discrete time queueing models statistical inference for the probability generating function p g f of the equilibrium waiting time distribution is considered the consistency of the posterior distribution for such a p g f as well as the weak convergence to a gaussian process of a suitable rescaling are proved as by products results on statistical inference for queueing characteristics are also ob tained finally the problem of estimating the probability of a long delay is considered 1 introduction and preliminaries discrete time queueing models have recently received considerable attention mainly because of their appli cations to telecommunication systems based on asynchronous transfer mode atm which is the standard transport vehicle of the broadband integrated let t be the r v number of time slots between i 1 th and ith batches i ith interarrival time and let s be the r v ith service time i e the size of i the ith batch the hypotheses on r v s t s and s s are ii

a game theoretic approach to h control for time varying systems a representation formula for all controllers that satisfy an mathcal l infty type constraint is derived for time varying systems it is now known that a formula based on two indefinite algebraic riccati equations may be found for time invariant systems over an infinite time support see j c doyle et al ieee trans automat control ac 34 1989 pp 831 847 k glover and j c doyle systems control lett 11 1988 pp 167 172 k glover et al siam j control optim 29 1991 pp 283 324 m green et al siam j control optim 28 1990 pp 1350 1371 d j n limebeer et al in proc ieee conf on decision and control austin tx 1988 g tadmor math control systems signal processing 3 1990 pp 301 324 in the time varying case two indefinite riccati differential equations are required a solution to the design problem exists if these equations have a solution on the optimization interval the derivation of the representation formula illustrated in this paper mak

oscillation stability and boundedness of second order differential systems with random impulses the model of second order linear differential systems with random impulses is brought forward in this paper then necessary and sufficient conditions for oscillation in mean p moment stability and p moment boundedness are obtained by several theorems that compare solutions of this system with the corresponding nonimpulsive differential system at last an example is presented to show the application of obtained results

distribution functions of means of a dirichlet process let be a random probability measure chosen by a dirichlet process on r b with parameter and such that x dx turns out to be a finite random variable the main concern of this paper is the statement of a suitable expression for the distribution function of that random variable such an expression is deduced through an extension of a procedure based on the use of generalized stieltjes transforms

nonparametric estimation in renewal theory i the empirical renewal function we introduce a nonparametric estimator for the renewal function and discuss its properties including consistency asymptotic normality and asymptotic validity of bootstrap confidence regions the underlying theme is that stochastic models can be regarded as functionals or nonlinear operators this view leads to nonparametric estimators in a natural way and statistical properties of the estimators can be related to the local behaviour of the functionals

remarks on a paper of c huang we prove oscillation and nonoscillation theorems for the second order linear differential equation e y q t y 0 where q t 0 and locally integrable on t these results are extensions of earlier results of huang j math anal appl 210 1997 712 723 furthermore we show that the oscillation criterion established for eq e can be extended to the delayed differential equation y q t y t 0 where t t and limt t

oscillation and non oscillation for second order linear difference equations abstract we prove new oscillation and non oscillation theorems for the second order linear difference equation 2xn 1 pnxn 0 where p n n 1 is a real sequence with pn 0 these results are extensions of earlier results of zhang and zhou comput math appl 39 2000 1 7

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

nonparametric estimation of the heterogeneity of a random medium using compound poisson process modeling of wave multiple scattering in this paper we present a nonparametric method to estimate the heterogeneity of a random medium from the angular distribution of intensity of waves transmitted through a slab of random material our approach is based on the modeling of forward multiple scattering using compound poisson processes on compact lie groups the estimation technique is validated through numerical simulations based on radiative transfer theory

inference for the limiting cluster size distribution of extreme values any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound poisson under appropriate long range dependence conditions typically exceedances appear in clusters the underlying poisson points represent the cluster positions and the multiplicities correspond to the cluster sizes in the present paper we introduce estimators of the limiting cluster size probabilities which are constructed through a recursive algorithm we derive estimators of the extremal index which plays a key role in determining the intensity of cluster positions we study the asymptotic properties of the estimators and investigate their finite sample behavior on simulated data

an analysis of bayesian inference for nonparametric regression abstract the observation model y sub i beta i n epsilon sub i 1 or n is considered where the epsilon s are i i d mean zero and variance sigma sq and beta is an unknown smooth function a gaussian prior distribution is specified by assuming beta is the solution of a high order stochastic differential equation the estimation error delta beta beta average is analyzed where beta average is the posterior expectation of beta asymptotic posterior and sampling distributional approximations are given for abs val del square when abs val square is one of a family of norms natural to the problem it is shown that the frequentist coverage probability of a variety of 1 alpha posterior probability regions tends to be larger than 1 alpha but will be infinitely often less than any epsilon 0 as n approaches infinity with prior probability 1 a related continuous time signal estimation problem is also studied keywords bayesian inference nonparametric regression confidence regions signal extraction smoothing splices

infinitely many nonoscillatory solutions for second order nonlinear neutral delay differential equations abstract in this paper we consider the second order nonlinear neutral delay differential equation a t x t b t x t h t x h 1 t x h 2 t x h k t f t x f 1 t x f 2 t x f k t g t t t 0 where 0 a b g c t 0 r with a t 0 for t t 0 h c 1 t 0 r k r f c t 0 r k r h l c 1 t 0 r and f l c t 0 r with lim t h l t lim t f l t l 1 k under suitable conditions by making use of the banach fixed point theorem we show the existence of infinitely many nonoscillatory solutions which are uncountable for the above equation suggest several mann type iterative approximation sequences with errors for these nonoscillatory solutions and establish some error estimates between the approximate solutions and the nonoscillatory solutions five nontrivial examples are given to illustrate the advantages of our results

oscillation nonoscillation criteria for linear second order differential equations new oscillation and nonoscillation criteria are given by generalizing a method of chunchao huang published recently in this journal

supremum metric on the space of fuzzy sets and common fixed point theorems for fuzzy mappings this paper generalizes a classical result about the space of bounded closed sets with the hausdorff metric and establishes the completeness of cb x with respect to the completeness of the metric space x where cb x is the class of fuzzy sets with nonempty bounded closed a cut sets equipped with the supremum metric d which takes the supremum on the hausdorff distances between the corresponding a cut sets in addition some common fixed point theorems for fuzzy mappings are proved and two examples are given to illustrate the validity of the main results in fixed point theory

nonparametric renewal function estimation abstract the renewal function is a basic tool used in many probabilistic models and sequential analysis based on a random sample of size n a nonparametric estimator of the renewal function is introduced asymptotic properties of the estimator such as the almost sure consistency and local asymptotic normality are developed a discussion of an application of the estimator is also provided keywords u statistics reverse martingales warranty analysis

integral averaging technique for the interval oscillation criteria of certain second order nonlinear differential equations abstract we present new interval oscillation criteria related to integral averaging technique for certain classes of second order nonlinear differential equations which 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 they generalize and improve some known results examples are also given to illustrate the importance of our results

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 and nonoscillation for second order linear difference equations new oscillation and nonoscillation theorems are obtained for the second order linear difference equation 2xn 1 pnxn 0 where if pn n 1 is a real sequence with pn 0

on the central controller characterizations via differential games and leqg control problems abstract we provide a game theoretic interpretation to the central controller which plays a central role in characterizing all controllers achieving disturbance attenuation in the sense of the h norm in the imperfect observation case we also establish a direct relation between the central controller and the stationary leqg controller for continuous time systems

a first approach to fuzzy differential game problem guarding a territory abstract in this paper the fuzzy differential game problem is proposed and the problem of guarding a territory is considered we reformulate this differential game problem by considering that the locations of the territory and or of one s opponent are imprecisely known to the players thus treating them as fuzzy information a fuzzy control strategy is proposed for this fuzzy differential game problem it will be seen that in the limiting case the result of the fuzzy differential game problem approaches that of the unfuzzified case some computer simulation results are provided in this paper