generalized symmetric duality for multiobjective variational problems with invexity abstract we formulate a pair of multiobjective nonlinear generalized symmetric dual variational problems involving vector valued functions which unify the wolfe and mond weir models for a special case our problems become the symmetric dual pair of d s kim and w j lee 1998 j math anal appl 218 34 48 under invexity assumptions we establish weak strong and converse duality theorems for our variational problems by using the concept of efficiency also we give the static case of our multiobjective generalized symmetric duality results several known results are obtained as special cases

direct learning of sparse changes in markov networks by density ratio estimation we propose a new method for detecting changes in markov network structure between two sets of samples instead of naively fitting two markov network models separately to the two data sets and figuring out their difference we directly learn the network structure change by estimating the ratio of markov network models this density ratio formulation naturally allows us to introduce sparsity in the network structure change which highly contributes to enhancing interpretability furthermore computation of the normalization term a critical bottleneck of the naive approach can be remarkably mitigated we also give the dual formulation of the optimization problem which further reduces the computation cost for large scale markov networks through experiments we demonstrate the usefulness of our method

a multivariate two sample test based on the number of nearest neighbor type coincidences for independent d variate random samples x 1 cdots x n 1 i i d f x y 1 cdots y n 2 i i d g x where the densities f and g are assumed to be continuous a e consider the number t of all k nearest neighbor comparisons in which observations and their neighbors belong to the same sample we show that if f g a e the limiting normal distribution of t as min n 1 n 2 rightarrow infty n 1 n 1 n 2 rightarrow tau 0 tau 1 does not depend on f an omnibus procedure for testing the hypothesis h 0 f g a e is obtained by rejecting h 0 for large values of t the result applies to a general distance generated by a norm on mathbb r d for determining nearest neighbors and it generalizes to the multisample situation

emden fowler equations involving critical exponents on considere le probleme y t k y 2 y 2k 3 0 t 0 pour t 2 0 0 soit t inf t 0 y 0 sur t alors t 0 0 on etudie comment la position t du premier zero de y t varie avec

symmetric duality with pseudo invexity in variational problems abstract weak and strong duality results are established under pseudo invexity hypotheses for symmetric dual variational problems self dual problems and static symmetric dual programs are included as special cases

symmetric duality for a class of multiobjective fractional programming problems this paper is concerned with symmetric duality for a class of nondifferentiable multiobjective fractional programming problems two weak duality theorems and two strong duality theorems are proved discussion on some special cases shows that results in this paper extend previous work in this area

elliptic equations with nearly critical growth n f 2 n 2 it has no solution for any star shaped domain 13 recently considerable interest has grown around problems like i in which the right hand side up is replaced by a perturbation f u of the pure power such as f u au up where 1 e iw and 0

generalized continuous nondifferentiable fractional programming problems with invexity abstract the concept of invexity has allowed the convexity requirements in a variety of mathematical programming problems to be weakened we extend a number of kuhn tucker type sufficient optimality criteria for a class of continuous nondifferentiable minmax fractional programming problems that involves several ratios in the objective with a nondifferentiable term in the numerators as an application of these optimality results various mond weir type duality results are proved under a variety of generalized invexity assumptions these results extend many well known duality results and also give a dynamic generalization of those of finite dimensional nonlinear programming problems recently explored

on efficiency and duality for multiobjective variational problems abstract the concept of efficiency pareto optimum is used to formulate duality for multiobjective variational problems wolfe and mond weir type duals are formulated under generalized f convexity assumptions on the functions involved weak and strong duality theorems are proved

extremal functions and best constants to an inequality involving hardy potential and critical sobolev exponent abstract in this paper we study the asymptotic behavior of radial extremal functions to an inequality involving hardy potential and critical sobolev exponent based on the asymptotic behavior at the origin and the infinity we shall deduce a strict inequality between two best constants finally as an application of this strict inequality we consider the existence of a nontrivial solution of a quasilinear brezis nirenberg type problem with hardy potential and critical sobolev exponent

uniqueness theorems for positive radial solutions of quasilinear elliptic equations in a ball we establish a new pohozaev type identity and use it to prove a theorem on the uniqueness of positive radial solutions to the quasilinear elliptic problem div u m 2emsp14 u f u 0 inb andu 0 on b wherebis a finite ball in rn n 3 and 1 0 and 1 p q n 2 n 2 has a unique positive solution whenn 6 this gives a complete answer to an open problem raised by brezis and nirenberg in 1983 in the casen 6 we shall also derive some partial results to the open problem in the casesn 3 4 5

symmetric duality for a class of nondifferentiable multi objective fractional variational problems abstract we introduce a symmetric dual pair for a class of nondifferentiable multi objective fractional variational problems weak strong converse and self duality relations are established under certain invexity assumptions the paper includes extensions of previous symmetric duality results for multi objective fractional variational problems obtained by kim lee and schaible d s kim w j lee s schaible symmetric duality for invex multiobjective fractional variational problems j math anal appl 289 2004 505 521 and symmetric duality results for the static case obtained by yang wang and deng x m yang s y wang x t deng symmetric duality for a class of multiobjective fractional programming problems j math anal appl 274 2002 279 295 to the dynamic case

statistical process control for shifts in mean or variance using a changepoint formulation statistical process control spc involves ongoing checks to ensure that neither the mean nor the variability of the process readings has changed conventionally this is done by pairs of charts shewhart x and s or r charts cumulative sum charts for mean and for variance or exponentially weighted moving average charts for mean and variance the traditional methods of calculating the statistical properties of control charts are based on the assumption that the in control true mean and variance were known exactly and use these assumed true values to set center lines control limits and decision intervals the reality however is that true parameter values are seldom if ever known exactly rather they are commonly estimated from a phase i sample the random errors in the estimates lead to uncertain run length distribution of the resulting charts an attractive alternative to the traditional charting methods is a single chart using the unknown parameter likelihood ratio test for a change in mean and o

on semilinear elliptic problems involving critical exponents abstract in this paper we study brezis nirenberg type results for radial solutions of a semilinear elliptic equation of the form u c x u b x u q 2 u a e x b r 0 r n r 0 u 0 on b r 0 where r q 2 and the weights b c are appropriate positive measurable radially symmetric functions

existence results for brezis nirenberg problems with hardy potential and singular coefficients abstract in this paper we consider the existence of non trivial solutions to semi linear brezis nirenberg type problems with hardy potential and singular coefficients first we shall study the corresponding eigenvalue problem and obtain some basic properties of eigenvalues and asymptotic estimates of the eigenfunctions and approximating eigenfunctions secondly we consider the extremal functions of the best embedding constant and get some crucial estimates for the cut off function of the extremal functions thirdly applying different variational theorems for distinct cases of those parameters appearing in the equation we obtain two existence results for non trivial solutions to semi linear brezis nirenberg type problems our existence results are divided into non resonant and resonant cases

symmetric duality for a class of nonlinear fractional programming problems abstract a pair of symmetric dual nonlinear fractional programming problems is presented and duality theorems are established under pseudoinvexity pseudoincavity and invexity incavity respectively type assumptions on the kernel function special cases are particularly discussed to show that this paper extends some work appeared in this area

symmetric duality for the multiobjective fractional variational problem with partial invexity a symmetric dual problem for a class of multiobjective fractional variational problems is first formulated under partial invexity assumptions on the functions involved dual theorems are proved through a parametric approach to related properly efficient solutions of the primal and dual problems finally self dual and related problems are considered

a pdf free change detection test based on density difference estimation the ability to detect online changes in stationarity or time variance in a data stream is a hot research topic with striking implications in this paper we propose a novel probability density function free change detection test which is based on the least squares density difference estimation method and operates online on multidimensional inputs the test does not require any assumption about the underlying data distribution and is able to operate immediately after having been configured by adopting a reservoir sampling mechanism thresholds requested to detect a change are automatically derived once a false positive rate is set by the application designer comprehensive experiments validate the effectiveness in detection of the proposed method both in terms of detection promptness and accuracy

nonexistence theorems for singular solutions of quasilinear partial differential equations on etudie les etats fondamentaux singuliers de l equation de poisson semilineaire u f u 0 et de son analogue quasi lineaire div a du du f u 0 ou est le laplacien a n dimensions et a p et f u sont des fonctions donnees

critical semilinear biharmonic equations in rn an existence theorem is obtained for a fourth order semilinear elliptic problem in r n involving the critical sobolev exponent n 4 n 4 n 4 a preliminary result is that the best constant in the sobolev embedding l 2n n 4 r n is attained by all translations and dilations of 1 x 2 4 n 2 the best constant is found to be

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

symmetric duality for multiobjective variational problems with invexity abstract we formulate a pair of multiobjective nonlinear symmetric dual variational problems for the single objective problems our problems become the symmetric dual pair of i smart and b mond j math anal appl 152 1990 536 545 under invexity assumptions we establish the weak strong converse and self duality theorems for our variational problems by using the concept of efficiency also we give the static case of our symmetric duality results

symmetric duality with invexity in variational problems abstract weak and strong duality results are established under invexity hypotheses for symmetric dual variational problems without positivity constraints self dual problems and static symmetric dual programs are included as special cases

multiplicity of positive solutions for p laplace equation with superlinear type nonlinearity abstract in this work we consider the problem p r p u u p u q u 0 in b r 0 u 0 on b r 0 where p 2 p np n p and b r 0 is the open ball of radius r centered about the origin in r n n 3 under the condition that p 1 q p 2 n p 1 we show that there exists r 0 such that p r admits atleast two solutions for all r r and no solution if r this extends the results of nonlinear anal tma 10 8 1986 755 to the case of p laplace equation

weakly efficient solutions and pseudoinvexity in multiobjective control problems abstract in this paper we introduce new pseudoinvexity conditions on functionals involved in a multiobjective control problem called w kt pseudoinvexity and w fj pseudoinvexity we prove that all kuhn tucker or fritz john points are weakly efficient solutions if and only if these conditions are fulfilled we relate weakly efficient solutions to optimal solutions of weighting control problems we generalize recently obtained optimality results of known mathematical programming problems and control problems we illustrate these results with an example

diagonals of green s functions and applications abstract we describe the diagonal of the green s function for some sturm liouville operators as it was introduced and studied in a number of papers already and we discuss a number of applications that depend on its properties semilinear elliptic pde s with rotationally invariant and possibly singular coefficients with power type nonlinearities provide a particularly well suited class of examples where the results of this article apply

existence and nonexistence of positive radial solutions for some semilinear elliptic problems in annular domains au f x u 0 in s u 0 on xj when n is some annulus and the above conditions in 4 29 are not necessarily satisfied in fact in our main result theorem 2 4 f is not necessarily c lim f t u u may not exist or may be u rn finite and f t u could be zero for u in some finite interval 0 p we also allow lim f t u u 0 corollary 2 6 and lim f t u u may not exist in example 2 3 below u o u 0 neither lim f u u nor lim f u u exists on the other hand we show that u 0 u m

a multivariate change point model for statistical process control multivariate statistical process control spc carries out ongoing checks to ensure that a process is in control these checks on the process are traditionally done by t2 multivariate cusum and multivariate exponentially weighted moving average control charts these traditional spc charts assume that the in control true parameters are known exactly and use these assumed true values to set the control limits the reality however is that true parameter values are seldom if ever known exactly rather they are commonly estimated from a phase i sample it is increasingly recognized that this phase i study needs to involve large samples if the parameter estimates are to provide run behavior matching that of the known parameter situation but apart from the general undesirability of large and thus expensive studies preliminary to actual charting some industrial settings have a paucity of relevant data for estimating the process parameters an attractive alternative to traditional charting methods when mon

multivariate two sample tests based on nearest neighbors abstract a new class of simple tests is proposed for the general multivariate two sample problem based on the possibly weighted proportion of all k nearest neighbor comparisons in which observations and their neighbors belong to the same sample large values of the test statistics give evidence against the hypothesis h of equality of the two underlying distributions asymptotic null distributions are explicitly determined and shown to involve certain nearest neighbor interaction probabilities simple infinite dimensional approximations are supplied the unweighted version yields a distribution free test that is consistent against all alternatives optimally weighted statistics are also obtained and asymptotic efficiencies are calculated each of the tests considered is easily adapted to a permutation procedure that conditions on the pooled sample power performance for finite sample sizes is assessed in simulations

symmetric duality for invex multiobjective fractional variational problems we introduce a symmetric dual for multiobjective fractional variational problems under certain invexity assumptions we establish weak strong and converse duality theorems as well as self duality relations the paper includes an extension of previous symmetric duality results for the static case obtained by weir to the dynamic case

green s function harmonic transplantation and best sobolev constant in spaces of constant curvature ass rrac t we extend the method of harmonic transplantation ft om euclidean domains to spaces of constant positive or negative curvature to this end the structure of the green s function of the corresponding laplacebeltrami operator is investigated by means of isoperimetric inequalities we derive complementary estimates for its distribution function we apply the method of harmonic transplantation to the question of whether the best sobolev constant for the critical exponent is attained i e whether there is an extremal function for the best sobolev constant in spaces of constant curvature a fairly complete answer is given based on a concentration compactness argument and a pohozaev identity the result depends on the curvature

generalized invexity and duality in multiple objective variational problems multiple objective programming problems with the concept of weak minima are extended to multiple objective variational problems a number of weak strong and converse duality theorems are given under a variety of generalized invexity conditions

duality for multiobjective fractional variational problems abstract a class of multiobjective fractional variational problems is considered and duals are formulated under concavity assumptions on the functions involved duality theorems are proved through a parametric approach to relate efficient solutions of the primal and dual problems we generalize those results for control problems also