environment induced superselection rules in markovian regime a generalization of the jacobs deleeuw glicksberg splitting for a quantum dynamical semigroup is introduced this generalization called the isometric sweeping decomposition is used to derive effective superselection rules in the quantum system

continuous location of dimensional structures abstract a natural extension of point facility location problems are those problems in which facilities are extensive i e those that cannot be represented by isolated points but as some dimensional structures such as straight lines line segments polygonal curves or circles in this paper a review of the existing work on the location of extensive facilities in continuous spaces is given gaps in the knowledge are identified and suggestions for further research are made

factorization of minty and stampacchia variational inequality systems abstract in this paper sufficient regularity and coercivity conditions for minty and stampacchia type variational inequality systems are offered the typical results state that if the independent inequalities are solvable and the functions involved are lower semicontinuous then the system has also a solution that is a factorization principle holds as an application a variational inequality system consisting of two partial differential inequalities is considered this result is analogous to that of chen journal of mathematical analysis and application 231 1999 177 obtained for one variational inequality

quantum markovian subsystems invariance attractivity and control we characterize the dynamical behavior of continuous time markovian quantum systems with respect to a subsystem of interest markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing subsystem encodings offering a general pathway to faithfully represent quantum information we provide explicit linear algebraic characterizations of the notion of invariant and noiseless subsystem for markovian master equations under different robustness assumptions for model parameter and initial state variations the stronger concept of an attractive quantum subsystem is introduced and sufficient existence conditions are identified based on lyapunov s stability techniques as a main control application we address the potential of output feedback markovian control strategies for quantum pure state stabilization and noiseless subspace generation in particular explicit results for the synthesis of stabilizing semigroups and noiseless subspaces in finite dimensional markovian systems are obtained

on pseudomonotone set valued mappings abstract in this paper a common generalization of the algebraic and topological pseudomonotonicity for set valued maps is introduced existence results for variational inequalities governed by such maps are given

minmax distance approximation and separation problems geometrical properties a center hyperplane in the d dimensional space minimizes the maximum of its distances from a finite set of points a with respect to possibly different gauges in this note it is shown that a center hyperplane exists which is at equal maximum distance from at least d 1 points of a moreover the projections of the points among these which lie above the center hyperplane cannot be separated by another hyperplane from the projections of those that are below it when all gauges involved are smooth all center hyperplanes satisfy these properties this geometric property allows us to improve and generalize previously existing results which were only known for the case in which all distances are measured using a common norm the results also extend to the constrained case where for some points it is prespecified on which side of the hyperplane above below or on they must lie in this case the number of points lying on the hyperplane plus those at maximum distance is at least d 1 it follows that solving such global optimization problems reduces to inspecting a finite set of candidate solutions extensions of these results to a separation problem are outlined

asymptotic behavior of markov semigroups on preduals of von neumann algebras we develop a new approach for investigation of asymptotic behavior of markov semigroup on preduals of von neumann algebras with using of our technique we establish several results about mean ergodicity statistical stability and constrictiviness of markov semigroups

locating least distant lines in the plane in this paper we deal with locating a line in a plane given a set of existing facilities represented by points in the plane our objective is to find a straight line l minimizing the sum of weighted distances to the existing facilities or minimizing the maximum weighted distance to the existing facilities respectively we show that for all distance measures derived from norms one of the lines minimizing the sum objective contains at least two of the existing facilities for the center objective we always get an optimal line which is at maximum distance from at least three of the existing facilities if all weights are equal there is an optimal line which is parallel to one facet of the convex hull of the existing facilities

the maximin line problem with regional demand abstract given a family p p 1 p m of m polygonal regions possibly intersecting in the plane we consider the problem of locating a straight line l intersecting the convex hull of p and such that mink d pk l is maximal we give an algorithm that solves the problem in time o m2 n log m log n using o m2 n space where n is the total number of vertices of p1 pm the previous best running time for this problem was o n2 j janardan f p preparata widest corridor problems nordic journal of computing 1 1994 231 245 we also improve the known complexity for several variants of this problem which include a three dimensional version the maximin plane problem the weighted problem and considering measuring distance different to the euclidean one

on the semi monotone operator theory and applications abstract in this paper eis a real banach space a e e e is a semi monotone operator we first study the variational inequality problem findu k such that a u u v u 0 wherek e is a closed convex subset then the operator equationa u u p and we also construct a degree theory for demi continuous semi monotone operators in reflexive banach spaces

the role of the atomic decoherence free subalgebra in the study of quantum markov semigroups we show that for a quantum markov semigroup qms with a faithful normal invariant state atomicity of the decoherence free subalgebra and environmental decoherence are equivalent moreover we prove that the predual of the decoherence free subalgebra is isometrically isomorphic to the subspace of reversible states we also describe in an explicit and constructive way the relationship between the decoherence free subalgebra and the fixed point subalgebra we show that for a quantum markov semigroup qms with a faithful normal invariant state atomicity of the decoherence free subalgebra and environmental decoherence are equivalent moreover we prove that the predual of the decoherence free subalgebra is isometrically isomorphic to the subspace of reversible states we also describe in an explicit and constructive way the relationship between the decoherence free subalgebra and the fixed point subalgebra

generalized vector complementarity type problems in topological vector spaces in this paper we introduced the generalized vector variational inequality type problem and the generalized vector complementarity type problem in the setting of topological vector space by utilizing a modified version of the fan kkm theorem we investigated the nonemptyness and compactness of solution sets of these problems without the demipseudomonotonicity assumption further we prove that solution sets of both the problems are equivalent to each other under some suitable conditions the results of this paper generalize and improve several results that appeared recently in the literature

classical properties of infinite quantum open systems long time asymptotic properties of a class of environmentally induced dynamical semigroups on arbitrary von neumann algebras are discussed such a semigroup selects observables called effective observables which are immune to the process of decoherence and so evolve in a reversible automorphic way in particular it is shown that effective observables of the quantum system in the thermodynamic limit subjected to a specific interaction with another quantum system obey classical dynamics

fixed point theory and nonlinear problems introduction among the most original and far reaching of the contributions made by henri poincare to mathematics was his introduction of the use of topological or qualitative methods in the study of nonlinear problems in analysis his starting point was the study of the differential equations of celestial mechanics and in particular of their periodic solutions his work on this topic began with his thesis in 1879 and was developed in detail in his great three volume work methodes nouvelles de la mechanique celeste which appeared in the early 1890s and summarized his many memoirs of the intervening period it continued until his memoir shortly before his death in 1912 in which he put forward the unproved fixed point result usually referred to as poincare s last geometric theorem the ideas introduced by poincare include the use of fixed point theorems the continuation method and the general concept of global analysis the writer s acquaintance with poincare s influence came through contact with solomon lefschetz and marston morse both of whom were very explicit as to the role of poincare as an initiator in this direction of mathematical development in 1934 in the foreword to his colloquium volume on the calculus of variations in the large morse had put this forward very forcefully in the first paragraph

on the generalized monotonicity of variational inequalities in this paper three new classes of generalized monotone operators are introduced the relaxed m pseudomonotone operator relaxed m quasimonotone operator and densely relaxed pseudomonotone operator the relations between these three classes and the relations between them and some other well known classes of generalized monotone operators are discussed in detail various existence results for variational inequalities in normed spaces are derived the results generalize some known results

generalized mixed equilibrium problems with generalized α η monotone bifunction in topological vector spaces the purpose of this paper is to introduce a new class of the generalized mixed equilibrium problems with a new definition of the relaxed monotonicity for bi functions in topological vector spaces by employing the kkm technique and under some appropriate assumptions on the considering nonlinear mappings we obtain the existence of a solution for the generalized mixed equilibrium problems with the new concept of the relaxed monotonicity and coercivity condition in order to relax the compactness of the domains of the nonlinear mappings in the setting of topological vector spaces moreover the compactness and convexness of the solution set are investigated the results in the paper extend and generalize the corresponding results especially sintunavarat 2013 20 in this area by providing mild assumptions in order to guarantee the existence of a solution for the generalized mixed equilibrium problem

a generalized vector variational inequality problem with a set valued semi monotone mapping abstract in this paper we first generalize the concept of semi monotonicity for a scalar single valued mapping to the case of a vector set valued mapping then we consider a generalized vector variational inequality problem concerning the vector set valued semi monotone mapping several existence results are obtained by using the kakutani fan glicksberg fixed point theorem which generalize some results for vector variational inequality problems studied in recent years

strongly positive semigroups and faithful invariant states let jf9 denote a ff algebra j a semigroup 0 of linear maps of j into j and a faithful invariant normal state over j we assume that is strongly positive in the sense that t a a t a t a for all aej and 0 therefore one can define a contraction semigroup t on t a aej where is the cyclic and separating vector associated with we prove 1 the fixed points ji of are given by j j r t j c e where e is the orthogonal projection onto the subspace of t invariant vectors 2 the state has a unique decomposition into ergodic states if and only if j or jiyje is abelian or equivalently if j is r abelian 3 the state is ergodic if and only if mkje is irreducible or if inf 0 eco o

continuity and generators of dynamical semigroups for infinite bose systems abstract for a class of quasifree quantum dynamical semigroups on the algebra of the canonical commutation relations ccr we give sufficient conditions for these semigroups to extend to ultraweakly continuous semigroups of normal operators on the von neumann algebra associated with a representation of the ccr then the explicit form of the generators of the extended semigroups is calculated

locating an obnoxious plane abstract let s be a set of n points in three dimensional euclidean space we consider the problem of positioning a plane intersecting the convex hull of s such that min d p p s is maximized in a geometric setting the problem asks for the widest empty slab through n points in space where a slab is the open region of r 3 that is bounded by two parallel planes that intersect the convex hull of s we give a characterization of the planes which are locally optimal and we show that the problem can be solved in o n3 time and o n2 space we also consider several variants of the problem which include constraining the obnoxious plane to contain a given line or point and computing the widest empty slab for polyhedral obstacles finally we show how to adapt our method for computing a largest empty annulus in the plane improving the known time bound o n3 log n j m diaz banez f hurtado h meijer d rappaport t sellares the largest empty annulus problem international journal of computational geometry and applications 13 4 2003 317 325

gradient flow and entropy inequalities for quantum markov semigroups with detailed balance abstract we study a class of ergodic quantum markov semigroups on finite dimensional unital c algebras these semigroups have a unique stationary state and we are concerned with those that satisfy a quantum detailed balance condition with respect to we show that the evolution on the set of states that is given by such a quantum markov semigroup is gradient flow for the relative entropy with respect to in a particular riemannian metric on the set of states this metric is a non commutative analog of the 2 wasserstein metric and in several interesting cases we are able to show in analogy with work of otto on gradient flows with respect to the classical 2 wasserstein metric that the relative entropy is strictly and uniformly convex with respect to the riemannian metric introduced here as a consequence we obtain a number of new inequalities for the decay of relative entropy for ergodic quantum markov semigroups with detailed balance

a generalized mixed vector variational like inequality problem abstract in this paper we introduce relaxed p monotone mapping and by utilizing kkm technique and nadler s lemma we establish some existence results for the generalized mixed vector variational like inequality problem further we give the concepts of complete semicontinuity and strong semicontinuity and prove the solvability for generalized mixed vector variational like inequality problem without monotonicity assumption by applying the brouwer s fixed point theorem the results presented in this paper are extensions and improvements of some earlier and recent results in the literature

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

existence results for stampacchia and minty type implicit variational inequalities with multivalued maps abstract stampacchia and minty type generalized implicit variational inequality problems are considered we extended the notion of dense pseudomonotonicity for multivalued maps and established several existence results for solutions of these problems in the setting of segment dense sets we also studied the existence of solutions of minty type generalized implicit quasi variational inequality problems some particular cases are also studied it is shown that our results contain several existing results in the literature as special cases

ergodic properties of diffusion type quantum dynamical semigroups we develop a framework for investigation of asymptotic behavior of quantum markov semigroups on c algebras associated with noncommutative elliptic generators an exponential rate of convergence toward the projection onto the fixed point subalgebra has been established and in a particular case of the semigroup selecting rotationally invariant states of a three dimensional quantum system the time factor of such a convergence has been estimated

computing the width of a set for a set of points p in three dimensional space the width of p w p is defined as the minimum distance between parallel planes of support of p it is shown that w p can be computed in o n log n i time and o n space where i is the number of antipodal pairs of edges of the convex hull of p and n is the number of vertices in the worst case i o n sup 2 for a convex polyhedra the time complexity becomes o n i if p is a set of points in the plane the complexity can be reduced to o nlog n for simple polygons linear time suffices

environment induced decoherence for markovian evolutions we study environmental decoherence for a quantum markov semigroup t acting on an arbitrary von neumann algebra m in particular we analyze the relationships between the decomposition of the algebra induced by decoherence and a sort of isometric sweeping decomposition for the space of states moreover when the semigroup has a faithful normal invariant state we embed the algebra m in its completion m with respect to the scalar product induced by the faithful state and we compare the decomposition induced by decoherence with some other kind of isometric sweeping decompositions of m and m

decoherence free subspaces of a quantum markov semigroup we give a full characterisation of decoherence free subspaces of a given quantum markov semigroup with generator in a generalised lindbald form which is valid also for infinite dimensional systems our results extending those available in the literature concerning finite dimensional systems are illustrated by some examples