how to project onto an isotone projection cone abstract the solution of the complementarity problem defined by a mapping f r n r n and a cone k r n consists of finding the fixed points of the operator p k i f where p k is the projection onto the cone k and i stands for the identity mapping for the class of isotone projection cones cones admitting projections isotone with respect to the order relation they generate and f satisfying certain monotonicity properties the solution can be obtained by iterative processes see g isac a b nemeth projection methods isotone projection cones and the complementarity problem j math anal appl 153 1 1990 258 275 and s z nemeth iterative methods for nonlinear complementarity problems on isotone projection cones j math anal appl 350 1 2009 340 347 these algorithms require computing at each step the projection onto the cone k in general computing the projection mapping onto a cone k is a difficult and computationally expensive problem in this note it is shown that the projection of an arbitrary point onto an isotone projection cone in r n can be obtained by projecting recursively at most n 1 times into subspaces of decreasing dimension this emphasizes the efficiency of the algorithms mentioned above and furnishes a handy tool for some problems involving special isotone projection cones as for example the non negative monotone cones occurring in reconstruction problems see e g section 5 13 in j dattorro convex optimization and euclidean distance geometry meboo 2005 v2009 04 11

equivalence of hardy submodules generated by polynomials abstract in this paper we obtain a complete classification under unitary equivalence for hardy submodules on the polydisk which are generated by ideals of polynomials let i be an ideal of polynomials in n variables since i is generated by finitely many polynomials i has a greatest common divisor p so i can be uniquely written as i p l which is called the beurling form of i let i 1 p 1 l 1 i 2 p 2 l 2 we prove that i 1 and i 2 are unitarily equivalent if and only if there are polynomials q 1 and q 2 with z q 1 d n z q 2 d n such that p 1 q 1 p 2 q 2 on t n and p 1 l 1 p 1 l 2 consequently two principal submodules p 1 and p 2 are unitarily equivalent if and only if there are polynomials q 1 and q 2 with z q 1 d n z q 2 d n such that p 1 q 1 p 2 q 2 on t n furthermore we give a complete similarity classification for submodules generated by homogeneous ideals finally we point out that in the case of the hardy module on the unit ball i 1 and i 2 are unitarily equivalent if and only if they are equal if i 1 and i 2 are homogeneous ideals then i 1 and i 2 are quasi similar if and only if i 1 i 2

solvability of variational inequalities on hilbert lattices this paper provides a systematic solvability analysis for generalized variational inequalities on separable hilbert lattices by contrast to a large part of the existing literature our approach is lattice theoretic and is not based on topological fixed point theory this allows us to establish the solvability of certain types of generalized variational inequalities without requiring the involved set valued maps be hemicontinuous or monotonic some of our results generalize those obtained in the context of nonlinear complementarity problems in earlier work and appear to have scope for applications this is illustrated by means of several applications to fixed point theory optimization and game theory

defect operators defect functions and defect indices for analytic submodules abstract this paper mainly concerns defect operators and defect functions of hardy submodules bergman submodules over the unit ball and hardy submodules over the polydisk the defect operator function carries key information about operator theory function theory and structure of analytic submodules the problem when a submodule has finite defect is attacked for both hardy submodules and bergman submodules our interest will be in submodules generated by polynomials the reason for choosing such submodules is to understand the interaction of operator theory function theory and algebraic geometry

projection methods isotone projection cones and the complementarity problem one studies some iterative methods for solving complementarity problems explicit or implicit in hilbert spaces the iterative methods presented are based on the fixed point theory on the coincidence equations on convex cones and on some properties of projection operators onto a special cone named the isotone projection cone the ordering defined by the cone is essential for the complementarity theory the idea is to use systematically the ordering in the iterative methods for solving complementarity problems in this sense one shows that the isotone projection cone is a good instrument

characteristic spaces and rigidity for analytic hilbert modules abstract it is well known that a polynomial in one variable is completely determined by its zeros counting multiplicities we generalize this result to an ideal of polynomials in several variables by introducing the characteristic spaces of the ideal one finds that the ideal is completely determined by its characteristic spaces on a characteristic set in particular a primary ideal is completely determined by its characteristic space at any zero point some straightforward applications of the above results yield the algebraic reduction theorem for analytic hilbert modules in several variables also we obtain some general rigidity results for analytic hilbert modules by using the techniques of af envelopes of analytic hilbert modules

invariant subspaces of finite codimension in banach spaces of analytic functions abstract we give a characterization of invariant subspaces of finite codimension in banach spaces of vector valued analytic functions in several variables where invariant refers to invariance under multiplication by any polynomial we obtain very weak conditions under which our characterization applies that unifies and improves a number of previous results in the vector valued case the results are new even for one complex variable as a concrete application in several variables we consider the bergman space on a strictly pseudo convex domain and we improve previous results assuming c boundary to the case of c 2 boundary

lattice like operations and isotone projection sets abstract by using some lattice like operations which constitute extensions of ones introduced by m s gowda r sznajder and j tao for self dual cones a new perspective is gained on the subject of isotonicity of the metric projection onto the closed convex sets the results of this paper are wide range generalizations of some results of the authors obtained for self dual cones the aim of the subsequent investigations is to put into evidence some closed convex sets for which the metric projection is isotonic with respect to the order relation which give rise to the above mentioned lattice like operations the topic is related to variational inequalities where the isotonicity of the metric projection is an important technical tool for euclidean sublattices this approach was considered by g isac and respectively by h nishimura and e a ok

some p properties for linear transformations on euclidean jordan algebras a real square matrix is said to be a p matrix if all its principal minors are positive it is well known that this property is equivalent to the nonsign reversal property based on the componentwise product of vectors the order p property based on the minimum and maximum of vectors uniqueness property in the standard linear complementarity problem lipschitzian homeomorphism property of the normal map corresponding to the nonnegative orthant in this article we extend these notions to a linear transformation defined on a euclidean jordan algebra we study some interconnections between these extended concepts and specialize them to the space s n of all n n real symmetric matrices with the semidefinite cone s n and to the space r n with the lorentz cone

optimal solutions to variational inequalities on banach lattices abstract we study the existence of maximum and minimum solutions to generalized variational inequalities on banach lattices the main tools of analysis are the variational characterization of the generalized metric projection operator and order theoretic fixed point theory

several extensions of the abian brown fixed point theorem and their applications to extended and generalized nash equilibria on chain complete posets abstract in this paper we provide several extensions of the abian brown fixed point theorem from single valued mappings to set valued mappings on chain complete posets then we examine some non monetized non cooperative games where both the collections of the strategies and the ranges of the utilities for the players are posets by applying the extensions of the abian brown fixed point theorem and by applying the order preserving property of mappings we prove some existence theorems of extended and generalized nash equilibria for non monetized non cooperative games on chain complete posets

a geometric dynamical approach to thermodynamics we present a geometric and dynamical approach to the micro canonical ensemble of classical hamiltonian systems we generalize the arguments in rugh 1997 phys rev lett 78 772 4 and show that the energy derivative of a micro canonical average is itself micro canonically observable in particular temperature specific heat and higher order derivatives of the entropy can be observed dynamically we give perturbative asymptotic formulae by which the canonical ensemble itself can be reconstructed from micro canonical measurements only using our geometrical tools we rederive formulae by lebowitz et al and pearson et al relating for example specific heat to fluctuations in the kinetic energy we show that under natural assumptions on the fluctuations in the kinetic energy the micro canonical temperature is asymptotically equivalent to the standard canonical definition using the kinetic energy

discrete fixed points models complexities and applications we study three discrete fixed point concept sperner dpzp brouwer under two different models the polynomial time function model and the oracle function model we fully characterize the computational complexities of these three problems the computational complexity unification of the above problems gives us more choices in the study of different applications as an example by a reduction from dpzp we derive asymptotically equal lower and upper bound for tucker in the oracle model the same reduction also allows us to derive a single proof for the ppad completeness of tucker in any constant dimension which is significantly simpler than the recent proofs

exceptional family of elements for general order complementarity problems abstract the notion of exceptional family of elements for general order complementarity problems in banach spaces will be introduced it will be shown that for general order complementarity problems defined by completely continuous fields the problem has either a solution or an exceptional family of elements finite dimensional examples and an application to integral operators will be given

existence results of partial differential mixed variational inequalities without lipschitz continuity abstract the aim of this paper is to use order theoretic approaches to investigate a class of partial differential mixed variational inequalities pdmvis for short which are receiving much attention recently to this end the order preservation properties of proximity mapping are explored applying these order preservation properties and combining with the knaster tarski fixed point theorem we prove the existence of solutions and the order preservation properties of solution mapping for mixed variational inequalities on hilbert lattices relying on the above obtained results as well as some order theoretic techniques the existence of mild solutions to pdmvi is established in contrast to many existing results on pdmvis the order theoretic approaches are new and the results obtained in this paper do not require the lipschitz continuity of the mapping associated to nonlinear evolution equation

an extension of tarski s fixed point theorem and its application to isotone complementarity problems tarski s fixed point theorem is extended to the case of set valued mappings and is applied to a class of complementarity problems defined by isotone set valued operators in a complete vector lattice

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

generalized f complementarity problems in banach spaces abstract in this paper a class of generalized f complementarity problems and three classes of variational inequalities are introduced in real banach spaces and the equivalences among them are established under certain conditions several coercivity conditions are introduced for the existence of solutions of the generalized f complementarity problem under some suitable assumptions it is shown that each of these coercivity conditions is equivalent to the nonemptyness and boundedness of the solution set for the generalized f complementarity problem in infinite dimensional banach spaces and even the nonemptyness and compactness of the solution set for the generalized f complementarity problem in finite dimensional spaces the existence of least elements for the feasible set of the generalized f complementarity problem is also presented under suitable conditions

finding solutions of implicit complementarity problems by isotonicity of the metric projection abstract isac and nemeth g isac and a b nemeth projection method isotone projection cones and the complementarity problem j math anal app 153 258 275 1990 proved that solving a coincidence point equation fixed point problem in turn solves the corresponding implicit complementarity problem nonlinear complementarity problem and they exploited the isotonicity of the metric projection onto isotone projection cones to solve implicit complementarity problems nonlinear complementarity problems defined by these cones in this paper the notion of isotone projection cones is employed and an iterative algorithm is presented in connection with an implicit complementarity problem on isotone projection cones it is proved that if the sequence generated through the defined algorithm is convergent then its limit is a solution of the coincidence point equation and thus solves the implicit complementarity problem sufficient conditions are given for this sequence to be convergent for implicit complementarity problems defined by isotone projection cones the question of finding nonzero solutions of these problems is also studied

a duality between the metric projection onto a convex cone and the metric projection onto its dual abstract if k and l are mutually dual pointed convex cones in r n with the metric projections onto them denoted by p k and p l respectively then the following two assertions are equivalent i p k is isotone with respect to the order induced by k i e v u k implies p k v p k u k ii p l is subadditive with respect to the order induced by l i e p l u p l v p l u v l for any u v r n

equivalence of nonlinear complementarity problems and least element problems in banach lattices a class of not necessarily linear operators a v v is introduced where the banach space v and its dual v carry dual vector lattice orderings these operators called z maps generalize the n n real matrices with nonnegative off diagonal elements if a is a strictly monotone z map with certain regularity and growth conditions and if f denotes the set of all vectors v v for which v 0 and av 0 then it is shown that the complementarity problem to find v f such that 0 and the least element problem to find v f with v w for all w f have the same unique solution some other problems equivalent to these and some examples are discussed

boundary representations and rigidity of submodules abstract this paper considers two problems on the fock type spaces f s 0 s 1 firstly it is shown that on the space f s 0 s 1 the identity representation of c i t 1 t n is a boundary representation for the banach subalgebra b i t 1 t n while on the space f 1 it is not secondly it is shown that all the submodules of f 1 are rigid

solving cone constrained convex programs by differential inclusions a differential inclusion is designed for solving cone constrained convex programs the method is of subgradient projection type it involves projection penalties and lagrangian relaxation nonsmooth data can be accommodated a novelty is that multipliers converge monotonically upwards to equilibrium levels an application to stochastic programming is considered

analytic hilbert spaces over the complex plane in this paper we study the structure of quasi invariant subspaces of analytic hilbert spaces over the complex plane we especially investigate when two quasi invariant subspaces are similar or unitarily equivalent for an analytic hilbert space over the complex plane

solving nonlinear complementarity problems by isotonicity of the metric projection abstract the main motivation for introducing the notion of isotone projection cones was to solve nonlinear complementarity problems the notion of isotone projection cones is introduced by this paper in a similar fashion iterative methods for finding solutions of complementarity problems on isotone projection cones are presented the problem of finding nonzero solutions of these problems is also considered

iterative algorithm for completely generalized set valued strongly nonlinear mixed variational like inequalities a class of completely generalized set valued strongly nonlinear mixed variational likeinequalities is introduced the auxiliary principle technique is extended to study this new class of mixed variational like inequalities the existence of a solution of the auxiliary problem for this new class of mixed variational like inequalities is shown the iterative algorithm for this new class of mixed variational like inequalities is given by virtue of this existence result moreover the existence of a solution of this new class of mixed variational like inequalities and the strong convergence of iterative sequences generated by the algorithm are shown the convergence criteria are different from some early and recent ones presented in the literature

generalized monotonicity and convexity of non differentiable functions the relationships between strict strong convexity of non differentiable functions and strict strong monotonicity of set valued mappings and strict strong sharp pseudo convexity of non differentiable functions and strict strong pseudo monotonicity of set valued mappings as well as quasi convexity of non differentiable functions and quasi monotonicity of set valued mappings are studied in this paper in addition the relations between generalized convexity of non differentiable functions and generalized co coerciveness of set valued mappings are also analyzed

isotonic regression and isotonic projection abstract the note describes the cones in the euclidean space admitting isotonic metric projection with respect to the coordinate wise ordering as a consequence it is shown that the metric projection onto the isotonic regression cone the cone defined by the general isotonic regression problem admits a projection which is isotonic with respect to the coordinate wise ordering

the linear order complementarity problem the classical complementarity problem in euclidean space can be viewed alternatively as a variational inequality or as a lattice orthogonality problem generalizations of the former have been extensively studied but infinite dimensional analogues of the latter have been largely ignored moreover as we show many well known results about the classical complementarity problem are more appropriately viewed order theoretically this is particularly true of least element solutions which are central to the present study of order complementarity in vector lattices we emphasize that the lattice theoretic descriptions we employ are very useful even in the standard finite dimensional setting

invariant subspaces quasi invariant subspaces and hankel operators abstract in this paper using the theory of hilbert modules we study invariant subspaces of the bergman spaces on bounded symmetric domains and quasi invariant subspaces of the segal bargmann spaces we completely characterize small hankel operators with finite rank on these spaces

d orientation sequences for continuous functions and nonlinear complementarity problems we introduce the new concept of d orientation sequence for continuous functions it is shown that if there does not exist a d orientation sequence for a continuous function then the corresponding complementarity problem cp has a solution we believe that such a result characterizes an intrinsic property of cps as the concept of exceptional family of elements the notion of d orientation sequence of a function is also a powerful tool for investigating the existence theorems of cps we use this new tool to establish among other things a new existence result for a class of p mapping cps

isotone retraction cones in hilbert spaces abstract a mapping is called isotone if it is monotone increasing with respect to the order induced by a pointed closed convex cone finding the pointed closed convex generating cones for which the projection mapping onto the cone is isotone is a difficult problem which was analyzed in isac and nemeth 1986 1990 1992 1 2 3 4 5 such cones are called isotone projection cones in particular it was shown that any isotone projection cone is latticial isac 1990 2 this problem is extended by replacing the projection mapping with continuous retractions onto the cone by introducing the notion of sharp mappings it is shown that a pointed closed convex generating cone is latticial if and only if there is a continuous retraction onto the cone whose complement is sharp several particular cases are considered and examples are given

temperature measurement from perturbations the notion of configuration temperature is extended to discontinuous systems by identifying the temperature as the nontrivial root of several integral equations regarding the distribution of the energy change upon configuration perturbations the relations are generalized to pressure and a distribution mean force

an alternative theorem for generalized variational inequalities and solvability of nonlinear quasi p m complementarity problems in this paper an alternative theorem and hence a sufficient solution condition is established for generalized variational inequality problems the concept of exceptional family for generalized variational inequality is introduced this concept is general enough to include as special cases the notions of exceptional family of elements and the d orientation sequence for continuous functions particularly we apply the alternative theorem for investigating the solvability of the nonlinear complementarity problems with so called quasi p m maps which are broad enough to encompass the quasi monotone maps and p maps as the special cases an existence theorem for this class of complementarity problems is established which significantly generalizes several previous existence results in the literature

the contraction principle for set valued mappings on a metric space with a graph let x d be a metric space and f x x be a set valued mapping we obtain sufficient conditions for the existence of a fixed point of the mapping f in the metric space x endowed with a graph g such that the set v g of vertices of g coincides with x and the set of edges of g is e g x y x y xxx

approximate proximal algorithms for generalized variational inequalities with paramonotonicity and pseudomonotonicity we propose an approximate proximal algorithm for solving generalized variational inequalities in hilbert space extension to bregman function based approximate proximal algorithm is also discussed weak convergence of these two algorithms are established under the paramonotonicity and pseudomonotonicity assumptions of the operators

integral fluctuation theorem for the housekeeping heat the housekeeping heat qhk is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states by analysing the evolution of its probability distribution we prove an integral fluctuation theorem exp qhk 1 valid for arbitrary driven transitions between steady states we discuss gaussian limiting cases and the difference between the new theorem and both the hatano sasa and the jarzynski relation

z transformations on proper and symmetric cones z transformations motivated by the similarities between the properties of z matrices on r n and lyapunov and stein transformations on the semidefinite cone mathcal s n we introduce and study z transformations on proper cones we show that many properties of z matrices extend to z transformations we describe the diagonal stability of such a transformation on a symmetric cone by means of quadratic representations finally we study the equivalence of q and p properties of z transformations on symmetric cones in particular we prove such an equivalence on the lorentz cone

finite codimensional invariant subspaces of bergman spaces abstract for a large class of bounded domains in c we describe thosefinite codimensional subspaces of the bergman space that are invariant undermultiplication by z using different techniques for certain domains in cn wedescribe those finite codimensional subspaces of the bergman space that areinvariant under multiplication by all the coordinate functions fix a positive integer n and let v denote lebesgue volume measure on cn sothat if n 1 then v is just area measure let q c c be a domain which asusual means that 0 is a nonempty open connected subset of c for an analyticfunction from 0 to c and 1 p oo the norm n p is defined by wfh r jn f pdv the bergman space l q is defined to be the set of analytic functions from fi toc such that n p oo our goal in this paper is to describe the closed finite codimensional subspaces oflpa 0 that are invariant under multiplication by the coordinate functions zi

new monte carlo algorithm entropic sampling we present a new monte carlo sampling algorithm with which one can obtain any desired distribution of the sampling in one monte carlo simulation the free energy and the entropy of a system can thus be obtained from a simple exercise of this algorithm the main idea is to sample directly the entropy of a system at infinite temperature importance sampling is shown to be a particular case of the new algorithm the algorithm is tested against the exact partition function of the ital l 4 simple cubic ising model a comparison with the multicanonical ensemble for the ital l 12 ital q 10 potts model shows that the new algorithm is more general and more efficient

domination of quadratic forms we study domination of quadratic forms in the abstract setting of ordered hilbert spaces our main result gives a characterization in terms of the associated forms this generalizes and unifies various earlier works along the way we present several examples

invariant subspaces of h2 on a torus abstract this paper answers two questions about unitarily equivalent pairs of invariant subspaces x1 and x2 of the hardy space h2 tn these satisfy x2 x1 for some unimodular l tn i must then be a quotient of inner functions ii if g 2 g 1 is such a quotient does it follow that the inner functions g1 and g2 can be so chosen that g 1 x 1 g 2 x 2 is an invariant subspace of h2 tn not merely of l2 tn when n 1 both answers are no

variational and generalized variational inequalities with discontinuous mappings abstract in this paper we derive several existence results for the variational and the generalized variational inequality problems where the mappings under consideration need not have any continuity properties uniqueness of the solution of the generalized variational inequality problem is also investigated as a by product we obtain several existence and uniqueness results for the generalized complementarity problem applications to minimization problems with generalized convex functions are considered

a duality between the metric projection onto a convex cone and the metric projection onto its dual in hilbert spaces abstract if k and l are mutually dual closed convex cones in a hilbert space h with the metric projections onto them denoted by p k and p l respectively then the following two assertions are equivalent i p k is isotone with respect to the order induced by k i e v u k implies p k v p k u k ii p l is subadditive with respect to the order induced by l i e p l u p l v p l u v l for any u v h this extends the similar result of a b nemeth and the author for euclidean spaces the extension is essential because the proof of the result for euclidean spaces is essentially finite dimensional and seemingly cannot be extended for hilbert spaces the proof of the result for hilbert spaces is based on a completely different idea which uses extended lattice operations

essentially normal hilbert modules and k homology this paper mainly concerns the essential normality of graded submodules essentially all of the basic hilbert modules that have received attention over the years are p essentially normal including the d shift hilbert module the hardy and bergman modules of the unit ball arveson conjectured graded submodules over the unit ball inherit this property and provided motivations to seek an affirmative answer some positive results have been obtained by arveson and douglas however the problem has been resistant in dimensions d 2 3 this paper shows that the arveson s conjecture is true in any dimension the paper also gives an affirmative answer in the case of the graded principal submodule finally the paper is associated with k homology invariants arising from graded quotient modules by which geometry of the quotient modules and geometry of algebraic varieties are connected in dimensions d 2 3 it is shown that k homology invariants determined by graded quotients are nontrivial the paper also establishes results on p smoothness of k homology elements and gives an explicit expression for k homology invariant in dimension d 2

polynomials having leading terms over c2 in the fock space we characterize polynomials p having leading terms over c2 in a generalized sense as applications we study a quasi invariant subspace p generated by p in the fock space and show that a quasi invariant subspace m is similar to p if and only if m q for some polynomial q having the same leading term as p these are generalizations of guo and hou s work

generalized vector variational inequalities with star pseudomonotone and discontinuous operators abstract it is well known that a vector variational inequality can be a very efficient model for use in studying vector optimization problems by using the ky fan fixed point theorem and the scalarization method we will prove some existence theorems for strong solutions for generalized vector variational inequalities where discontinuous and star pseudomonotone operators are involved our results can be applied to the study of the existence of solutions of vector optimal problems some examples are given and analyzed

a new projection method for variational inequality problems we propose a new projection algorithm for solving the variational inequality problem where the underlying function is continuous and satisfies a certain generalized monotonicity assumption e g it can be pseudomonotone the method is simple and admits a nice geometric interpretation it consists of two steps first we construct an appropriate hyperplane which strictly separates the current iterate from the solutions of the problem this procedure requires a single projection onto the feasible set and employs an armijo type linesearch along a feasible direction then the next iterate is obtained as the projection of the current iterate onto the intersection of the feasible set with the halfspace containing the solution set thus in contrast with most other projection type methods only two projection operations per iteration are needed the method is shown to be globally convergent to a solution of the variational inequality problem under minimal assumptions preliminary computational experience is also reported

on the equivalence of nonlinear complementarity problems and least element problems strictly pseudomonotonez maps operating on banach lattices are considered equivalence of complementarity problems and least element problems is established under certain regularity and growth conditions this extends a recent result by riddell 1981 for strictly monotonez maps to the pseudomonotone case some other problems equivalent to the above are discussed as well

inverse m matrices abstract this is an attempt at a comprehensive expository study of those nonnegative matrices which happen to be inverses of m matrices and is aimed at an audience conversant with basic ideas of matrix theory a theme is the parallels anddifferences between the class of m matrices and the class of inverse m matrices among the primary tools used are diagonal multiplications the neumann expansion and the form of the inverse of a partitioned matrix some of the results seem not to have appeared before and several unsolved problems are mentioned

a uniqueness theorem for the generalized order linear complementary problem associated with m matrices abstract in this paper we prove a uniqueness theorem for a class of complementarity problems involving m matrices

the rational complementarity problem abstract an extension of the linear complementarity problem lcp of mathematical programming is the so called rational complementarity problem rcp this problem occurs if complementarity conditions are imposed on input and output variables of linear dynamical input state output systems the resulting dynamical systems are called linear complementarity systems since the rcp is crucial both in issues concerning existence and uniqueness of solutions to complementarity systems and in time simulation of complementarity systems it is worthwhile to consider existence and uniqueness questions of solutions to the rcp in this paper necessary and sufficient conditions are presented guaranteeing existence and uniqueness of solutions to the rcp in terms of corresponding lcps using these results and proving that the corresponding lcps have certain properties we can show uniqueness and existence of solutions to linear mechanical systems with unilateral constraints electrical networks with diodes and linear dynamical systems subject to relays and or coulomb friction

toeplitz algebras subnormal tuples and rigidity on reproducing c z1 zd modules this paper mainly considers toeplitz algebras subnormal tuples and rigidity concerning reproducing c z1 zd modules by making use of arveson s boundary representation theory we find there is more rigidity in several variables than there is in single variable we specialize our attention to reproducing c z1 zd modules with u invariant kernels by examining the spectrum and the essential spectrum of the d tuple mz1 mzd and deducing an exact sequence of c algebras associated with toeplitz algebra finally we deal with toeplitz algebras defined on arveson submodules and rigidity of arveson submodules

a geometrical approach to iterative isotone regression in the present paper we propose and analyze a novel method for estimating a univariate regression function of bounded variation the underpinning idea is to combine two classical tools in nonparametric statistics namely isotonic regression and the estimation of additive models a geometrical interpretation enables us to link this iterative method with von neumann s algorithm moreover making a connection with the general property of isotonicity of projection onto convex cones we derive another equivalent algorithm and go further in the analysis

star generating vectors of rudin s quotient modules abstract the purpose of this paper is to study a class of quotient modules of the hardy module h 2 d n along with the two variables quotient modules introduced by w rudin we introduce and study a large class of quotient modules namely rudin s quotient modules of h 2 d n by exploiting the structure of minimal representations we obtain an explicit co rank formula for rudin s quotient modules

regularizing the abstract convex program abstract characterizations of optimality for the abstract convex program inf p x g x s x p where s is an arbitrary convex cone in a finite dimensional space is a convex set and p and g are respectively convex and s convex on were given in 10 these characterizations hold without any constraint qualification they use the minimal cone s f of p and the cone of directions of constancy d g s f in the faithfully convex case these cones can be used to regularize p i e transform p into an equivalent program p r for which slater s condition holds we present an algorithm that finds both s f and d g s f the main step of the algorithm consists in solving a particular complementarity problem we also present a characterization of optimality for p in terms of the cone of directions of constancy of a convex functional d g rather than d g s f

on the existence of pareto efficient points we prove some general theorems on the existence of minimal points of compact sets in linear spaces with respect to closed convex orderings these results are compared to the axiom of choice

iterative methods for nonlinear complementarity problems on isotone projection cones in this paper we present a recursion related to a nonlinear complementarity problem defined by a closed convex cone in a hilbert space and a continuous mapping defined on the cone if the recursion is convergent then its limit is a solution of the nonlinear complementarity problem in the case of isotone projection cones sufficient conditions are given for the mapping so that the recursion to be convergent