asymptotic stability of impulsive stochastic partial differential equations with infinite delays in this paper we study the existence and asymptotic stability in pth moment of mild solutions to nonlinear impulsive stochastic partial differential equations with infinite delay by employing a fixed point approach sufficient conditions are derived for achieving the required result these conditions do not require the monotone decreasing behaviour of the delays

fixed points and stability of neutral stochastic delay differential equations in this paper we consider a linear scalar neutral stochastic differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by means of fixed point theory these conditions do not require the boundedness of delays nor do they ask for a fixed sign on the coefficient functions an asymptotic mean square stability theorem with a necessary and sufficient condition is proved some well known results are improved and generalized

controllability of impulsive neutral stochastic functional differential inclusions with infinite delay this paper deals with the controllability of a class of impulsive neutral stochastic functional differential inclusions with infinite delay in an abstract space sufficient conditions for the controllability are derived with the help of the fixed point theorem for discontinuous multi valued operators due to dhage an example is provided to illustrate the obtained theory

bayesian inference and life testing plan for the weibull distribution in presence of progressive censoring this article deals with the bayesian inference of unknown parameters of the progressively censored weibull distribution it is well known that for a weibull distribution while computing the bayes estimates the continuous conjugate joint prior distribution of the shape and scale parameters does not exist in this article it is assumed that the shape parameter has a log concave prior density function and for the given shape parameter the scale parameter has a conjugate prior distribution as expected when the shape parameter is unknown the closed form expressions of the bayes estimators cannot be obtained we use lindley s approximation to compute the bayes estimates and the gibbs sampling procedure to calculate the credible intervals for given priors we also provide a methodology to compare two different censoring schemes and thus find the optimal bayesian censoring scheme monte carlo simulations are performed to observe the behavior of the proposed methods and a data analysis is onducted for ill

exponential stability for stochastic neutral partial functional differential equations abstract in this paper we consider a class of stochastic neutral partial functional differential equations in a real separable hilbert space some conditions on the existence and uniqueness of a mild solution of this class of equations and also the exponential stability of the moments of a mild solution as well as its sample paths are obtained the known results in govindan t e govindan almost sure exponential stability for stochastic neutral partial functional differential equations stochastics 77 2005 139 154 liu and truman k liu a truman a note on almost sure exponential stability for stochastic partial functional differential equations statist probab lett 50 2000 273 278 and taniguchi t taniguchi almost sure exponential stability for stochastic partial functional differential equations stoch anal appl 16 1998 965 975 t taniguchi asymptotic stability theorems of semilinear stochastic evolution equations in hilbert spaces stochastics 53 1995 41 52 are generalized and improved

fast approximate k nn graph construction for high dimensional data via recursive lanczos bisection nearest neighbor graphs are widely used in data mining and machine learning a brute force method to compute the exact knn graph takes dn2 time for n data points in the d dimensional euclidean space we propose two divide and conquer methods for computing an approximate knn graph in dnt time for high dimensional data large d the exponent t 1 2 is an increasing function of an internal parameter which governs the size of the common region in the divide step experiments show that a high quality graph can usually be obtained with small overlaps that is for small values of t a few of the practical details of the algorithms are as follows first the divide step uses an inexpensive lanczos procedure to perform recursive spectral bisection after each conquer step an additional refinement step is performed to improve the accuracy of the graph finally a hash table is used to avoid repeating distance calculations during the divide and conquer process the combination of these techniques is shown to yield quite effective algorithms for building knn graphs

exponential stability for nonautonomous impulsive neutral partial stochastic evolution equations with delay abstractin this paper we give sufficient conditions for the exponential stability of pseudo almost periodic in distribution mild solutions for nonautonomous impulsive neutral partial stochastic ev

optimum accelerated life tests wth a nonconstant scale parameter previous work on planning accelerated life tests has assumed that the scale parameter for a location scale distribution of log lifetime remains constant over all stress levels this assumption is however inappropriate for many applications including accelerated tests for metal fatigue and certain electronic components this article extends the existing maximum likelihood theory for test planning to the nonconstant model and presents test plans for a large range of practical testing situations the test plans are optimum in that they minimize the asymptotic variance of the maximum likelihood estimator of a specified quantile at the design stress the development and discussion in the article as well as the theory given in the appendix applies to accelerated life test models in which the log time to failure can be modeled as a location scale distribution the test setup assumes simultaneous testing of units with time censoring we give particular numerical results for the weibull failure time distr

existence uniqueness and stability of mild solutions for second order neutral stochastic evolution equations with infinite delay and poisson jumps in this paper we study a class of second order neutral stochastic evolution equations with infinite delay and poisson jumps snseeips in which the initial value belongs to the abstract space b we establish the existence and uniqueness of mild solutions for snseeips under non lipschitz condition with lipschitz condition being considered as a special case by means of the successive approximation furthermore we give the continuous dependence of solutions on the initial data by means of a corollary of the bihari inequality an application to the stochastic nonlinear wave equation with infinite delay and poisson jumps is given to illustrate the theory

analysis of the symmetric lanczos algorithm with reorthogonalization methods we present an error analysis of the symmetric lanczos algorithm in finite precision arithmetic the loss of orthogonality among the computed lanczos vectors is explained with the help of a recurrence formula a backward error analysis shows that semiorthogonality among the lanczos vectors is enough to guarantee the accuracy of the computed quantities up to machine precision the results of this analysis are then extended to the more general case of the lanczos algorithm with a semiorthogonalization strategy based on the recurrence formula a new reorthogonalization method called partial reorthogonalization is introduced we show that both partial reorthogonalization and selective orthogonalization as introduced by parlett and scott 15 are semiorthogonalization strategies finally we discuss the application of our results to the solution of linear systems of equations and to the eigenvalue problem

estimation of exponential population with nonconstant parameters under constant stress model abstract accelerated life test alt was introduced which provides a feasible and efficient way by testing units at higher than use condition this paper considers inference of constant stress alt model for exponential population under a general assumption that both exponential scale and location parameters are nonconstant and follow log linear life stress model with stress level under progressive type ii censoring maximum likelihood and pivotal quantities based point estimates for unknown coefficient parameters are proposed confidence interval estimates are also constructed by using asymptotic theory and bootstrap techniques simulation study and an illustrative example are provided for illustrative purpose

the existence and exponential stability of semilinear functional differential equations with random impulses under non uniqueness a b s t r a c t in this paper the existence and exponential stability of mild solutions of semilinear differential equations with random impulses are studied under non uniqueness in a real separable hilbert space the results are obtained by using the leray schauder alternative fixed point theorem

pth moment asymptotic stability for neutral stochastic functional differential equations with levy processes in this paper we will consider a class of neutral stochastic functional differential equations with levy processes levy processes contain a number of very important processes as special cases such as brownian motion the poisson process stable and self decomposable processes and subordinators and so on but its sample paths are discontinuity which makes the analysis more difficult in this paper we try to get over this difficulty the contributions of this paper are as follows a we will use lyapunov functional method to study the pth moment asymptotic stability and almost sure asymptotic stability of neutral stochastic functional differential equations with levy processes b under the result of a we will investigate two types of continuity of the solution continuous in the pth moment and continuous in probability finally we provide an example to illustrate the usefulness of the obtained results

exponential stability in mean square of neutral stochastic differential functional equations abstract the aim of this paper is to investigate the exponential stability in mean square for a neutral stochastic differential functional equation of the form d x t g xt f t x t g t xt dt t xt dw t where xt x t s s 0 with 0 is the past history of the solution several interesting examples are a given for illustration

existence uniqueness and asymptotic behavior of mild solutions to stochastic functional differential equations in hilbert spaces abstract in this paper we shall consider the existence uniqueness and asymptotic behavior of mild solutions to stochastic partial functional differential equations with finite delay r 0 dx t ax t f t x t dt g t x t dw t where we assume that a is a closed densely defined linear operator and the generator of a certain analytic semigroup f c h g c l 0 2 k h are two locally lipschitz continuous functions where c c r 0 d a l 0 2 k h are two proper infinite dimensional spaces 0 w t is a given k valued wiener process and both h and k are separable hilbert spaces

the lanczos algorithm with partial reorthogonalization the lanczos algorithm is becoming accepted as a powerful tool for finding the cigenvalues and for solving linear systems of equations any practical implementation of the algorithm suffers however from roundoff errors which usually cause the lanczos vectors to lose their mutual orthogonality in order to maintain some level of orthogonality full reorthogonalization fro and selective orthogonalization so have been used in the past as a remedy here partial reorthogonalization pro is proposed as a new method for maintain ing semiorthogonality among the lanczos vectors pro is based on a simple recurrence which allows us to monitor the loss of orthogonality among the lanczos vectors directly wvithout computing the inner products based on the information from the recurrence reorthogonalizations occur only when necessary thus substantial savings are made as compared to fro in some numerical examples we apply the lanczos algorithm with pro to the solution of large symmetric systems of linear equations and show that it is a robust and efficient algorithm for maintaining semiorthogonality among the lanczos vectors the results obtained compare favorably with the conjugate gradient method

existence of solutions for nonlinear fractional stochastic differential equations abstract the fractional stochastic differential equations have wide applications in various fields of science and engineering this paper addresses the issue of existence of mild solutions for a class of fractional stochastic differential equations with impulses in hilbert spaces using fractional calculations fixed point technique stochastic analysis theory and methods adopted directly from deterministic fractional equations new set of sufficient conditions are formulated and proved for the existence of mild solutions for the fractional impulsive stochastic differential equation with infinite delay further we study the existence of solutions for fractional stochastic semilinear differential equations with nonlocal conditions examples are provided to illustrate the obtained theory

bilinear lanczos components for fast dimensionality reduction and feature extraction matrix based methods such as generalized low rank approximations of matrices glram have gained wide attention from researchers in pattern recognition and machine learning communities in this paper a novel concept of bilinear lanczos components blc is introduced to approximate the projection vectors obtained from eigen based methods without explicit computing eigenvectors of the matrix this new method sequentially reduces the reconstruction error for a frobenius norm based optimization criterion and the resulting approximation performance is thus improved during successive iterations in addition a theoretical clue for selecting suitable dimensionality parameters without losing classification information is presented in this paper the blc approach realizes dimensionality reduction and feature extraction by using a small number of lanczos components extensive experiments on face recognition and image classification are conducted to evaluate the efficiency and effectiveness of the proposed algorithm results show that the new approach is competitive with the state of the art methods while it has a much lower training cost

inference for accelerated competing failure models from weibull distribution under type i progressive hybrid censoring this paper considers constant stress accelerated competing failure models under type i progressive hybrid censoring with binomial random removals a weibull distributed life of test units is assumed for a specific cause and by the newton raphson iteration and asymptotic likelihood theory the maximum likelihood estimates mles and asymptotic confidence intervals of the unknown parameters are obtained based on the noninformative prior a gibbs sampling algorithm using adaptive rejection sampling is presented to obtain bayesian estimates and the monte carlo mc method is employed to construct the hpd credible intervals the simulation results are provided to show that bayesian estimates perform better than mles and the change of the removal probability has a significant effect on mles

a note on exponential stability for impulsive neutral stochastic partial functional differential equations in this note the problem on the exponential stability in mean square moment of mild solution to impulsive neutral stochastic partial functional differential equations is considered by employing the inequality technique some sufficient conditions are established for the concerned problem and some existing results are generalized and improved finally an illustrative example is given to demonstrate the effectiveness of the obtained result

low rank matrix approximation using the lanczos bidiagonalization process with applications low rank approximation of large and or sparse matrices is important in many applications and the singular value decomposition svd gives the best low rank approximations with respect to unitarily invariant norms in this paper we show that good low rank approximations can be directly obtained from the lanczos bidiagonalization process applied to the given matrix without computing any svd we also demonstrate that a so called one sided reorthogonalization process can be used to maintain an adequate level of orthogonality among the lanczos vectors and produce accurate low rank approximations this technique reduces the computational cost of the lanczos bidiagonalization process we illustrate the efficiency and applicability of our algorithm using numerical examples from several applications areas

existence of pseudo almost automorphic mild solutions to stochastic fractional differential equations abstract fractional stochastic differential equations have gained considerable importance due to their application in various fields of science and engineering this paper is concerned with the square mean pseudo almost automorphic solutions for a class of fractional stochastic differential equations in a hilbert space the main objective of this paper is to establish the existence and uniqueness of square mean pseudo almost automorphic mild solutions to a linear and semilinear case of these equations a new set of sufficient conditions is obtained to achieve the required result by using the stochastic analysis theory and fixed point strategy finally an example is provided to illustrate the obtained theory

some new theorems for cyclic contractions in gb metric spaces and some applications abstract in this paper some new theorems for various cyclic contractions are established in gb metric spaces to discuss the existence and uniqueness of the solutions for a class of the operator equations which generalize many known results in corresponding literatures on the other hand we introduce the notion of the cyclic contractive mappings in gb metric spaces and establish a new fixed point theorem which is applied to consider the existence of the solutions of the integral equations and ordinary differential equations moreover some examples are given to support our main results

estimation of constant stress accelerated life test for weibull distribution with nonconstant shape parameter abstract statistical inference is considered on constant stress accelerated life test when the failure data are progressively type ii censored under the assumption that the weibull shape parameter is nonconstant and both weibull parameters follow log linear life stress model with stress the unknown coefficient parameters are estimated by using methods of maximum likelihood and expectation maximization based estimations as well as approximation maximum likelihood estimation the confidence intervals of unknown parameters are also constructed based on asymptotic theory and bootstrap technique simulation study and a real data example are presented for illustrative purpose

matrix free krylov iteration for implicit convolution of numerically low rank data evaluating the response of a linear shift invariant system is a problem that occurs frequently in a wide variety of science and engineering problems calculating the system response via a convolution may be done efficiently with fourier transforms when one must compute the response of one system to m input signals or the response of m systems to one signal it may be the case that one may approximate all system responses without having to compute all m fourier transforms this can lead to substantial computational savings rather than process each point individually one may only process basis vectors that span the output data space however to get a low error approximation it is necessary that the output vectors have low numerical rank if they were assembled into a matrix we develop theory that shows how the singular value decay of a matrix a that is a product of a convolution operator and an arbitrary matrix a depends in a linear fashion on the singular value decays of and a we propose gap rank a measure of the relative numerical rank of a matrix we show that convolution cannot destroy the numerical low rank ness of a data with only modest assumptions we then develop a new method that exploits low rank problems with block golub kahan iteration in a krylov subspace to approximate the low rank problem our method can exploit parallelism in both the individual convolutions and the linear algebra operations in the block golub kahan algorithm we present numerical examples from signal and image processing that show the low error and scalability of our method

exponential stability for second order neutral stochastic differential equations with impulses in this paper we investigate the problem on the exponential stability of mild solution for the second order neutral stochastic partial differential equations with impulses by utilising the cosine function theory a set of novel sufficient conditions is derived by establishing an impulsive integral inequality as a final point an example is given to illustrate the effectiveness of the obtained theory

reliability estimation of multicomponent stress strength model based on copula function under progressively hybrid censoring abstract in reliability analysis of the stress strength models the stress and strength variables are typically assumed as independent however such an assumption may be unrealistic in some applications it is a meaningful issue to estimate the reliability of the stress strength model for dependent stress and strength variables in this paper we estimate the reliability of multicomponent stress strength model by assuming the dependent weibull stress variables and exponential strength variables based on gumbel copula under type i progressively hybrid censoring scheme the estimators of the unknown parameters and reliability are obtained by using the maximum likelihood estimation method also the asymptotic confidence intervals and bootstrap percentile confidence intervals of the unknown parameters and reliability of stress strength model are derived monte carlo simulations are used to evaluate the performance of the maximum likelihood estimators asymptotic confidence intervals and bootstrap percentile confidence intervals finally real data are analyzed to demonstrate the practicability of the stress strength model in this article

proper orthogonal decomposition and its applications part i theory abstract in view of the increasing popularity of the application of proper orthogonal decomposition pod methods in engineering fields and the loose description of connections among the pod methods the purpose of this paper is to give a summary of the pod methods and to show the connections among these methods firstly the derivation and the performance of the three pod methods karhunen loeve decomposition kld principal component analysis pca and singular value decomposition svd are summarized then the equivalence problem is discussed via a theoretical comparison among the three methods the equivalence of the matrices for processing the objective functions the optimal basis vectors the mean square errors and the asymptotic connections of the three methods are demonstrated and proved when the methods are used to handle the pod of discrete random vectors

a note on exponential stability for second order neutral stochastic partial differential equations with infinite delays in the presence of impulses in this work the problem on the exponential stability for second order neutral stochastic partial differential equations with infinite delays is considered in the presence of impulses under some conditions by employing the new integral inequality technique some algebraic criteria of stability are established for the concerned problem and some existing results are generalized and improved finally an illustrative example is given to demonstrate the effectiveness of the obtained results

theoretical comparison of bootstrap confidence intervals we develop a unified framework within which many commonly used bootstrap critical points and confidence intervals may be discussed and compared in all seven different bootstrap methods are examined each being usable in both parametric and nonparametric contexts emphasis is on the way in which the methods cope with first and second order departures from normality percentile t and accelerated bias correction emerge as the most promising of existing techniques certain other methods are shown to lead to serious errors in coverage and position of critical point an alternative approach based on shortest bootstrap confidence intervals is developed we also make several more technical contributions in particular we confirm efron s conjecture that accelerated bias correction is second order correct in a variety of multivariate circumstances and give a simple interpretation of the acceleration constant

existence and controllability results for second order impulsive stochastic evolution systems with state dependent delay in this paper we discuss a kind of impulsive second order stochastic evolution systems with state dependent delay in a real separable hilbert space the results concerning the existence and controllability of mild solutions have been addressed by means of the fixed point techniques some sufficient conditions are formulated as well as an application involving partial differential equation with impulses is presented

inference of accelerated dependent competing risks model for marshall olkin bivariate weibull distribution with nonconstant parameters abstract in this paper we discuss the statistical inference of constant stress accelerated dependent competing risks model under type ii hybrid censoring schemes the dependency structure is modeled by a marshall olkin bivariate weibull distribution both the shape and the scale parameters in the model are assumed to be dependent on the stress levels through a log linear relationship the maximum likelihood estimates mles of the model parameters are derived confidence intervals cis of the model parameters are constructed based on the asymptotic normality of mles and the bias corrected percentile bootstrap method bayes estimates with the squared error loss function and the highest posterior density hpd credible intervals cis are obtained by using an importance sampling method in addition the estimates for the accelerated coefficients and the reliability under normal use stress level at mission time are derived a monte carlo simulation study is used to evaluate the performance of the proposed statistical inference methods a real data example is used to illustrate the methodologies proposed in this paper and to compare the proposed model with the copula model

asymptotic stability of second order neutral stochastic differential equations in this paper we study the existence and asymptotic stability in pth moment of mild solutions to second order nonlinear neutral stochastic differential equations further this result is extended to establish stability criterion for stochastic equations with impulsive effects with the help of fixed point strategy stochastic analysis technique and semigroup theory a set of novel sufficient conditions are derived for achieving the required result finally an example is provided to illustrate the obtained result

on the exponential stability in mean square of neutral stochastic functional differential equations in 1 2 some efforts have been devoted to the investigation of exponential stability in mean square of neutral stochastic functional differential equations however the results derived there are either difficult to demonstrate in a straightforward way for practical situations or somewhat too restricted to be applied to general neutral stochastic functional differential equations for instance nonautonomous cases in this paper we shall establish some results which are more effective and relatively easy to verify to obtain the required stability