a new neural network for solving linear and quadratic programming problems a new neural network for solving linear and quadratic programming problems is presented and is shown to be globally convergent the new neural network improves existing neural networks for solving these problems it avoids the parameter turning problem it is capable of achieving the exact solutions and it uses only simple hardware in which no analog multipliers for variables are required furthermore the network solves both the primal problems and their dual problems simultaneously

coincidence of extendible vector valued ideals with their minimal kernel abstract we provide coincidence results for vector valued ideals of multilinear operators more precisely if a is an ideal of n linear mappings we give conditions for which the equality a e 1 e n f a min e 1 e n f holds isometrically as an application we obtain in many cases that the monomials form a schauder basis of the space a e 1 e n f several structural and geometric properties are also derived using this equality we apply our results to the particular case where a is the classical ideal of extendible or pietsch integral multilinear operators similar statements are given for ideals of vector valued homogeneous polynomials

analytic approximation onc0 the banach spacec0is shown to possess the analytic approximation property more precisely given any uniformly continuous function on an open setg c0 an analytic map is constructed which uniformly approximates the given function

uniform homeomorphisms of banach spaces and asymptotic structure we give a general result on the behavior of spreading models in banach spaces which coarse lipschitz embed into asymptotically uniformly convex spaces we use this result to study the uniqueness of the uniform structure in p sums of finite dimensional spaces for 1 p in particular we give some new examples of spaces with unique uniform structure

trees and branches in banach spaces an infinite dimensional notion of asymptotic structure is considered this notion is developed in terms of trees and branches on banach spaces every countably infinite countably branching tree t of a certain type on a space x is presumed to have a branch with some property it is shown that then x can be embedded into a space with an fdd e i so that all normalized sequences in x which are almost a skipped blocking of e i have that property as an application of our work we prove that if x is a separable reflexive banach space and for some 1 0 there exists a subspace of x having finite codimension which c 2 e embeds into the l p sum of finite dimensional spaces

bases in spaces of multilinear forms over banach spaces fil dimant veronica universidad de san andres departamento de matematica y ciencias argentina

primal dual solution for the linear programming problems using neural networks in this paper we represent two new methods for the solution of canonical form linear programming problems in order to solve this linear programming problem we must minimize energy function of the corresponding neural network here energy function is considered as a liapunov function and we use treated hopfield neural network first new method finds optimal solution for primal problem using neural network while second new method composes primal and dual problem and therefore finds optimal solution for both problems numerical results compared with simplex solution and find that the convergence of two new methods to the correct solution is too fast even faster than neguyen s method the new methods are fully stable

polynomial approximation in banach spaces abstract we define new classes of topological algebras of holomorphic functions on open subsets of banach spaces and on open subsets of dual banach spaces we investigate properties and derive results concerning polynomial approximation on such algebras we give an explicit description of their spectra derive results on finitely generated ideals and theorems of banach stone type we show that under certain conditions on the open subset u this new algebra coincides with h w u u deriving new results on h w u u

a novel neural network for variational inequalities with linear and nonlinear constraints variational inequality is a uniform approach for many important optimization and equilibrium problems based on the sufficient and necessary conditions of the solution this paper presents a novel neural network model for solving variational inequalities with linear and nonlinear constraints three sufficient conditions are provided to ensure that the proposed network with an asymmetric mapping is stable in the sense of lyapunov and converges to an exact solution of the original problem meanwhile the proposed network with a gradient mapping is also proved to be stable in the sense of lyapunov and to have a finite time convergence under some mild conditions by using a new energy function compared with the existing neural networks the new model can be applied to solve some nonmonotone problems has no adjustable parameter and has lower complexity thus the structure of the proposed network is very simple since the proposed network can be used to solve a broad class of optimization problems it has great application potential the validity and transient behavior of the proposed neural network are demonstrated by several numerical examples

a general methodology for designing globally convergent optimization neural networks we present a general methodology for designing optimization neural networks we prove that the neural networks constructed by using the proposed method are guaranteed to be globally convergent to solutions of problems with bounded or unbounded solution sets in contrast with the gradient methods whose convergence is not guaranteed we show that the proposed method contains both the gradient methods and nongradient methods employed in existing optimization neural networks as special cases based on the theoretical results of the proposed method we study the convergence and stability of general gradient models in the case of unisolated solutions using the proposed method we derive some new neural network models for a very large class of optimization problems in which the equilibrium points correspond to exact solutions and there is no variable parameter finally some numerical examples show the effectiveness of the method

extensions of multilinear operators and banach space properties a new characterization of the dunford pettis property in terms of the extensions of multilinear operators to the biduals is obtained for the first time multilinear characterizations of the reciprocal dunford pettis property and pelczynski s property v are also found polynomial and holomorphic versions of these properties are given as well

a discrete time neural network for solving nonlinear convex problems with hybrid constraints this paper investigates a discrete time neural network model for solving nonlinear convex programming problems with hybrid constraints the neural network finds the solution of both primal and dual problems and converges to the corresponding exact solution globally we prove here that the proposed neural network is globally exponentially stable furthermore we extend the proposed neural network for solving a class of monotone variational inequality problems with hybrid constraints compared with other existing neural networks for solving such problems the proposed neural network has a low complexity for implementation without a penalty parameter and converge an exact solution to convex problem with hybrid constraints some numerical simulations for justifying the theoretical analysis are also given the numerical simulations are shown that in the new model note only the cost of the hardware implementation is not relatively expensive but also accuracy of the solution is greatly good

a neural network based on the generalized fischer burmeister function for nonlinear complementarity problems in this paper we consider a neural network model for solving the nonlinear complementarity problem ncp the neural network is derived from an equivalent unconstrained minimization reformulation of the ncp which is based on the generalized fischer burmeister function f p a b email protected a b p a b we establish the existence and the convergence of the trajectory of the neural network and study its lyapunov stability asymptotic stability as well as exponential stability it was found that a larger p leads to a better convergence rate of the trajectory numerical simulations verify the obtained theoretical results

symmetry of the unsteady linearized boltzmann equation in a fixed bounded domain a symmetric relation between time dependent problems described by the linearized boltzmann equation is obtained for a gas in a fixed bounded domain general representations of the total mass momentum and energy in the domain as well as their fluxes through the boundary in terms of an appropriate green function are derived from that relation several application examples are presented similarities to the fluctuation dissipation theorem in the linear response theory and its generalization to gas systems of arbitrary knudsen numbers are also discussed the present paper is an extension of the previous work of the author takata in j stat phys 136 751 784 2009 to time dependent problems

on m ideals of compact operators in lorentz sequence spaces abstract let x d v p and y d w q be lorentz sequence spaces we investigate when the space k x y of compact linear operators acting from x to y forms or does not form an m ideal in the space of bounded linear operators we show that k x y fails to be a non trivial m ideal whenever p 1 or p q in the case when 1 p q we establish a general essential condition guaranteeing that k x y is not an m ideal in contrast we prove that non trivial m ideals k x y do exist whenever 1 p q and we give a description of them

weakly p compact p banach saks and super reflexive banach spaces abstract new techniques are introduced to extract subsequences satisfying certain upper estimates in suitable banach spaces using these methods alternative proofs of results of rakov math notes 26 1979 909 916 and godun and rakov math notes 31 1982 32 39 are obtained moreover these methods provide a useful tool to obtain new examples of spaces in the sense of carne et al trans amer math soc 314 1989 639 659

real analytic approximation of lipschitz functions on hilbert space and other banach spaces let x be a separable banach space with a separating polynomial we show that there exists c 1 depending only on x such that for every lipschitz function f x r and every epsilon 0 there exists a lipschitz real analytic function g x r such that vertical bar f x g x vertical bar epsilon e and lip g c lip f this result is new even in the case when x is a hilbert space furthermore in the hilbertian case we also show that c can be assumed to be any number greater than i

a posteriori error bounds for the linearly constrained varitional inequality problem in this paper we derive a posteriori error bound of an approximate solution to a linearly constrained variational inequality problem three measures of error are used with each depending on a particular characterization of an exact solution and related to a certain class of iterative methods

new discrete time recurrent neural network proposal for quadratic optimization with general linear constraints in this brief the quadratic problem with general linear constraints is reformulated using the wolfe dual theory and a very simple discrete time recurrent neural network is proved to be able to solve it conditions that guarantee global convergence of this network to the constrained minimum are developed the computational complexity of the method is analyzed and experimental work is presented that shows its high efficiency

numerical solutions for constrained quadratic problems using high performance neural networks two new classes of neural networks for solving constrained quadratic programming problems are presented the main advantage of these networks is the requirement to use economic analog multipliers for variables the numerical simulations demonstrate that in the new neural networks not only the cost of the hardware implementation is not relatively expensive but also accuracy of the solution is greatly good the network dynamic behaviors are discussed the numerical simulations are shown that an optimal solution of the quadratic problems is an equilibrium point of the neural dynamics and vise versa we show that these networks find the solution of both primal and dual problems and converge to the corresponding exact solutions globally the proposed new neural networks models are fully stable

onsager casimir reciprocity relations for open gaseous systems at arbitrary rarefaction iii theory and its application for gaseous mixtures abstract the statistical approach to the nonequilibrium thermodynamics based on fundamental properties of the boltzmann equation and boundary condition for the distribution function is generalized for mixtures of nonreactive gases as an application of the approach several problems of gaseous mixture flows are considered the problems are as follows evaporation and condensation of the mixture between two parallel plates two dimensional mixture flow through a capillary mixture flow past a particle the explicit expressions of the thermodynamic fluxes and kinetic coefficients satisfying the onsager casimir reciprocity relations are derived the couplings between cross effects arising in the mixture flows are obtained from these relations

small subspaces of l_p we prove that if x is a subspace of lp 2 p 1 then either x embeds isomorphically into p 2 or x contains a subspace y which is isomorphic to p 2 we also give an intrinsic characterization of when x embeds into p 2 in terms of weakly null trees in x or equivalently in terms of the innite asymptotic game played in x this solves problems concerning small subspaces of lp originating in the 1970 s the techniques used were developed over several decades the most recent being that of weakly null trees developed in the 2000 s

lifting convex approximation properties from banach spaces to their dual spaces and the related local reflexivity abstract our main result demonstrates that rather weak forms of the extendable local reflexivity and of the principle of local reflexivity are needed for the lifting of bounded convex approximation properties from banach spaces to their dual spaces this provides a unified approach to the lifting of various bounded approximation properties including besides the classical ones the approximation property for pairs of banach spaces and the positive approximation property of banach lattices

entire functions on banach spaces with a separable dual abstract let e and f be complex banach spaces we show that if e has a separable dual then every holomorphic function from e into f which is bounded on weakly compact sets is bounded on bounded sets

a norm convergence result on random products of relaxed projections in hilbert space suppose x is a hilbert space and c 1 ldots c n are closed convex intersecting subsets with projections p 1 ldots p n suppose further r is a mapping from bbb n onto 1 ldots n that assumes every value infinitely often we prove a more general version of the following result begin quote if the n tuple c 1 ldots c n is innately boundedly regular then the sequence x n defined by x 0 in x mbox arbitrary x n 1 p r n x n mbox for all n geq 0 converges in norm to some point in bigcap i 1 n c i end quote examples without the usual assumptions on compactness are given methods of this type have been used in areas like computerized tomography and signal processing

entire functions on c0 abstract it is shown that every holomorphic function on c 0 which is bounded on weakly compact sets is bounded on bounded sets

symmetry of the linearized boltzmann equation and its application a symmetric relation of macroscopic quantities between two different steady problems of the linearized boltzmann equation is derived a few applications to half space problems are presented first then for the gas in bounded or unbounded domains such that solid bodies or condensed phases are confined in a finite region general representations of the mass momentum and heat fluxes through the boundary possibly at a point on or on a part of it are derived from the symmetric relation linked to the separability of boundary data this result implies a reduction of the original problem to a single elemental problem in the same domain as far as the fluxes are concerned many applications are also presented

a recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints this paper presents a continuous time recurrent neural network model for nonlinear optimization with any continuously differentiable objective function and bound constraints quadratic optimization with bound constraints is a special problem which can be solved by the recurrent neural network the proposed recurrent neural network has the following characteristics 1 it is regular in the sense that any optimum of the objective function with bound constraints is also an equilibrium point of the neural network if the objective function to be minimized is convex then the recurrent neural network is complete in the sense that the set of optima of the function with bound constraints coincides with the set of equilibria of the neural network 2 the recurrent neural network is primal and quasiconvergent in the sense that its trajectory cannot escape from the feasible region and will converge to the set of equilibria of the neural network for any initial point in the feasible bound region 3 the recurrent neural network has an attractivity property in the sense that its trajectory will eventually converge to the feasible region for any initial states even at outside of the bounded feasible region 4 for minimizing any strictly convex quadratic objective function subject to bound constraints the recurrent neural network is globally exponentially stable for almost any positive network parameters simulation results are given to demonstrate the convergence and performance of the proposed recurrent neural network for nonlinear optimization with bound constraints

decompositions of the free additive convolution we introduce and study a new type of convolution of probability measures denoted and called the s free additive convolution which is defined by the subordination functions associated with the free additive convolution we derive an alternating decomposition of for compactly supported and using another convolution called orthogonal additive convolution this decomposition leads to two types of complete alternating decompositions of the free additive convolution more importantly we develop an operatorial approach to the subordination property and introduce the associated notion of s free independence moreover we establish relations between convolutions associated with the main notions of noncommutative independence free monotone and boolean finally our result leads to natural decompositions of the free product of rooted graphs

all schatten spaces endowed with the schur product are q algebras we prove that the banach algebra formed by the space of compact operators on a hilbert space endowed with the schur product is a quotient of a uniform algebra also known as a q algebra together with a similar result of perez garcia for the trace class this completes the answer to a long standing question of varopoulos

lp harmonic analysis and radon transforms on the heisenberg group in this paper harmonic analysis in the heisenberg group heisn cn r with group law z t z t z z t t 12im z z is taken to mean the joint spectral theory of the operators l heisenberg laplacian and t t the spectral decomposition of e l2 is given explicitly as e 0 e d where e 1 k 0 1 2 and e z t n 2 n 1 n 2k n 1 exp ie tn 2k exp z 24 n 2k lkn 1 z 22 n 2k where lkn 1 denotes the laguerre polynomial the eigenvalues are it e e n 2k e and l k e k e this decomposition is essentially well known but has not previously been described in this light it is also the decomposition into irreducibles of the representation of the heisenberg motion group semi direct product of heisn and u n on l2 heisn the main result is a summability in lp of the decomposition for e lp 1 p limr 1 rk 0 ed for p 1 only a weaker substitute is available and for p the decomposition is false there is also a plancherel formula for l2 2 2 k e n 2k 0 k e z 0 2dzd a number of explicit examples of the decomposition are computed including part of the schrodinger propagator eisl the heisenberg radon transform is defined by r z t n z t w 0 dw this operator was studied by geller and stein it is shown to be bounded from lp to lq if and only if p 2n 2 2n 1 and q 2n 2 some generalizations of these results to the free step two nilpotent lie groups are given but the results are not as complete

weak strong continuity of multilinear mappings and the pelczynski pitt theorem abstract in generalizing a result of pelczynski the sequential weak to norm continuity ofn linear mappings between certain banach spaces including spaces of type and cotype will be studied in particular it is shown that everyn linear continuous mapping from lp1 lpninto lqis compact if and only if i 1n 1 pi

weakly continuous mappings on banach spaces abstract it is shown that every n homogeneous continuous polynomial on a banach space e which is weakly continuous on the unit ball of e is weakly uniformly continuous on the unit ball of e applications of the result to spaces of polynomials and holomorphic mappings on e are given

solving convex programming problems with equality constraints by neural networks abstract this paper presents a neural network approach for solving convex programming problems with equality constraints after defining the energy function and neural dynamics of the proposed neural network we show the existence of an equilibrium point at which the neural dynamics becomes asymptotically stable it is shown that under proper conditions an optimal solution of the underlying convex programming problems is an equilibrium point of the neural dynamics and vise versa the configuration of the proposed neural network with an exact layout is provided for solving linear programming problems the operational characteristics of the neural network are demonstrated by numerical examples

atomic decompositions for tensor products and polynomial spaces abstract we study the existence of atomic decompositions for tensor products of banach spaces and spaces of homogeneous polynomials if a banach space x admits an atomic decomposition of a certain kind we show that the symmetrized tensor product of the elements of the atomic decomposition provides an atomic decomposition for the symmetric tensor product s n x for any symmetric tensor norm in addition the reciprocal statement is investigated and analogous consequences for the full tensor product are obtained finally we apply the previous results to establish the existence of monomial atomic decompositions for certain ideals of polynomials on x

multilinear forms subsymmetric polynomials and spreading models on banach spaces abstract some applications of ramsey theory to the study of multilinear forms and polynomials on banach spaces are given related to the existence of lower l q estimates of sequences we give an explicit representation of subsymmetric polynomials in banach spaces with subsymmetric basis finally we apply our results to get approximation of polynomials by subsymmetric polynomials and to the problem of stabilization of a certain chain of algebras generated by polynomials

beurling fourier algebras on compact groups spectral theory for a compact group g we define the beurling fourier algebra a omega g on g for weights omega defined on the dual what g and taking positive values the classical fourier algebra corresponds to the case omega is the constant weight 1 we study the gelfand spectrum of the algebra realizing it as a subset of the complexification g mathbb c defined by mckennon and cartwright and mcmullen in many cases such as for polynomial weights the spectrum is simply g we discuss the questions when the algebra a omega g is symmetric and regular we also obtain various results concerning spectral synthesis for a omega g

quasi completely continuous multilinear operators we introduce the concept of quasi completely continuous multilinear operators and use this concept to characterize for a wide class of banach spaces x1 xk the multilinear operators t x1 xk x with an x valued aron berner extension

a novel neural network for solving semidefinite programming problems with some applications abstract in this paper we present a neural network model for solving semidefinite programming we show that the equilibrium point of the proposed neural network and the kkt point of the semidefinite programming are equal by employing lyapunov function approach it is also shown that the suggested neural network model is stable in the sense of lyapunov and globally convergent to an exact optimal solution of the original problem some applications of the proposed scheme are stated by modeling of some important problems as semidefinite programming problems numerical simulations verify the obtained theoretical results

descriptive complexity of some isomorphism classes of banach spaces abstract we present a topological frame in which it is possible to estimate the complexity of some borel families of separable banach spaces we use this frame for evaluating the complexity of the isomorphism class of the hilbert space l 2 of certain asymptotically hilbertian spaces and of the l p spaces under the condition 1 p the complexity appears to increase with the distance to the hilbert space commented open problems conclude the article

relationships between properties that imply the weak fixed point property a number of banach space properties have previously been shown to imply the weak fixed point property we investigate various connections between these properties

a lagrangian network for kinematic control of redundant robot manipulators a recurrent neural network called the lagrangian network is presented for the kinematic control of redundant robot manipulators the optimal redundancy resolution is determined by the lagrangian network through real time solution to the inverse kinematics problem formulated as a quadratic optimization problem while the signal for a desired velocity of the end effector is fed into the inputs of the lagrangian network it generates the joint velocity vector of the manipulator in its outputs along with the associated lagrange multipliers the proposed lagrangian network is shown to be capable of asymptotic tracking for the motion control of kinematically redundant manipulators

bases in the space of regular multilinear operators on banach lattices abstract for banach lattices e 1 e m and f with 1 unconditional bases we show that the monomial sequence forms a 1 unconditional basis of l r e 1 e m f the banach lattice of all regular m linear operators from e 1 e m to f if and only if each basis of e 1 e m is shrinking and every positive m linear operator from e 1 e m to f is weakly sequentially continuous as a consequence we obtain necessary and sufficient conditions for which the m fold fremlin projective tensor product e 1 e m resp the m fold positive injective tensor product e 1 e m has a shrinking basis or a boundedly complete basis

unbounded violation of tripartite bell inequalities we prove that there are tripartite quantum states constructed from random unitaries that can lead to arbitrarily large violations of bell inequalities for dichotomic observables as a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model this is in sharp contrast with the bipartite case where all violations are bounded by grothendieck s constant we will discuss the possibility of determining the hilbert space dimension from the obtained violation and comment on implications for communication complexity theory moreover we show that the violation obtained from generalized greenberger horne zeilinger ghz states is always bounded so that in contrast to many other contexts ghz states do not lead to extremal quantum correlations in this case in order to derive all these physical consequences we will have to obtain new mathematical results in the theories of operator spaces and tensor norms in particular we will prove the existence of bounded but not completely bounded trilinear forms from commutative c algebras finally we will relate the existence of diagonal states leading to unbounded violations with a long standing open problem in the context of banach algebras

rolle s theorem for polynomials of degree four in a hilbert space in an infinite dimensional real hilbert space we introduce a class of fourth degree polynomials which do not satisfy rolle s theorem in the unit ball extending what happens in the finite dimensional case we show that every fourth degree polynomial defined by a compact operator satisfies rolle s theorem

the approximation property for spaces of holomorphic functions on infinite dimensional spaces ii let h u denote the vector space of all complex valued holomorphic functions on an open subset u of a banach space e let and respectively denote the compact ported topology and the bornological topology on h u we show that if e is a banach space with a shrinking schauder basis and with the property that every continuous polynomial on e is weakly continuous on bounded sets then h u and h u have the approximation property for every open subset u of e the classical space c0 the original tsirelson space t and the tsirelson james space tj are examples of banach spaces which satisfy the hypotheses of our main result our results are actually valid for riemann domains

reciprocal relations based on the non stationary boltzmann equation abstract the reciprocal relations for open gaseous systems are obtained on the basis of main properties of the non stationary boltzmann equation and gas surface interaction law it is shown that the main principles to derive the kinetic coefficients satisfying the reciprocal relations remain the same as those used for time independent gaseous systems f sharipov onsager casimir reciprocal relations based on the boltzmann equation and gas surface interaction law single gas phys rev 73 2006 026110 first the kinetic coefficients are obtained from the entropy production expression then it is proved that the coefficient matrix calculated for time reversed source functions is symmetric the proof is based on the reversibility of the gas gas and gas surface interactions three examples of applications of the present theory are given none of these examples can be treated in the frame of the classical onsager casimir reciprocal relations which are valid only in a particular case when the kinetic coefficients are odd or even with respect to the time reversion the approach is generalized for gaseous mixtures

a note on the range of the derivatives of analytic approximations of uniformly continuous functions on c0 this paper is a contribution to the body of results concerning the size of the set of derivatives of differentiable functions on a banach space the results so far have consisted of examples of highly differentiable bump functions or functions approximating a given continuous function whose set of derivatives either is surprisingly small or has a given shape the paper under review treats the case of analytic smoothness the main result states that every uniformly continuous function on c0 more generally on a space with property k can be approximated by a real analytic function whose set of derivatives is contained in t p 0 lp this is a significant step forward as analytic functions are substantially harder to deal with than c1 smooth ones indeed a local perturbation of an analytic function necessarily changes the values of the function everywhere also of particular value is the quite precise and elegant description of the set of derivatives of the approximating function

an alternating projection that does not converge in norm this paper proves that the method of alternating projections between two closed convex intersecting sets does not always converge in norm weak convergence was established by bregman soviet math dokl 6 1965 688 but the status of norm convergence was undetermined an explicit counterexample is provided

absolutely continuous multilinear operators abstract we introduce the new class of the p p 1 p m absolutely continuous multilinear operators that is defined using a summability property that provides the multilinear version of the p absolutely continuous operators we give an analogue of the pietsch domination theorem and a multilinear version of the associated factorization theorem that holds for p absolutely continuous operators obtaining in this way a rich factorization theory we present also a tensor norm which represents this multi ideal by trace duality as an application we show that p p 1 p m absolutely continuous multilinear operators are compact under some requirements applications to factorization of linear maps on banach function spaces through interpolation spaces are also given

symmetry of the linearized boltzmann equation ii entropy production and onsager casimir relation this is the second part of the study by the author on the symmetry of the linearized boltzmann equation the issue of the present part is the entropy production and the onsager casimir reciprocity relation in the steady non equilibrium systems after the discussions on the definition of the entropy entropy flow and entropy production in the non equilibrium gas systems the expression of the entropy production in the steady state is presented then for the systems weakly perturbed from a uniform equilibrium state the entropy production is shown to be expressed in terms of the solution of the linearized boltzmann equation the thermodynamic forces and fluxes and the kinetic coefficients are defined solely from the expression of the entropy production the conventional type onsager casimir relation is shown to hold for the entire range of the knudsen number in bounded and unbounded domain systems provided that the state of the gas in a far field is a local maxwellian satisfying the boltzmann equation for the latter as to the other unbounded domain systems a nonconventional reciprocity is shown to hold

multi variable subordination distributions for free additive convolution abstract let k be a positive integer and let d c k denote the space of joint distributions for k tuples of selfadjoint elements in c probability space the paper studies the concept of subordination distribution of with respect to for d c k where is the operation of free additive convolution on d c k the main tools used in this study are combinatorial properties of r transforms for joint distributions and a related operator model with operators acting on the full fock space multi variable subordination turns out to have nice relations to a process of evolution towards infinite divisibility on d c k that was recently found by belinschi and nica arxiv 0711 3787 most notably one gets better insight into a connection which this process was known to have with free brownian motion

factorization of holomorphic mappings in infinite dimensions this note is concerned with a generalization of the first identity to the non linear setting of holomorphic i e complex analytic functions on e in fact our interest in this generalization arose from a study made by the second author 15 of a suitable generalization of the second identity to the holomorphic setting however our results and methods have little in common with 15 in somewhat simplistic terms our results provide further evidence that in many situations one is justified in regarding the space h e of holomorphic functions on e as the holomorphic dual of e which shares many properties with the standard linear dual of e see for example 6 a brief outline of this paper follows after which we recall some basic results about holomorphic mappings between infinite dimensional locally convex spaces in section 2 we investigate when a holomorphic function f u c on a balanced open subset u of e admits a factorization through u a characterization of factorizable functions is given in terms of the derivative o f f our basic technique is

analytic approximations of uniformly continuous functions in real banach spaces abstract it is shown that if a separable real banach space x admits a separating analytic function with an additional condition property k concerning uniform behaviour of radii of convergence then every uniformly continuous mapping on x into any real banach space y can be approximated by analytic operators in particular the result applies to c0

weakly continuous holomorphic functions on banach spaces with a shrinking and unconditional basis let e and f be complex banach spaces and let u be an open ball in e we show that if e has a shrinking and unconditional basis then every holomorphic function f u f that is weakly continuous on u bounded sets is weakly uniformly continuous on u bounded sets

weakly sequentially continuous differentiable mappings abstract it is well known that a linear operator t l x y between banach spaces is completely continuous if and only if its adjoint t l y x takes bounded subsets of y into uniformly completely continuous subsets often called l subsets of x we give similar results for differentiable mappings more precisely if u x is an open convex subset let f u y be a differentiable mapping whose derivative f u l x y is uniformly continuous on u bounded subsets we prove that f takes weak cauchy u bounded sequences into convergent sequences if and only if f takes rosenthal u bounded subsets of u into uniformly completely continuous subsets of l x y as a consequence we extend a result of p hajek and answer a question raised by r deville and e matheron we derive differentiable characterizations of banach spaces not containing l 1 and of banach spaces without the schur property containing a copy of l 1 analogous results are given for differentiable mappings taking weakly convergent u bounded sequences into convergent sequences finally we show that if x has the hereditary dunford pettis property then every differentiable function f u r as above is locally weakly sequentially continuous

almost square banach spaces abstract we single out and study a natural class of banach spaces almost square banach spaces in an almost square space we can find given a finite set x 1 x 2 x n in the unit sphere a unit vector y such that x i y is almost one these spaces have duals that are octahedral and finite convex combinations of slices of the unit ball of an almost square space have diameter 2 we provide several examples and characterizations of almost square spaces we prove that non reflexive spaces which are m ideals in their biduals are almost square we show that every separable space containing a copy of c 0 can be renormed to be almost square a local and a weak version of almost square spaces are also studied

polynomial algebras and smooth functions in banach spaces abstract let a n x be the algebra of polynomials on a real banach space x which is generated by all continuous polynomials of degree not exceeding n let m be the minimal integer such that there is a non compact m homogeneous polynomial p p x m l 1 then n m implies that the uniform closure of a n x does not contain all polynomials of degree n 1 and hence the chain of closures a n x n m is strictly increasing in the rest of the note we give solutions to three problems concerning the behaviour of smooth functions on banach spaces posed in the literature in particular we construct an example of a uniformly differentiable real valued function f on the unit ball of a certain banach space x such that there exists no uniformly differentiable function g on b x for any 1 which coincides with f in some neighbourhood of the origin

generalizations of the busemann petty problem for sections of convex bodies abstract we present generalizations of the busemann petty problem for dual volumes of intermediate central sections of symmetric convex bodies it is proved that the answer is negative when the dimension of the sections is greater than or equal to 4 for two three dimensional sections both negative and positive answers are given depending on the orders of dual volumes involved and certain cases remain open for bodies of revolution a complete solution is obtained in all dimensions

extensions of smooth mappings into biduals and weak continuity abstract we study properties of uniformly differentiable mappings between real banach spaces among our main results are generalizations of a number of classical results for linear operators on l spaces into the setting of uniformly differentiable mappings denote by b x the closed unit ball of a banach space x let x be a l space 1 and let y be a banach space let t b x y be a continuous mapping which is uniformly differentiable in the open unit ball of x assuming that t is weakly compact then t can be extended preserving its best smoothness properties into the mapping from the 1 multiple of the unit ball of any superspace of the domain space x into the same range space y we also show that t maps weakly cauchy sequences from b x into norm convergent sequences in y this is a uniformly smooth version of the dunford pettis property for the l spaces we also show that a uniformly differentiable mapping t which is not necessarily weakly compact still maps weakly cauchy sequences from b x into norm convergent sequences in y provided y does not contain an isomorphic copy of c 0 we prove that for certain pairs of banach spaces the completion of the space of polynomials equipped with the topology of uniform convergence on the bounded sets of the functions and their derivatives up to order k coincides with the space of uniformly differentiable up to order k mappings our work is based on a number of tools that are of independent interest we prove for every pair of banach spaces x y that any continuous mapping t b x y which is uniformly differentiable of order up to k in the interior of b x can be extended preserving its best smoothness into a bidual mapping t b x y another main tool is a result of zippin s type we show that weakly cauchy sequences in x c k can be uniformly well approximated by weakly cauchy sequences from a certain c 0 is a countable ordinal subspace of x

polynomial properties of banach spaces abstract several properties defined by polynomials on a banach space are introduced and briefly studied we apply them to give necessary and sufficient conditions for the non containment of l 1 in a symmetric projective tensor product of banach spaces

polynomial sequential continuity on c k e spaces we show that for bounded sequences in c k e the polynomial sequential convergence is not equivalent to the pointwise polynomial sequential convergence we introduce several conditions on e under which different versions of the result are true when k is a scattered compact space these conditions are related with some others appeared in the literature and they seem to be of independent interest

asymptotic structure lp estimates of sequences and compactness of multilinear mappings abstract we relate the moduli of asymptotic uniform smoothness and convexity of a banach space with the existence of upper and lower l p estimates of sequences in the space to this end we introduce two properties which are related to the m p property defined by kalton and werner in this way we obtain a connection between the moduli of asymptotic uniform smoothness and convexity and compactness or weak sequential continuity of multilinear mappings finally we give some applications to the existence of analytic and asymptotically flat norms on a banach space

szlenk indices and uniform homeomorphisms we prove some rather precise renorming theorems for banach spaces with szlenk index wo we use these theorems to show the invariance of certain quantitative szlenk type indices under uniform homeomorphisms

factorization of injective ideals by interpolation we construct a factorization of certain multilinear mappings through linear operators belonging to closed injective operator ideals using interpolation technique an extension of the duality theorem for interpolation spaces is also obtained

weak sequential completeness of spaces of homogeneous polynomials abstract let p w e n f be the space of all continuous n homogeneous polynomials from a banach space e into another f that are weakly continuous on bounded sets we give sufficient conditions for the weak sequential completeness of p w e n f these sufficient conditions are also necessary if both e and f have the bounded compact approximation property we also show that the weak sequential completeness and the reflexivity of p w e n f are equivalent whenever both e and f are reflexive

weak amenability and 2 weak amenability of beurling algebras abstract let l 1 g be a beurling algebra on a locally compact abelian group g we look for general conditions on the weight which allows the vanishing of continuous derivations of l 1 g this leads us to introducing vector valued beurling algebras and considering the translation of operators on them this is then used to connect the augmentation ideal to the behavior of the derivation space we apply these results to give examples of various classes of beurling algebras which are weakly amenable 2 weakly amenable or fail to be even 2 weakly amenable

duality in spaces of nuclear and integral polynomials abstract we study the spaces of nuclear and integral vector valued polynomials and their duals we prove that if e is asplund p n ne f p i ne f isometrically for any banach space f we describe p n ne f as a subspace of p ne f in terms of weak star continuous polynomials we show that p w ne f p c ne f when e has the approximation property

some geometric properties of read s space abstract we study geometric properties of the banach space r constructed recently by c read 8 which does not contain proximinal subspaces of finite codimension greater than or equal to two concretely we show that the bidual of r is strictly convex that the norm of the dual of r is rough and that r is weakly locally uniformly rotund but it is not locally uniformly rotund apart of the own interest of the results they provide a simplification of the proof by m rmoutil 9 that the set of norm attaining functionals over r does not contain any linear subspace of dimension greater than or equal to two note that if a banach space x contains proximinal subspaces of finite codimension at least two then the set of norm attaining functionals over x contain two dimensional linear subspaces of x our results also provides positive answer to the questions of whether the dual of r is smooth and of whether r is weakly locally uniformly rotund 9 finally we present a renorming of read s space which is smooth whose dual is smooth and such that its set of norm attaining functionals does not contain any linear subspace of dimension greater than or equal to two so the renormed space does not contain proximinal subspaces of finite codimension greater than or equal to two

solving complementarity and variational inequalities problems using neural networks in this paper we propose a recurrent neural network model for solving a class of monotone variational inequalities problem with linear constraints the neural network is stable in the sense of lyapunov and globally convergent to an optimal solution compared with the existing convergence results the present proof do not require lipschitz continuity condition on the objective function this neural network model has no adjustable parameter thus its structure is very simple variational inequalities problem with general set of constraints plus a general form of the complementarity problems are solved using the proposed neural networks some examples demonstrated to show the applicability of the proposed neural networks to solve various nonlinear optimization problems numerically