existence of sign changing solutions for a nonlinear elliptic problem on rn with a hardy term abstract let n 3 1 p n 2 n 2 and 0 n 2 2 4 we study the existence of multiple sign changing solutions of u h 1 r n u u u x 2 u p 1 u in r n which are not radially symmetric

multiple positive solutions for a quasilinear elliptic equation involving singular potential and critical sobolev exponent in this paper we are concerned with a class of quasilinear elliptic equation in which the potential is singular at the origin and the nonlinearity is p sublinear near the origin by the ekeland variational principle and mountain pass theorem we prove that there exist at least two positive solutions under suitable assumptions on the potential and the nonlinearity

state estimation for discrete time markov jump linear systems with time correlated measurement noise abstract in this paper the state estimation problem for discrete time markov jump linear systems affected by time correlated measurement noise is considered where the time correlated measurement noise is described by a linear system model with white noise as a result two algorithms are proposed to estimate the state of the system under consideration based on a measurement sequence the first algorithm is optimal in the sense of minimum mean square error which is obtained based on the measurement differencing method bayes rule and some results derived in this paper the second algorithm is a suboptimal algorithm obtained by using a lot of gaussian hypotheses the proposed suboptimal algorithm is finite dimensionally computable and does not increase computational and storage load with time computer simulations are carried out to evaluate the performance of the proposed suboptimal algorithm

optimal recursive estimation for networked stochastic uncertain systems with fading measurements and time correlated channel noises abstract this paper is concerned with the optimal linear estimation problem for discrete time stochastic system with time correlated channel noises correlated multiplicative noises and fading measurements the time correlated channel noises are described by a seemingly arma autoregressive moving average model by an equivalent transformation the original system is transformed into the same dimension system with finite step correlated virtual noises and multiple measurement delays the statistical properties of correlation functions among noise state and measurement are analyzed further the optimal linear state estimators including filter predictor and smoother are derived by using an innovation analysis approach a simulation example shows the effectiveness of the proposed algorithms

on an elliptic problem with critical exponent and hardy potential in this paper we study the following elliptic problem with critical exponent and a hardy potential u x 2u u u 2 2u u h01 where is a smooth open bounded domain in rn n 3 which contains the origin and 2 is the critical sobolev exponent we show that if n 5 and 0 n 22 2 n 2n 2 this problem has a ground state solution for each fixed 0 moreover we give energy estimates from below and bounds on the number of nodal domains for these ground state solutions if n 7 and 0 n 22 2 4 this problem has infinitely many sign changing solutions for each fixed 0

on the quasilinear elliptic problems with critical sobolev hardy exponents and hardy terms abstract let r n be a smooth bounded domain such that 0 n 3 in this paper we study the critical quasilinear elliptic problems p u u p 2 u x p u p t 2 x t u u q 2 x s u u w 0 1 p with dirichlet boundary condition where p u div u p 2 u 1 p n 0 n p p p 0 0 s t p p q p s p n s n p p t p n t n p p s and p t are the critical sobolev hardy exponents via variational methods we deal with the conditions that ensure the existence of positive solutions for the equation the results depend crucially on the parameters p q s and

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

multiple model estimation with variable structure existing multiple model mm estimation algorithms have a fixed structure i e they use a fixed set of models an important fact that has been overlooked for a long time is how the performance of these algorithms depends on the set of models used limitations of the fixed structure algorithms are addressed first in particular it is shown theoretically that the use of too many models is performance wise as bad as that of too few models apart from the increase in computation this paper then presents theoretical results pertaining to the two ways of overcoming these limitations select construct a better set of models and or use a variable set of models this is in contrast to the existing efforts of developing better implementable fixed structure estimators both the optimal mm estimator and practical suboptimal algorithms with variable structure are presented a graph theoretic formulation of multiple model estimation is also given which leads to a systematic treatment of model set adaptation and opens up new avenues for the study and design of the mm estimation algorithms the new approach is illustrated in an example of a nonstationary noise identification problem

solutions of the quasilinear elliptic problem with a critical sobolev hardy exponent and a hardy type term abstract in the present paper the quasilinear elliptic problem with a critical sobolev hardy exponent and a hardy type term is considered by means of a variational method the existence of nontrivial solutions to the problem is obtained

solutions of a quasilinear elliptic problem involving a critical sobolev exponent and multiple hardy type terms in the present paper a quasilinear elliptic problem with a critical sobolev exponent and multiple hardy type terms is considered by means of a variational method the existence of positive solutions of the problem is obtained

iterative algorithms for state estimation of jump markov linear systems jump markov linear systems jmlss are linear systems whose parameters evolve with time according to a finite state markov chain given a set of observations our aim is to estimate the states of the finite state markov chain and the continuous in space states of the linear system in this paper we present original deterministic and stochastic iterative algorithms for optimal state estimation of jmlss the first stochastic algorithm yields minimum mean square error mmse estimates of the finite state space markov chain and of the continuous state of the jmls a deterministic and a stochastic algorithm are given to obtain the marginal maximum a posteriori mmap sequence estimate of the finite state markov chain finally a deterministic and a stochastic algorithm are derived to obtain the mmap sequence estimate of the continuous state of the jmls computer simulations are carried out to evaluate the performance of the proposed algorithms the problem of deconvolution of bernoulli gaussian bg processes and the problem of tracking a maneuvering target are addressed

on the elliptic problems involving multi singular inverse square potentials and multi critical sobolev hardy exponents abstract let r n n 3 be a smooth bounded domain such that the different points a i i 1 2 k k 2 0 i n 2 2 2 0 s i 2 p i 2 n s i n 2 are the critical sobolev hardy exponents we deal with the conditions that ensure the existence of positive solutions for the multi singular and multi critical elliptic problem u i 1 k i x a i 2 u i 1 k u p i 1 x a i s i with the dirichlet boundary condition involving the hardy inequality and the sobolev hardy inequality the results depend crucially on the parameters s i and i i 1 2 k

convergence of optimal linear estimator with multiplicative and time correlated additive measurement noises in this paper the problem of convergence for the optimal linear estimator of discrete time linear systems with multiplicative and time correlated additive measurement noises is studied by defining a new random vector that consists of the innovation error and part of the noise in the new measurement obtained from the measurement differencing method we obtain convergence conditions of the optimal linear estimator by equivalently studying the convergence of the expectation of a random matrix where the random matrix is the product of the new vector and its transpose it is also shown that the state error covariance matrix of the optimal linear estimator converges to a unique fixed point under appropriate conditions and moreover this fixed point can be obtained by solving a set of matrix equations

nodal and positive solutions for singular semilinear elliptic equations with critical exponents in symmetric domains abstract in this paper we consider the semilinear elliptic problem u u x 2 u k x u 2 2 u in u 0 on where is a smooth bounded domain in r n n 4 0 n 2 2 4 2 2 n n 2 is the critical sobolev exponent k x is a continuous function when and k x are invariant under a group of orthogonal transformations we prove the existence of nodal and positive solutions for 0 1 where 1 is the first dirichlet eigenvalue of x 2 on

on a neumann problem with critical exponents and hardy potentials abstract in this paper we consider the neumann problem of the potential elliptic system with hardy terms and critical exponents on a bounded domain using the critical point theory we first find infinitely many solutions for the corresponding perturbed subcritical problem analyzing concentration points in the bubbles carefully which appear in the approximate solutions we establish the concentration estimates and then obtain infinitely many solutions with positive energy by passing to a limit

quasilinear elliptic problems involving multiple critical hardy sobolev exponents in this paper we study a kind of quasilinear elliptic problem which involves multiple critical hardy sobolev exponents and hardy terms by employing the variational methods and analytical techniques the existence of sign changing solutions to the problem is obtained

particle filters for state estimation of jump markov linear systems jump markov linear systems jmls are linear systems whose parameters evolve with time according to a finite state markov chain in this paper our aim is to recursively compute optimal state estimates for this class of systems we present efficient simulation based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed lag smoothing problem our algorithms combine sequential importance sampling a selection scheme and markov chain monte carlo methods they use several variance reduction methods to make the most of the statistical structure of jmls computer simulations are carried out to evaluate the performance of the proposed algorithms the problems of on line deconvolution of impulsive processes and of tracking a maneuvering target are considered it is shown that our algorithms outperform the current methods

existence results for singular critical elliptic problems in rn abstract in the paper we consider the following semilinear elliptic problems with critical sobolev hardy exponents p s u x 2 u v x u k x u 2 s 2 x s u in r n lim x u x 0 where n 3 0 n 2 2 2 0 0 s 2 2 s 2 n s n 2 under suitable conditions we prove that p s has at least one nontrivial solution by means of linking theorem also via the pseudo index theory we consider the multiplicity of nontrivial solutions for p s

solutions to critical elliptic equations with multi singular inverse square potentials abstract let be an open bounded domain in r n n 3 with smooth boundary we are concerned with the multi singular critical elliptic problem u i 1 k i u x a i 2 q x u 2 2 u u h 0 1 where i r 2 2 n n 2 a i 1 i k and q x is a positive bounded function on using moser iteration we prove the asymptotic behavior of solutions for at points a i 1 i k by exploiting the effect of the coefficient of the critical nonlinearity we by means of a variational method establish the existence of positive and sign changing solutions for problem

state estimation for discrete time markov jump linear systems with time correlated and mode dependent measurement noise abstract the state estimation problem for discrete time markov jump linear systems corrupted by time correlated and mode dependent measurement noise is considered where the time correlated and mode dependent measurement noise is described via a discrete time stochastic system with markov parameter and kronecker delta function by defining the measurement noise in this manner both time correlation and periodic step change caused by the change of system environment or structure can be embodied in the measurement noise a novel distributed measurement differencing method is applied to the problem of state estimation under consideration so that two algorithms are obtained using some results presented in this paper the first algorithm is optimal in the sense of minimum mean square error which can exactly compute the minimum mean square error estimate of system state the second algorithm is suboptimal and the suboptimality of the algorithm is caused by using some gaussian hypotheses the two proposed algorithms are recursive and the proposed suboptimal algorithm has a time independent complexity the performance of the proposed suboptimal algorithm is illustrated using computer simulations

existence of positive solutions for the p laplacian with p gradient term abstract in this paper we study the existence of positive solutions for the p laplacian involving a p gradient term due to the non variational structure and the fact that the nonlinearity may be critical or supercritical the variational method is no longer valid taking advantage of global c 1 estimates and the liouville type theorems we employ the blow up argument to obtain the a priori estimates on solutions and finally obtain the existence result based on the krasnoselskii fixed point theorem

brief paper detection and estimation for abruptly changing systems the problem of state estimation and system structure detection for discrete stochastic dynamical systems with parameters which may switch among a finite set of values is considered the switchings are modelled by a markov chain with known transition probabilities a brief survey and a unified treatment of the existing suboptimal algorithms are provided the optimal algorithms require exponentially increasing memory and computations with time simulation results comparing the various suboptimal algorithms are presented

ground states of nonlinear schrodinger equations with sum of periodic and inverse square potentials abstract we study the existence of solutions of the following nonlinear schrodinger equation u v x x 2 u f x u for x r n 0 where v r n r and f r n r r are periodic in x r n we assume that 0 does not lie in the spectrum of v and n 2 2 4 n 3 the superlinear and subcritical term f satisfies a weak monotonicity condition for sufficiently small 0 we find a ground state solution as a minimizer of the energy functional on a natural constraint if 0 and 0 lies below the spectrum of v then ground state solutions do not exist

on the elliptic problems with critical weighted sobolev hardy exponents abstract let r n be a smooth bounded domain such that 0 n 3 in this paper we deal with the conditions that ensure the existence of nontrivial solutions for the elliptic equation div x 2 a u u x 2 1 a u p 2 x b p u u with dirichlet boundary condition which involving the caffarelli kohn nirenberg inequalities the results depend crucially on the parameters a b and

brief paper risk sensitive filtering for jump markov linear systems in this paper a risk sensitive multiple model filtering algorithm is derived using the reference probability methods first the approximation of the interacting multiple model imm algorithm is identified in the reference probability domain then the same type of approximation is used to derive the finite dimensional risk sensitive filtering algorithm the derived algorithm reduces to the imm filter when the risk sensitive parameter goes to zero and reduces to the risk sensitive filter for linear gauss markov systems when the number of models is unity the algorithm performs better in a simulated uncertain parameter scenario than the imm filter

a new multiple model filter with switch time conditions the interacting multiple model filter has long been the method of choice for performing target tracking using multiple motion models the filter finds a suboptimal solution to a problem which has the implicit assumption that immediate model shifts have the highest probability when the sampling rate of the underlying continuous process is high compared to the target dynamics this is not a reasonable assumption instead changes in dynamics persist for some time in this paper we propose an alternative switching model which forces the dynamic models to persist for at least a model specific time the model is semi markov in nature with a sojourn time probability mass function which is zero for a model specific number of time steps and then follows a geometrical distribution through this assumption a less complex problem in terms of model hypotheses arises and to that problem we derive a state estimation algorithm that is close to optimal when the model assumptions are valid three other semi markov based multiple model filters are discussed and compared to in a qualitative sense we also derive a new aircraft motion model for start and termination of turns finally the proposed filter is evaluated on a benchmark scenario for tracking and the results show a performance increase compared to the interacting multiple model imm filter for the trajectories considered

elliptic problems with critical exponents and hardy potentials this paper is devoted to the existence of positive solutions of a dirichlet problem with critical exponent and a singular potential under various assumption on the domain omega which include some kinds of unbounded domains we prove the existence of ground states and of symmetric solutions c 2002 elsevier science usa all rights reserved

a switched imm extended viterbi estimator based algorithm for maneuvering target tracking this paper presents a new algorithm for tracking a maneuvering target modeled as a class of markov jump linear systems the proposed algorithm consists of two interacting multiple model extended viterbi imm ev algorithms coupled with proposed detection schemes for maneuver occurrences and terminations as well as for switching initializations combined performance strengths of the two imm ev algorithms are utilized via switching from one imm ev algorithm to the other appropriate design parameter values are derived for the detection schemes of maneuver occurrences and terminations the results demonstrate that the proposed algorithm can be a viable alternative to several well known tracking methods

on the singular critical quasilinear problems in rn abstract in this paper we study the following quasilinear problem p u u p 2 u u p 2 u x p u p 2 u f u u w r 1 p r n where n 3 2 p n p n p n p and f u satisfies some kinds of assumptions by employing the variational methods and analytic techniques we obtain the existence of a nontrivial solution to the problem under some assumptions for the parameters p n and at last we manage to prove that the problem has at least a pair of nodal solutions u k for each k n and both u k possess exactly k nodes

on schrodinger operators with multipolar inverse square potentials abstract positivity essential self adjointness and spectral properties of a class of schrodinger operators with multipolar inverse square potentials are discussed in particular a necessary and sufficient condition on the masses of singularities for the existence of at least a configuration of poles ensuring the positivity of the associated quadratic form is established

linear minimum mean square error estimation for discrete time markovian jump linear systems the linear minimum mean square error estimator lmmse for discrete time linear systems subject to abrupt changes in the parameters modeled by a markov chain spl theta k spl epsiv 1 n is considered the filter equations are derived from geometric arguments in a recursive form resulting in an on line algorithm suitable for computer implementation the author s approach is based on estimating x k 1 sub spl theta k i instead of estimating directly x k the uncertainty introduced by the markovian jumps increases the dimension of the filter to n n 1 where n is the dimension of the state variable an example where the dimension of the filter can be reduced to n is presented as well as a numerical comparison with the imm filter

on a class of quasilinear elliptic systems with critical growth abstract a class of quasilinear elliptic systems with critical growth are considered in a bounded domain employing critical point theory and concentration estimates we establish the existence of infinitely many solutions in higher values of dimension n p 2 p 1 p n

a generalized linear models approach to spatial scan statistics for covariate adjustment the spatial scan statistic proposed by kulldorff commun statist theory methods 1997 26 1481 1496 is one of the most widely used methods for detecting spatial clusters and evaluating their statistical significance however it is not fully capable of adjusting for all types of confounding covariates in this article a generalized linear models glm approach to construct spatial scan statistics which is readily in a form for covariate adjustment is proposed using glm spatial scan statistics for different probability models can be formulated in a single framework the test statistic is based on the log likelihood ratio test statistic and evaluated using monte carlo hypothesis testing the proposed method is illustrated using texas female breast cancer data concerning late versus early stage cancer cases with covariates of race ethnicity and age group

multiple positive solutions for a quasilinear elliptic problem involving critical sobolev hardy exponents and concave convex nonlinearities abstract let r n n 3 be a bounded smooth domain containing the origin in this paper by using variational methods the multiplicity of positive solutions is obtained for a quasilinear elliptic problem p u u p 2 u x p u p t 2 x t u u q 2 x s u u w 0 1 p with dirichlet boundary condition where p u div u p 2 u 1 p n 0 n p p p 0 0 s t p 1 q p and p t p n t n p is the critical sobolev hardy exponent

optimal filtering for discrete time linear systems with time correlated multiplicative measurement noises in this note the filtering problem for discrete time linear systems with time correlated multiplicative measurement noises is considered where the vector consisting of all the multiplicative measurement noises can be described by a linear system model with white noise by introducing several new recursive terms a novel algorithm for optimal filtering of the system under consideration is proposed in the sense of linear minimum mean square error the proposed algorithm is recursive and has time independent complexity computer simulations are provided to illustrate the performance of the proposed algorithm

an improvement to the interacting multiple model imm algorithm computing the optimal conditional mean state estimate for a jump markov linear system requires exponential complexity and hence practical filtering algorithms are necessarily suboptimal in the target tracking literature suboptimal multiple model filtering algorithms such as the interacting multiple model imm method and generalized pseudo bayesian gpb schemes are widely used for state estimation of such systems we derive a reweighted interacting multiple model algorithm although the imm algorithm is an approximation of the conditional mean state estimator our algorithm is a recursive implementation of a maximum a posteriori map state sequence estimator this map estimator is an instance of a previous version of the em algorithm known as the alternating expectation conditional maximization aecm algorithm computer simulations indicate that the proposed reweighted imm algorithm is a competitive alternative to the popular imm algorithm and gpb methods

nonlinear gaussian smoothers with colored measurement noise this paper is concerned with the gaussian approximation ga smoothing estimation for the nonlinear system with the colored measurement noise modeled as an autoregressive process firstly based on measurement differencing scheme designing the ga smoothers with the colored measurement noise is transformed into deriving the ga ones with delayed state secondly the novel fixed interval fixed point and fixed lag ga smoothers are proposed via the recursive operation of analytical computation and nonlinear integrals as the general and unifying frameworks they are applicable for both linear and nonlinear systems by setting the noise correlation parameter as zero they can automatically reduce to the standard ga smoothers with uncorrelated white noises many implementations of the ga frameworks can be developed through utilizing different numerical technologies for computing such nonlinear integrals e g the cubature rule based cubature kalman smoothers ckss with the colored measurement noise finally the superior performance in estimation accuracy and computation efficiency of the proposed smoothing methods is demonstrated with a multi sensor target tracking example

brief paper a maximum likelihood kalman filter for switching discrete time linear systems state estimation is addressed for a class of discrete time systems that may switch among different modes taken from a finite set the system and measurement equations of each mode are assumed to be linear and perfectly known but the current mode of the system is unknown moreover additive independent normally distributed noises are assumed to affect the dynamics and the measurements first relying on a well established notion of mode observability developed ad hoc for switching systems an approach to system mode estimation based on a maximum likelihood criterion is proposed second such a mode estimator is embedded in a kalman filtering framework to estimate the continuous state under the unique assumption of mode observability stability properties in terms of boundedness of the mean square estimation error are proved for the resulting filter simulation results showing the effectiveness of the proposed filter are reported

inference for likelihood ratio ordering in the two sample problem abstract we obtain the maximum likelihood estimators of two multinomial probability vectors under the constraint that they are likelihood ratio ordered we extend this estimation approach to the case of two univariate distributions and show strong consistency of the estimators we also derive and study the asymptotic distribution of the likelihood ratio statistic for testing the equality of two discrete probability distributions against the alternative that one distribution is greater than the other in the likelihood ratio ordering sense finally we examine a data set pertaining to average daily insulin dose from the boston collaborative drug surveillance program and compare our testing procedure to testing procedures for other stochastic orderings

elliptic systems involving the critical exponents and potentials abstract in this paper we investigate a singular elliptic system which involves the critical sobolev exponent and multiple hardy type terms by employing variational methods the existence of its positive solutions is established by the moser iteration method some asymptotic properties of its nontrivial solutions at the singular points are verified

exact hybrid filters in discrete time using the reference probability method and the change of measure in discrete time the state estimator problem is considered for linear systems observed in gaussian noise when the coefficients are functions of a noisily observed finite state markov chain the methods are new and finite dimensional filters are obtained however the number of statistics increases in time a numerical comparison of this filter with the interactive multiple model algorithm introduced by blom and bar shalom 1988 is given

a note on the sign changing solutions to elliptic problems with critical sobolev and hardy terms let rn be a bounded domain such that 0 n 7 2 2nn 2 we obtain existence of sign changing solutions for the dirichlet problem u u x 2 u 2 2u u on u 0 on for suitable positive numbers and

positive ground state solutions for an elliptic system with hardy sobolev critical exponent growth this paper considers a nonlinear elliptic system with hardy sobolev critical exponent growth several existence results on the positive ground state solutions to the system are established under proper conditions this paper considers a nonlinear elliptic system with hardy sobolev critical exponent growth several existence results on the positive ground state solutions to the system are established under proper conditions

optimal estimation for discrete time linear systems in the presence of multiplicative and time correlated additive measurement noises in this paper the state estimation problem for discrete time linear systems influenced by multiplicative and time correlated additive measurement noises is considered where the multiplicative noises are zero mean white noise sequences and the time correlated additive noise is described by a linear system model with white noise an optimal linear estimator for the system under consideration is proposed which does not require computing the inverse of state transition matrix the proposed estimator has a recursive structure and has time independent computation and storage load computer simulations are carried out to demonstrate the performance of the proposed estimator the simulation results show the superiority of the proposed estimator

solutions for a singular critical growth problem with a weight in this paper we consider some semilinear elliptic equations with hardy potential by using linking theorem in p rabinowitz minimax methods in critical points theory with applications to differential equations cbms reg conf ser math vol 65 amer math soc providence ri 1986 and analyzing the effect of nonlinearities we establish the existence of nontrivial solutions

existence of multiple positive solutions to singular elliptic systems involving critical exponents abstract this paper is devoted to investigate multiple positive solutions to a singular elliptic system where the nonlinearity involves a combination of concave and convex terms by exploiting the effect of the coefficient of the critical nonlinearity and a variational method we establish the main result which is based on the argument of the compactness

on the quasilinear elliptic problem with a critical hardy sobolev exponent and a hardy term abstract in the present paper a quasilinear elliptic problem with a critical sobolev exponent and a hardy type term is considered by means of a variational method the existence of nontrivial solutions for the problem is obtained the result depends crucially on the parameters p t s and

on the elliptic problems involving multi singular inverse square potentials and critical sobolev exponent abstract assume that r n n 3 is a smooth bounded domain a i are different points in i 1 2 k k 2 0 2 q 2 n 2 2 2 2 2 n n 2 is the critical sobolev exponent we study the existence and asymptotic behavior of solutions to the multi singular critical elliptic problem u u i 1 k x a i 2 u 2 2 u u q 2 u with dirichlet boundary condition the results depend crucially on the parameters and q

existence of sign changing solutions for semilinear singular elliptic equations with critical sobolev exponents we consider the semilinear elliptic problem u u x 2 f x u k x u 2 2u in u 0 on where 0 is a smooth bounded domain in rn n 4 0 0 is continuous we prove the existence of sign changing solutions under different assumptions when is a usual domain and a symmetric domain respectively

p value approximations for spatial scan statistics using extreme value distributions spatial scan statistics are widely applied to identify spatial clusters in geographic disease surveillance to evaluate the statistical significance of detected clusters monte carlo hypothesis testing is often used because the null distribution of spatial scan statistics is not known a drawback of the method is that we have to increase the number of replications to obtain accurate p values gumbel based p value approximations for spatial scan statistics have recently been proposed and evaluated for poisson and bernoulli models in this study we examine the use of a generalized extreme value distribution to approximate the null distribution of spatial scan statistics as well as the gumbel distribution through simulation p value approximations using extreme value distributions for spatial scan statistics are assessed for multinomial and ordinal models in addition to poisson and bernoulli models copyright 2014 john wiley sons ltd

solutions for semilinear elliptic equations with critical exponents and hardy potential abstract in this paper we answer affirmatively an open problem cf theorem 4 in ferrero and gazzola j differential equations 177 2001 494 let 0 be an open bounded domain r n n 5 and assume that 0 n 2 2 2 n 2 n 2 then for all 0 there exists a nontrivial solution with critical level in the range 0 1 n s n 2 for the problem u u x 2 u u 2 2 u in u 0 on

spatial cluster detection for ordinal outcome data in geographical disease surveillance spatial scan statistics are used to identify areas having unusually high or low rates of disease outcomes and to determine the statistical significance of detected clusters the spatial scan statistic for ordinal data such as stage of cancer has been developed to detect clusters representing areas with high rates of more serious stages compared with the surrounding areas such areas were expressed using likelihood ratio ordering which is a rather strict order restriction and hence the method might fail to detect spatial clusters with high rates of worse categories e g later stage in this paper we relax the order restriction using stochastic ordering and examine differences between the two approaches in detecting spatial clusters through simulation studies we show that the stochastic ordering based approach has higher power sensitivity and positive predictive value under several scenarios we illustrate the two methods with the use of a real data example copyright 2012 john wiley sons ltd

optimal state estimation for discrete time markovian jump linear systems in the presence of delayed output observations we investigate the design of optimal state estimators for markovian jump linear systems we consider that the output observations and the mode observations are affected by delays not necessarily identical our objective is to design optimal estimators for the current state given current and past observations we provide a solution to this paradigm by giving an optimal recursive estimator for the state in the minimum mean square sense and a finitely parameterized recursive scheme for computing the probability mass function of the current mode conditioned on the observed output we also show that if the output delay is less then the one in observing the mode then the optimal state estimation becomes nonlinear in the output observations

state estimation for asynchronous sensor systems with markov jumps and multiplicative noises abstract this paper is concerned with the asynchronous state estimation problem for sensor systems subject to markov jump parameters and multiplicative noises the asynchronous sensors considered can have arbitrary sampling rates and arbitrary initial sampling instants by transforming the asynchronous measurements within each fusion interval into an augmented measurement the equivalent measurement equation and state equation at the fusion time instant are constructed based on the two equations a linear minimum mean squared error lmmse estimator is developed using the orthogonality projection principle due to the existence of the common process noise in the equivalent process and measurement noises the equivalent process and measurement noises are cross correlated and the equivalent measurement noises are autocorrelated these correlations are taken into account in the estimator design the stationary case is also studied and the sufficient condition is established for the stability of the proposed estimator a target tracking example is provided to illustrate the effectiveness of the proposed estimator

existence and multiplicity of positive solutions for some hardy sobolev critical elliptic equation with boundary singularities abstract in this paper by ekeland s variational principle and strong maximum principle we consider the existence and multiplicity of positive solutions for some semilinear elliptic equation involving critical hardy sobolev exponents and hardy terms with boundary singularities

the existence of solutions for quasilinear elliptic problems with combined critical sobolev hardy terms abstract in this paper we investigate the quasilinear elliptic equations with dirichlet boundary conditions and combined critical sobolev hardy terms on bounded smooth domains r n n 3 and prove the existence and multiplicity of solutions by employing ekeland s variational principle

multiple positive solutions for semilinear elliptic equations with critical weighted hardy sobolev exponents abstract the existence and multiplicity of positive solutions are obtained for a class of semilinear elliptic equations with critical weighted hardy sobolev exponents and the concave convex nonlinearity by variational methods and some analysis techniques

multiple positive solutions for p laplace elliptic equations involving concave convex nonlinearities and a hardy type term abstract in this paper the following problem is considered p u u p 2 u x p f x u q 2 u g x u p 2 u x u 0 x where r n is a bounded domain such that 0 1 q p 0 f and g are nonnegative functions n p p p is the best hardy constant and p n p n p is the critical sobolev exponent by extracting the palais smale sequence in the nehari manifold the existence of multiple positive solutions to this equation is verified

quasilinear elliptic problems with critical exponents and hardy terms abstract let 0 be an open bounded domain r n n p 2 we are concerned with the multiplicity of positive solutions of p u u p 2 u x p u p 2 u q x u p 2 u u w 0 1 p where p u div u p 2 u 1 p n p np n p 0 n p p p 0 and q x is a nonnegative function on by investigating the effect of the coefficient of the critical nonlinearity we by means of variational method prove the existence of multiple positive solutions

multiplicity result for a class of elliptic equations with singular term abstract we consider the existence of nontrivial solutions of the equation u x 2 u u 2 2 u x 2 u f x u x 0 u h 0 1 where 0 is a smooth bounded domain in r n n 3 by variational methods and nehari set techniques we show that this problem under some additional hypotheses on 0 0 0 0 1 and f l has four nontrivial solutions in h 0 1 and that least one of them is sign changing

positive solutions to the weighted critical quasilinear problems in a bounded domain with smooth boundary we consider a kind of weighted quasilinear elliptic problem which satisfies dirichlet boundary condition and involves the hardy sobolev inequality by the analytic techniques we first get the properties of the extremal functions by which the best hardy sobolev constant is achieved then by the variational methods the existence of positive solutions to the problem is verified by careful estimates and computations

existence and multiplicity of solutions to a singular elliptic system with critical sobolev hardy exponents and concave convex nonlinearities abstract this paper is concerned with a singular elliptic system which involves the caffarelli kohn nirenberg inequality and critical sobolev hardy exponents the existence and multiplicity results of positive solutions are obtained by variational methods

expectation maximization algorithms for map estimation of jump markov linear systems in a jump markov linear system the state matrix observation matrix and the noise covariance matrices evolve according to the realization of a finite state markov chain given a realization of the observation process the aim is to estimate the state of the markov chain assuming known model parameters computing conditional mean estimates is infeasible as it involves a cost that grows exponentially with the number of observations we present three expectation maximization em algorithms for state estimation to compute maximum a posteriori map state sequence estimates which are also known as bayesian maximum likelihood state sequence estimates mlses the first em algorithm yields the map estimate for the entire sequence of the finite state markov chain the second em algorithm yields the map estimate of the continuous state of the jump linear system the third em algorithm computes the joint map estimate of the finite and continuous states the three em algorithms optimally combine a hidden markov model hmm estimator and a kalman smoother ks in three different ways to compute the desired map state sequence estimates unlike the conditional mean state estimates which require computational cost exponential in the data length the proposed iterative schemes are linear in the data length