total positivity in markov structures we discuss properties of distributions that are multivariate totally positive of order two mtp2 related to conditional independence in particular we show that any independence model generated by an mtp2 distribution is a compositional semi graphoid which is upward stable and singletontransitive in addition we prove that any mtp2 distribution satisfying an appropriate support condition is faithful to its concentration graph finally we analyze factorization properties of mtp2 distributions and discuss ways of constructing mtp2 distributions in particular we give conditions on the log linear parameters of a discrete distribution which ensure mtp2 and characterize conditional gaussian distributions which satisfy mtp2

a general central limit theorem for fkg systems a central limit theorem is given which is applicable to not necessarily monotonic functions of random variables satisfying the fkg inequalities one consequence is convergence of the block spin scaling limit for the magnetization and energy densities jointly to the infinite temperature fixed point of independent gaussian blocks for a large class of ising ferromagnets whenever the susceptibility is finite another consequence is a central limit theorem for the density of thesurface of the infinite cluster in percolation models

on a class of nonconvex equilibrium problems in this paper we introduce a new class of equilibrium problems known as nonconvex equilibrium problems we suggest some algorithms for solving nonconvex equilibrium problems by using the auxiliary principle technique the convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomononicity we also introduce the concept of well posedness for the nonconvex equilibrium problems as special cases we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems our results can be considered a significant improvement of the previously known results

invex equilibrium problems in this paper we introduce a new class of equilibrium problems known as invex equilibrium problems in the setting of invexity this class of equilibrium problems includes equilibrium problems variational inequalities and variational like inequalities as special cases we use the auxiliary principle technique to suggest and analyze some iterative schemes for solving invex equilibrium problems and study the convergence criteria of these methods under some mild conditions we also consider the concept of well posedness for invex equilibrium problems our results represent significant and important refinements of the previously known results

a variational like inequality for multifunctions with applications abstract we study a variational like inequality problem for a multifunction a certain relevant complementarity problem is defined we establish some existence theorems for the above two problems an application to convex mathematical programming is also shown

perturbed proximal point algorithms for general quasi variational like inclusions in this paper we introduce two new concepts of subdifferential and proximal mappings of proper functionals on hilbert spaces the existence and lipschitz continuity of proximal mapping of a proper functional are proved by applying these concepts we introduce and study a class of general quasi variational like inclusions and develop some new perturbed proximal point algorithms of mann and ishikawa type for finding the approximate solutions of the general quasi variational like inclusions the convergence criteria of the sequences of approximate solutions generated by these new algorithms are also discussed our algorithms and results improve and generalize many known results in the literature

auxiliary principle and iterative algorithms for generalized set valued strongly nonlinear mixed variational like inequalities in this paper we extend the auxiliary principle technique to study a class of generalized set valued strongly nonlinear mixed variational like inequalities we prove the existence of a solution of the auxiliary problem for the generalized set valued strongly nonlinear mixed variational like inequalities construct the iterative algorithm for the generalized set valued strongly nonlinear mixed variational like inequalities and show the existence of a solution of the generalized set valued strongly nonlinear mixed variational like inequality by using the auxiliary principle technique we also prove the convergence of iterative sequences generated by the algorithm

on a predictor corrector method for solving invex equilibrium problems abstract in this paper we use the auxiliary principle technique in conjunction with the bregman function to suggest and analyze a predictor corrector method for solving invex equilibrium problems we also study the convergence criteria of this new method under some mild conditions we obtain as special cases new and known methods for solving variational like inequalities and equilibrium problems

criteria for generalized invex monotonicities abstract in this paper under appropriate conditions we establish that i if the gradient of a function is strictly pseudo monotone then the function is strictly pseudo invex ii if the gradient of a function is quasi monotone then the function is quasi invex and iii if the gradient of a function is strong pseudo monotone then the function is strong pseudo invex

a glivenko cantelli lemma and weak convergence for empirical processes of associated sequences with the help of an extension of hoeffding s equality we develop a way for estimating the covariance structures for empirical functions of associated sequences in terms of covariances of the original random variables based on these estimations a glivenko cantelli lemma for associated sequences and weak convergence for empirical processes of stationary associated sequences are obtained all under the conditions on covariances of the original random variables

a proof for antczak s mean value theorem in invexity analysis abstract this paper provides another proof for antczak s mean value theorem in invexity analysis

stochastic renormalization group in percolation i fluctuations and crossover abstract a generalization of the renormalization group which describes order parameter fluctuations in finite systems is developed in the specific context of percolation this stochastic renormalization group srg expresses statistical self similarity through a non stationary branching process the srg provides a theoretical basis for analytical or numerical approximations both at and away from criticality whenever the correlation length is much larger than the lattice spacing regardless of the system size for example the srg predicts order parameter distributions and finite size scaling functions for the complete crossover between phases for percolation the simplest srg describes structural quantities conditional on spanning such as the total cluster mass or the minimum chemical distance between two boundaries in these cases the central limit theorem for independent random variables holds at the stable off critical fixed points while a fractal central limit theorem describing long range correlations holds at the unstable critical fixed point this first part of a series of articles explains these basic concepts and a general theory of crossover subsequent parts will focus on limit theorems and comparisons of small cell srg approximations with simulation results

generalized mixed quasi variational like inequalities in this paper we use the auxiliary principle technique to suggest and analyze some iterative methods for solving generalized mixed quasi variational like inequalities we show that the convergence of the proposed method requires either pseudomonotonicity or partially relaxed strongly monotonicity under some mild condition as special cases one can obtain a number of new and known algorithms for solving variational inequalities and complementarity problems our results represent significant and important refinements of the previously known results

on vector variational like inequality problems abstract in this paper we establish some relationships between vector variational like inequality and vector optimization problems under the assumptions of invex functions we identify the vector critical points the weakly efficient points and the solutions of the weak vector variational like inequality problems under pseudo invexity assumptions these conditions are more general than those of existing ones in the literature in particular this work extends the earlier work of ruiz garzon et al g ruiz garzon r osuna gomez a rufian lizan relationships between vector variational like inequality and optimization problems european j oper res 157 2004 113 119 to a wider class of functions namely the pseudo invex functions studied in a recent work of noor m a noor on generalized preinvex functions and monotonicities j inequal pure appl math 5 2004 1 9

criteria for generalized invex monotonicities without condition c in this paper some necessary conditions of strictly pseudo invex monotonicity and quasi invex monotonicity are established with the condition that is affine in the first argument and skew instead of condition c

optimality and invexity in optimization problems in banach algebras spaces abstract in this paper we introduce into nonsmooth optimization theory in banach algebras a new class of mathematical programming problems which generalizes the notion of smooth kt p r invexity in fact this paper focuses on the optimality conditions for optimization problems in banach algebras regarding the generalized kt p r invexity notion and kuhn tucker points

the sugeno integral with respect to α preinvex functions abstract in this paper we establish the left hand side of the hermite hadamard inequality for preinvex functions and illustrate that the hermite hadamard inequality for preinvex functions is not valid for the sugeno integral moreover we give several upper bounds for the sugeno integral related to preinvex functions some examples are also provided to show the validity of our results

infinite clusters in percolation models the qualitative nature of infinite clusters in percolation models is investigated the results which apply to both independent and correlated percolation in any dimension concern the number and density of infinite clusters the size of their external surface the value of their total surface to volume ratio and the fluctuations in their density in particular it is shown thatn0 the number of distinct infinite clusters is either 0 1 or and the casen0 which might occur in sufficiently high dimension is analyzed

generalized invex monotonicity abstract in this paper the generalized invex monotone functions are defined as an extension of monotone functions a series of sufficient and necessary conditions are also given that relate the generalized invexity of the function with the generalized invex monotonicity of its gradient function this new class of functions will be important in order to characterize the solutions of the variational like inequality problem and mathematical programming problem

on iterative methods for equilibrium problems abstract in this paper we introduce a hybrid iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of finitely many nonexpansive mappings we prove that the approximate solution converges strongly to a solution of a class of variational inequalities under some mild conditions which is the optimality condition for some minimization problem we also give some comments on the results of plubtieng and punpaeng s plubtieng r punpaeng a general iterative method for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 336 2007 455 469 results obtained in this paper may be viewed as an improvement and refinement of the previously known results in this area

on optimality conditions for multiobjective optimization problems in topological vector space abstract in this paper we are concerned with a differentiable multiobjective programming problem in topological vector spaces an alternative theorem for generalized k subconvexlike mappings is given this permits the establishment of optimality conditions in this context several generalized fritz john conditions in line to those in hu and ling y hu c ling the generalized optimality conditions of multiobjective programming problem in topological vector space j math anal appl 290 2004 363 372 are obtained and in the presence of the generalized slater s constraint qualification the karush kuhn tucker necessary optimality conditions

co coercivity and its role in the convergence of iterative schemes for solving variational inequalities this paper stresses the role of co coercivity and related notions in the convergence of iterative schemes for solving monotone but not necessarily strongly or even strictly monotone variational inequalities the analysis will be conducted within the conceptual framework of the auxiliary problem principle

some relations between variational like inequality problems and vectorial optimization problems in banach spaces in this work we will establish some relations between variational like inequality problems and vectorial optimization problems in banach spaces under invexity hypotheses this paper extends the earlier work of ruiz garzon et al g ruiz garzon r osuna gomez a rufian lizana relationships between vector variational like inequality and optimization problems european j oper res 157 2004 113 119

hemiequilibrium like problems abstract in this paper we introduce and consider a new class of equilibrium problems known as hemiequilibrium like problems this new class includes hemiequilibrium equilibrium like problems and several classes of variational inequalities as special cases a number of iterative methods for solving hemiequilibrium like problems are suggested and analyzed by using the auxiliary principle technique we also study the convergence analysis of these iterative methods under some mild conditions the results obtained in this paper can be considered as a novel application of the auxiliary principle technique

central limit theorems for percolation models letp 1 2 be the open bond probability in broadbent and hammersley s percolation model on the square lattice letwxbe the cluster of sites connected tox by open paths and let n be any sequence of circuits with interiors mathop gamma limits circ n to infty it is shown that for certain sequences of functions fn s n sum x in mathop gamma limits circ n f n w x converges in distribution to the standard normal law when properly normalized this result answers a problem posed by kunz and souillard proving that the numbersnof sites inside n which are connected by open paths to n is approximately normal for large circuits n

some characterizations of strongly preinvex functions in this paper a new class of generalized convex function is introduced which is called the strongly preinvex function we study some properties of strongly preinvex function in particular we establish the equivalence among the strongly preinvex functions strongly invex functions and strongly monotonicity under some suitable conditions as special cases one can obtain several new and previously known results for preinvex invex functions

relationships between pre invex concepts abstract it is well known that some properties of convex optimization problems especially sufficient conditions for optimality and duality conditions are preserved when convexity is weakened to pre invexity however there are several distinct pre invex concepts b vex b pre invex pre univex p r pre invex and these are not equivalent the pre invexity concepts mentioned above have also some properties which are characteristic and invariant for functions belonging to these classes of functions

statistical mechanics of probabilistic cellular automata we investigate the behavior of discrete time probabilistic cellular automata pca which are markov processes on spin configurations on ad dimensional lattice from a rigorous statistical mechanics point of view in particular we exploit whenever possible the correspondence between stationary measures on the space time histories of pcas on d and translation invariant gibbs states for a related hamiltonian on d 1 this leads to a simple large deviation formula for the space time histories of the pca and a proof that in a high temperature regime the stationary states of the pca are gibbsian we also obtain results about entropy fluctuations and correlation inequalities and demonstrate uniqueness of the invariant state and exponential decay of correlations in a high noise regime we discuss phase transitions in the low noise or low temperature regime and review toom s proof of nonergodicity of a certain class of pcas

hemivariational like inequalities in this paper we introduce and consider a new class of variational inequalities known as the hemivariational like inequalities it is shown that the hemivariational like inequalities include hemivariational inequalities variational like inequalities and the classical variational inequalities as special cases the auxiliary principle is used to suggest and analyze some iterative methods for solving hemivariational like inequalities under mild conditions the results obtained in this paper can be considered as a novel application of the auxiliary principle technique

multivalued general equilibrium problems in this paper we use the auxiliary principle technique to suggest some new classes of iterative algorithms for solving multivalued equilibrium problems the convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomonotonicity as special cases we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems since multivalued equilibrium problems include equilibrium variational inequality and complementarity problems as specials cases our results continue to hold for these problems

generalized invexity of nonsmooth functions abstract in this paper the concepts of weak invexity and weak quasi invexity are introduced and the relations among several kinds of generalized invexity are studied for nonsmooth functions by means of the properties of limiting subdifferentials in addition the relations between generalized invexity of a nonsmooth function and generalized invariant monotonicity of its limiting subdifferential mapping are researched our results here are an extension and generalization of those presented by m soleimani damaneh

hardy littlewood polya type theorems for invex functions in this paper the hardy littlewood polya theorem on majorization is extended from convex functions to invex ones some variants for pseudo invex and quasi invex functions are also considered the framework used is that of similarly separable vectors the results obtained are illustrated for monotonic monotonic in mean and star shaped vectors respectively applications to relative invexity are given

new high order sufficient conditions for configuration tracking in this paper we propose new conditions guaranteeing that the trajectories of a mechanical control system can track any curve on the configuration manifold we focus on systems that can be represented as forced affine connection control systems and we generalize the sufficient conditions for tracking known in the literature the new results are proved by a combination of averaging procedures by highly oscillating controls with the notion of kinematic reduction

on minty vector variational like inequality this paper is devoted to the study of relationships between solutions of minty vector variational like inequalities mvvli and solutions of vector optimization problems vop as well as some relations between solutions of mvvli and stampacchia vector variational like inequalities svvli moreover some relations between mvvli and perturbed vector variational like inequalities are established our results generalize some known results

generalized quasi variational like inclusions with nonconvex functionals in this paper two new concepts of h subdifferential and h proximal mappings of a proper functional is introduced in hilbert spaces the existence and lipschitz continuity of h proximal mapping of a proper functional are proved by applying these concepts we introduce and study a class of generalized quasi variational like inclusions with a nonconvex functional a new iterative algorithms for finding the approximate solutions and the convergence criteria of the iterative sequences generated by the algorithm are also given these algorithm and existence result generalize many known results in the literature

on differential systems with quadratic impulses and their applications to lagrangian mechanics this paper is concerned with the basic dynamics and a class of variational problems for control systems of the form text e qquad dot x f t x u g t x u dot u h t x u dot u 2 these systems have impulsive character due to the presence of the time derivative dot u of the control it is shown that trajectories can be well defined when the controls u are limits in a suitable weak sense of sequences u n contained in the sobolev space w 1 2 roughly speaking one can say that in this case the dot u n tend to the square root of a measure actually this paper shows that the system e is essentially equivalent to an affine impulsive system of the form dot x f x g x v h x dot w where v in l 2 and dot w is a nonnegative radon measure not smaller than v 2 this provides a characterization of the closure of the set of trajectories of e as the controls u range inside a fixed ball of w 1 2 the existence of generalized optimal controls for va

geometric aspects of quantum spin states a number of interesting features of the ground states of quantum spin chains are analyzed with the help of a functional integral representation of the system s equilibrium states methods of general applicability are introduced in the context of the su 2s 1 invariant quantum spin s chains with the interaction p o wherep o is the projection onto the singlet state of a pair of nearest neighbor spins the phenomena discussed here include the absence of neel order the possibility of dimerization conditions for the existence of a spectral gap and a dichotomy analogous to one found by affleck and lieb stating that the systems exhibit either slow decay of correlations or translation symmetry breaking our representation elucidates the relation evidence for which was found earlier of the p o spin s systems with the potts and the fortuin kasteleyn random cluster models in one more dimension the method reveals the geometric aspects of the listed phenomena and gives a precise sense to a picture of the ground state in which the spins are grouped into random clusters of zero total spin e g within such structure the dichotomy is implied by a topological argument and the alternatives correspond to whether or not the clusters are of finite mean length

generalizations of e convex and b vex functions a class of functions called e b vex functions is defined as a generalization of e convex and b vex functions similarly a class of e b preinvex functions which are generalizations of e convex and b preinvex functions is introduced in addition the concept of b linear functions is also generalized to e b linear functions some properties of these proposed classes are studied furthermore the equivalence between the class of e b vex functions and that of e quasiconvex functions is proved

microcanonical distributions for lattice gases in this article a large deviation principle cf theorem 1 3 for the empirical distribution functional is applied to prove a rather general version of boltzmann s principle cf theorem 3 5 for models with shift invariant finite range potentials the final section contains an application of these considerations to the two dimensional ising model at sub critical temperature

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

some quantum integral inequalities via preinvex functions in this paper we obtain some new quantum analogues of hermite hadamard and iyengar type inequalities for some classes of preinvex functions some special cases are also discussed

on fuzzy generalized convex mappings and optimality conditions for fuzzy weakly univex mappings in this paper we first introduce the weakly invex fuzzy mappings based on weakly differentiable functions and discuss the relationships between several kinds of fuzzy generalized convex mappings then a kind of fuzzy weakly univex functions are introduced and some properties of them are investigated furthermore optimality and duality results are derived for a class of generalized convex optimization problems with fuzzy weakly univex functions

central limit theorems for additive functionals of the simple exclusion process definition 2 1 in the above paper is incorrectly stated in the proof of theo rem 2 1 which gives an invariance principle for certain processes satisfying defi nition 2 1 conditions in definition 2 1 are sufficient to deduce finite dimensional convergence but not enough to apply a maximal inequality for demimartingales to obtain tightness the problem is definition 2 1 as stated only considers pair increment associations and not more general associations needed for the demi martingale property we slightly strengthen the definition here in this correction so that the proof of tightness in theorem 2 1 holds details of how this is accom plished are given below by substituting the corrected definition 2 1 for the previous one all results in the article hold as written in particular proposition 2 1 which is the link between theorem 2 1 and the main results and which states certain additive processes sat isfy definition 2 1 holds with the same argument

on the controllability of lagrangian systems by active constraints abstract we consider a mechanical system which is controlled by means of moving constraints namely we assume that some of the coordinates can be directly assigned as functions of time by implementing frictionless constraints this leads to a system of ode s whose right hand side depends quadratically on the time derivative of the control in this paper we introduce a simplified dynamics described by a differential inclusion we prove that every trajectory of the differential inclusion can be uniformly approximated by a trajectory of the original system on a sufficiently large time interval starting at rest under a somewhat stronger assumption we show this second trajectory reaches exactly the same terminal point

a class of nonconvex functions and pre variational inequalities abstract a class of nonconvex functions is introduced called semi preinvex function which includes the classes of preinvex functions and arc connected convex functions the fritz john conditions of the mathematical programming problem are derived for these kinds of functions the pre variational inequality is given as a necessary condition and also a sufficient condition for a mathematical programming for invex functions the type i function related to unconstrained problems is given as an equivalent form of the pre variational inequality existence theorems for the solution of the pre variational inequality are also proved

some developments in general variational inequalities general variational inequalities provide us with a unified natural novel and simple framework to study a wide class of equilibrium problems arising in pure and applied sciences in this paper we present a number of new and known numerical techniques for solving general variational inequalities using various techniques including projection wiener hopf equations updating the solution auxiliary principle inertial proximal penalty function dynamical system and well posedness we also consider the local and global uniqueness of the solution and sensitivity analysis of the general variational inequalities as well as the finite convergence of the projection type algorithms our proofs of convergence are very simple as compared with other methods our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems since the general variational inequalities include quasi variational inequalities and quasi implicit complementarity problems as special cases results presented here continue to hold for these problems several open problems have been suggested for further research in these areas

equilibrium problems with set valued mappings in banach spaces abstract in this paper we consider two classes of equilibrium problems which imply general pseudomonotonicity and general semipseudomonotonicity relative to a set valued map on reflexive and nonreflexive banach spaces respectively using the classical kkm technique we obtain some existence results under boundedness as well as under unboundedness assumptions some examples are given

scaling limit of the energy variable for the two dimensional ising ferromagnet the critical point limit law scaling limit of the suitably renormalized energy variable is explicitly calculated for the two dimensional nearest neighbour ising cylinder with free edges it is shown that the renormalization factor has to behave as 2m 2n lnn 1 2 where 2m denotes the number of rows and 2n the number of columns by first taking the limitm and thenn the limit law is proven to be gaussian

on invex sets and preinvex functions abstract in this paper we consider the class of the invex function introduced by hanson we show that under certain condition an invex function defined on an invex set a is preinvex on a similarly a quasiinvex function defined on an invex set a is pre quasiinvex

on limit theorems for the bivariate magnetization energy variable at the critical point the limiting magnetization energy bivariate variable is studied for ising ferromagnets at the critical point the factorization property of the limiting bivariate moment generating function is shown to be intimately connected to critical point exponent inequalities and to the behaviour of the scaling limit near and at the critical point the validity of this can be deduced from the study of the second and the fourth magnetization cumulants at zero external field the limiting bivariate variable is exactly calculated at the critical point for the curie weiss model mf and for the edge of a two dimensional ising ferromagnet wrapped on a cylinder it is shown that the mean field case leads to a non gaussian limiting distribution in contradistinction with the particular ising model we consider for which we obtain a product of two gaussian probability distributions

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

high order sufficient conditions for configuration tracking of affine connection control systems in this paper we study under which conditions the trajectories of a mechanical control system can track any curve on the configuration manifold we focus on systems that can be represented as forced affine connection control systems and we generalize the sufficient conditions for tracking known in the literature the sufficient conditions are expressed in terms of convex cones of vector fields defined through particular brackets of the control vector fields of the system the tracking control laws obtained by our constructions depend on several parameters by imposing suitable asymptotic conditions on such parameters we construct algorithmically one parameter tracking control laws the theory is supported by examples of control systems associated with elliptic hovercrafts and ellipsoidal submarines

normal approximation for associated point processes via stein s method with applications to determinantal point processes abstract we use stein s method to provide non asymptotic l 1 bounds also known as wasserstein bounds to the normal for functionals of associated point processes as for supporting tools we use the connection between association and mixing properties that was recently uncovered by 29 we apply our main results to determinantal point processes which are known to be negatively associated a potential application to determinantal point processes in the laguerre gaussian family is also presented

pre invex functions in multiple objective optimization and called such functions convexlike if s is a convex set and if f is a convex function then clearly f is convexlike elster and nehse obtained a saddlepoint optimality condition for convexlike mathematical programs hayashi and komiya 9 also considered convexlike functions and developed a gordan type theorem of the alternative involving convexlike functions and in addition considered lagrangian duality for convexlike programs hanson 7 considered differentiable functions f s r for which there exists an n dimensional vector function q q u such that for all x u e s

the central limit theorem for supercritical oriented percolation in two dimensions we consider the cardinality of supercritical oriented bond percolation in two dimensions we show that whenever the the origin is conditioned to percolate the process appropriately normalized converges asymptotically in distribution to the standard normal law this resolves a longstanding open problem pointed out to in several instances in the literature the result applies also to the continuous time analog of the process viz the basic one dimensional contact process we also derive general random indices central limit theorems for associated random variables as byproducts of our proof

vector nonsmooth variational like inequalities and optimization problems abstract in this paper we first extend the concepts of clarke s generalized derivation and subdifferential for a function whose domain is a subset of a metrizable topological vector space we also introduce and consider a new class of variational like inequalities which are called the vector nonsmooth variational like inequalities we also establish the relationship between the nonsmooth variational like inequalities and vector optimization problems under some suitable conditions in particular our results extend and generalize the results of mishra and wang s k mishra s y wang vector variational like inequalities and nonsmooth vector optimization problems nonlinear anal 64 2006 1939 1945 and mishra and noor s k mishra m aslam noor on vector variational like inequality problems j math anal appl 311 2005 69 75

on strongly α preinvex functions in this paper by means of a series of counterexamples we study in a systematic way the relationships among pseudo quasi preinvexity strict strong pseudo quasi invexity and strict strong pseudo quasi monotonicity results obtained in this paper can be viewed as a refinement and improvement of the results of noor and noor m a noor k i noor some characterizations of strongly preinvex functions j math anal appl 316 2006 697 706

optimality conditions and duality for nondifferentiable multiobjective programming problems involving d r type i functions in this paper new classes of nondifferentiable functions constituting multiobjective programming problems are introduced namely the classes of d r type i objective and constraint functions and moreover the various classes of generalized d r type i objective and constraint functions are defined for directionally differentiable multiobjective programming problems sufficient optimality conditions and various mond weir duality results are proved for nondifferentiable multiobjective programming problems involving functions of such type finally it is showed that the introduced d r type i notion with r 0 is not a sufficient condition for wolfe weak duality to hold these results are illustrated in the paper by suitable examples

sampling from a gibbs measure with pair interaction by means of pca we consider the problem of approximate sampling from the finite volume gibbs measure with a general pair interaction we exhibit a parallel dynamics probabilistic cellular automaton which efficiently implements the sampling in this dynamics the product measure that gives the new configuration in each site contains a term that tends to favour the original value of each spin this is the main ingredient that allows one to prove that the stationary distribution of the pca is close in total variation to the gibbs measure the presence of the parameter that drives the inertial term mentioned above gives the possibility to control the degree of parallelism of the numerical implementation of the dynamics