some results on almost square banach spaces abstract we study almost square banach spaces under a topological point of view indeed we prove that the class of banach spaces which admits an equivalent norm to be asq is that of those banach spaces which contain an isomorphic copy of c 0 we also prove that the symmetric projective tensor products of an almost square banach space have the strong diameter two property

characterization of real inner product spaces by means of symmetrical bilinear forms abstract we investigate those normed spaces e for which the norm of any continuous symmetric bilinear form on e has the same value as the norm of the associated homogeneous polynomial in the real case we show that this property characterizes an inner product space i p s we also give some other characterizations of an i p s through symmetric bilinear forms

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

brief paper global stabilization of semilinear systems using switching controls this paper considers feedback stabilization of distributed semilinear systems using switching controls the semilinear processes together with the switched controllers constitute a type of switched nonlinear system three kinds of stabilizabilities namely weak strong and exponential stabilizabilities are investigated one by one sets of sufficient conditions are obtained for each case a necessary condition for strong stabilizability is given the stabilizing control is characterized using a minimization problem applications to parabolic and hyperbolic like equations are considered

geometric aspects of the daugavet property let x be a closed subspace of a banach space y and j be the inclusion map we say that the pair x y has the daugavet property if for every rank one bounded linear operator t from x to y the following equality kj tk 1 ktk 1 holds a new characterization of the daugavet property in terms of weak open sets is given it is shown that the operators not xing

on independence and conditioning on wiener space notant i f et i g des integrales de wiener ito multiples d ordre p et q respectivement on donne une condition necessaire et suffisante sur le couple f g sous laquelle les variables aleatoires i f et i g sont independantes ceci est base sur une caracterisation generale de l independance de variables aleatoires dans l espace de wiener dans le contexte d un calcul variationnel stochastique

the dth linear polarization constant of rd in c benitez y sarantopoulos a tonge lower bounds for norms of products of polynomials math proc cambridge philos soc 124 3 1998 395 408 it was conjectured that for all unit vectors u1 ud in rd x u1 ud supx rd x 2 d i 1d x ui 2 1 with equality occurring iff u1 ud are orthonormal we relate this to a conjecture about solutions of ay y 1 where a ui uj and show that if the conjecture fails then the u1 ud minimizing x must be linearly dependent we also show x u1 ud 1 for certain families of u1 ud

control of wave processes with distributed controls supported on a subregion it is proved that solutions of one dimensional wave equations satisfying general boundary conditions at the ends of a bounded interval i can be exactly controlled to any finite energy state by means of distributed controls which vanish outside of any fixed nonempty subinterval of i an example is given which shows that no such general analogous result can hold in higher dimensions in this case for a spherical region those states are characterized which can be exactly controlled to zero by means of controls supported in an annulus within the region it is found that very strong controllability obtains when the controls are distributed near the boundary but that only rather weak controllability is possible with controls supported in an interior annulus applications of these results to boundary control problems in annular regions are also discussed

first passage time statistics of brownian motion with purely time dependent drift and diffusion abstract systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a brownian motion bm driven by time dependent drift and diffusion coefficients modeling such systems requires solving the associated fokker planck equation subject to an absorbing barrier transitional probabilities are derived via the method of images whose applicability to time dependent problems is shown to be limited to state independent drift and diffusion coefficients that only depend on time and are proportional to each other first passage time statistics such as the survival probabilities and first passage time densities are obtained analytically the analysis includes the study of different functional forms of the time dependent drift and diffusion including power law time dependence and different periodic drivers as a case study of these theoretical results a stochastic model of water resources availability in snowmelt dominated regions is presented where both temperature effects and snow precipitation input are incorporated

relatively weakly open subsets of the unit ball in functions spaces for an infinite hausdorff compact set k and for any banach space x we show that every nonempty weak open subset relative to the unit ball of the space of x valued functions that are continuous when x is equipped with the weak respectively norm weak topology has diameter 2 as consequence we improve known results about nonexistence of denting points in these spaces also we characterize when every nonempty weak open subset relative to the unit ball has diameter 2 for the spaces of bochner integrable and essentially bounded measurable x valued functions

radius of analyticity of analytic functions on banach spaces abstract we examine the question of when the radius of analyticity of a real analytic function on a real banach space is equal to its radius of uniform convergence we will see that a positive solution to this problem on l 1 implies a positive solution on all banach spaces in the final section we show that our question has an affirmative answer for power series of positive polynomials on banach lattices

a first passage kinetic monte carlo algorithm for complex diffusion reaction systems we develop an asynchronous event driven first passage kinetic monte carlo fpkmc algorithm for continuous time and space systems involving multiple diffusing and reacting species of spherical particles in two and three dimensions the fpkmc algorithm presented here is based on the method introduced in oppelstrup et al 10 and is implemented in a robust and flexible framework unlike standard kmc algorithms such as the n fold algorithm fpkmc is most efficient at low densities where it replaces the many small hops needed for reactants to find each other with large first passage hops sampled from exact time dependent green s functions without sacrificing accuracy we describe in detail the key components of the algorithm including the event loop and the sampling of first passage probability distributions and demonstrate the accuracy of the new method we apply the fpkmc algorithm to the challenging problem of simulation of long term irradiation of metals relevant to the performance and aging of nuclear materials in current and future nuclear power plants the problem of radiation damage spans many decades of time scales from picosecond spikes caused by primary cascades to years of slow damage annealing and microstructure evolution our implementation of the fpkmc algorithm has been able to simulate the irradiation of a metal sample for durations that are orders of magnitude longer than any previous simulations using the standard object kmc or more recent asynchronous algorithms

semidefinite extreme points of the unit ball in a polynomial space abstract let be the triangle in r 2 bounded by the lines x 0 y 0 x y 1 the standard simplex in r 2 denote by 2 the set of all real bivariate algebraic polynomials of total degree at most two let b be the unit ball of the space 2 endowed with the supremum norm on we give a full description of the semidefinite extreme points of b the present paper completes the description of the set e of all extreme points of b started in milev and naidenov 2008 13 and milev and naidenov 2011 14 we study as an application the path connectedness of e the conclusion is that e 1 consists of two path connected components

feedback stabilization for a bilinear control system under weak observability inequalities abstract in this paper we discuss the feedback stabilization of bilinear systems under weak observation properties in this case the uniform stability is not guaranteed thus we provide an explicit weak decay rate for all regular initial data applications to schrodinger and wave equations are provided

gaussian variables polynomials and permanents abstract we prove that given n unit vectors aj nj 1 in a complex hilbert space there exists a unit vector x such that x a 1 x a n n n 2 this answers a question about the best constant in an inequality for polynomials in several variables the proof depends on a relation between gaussian variables and permanents

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

exponential stability of nondissipative linear system in banach space and application to unbounded bilinear systems abstract we consider linear control systems of the form d z t d t a z t b z t where is a real parameter a is the infinitesimal generator of a linear c 0 semigroup of contractions s 0 t on a banach space x and the linear perturbation b is a relatively bounded operator with respect to a we provide necessary and sufficient conditions for exponential stability of the above system our stability results are then applied to establish uniform exponential stabilization of linear and bilinear systems with unbounded control operators applications to hyperbolic like equations are considered

lower bounds for norms of products of polynomials via bombieri inequality in this paper we give a different interpretation of bombieri s norm this new point of view allows us to work on a problem posed by beauzamy about the behavior of the sequence sn p supqn pqn 2 where p is a fixed m homogeneous polynomial and qn runs over the unit ball of the hilbert space of n homogeneous polynomials we also study the factor problem for homogeneous polynomials defined on c and we obtain sharp inequalities whenever the number of factors is no greater than n in particular we prove that for the product of homogeneous polynomials on infinite dimensional complex hilbert spaces our inequality is sharp finally we use these ideas to prove that any set zk k 1 of unit vectors in a complex hilbert space for which sup z 1 z z1 z zn is minimum must be an orthonormal system

geometry of 2 homogeneous polynomials on lp spaces 1 p abstract we characterise extreme 2 homogeneous polynomials of diagonal form on l p with p 2 and give a class of examples of smooth points we describe the unit ball of p 2 l p 2 for both the cases p 2 and p we apply the results thus found to study the geometry of the predual of p 2 l p 2 and to show that for p 2 an extreme 2 homogeneous polynomial on l p 2 remains extreme when regarded as a polynomial on l p

weak and strong stabilisation of bilinear systems in a banach space abstractin this paper we study the feedback stabilisation of homogeneous bilinear systems on a banach state space sufficient conditions for weak and strong stabilisation are given a decay rate o

geometry of three homogeneous polynomials on real hilbert spaces let h be a two dimensional real hilbert space we give a characterisation of the extreme and the smooth points of the unit ball of the space of three homogeneous polynomials on h in terms of the coefficients of the polynomial we also determine the smooth points of the unit ball of the predual of the space of three homogeneous polynomials

weak closure and polarization constant by gaussian measure let x be a banach space and x n subset x we study under which condition on xn the set xn n 0 is weakly closed our results depend on the geometry of x

on the global finite time stabilization of bilinear systems by homogeneous feedback laws applications to some pde s abstract in this paper the problem of global finite time stabilization of bilinear control systems by means of homogeneous feedback law is investigated we prove under some reasonable assumptions on the operators a and b that continuous bounded and discontinuous unbounded feedbacks stabilize globally in finite time the closed loop system for illustrative the examples of heat schrodinger and transport equations are considered where homogeneous stabilizing feedback is built for these systems

stabilisation and polynomial decay estimate for distributed semilinear systems in this article we propose a family of feedback controls that guarantee weak and strong stabilisability for distributed semilinear systems in the case of strong stabilisation an optimal decay of the state is estimated applications to wave equations are provided

feedback stabilisation and polynomial decay estimate for time delay bilinear systems in this paper we are concerned with the question of weak and strong stabilisation for distributed bilinear systems with time delay using continuous feedback controls in the case of strong stabili

improving point selection in cubature by a new discrepancy reasonable point set selection is of paramount importance to the accuracy of high dimensional integrals that will be encountered in various disciplines in the present paper to improve the point selection and to overcome the computational complexity of evaluating classical discrepancies the concept of extended f discrepancy ef discrepancy and generalized f discrepancy gf discrepancy of a point set is introduced and justified by comparative studies with other existing discrepancies meanwhile the extensions of the koksma hlawka inequality for ef discrepancy are proved and a conjecture for gf discrepancy is put forward and discussed this gf discrepancy is then employed as the objective function when selecting the optimal rotation angles in the rotation transform of the quasi symmetric point method q spm meanwhile it is also proved that the rotation transform will keep the degree of algebraic accuracy a genetic algorithm is adopted to solve the optimization problem several numerical examples a

centralisers of spaces of symmetric tensor products and applications we show that the centraliser of the space of n fold symmetric injective tensors n 2 on a real banach space is trivial with a geometric condition on the set of extreme points of its dual the space of integral polynomials we obtain the same result for complex banach spaces we give some applications of this results to centralisers of spaces of homogeneous polynomials and complex banach spaces in addition we derive a banach stone theorem for spaces of vector valued approximable polynomials

relatively weakly open sets in closed balls of banach spaces and real jb triples of finite rank we prove that given a real jb triple x there exists a nonempty relatively weakly open subset of the closed unit ball of x with diameter less than 2 if and only if the banach space of x is isomorphic to a hilbert space moreover we give the structure of real jb triples whose banach spaces are isomorphic to hilbert spaces such real jb triples are also characterized in two different purely algebraic ways

averages of norms and quasi norms we compute the number of summands in q averages of norms needed to approximate an euclidean norm it turns out that these numbers depend on the norm involved essentially only through the maximal ratio of the norm and the euclidean norm particular attention is given to the case q in which the average is replaced with the maxima this is closely connected with the behavior of certain families of projective caps on the sphere

isometries between spaces of homogeneous polynomials abstract we derive banach stone theorems for spaces of homogeneous polynomials we show that every isometric isomorphism between the spaces of homogeneous approximable polynomials on real banach spaces e and f is induced by an isometric isomorphism of e onto f with an additional geometric condition we obtain the analogous result in the complex case isometries between spaces of homogeneous integral polynomials and between the spaces of all n homogeneous polynomials are also investigated

the three dimensional gaussian product inequality abstract we prove the 3 dimensional gaussian product inequality i e for any real valued centered gaussian random vector x y z and m n it holds that e x 2 m y 2 m z 2 m e x 2 m e y 2 m e z 2 m this settles positively the gaussian product conjecture in the 3 dimensional case our proof is based on some improved inequalities on multi term products involving 2 dimensional gaussian random vectors the improved inequalities are derived using the gaussian hypergeometric functions and are of independent interest as by products several new combinatorial identities and inequalities are obtained

geometry of banach spaces of trinomials abstract for each pair of numbers m n n with m n we consider the norm on r 3 given by a b c m n sup a x m b x n c x 1 1 for every a b c r 3 we investigate some geometrical properties of these norms we provide an explicit formula for m n a full description of the extreme points of the corresponding unit balls and a parametrization and a plot of their unit spheres

feedback stabilisation and polynomial decay estimate for distributed bilinear parabolic systems with time delay in this paper we examine the feedback stabilisation for distributed bilinear parabolic systems described by partial differential equation with time delay the stabilisation of a such system reduce

properties of q reflexive banach spaces abstract we investigate whether the q reflexive banach spaces have the following properties containment of l p reflexivity dunford pettis property etc

relatively weakly open sets in closed balls of banach spaces and the centralizer we prove that if the centralizer of a banach space x is infinite dimensional then every nonempty relatively weakly open subset of the closed unit ball of x has diameter equal to 2 this result together with a suitable refinement also proven in the paper contains and improves in some cases previously known facts for c algebras jb triples spaces of vector valued continuous functions and spaces of operators

factorization of q p summing polynomials through lorentz spaces abstract we present a vector valued duality between factorable q p summing polynomials and q p summing linear operators on symmetric tensor products of banach spaces several applications are provided first we prove a polynomial characterization of cotype of banach spaces we also give a variant of pisier s factorization through lorentz spaces of factorable q p summing polynomials from c k spaces finally we show a coincidence result for q p concave polynomials

an adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations in recent years there has been a growing interest in analyzing and quantifying the effects of random inputs in the solution of ordinary partial differential equations to this end the spectral stochastic finite element method ssfem is the most popular method due to its fast convergence rate recently the stochastic sparse grid collocation method has emerged as an attractive alternative to ssfem it approximates the solution in the stochastic space using lagrange polynomial interpolation the collocation method requires only repetitive calls to an existing deterministic solver similar to the monte carlo method however both the ssfem and current sparse grid collocation methods utilize global polynomials in the stochastic space thus when there are steep gradients or finite discontinuities in the stochastic space these methods converge very slowly or even fail to converge in this paper we develop an adaptive sparse grid collocation strategy using piecewise multi linear hierarchical basis functions hierarchical surplus is used as an error indicator to automatically detect the discontinuity region in the stochastic space and adaptively refine the collocation points in this region numerical examples especially for problems related to long term integration and stochastic discontinuity are presented comparisons with monte carlo and multi element based random domain decomposition methods are also given to show the efficiency and accuracy of the proposed method

exact controllability of the one dimensional wave equation with locally distributed control the one dimensional wave equation with variable wave speed and locally distributed control is considered it is shown that the adjoint system is observable using a multiplier method with a multiplier being the solution of an ordinary differential equation it is also shown that a sufficient condition for exact controllability is that a related minimization problem always has an optimal solution since the objective function for this minimization problem would be coercive if the adjoint system is observable this establishes the exact controllability of the original system

stabilization and decay estimate for distributed bilinear systems abstract in this paper we consider the problem of feedback stabilization for the distributed bilinear system y t ay t u t by t here a is the infinitesimal generator of a linear c0 semigroup of contractions on a hilbert space h and b h h is a linear bounded operator a sufficient condition for feedback stabilization is given and explicit decay estimate is established applications to vibrating systems are presented

duality in spaces of polynomials of degree at most n abstract we study spaces of continuous polynomials of degree at most n between banach spaces using symmetric tensor products we show that any polynomial of degree at most n has a natural linearisation and that the space of all scalar valued polynomials of degree at most n has an isometric predual we introduce the spaces of integral and nuclear polynomials of degree at most n and endow them with norms that allows us to develop a duality theory for spaces of polynomials of degree at most n

the symmetric radon nikodým property for tensor norms abstract we introduce the symmetric radon nikod m property srn property for finitely generated s tensor norms of order n and prove a lewis type theorem for s tensor norms with this property as a consequence if is a projective s tensor norm with the srn property then for every asplund space e the canonical mapping n s e n s e is a metric surjection this can be rephrased as the isometric isomorphism q min e q e for some polynomial ideal q we also relate the srn property of an s tensor norm with the asplund or radon nikod m properties of different tensor products as an application results concerning the ideal of n homogeneous extendible polynomials are obtained as well as a new proof of the well known isometric isomorphism between nuclear and integral polynomials on asplund spaces an analogous study is carried out for full tensor products

squared chaotic random variables new moment inequalities with applications abstract we prove a new family of inequalities involving squares of random variables belonging to the wiener chaos associated with a given gaussian field our result provides a substantial generalization as well as a new analytical proof of an estimate by frenkel 2007 10 and also constitutes a natural real counterpart to an inequality established by arias de reyna 1998 2 in the framework of complex gaussian vectors we further show that our estimates can be used to deduce new lower bounds on homogeneous polynomials thus partially improving results by pinasco 2012 19 as well as to obtain a novel probabilistic representation of the remainder in hadamard inequality of matrix analysis

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

weakly open sets in the unit ball of the projective tensor product of banach spaces abstract a banach space is said to have the diameter two property if every non empty relatively weakly open subset of its unit ball has diameter two we prove that the projective tensor product of two banach spaces whose centralizer is infinite dimensional has the diameter two property the same statement also holds for x y if the centralizer of x is infinite dimensional and the unit sphere of y contains an element of numerical index one we provide examples of classical banach spaces satisfying the assumptions of the results if k is any infinite compact hausdorff topological space then c k y has the diameter two property for any nonzero banach space y we also provide a result on the diameter two property for the injective tensor product

strong stabilization with decay estimate of semilinear systems this paper considers feedback stabilization for distributed semilinear systems a sufficient condition for an appropriate feedback control to ensure strong stabilization with explicit decay rate is given application to petrowsky equation is presented

non sequential weak supercyclicity and hypercyclicity abstract a bounded linear operator t acting on a banach space b is called weakly hypercyclic if there exists x b such that the orbit t n x n 0 1 is weakly dense in b and t is called weakly supercyclic if there is x b for which the projective orbit t n x c n 0 1 is weakly dense in b if weak density is replaced by weak sequential density then t is said to be weakly sequentially hypercyclic or supercyclic respectively it is shown that on a separable hilbert space there are weakly supercyclic operators which are not weakly sequentially supercyclic this is achieved by constructing a borel probability measure on the unit circle for which the fourier coefficients vanish at infinity and the multiplication operator m f z z f z acting on l 2 is weakly supercyclic it is not weakly sequentially supercyclic since the projective orbit under m of each element in l 2 is weakly sequentially closed this answers a question posed by bayart and matheron it is proved that the bilateral shift on l p z 1 p is weakly supercyclic if and only if 2 p and that any weakly supercyclic weighted bilateral shift on l p z for 1 p 2 is norm supercyclic it is also shown that any weakly hypercyclic weighted bilateral shift on l p z for 1 p 2 is norm hypercyclic which answers a question of chan and sanders

on the norm of products of polynomials on ultraproducts of banach spaces abstract the purpose of this article is to study the problem of finding sharp lower bounds for the norm of the product of polynomials in the ultraproducts of banach spaces x i u we show that under certain hypotheses there is a strong relation between this problem and the same problem for the spaces x i

symmetric multilinear forms on hilbert spaces where do they attain their norm abstract we characterize the sets of norm one vectors x 1 x k in a hilbert space h such that there exists a k linear symmetric form attaining its norm at x 1 x k we prove that in the bilinear case any two vectors satisfy this property however for k 3 only collinear vectors satisfy this property in the complex case while in the real case this is equivalent to x 1 x k spanning a subspace of dimension at most 2 we use these results to obtain some applications to symmetric multilinear forms symmetric tensor products and the exposed points of the unit ball of l s h k

the unit ball of the complex mathcal p 3h let h be a two dimensional complex hilbert space and mathcal p 3h the space of 3 homogeneous polynomials on h we give a characterization of the extreme points of its unit ball mathsf b mathcal p 3h from which we deduce that the unit sphere of mathcal p 3h is the disjoint union of the sets of its extreme and smooth points we also show that an extreme point of mathsf b mathcal p 3h remains extreme as considered as an element of mathsf b mathcal l 3h finally we make a few remarks about the geometry of the unit ball of the predual of mathcal p 3h and give a characterization of its smooth points

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

geometry of integral polynomials m ideals and unique norm preserving extensions we use the aron berner extension to prove that the set of extreme points of the unit ball of the space of integral k homogeneous polynomials over a real banach space x is k x 1 with this description we show that for real banach spaces x and y if x is a nontrivial m ideal in y then ek sk sx the k th symmetric tensor product of x endowed with the injective symmetric tensor norm is never an m ideal in ek sk sy this result marks up a difference with the behavior of nonsymmetric tensors since when x is an m ideal in y it is known that ekkx the k th tensor product of x endowed with the injective tensor norm is an m ideal in ekky nevertheless if x is also asplund we prove that every integral k homogeneous polynomial in x has a unique extension to y that preserves the integral norm other applications to the metric and isomorphic theory of symmetric tensor products and polynomial ideals are also given

reinhardt domains of holomorphy in banach spaces abstract it is known that in c 0 the holomorphic functions representable by multiple power series the series of monomials are those of nuclear type in this article we show that in a banach space with unconditional schauder basis every domain of existence is the domain of existence of a holomorphic function representable by a multiple power series and in fact the domain of convergence of such a series

the plank problem for symmetric bodies given a symmetric convex bodyc andn hyperplanes in an euclidean space there is a translate of a multiple ofc at least frac 1 n 1 times as large insidec whose interior does not meet any of the hyperplanes the result generalizes bang s solution of the plank problem of tarski and has applications to diophantine approximation

strong stabilisation and decay estimate for unbounded bilinear systems in this article we deal with distributed bilinear systems where the operator of control is supposed to be unbounded in the sense that it is bounded from the state space into some extension then we give sufficient conditions for strong stabilisation also the rate of convergence of the state is estimated an illustrating example is given

geometry of homogeneous polynomials on two dimensional real hilbert spaces we describe a method which characterises extreme points of the unit ball of the space of homogeneous polynomials of degrees 3 and 4 on two dimensional hilbert spaces and provides classes of examples of extreme and smooth polynomials of an arbitrary degree n

polynomials on riesz spaces abstract in this paper we investigate polynomial mappings on riesz spaces we give a characterization of positivity of homogeneous polynomials in terms of forward differences finally we prove hahn banach type extension theorems for positive and regular polynomial mappings

partial stabilisation of semilinear systems using bounded controls this paper studies a partial stabilisation problem for distributed semilinear systems this consists of steering only a part of the system s state to its equilibrium constrained controls are proposed to force the desired part of the state to approach the equilibrium necessary and sufficient conditions for weak and strong partial stabilisation are given applications are presented

a geometric estimate on the norm of product of functionals abstract the open problem of determining the exact value of the n th linear polarization constant c n of r n has received considerable attention over the past few years this paper makes a contribution to the subject by providing a new lower bound on the value of sup y 1 x 1 y x n y where x 1 x n are unit vectors in r n the new estimate is given in terms of the eigenvalues of the gram matrix x i x j and improves upon earlier estimates of this kind however the intriguing conjecture c n n n 2 remains open

path integral solutions of the governing equation of sdes excited by levy white noise abstract in this paper the probability density functions pdfs of scalar stochastic differential equations sdes subject to stable levy white noise are investigated the path integral pi method is extended to solve one dimensional space fractional fokker planck kolmogorov fpk equations which are the governing equations corresponded to scalar sdes excited by stable levy white noise first we derive a short time solution of the one dimensional space fractional fpk equation which is used in the chapman kolmogorov smoluchowski cks equation to obtain the pi solution then the accuracy of the pi solution is analyzed theoretically in terms of its characteristic function our results demonstrate that the pi method has a higher accuracy than the first order finite difference method for one step iteration in time finally several illustrative examples are carried out in detail to verify the feasibility and effectiveness of the pi method for solving one dimensional space fractional fpk equations we find that the pi solution agrees well with the exact solution or the monte carlo one

weakly open sets in the unit ball of some banach spaces and the centralizer abstract we show that every banach space x whose centralizer is infinite dimensional satisfies that every non empty weakly open set in b y has diameter 2 where y n s x n fold symmetric projective tensor product of x endowed with the symmetric projective norm for every natural number n we provide examples where the above conclusion holds that includes some spaces of operators and infinite dimensional c algebras we also prove that every non empty weak open set in the unit ball of the space of n homogeneous and integral polynomials on x has diameter two for every natural number n whenever the cunningham algebra of x is infinite dimensional here we consider the space of n homogeneous integral polynomials as the dual of the space n s e x n fold symmetric injective tensor product of x endowed with the symmetric injective norm for instance every infinite dimensional l 1 satisfies that its cunningham algebra is infinite dimensional we obtain the same result for every non reflexive l embedded space and so for every predual of an infinite dimensional von neumann algebra

plank type problems for polynomials on banach spaces abstract in this work we prove plank type problems for polynomials on banach spaces we give estimates in the case of complex banach spaces and in particular in the case of complex hilbert spaces moreover we get optimal results in the case of 2 homogeneous polynomials on real hilbert spaces we have also derived estimates in the case of the classical l p spaces

exponential stabilization of distributed semilinear systems by optimal control this paper studies exponential stabilization of distributed semilinear systems the paper i gives a constrained feedback control that ensure the exponential stabilizability and ii shows that this control is the unique solution of an appropriate minimization problem examples of hyperbolic partial equations are provided

integral representation of holomorphic functions on banach spaces abstract in this paper we discuss the problem of integral representation of analytic functions over a complex banach space e we obtain for a wide class of functions integral representations of the form f x e e x f 1 d w and f x e 1 1 x f 2 d w where w is an abstract wiener measure on e and f 1 f 2 are transformations of f involving the covariance operator of w

complex vector lattices via functional completions abstract we show that the fremlin tensor product c x c y is not square mean complete when x and y are uncountable metrizable compact spaces this motivates the definition of complexification of archimedean vector lattices the fremlin tensor product of archimedean complex vector lattices and a theory of powers of archimedean complex vector lattices

fourth moment theorems for markov diffusion generators abstract inspired by the insightful article 4 we revisit the nualart peccati criterion 13 now known as the fourth moment theorem from the point of view of spectral theory of general markov diffusion generators we are not only able to drastically simplify all of its previous proofs but also to provide new settings of diffusive generators laguerre jacobi where such a criterion holds convergence towards gamma and beta distributions under moment conditions is also discussed

geometry of spaces of polynomials abstract connections between the shape of the unit ball of a banach space and analytic properties of the banach space have been studied for many years in this article some geometric properties of spaces related ton homogeneous polynomials are considered in particular the rotundity and smoothness of spaces of continuousn homogeneous polynomials and its preduals are studied furthermore an inequality relating the product of the norms of linear functionals on a banach space with the norm of the continuousn homogeneous polynomial determined by the product of the linear functionals is derived this inequality is used to study the strongly exposed points of the predual of the space of continuous 2 homogeneous polynomials

linear polarization constants of hilbert spaces abstract this paper has been motivated by previous work on estimating lower bounds for the norms of homogeneous polynomials which are products of linear forms the purpose of this work is to investigate the so called n th linear polarization constant c n x of a finite dimensional banach space x and in particular of a hilbert space note that c n x is an isometric invariant of the space it has been proved by j arias de reyna linear algebra appl 285 1998 395 408 that if h is a complex hilbert space of dimension at least n then c n h n n 2 the same value of c n h for real hilbert spaces is only conjectured but estimates were obtained in many cases in particular it is known that the n th linear polarization constant of a d dimensional real or complex hilbert space h is of the approximate order d n 2 for n large enough and also an integral form of the asymptotic quantity c h that is the linear polarization constant of the hilbert space h where dim h d was obtained together with an explicit form for real spaces here we present another proof we find the explicit form even for complex spaces and we elaborate further on the values of c n h and c h in particular we answer a question raised by j c garcia vazquez and r villa mathematika 46 1999 315 322 also we prove the conjectured c n h n n 2 for real hilbert spaces of dimension n 5 a few further estimates have been also derived

a new approach for time variant probability density function of the maximal value of stochastic dynamical systems abstract the extreme value distribution evd of stochastic processes is an important but still challenging problem for the determination of reliability function and distribution of first excursion time in various science and engineering fields in the present paper a new method to evaluate the time variant probability density function pdf of the maximal value of a markov process or markov vector process is proposed in this method a joint maximum state vector process is constructed by combining the maximal value process mvp and its underlying markov process the markov property of the joint maximum state vector process is rigorously proved incorporated with the ito stochastic differential equation sde governing the underlying markov process a numerical method is developed based on the chapman kolmogorov equation in particular the short time transition probability density function of the joint maximum state process in the path integral solution pis is derived the detailed algorithms for the proposed method in two and three dimensional cases respectively are elaborated several examples are illustrated demonstrating the effectiveness of the proposed method problems to be further studied are also discussed

geometric theory of spaces of integral polynomials and symmetric tensor products abstract we investigate the nature of extreme weak exposed and weak strongly exposed points of the unit ball of spaces of n homogeneous integral polynomials on and n fold symmetric products of a banach space e for the space of integral polynomials we show the set of extreme points is contained in the set n e 1 we give smul yan type theorems for spaces of n homogeneous polynomials and n fold symmetric tensors that characterise weak exposed resp weak strongly exposed points in terms of g teaux resp frechet differentiability of the norm on various spaces of tensor products and polynomials our study of the geometry of these spaces has many applications when e has the radon nikod m property we show that the spaces of n homogeneous integral and nuclear polynomials are isomerically isomorphic for each integer n when the dimensions of e and n are both at least 2 then the space of n homogeneous polynomials on e is neither smooth nor rotund for a certain class of reflexive banach space the space of n homogeneous approximable polynomials on e is either reflexive or is not isometric to a dual banach space we conclude with a choquet theorem for a space of homogeneous polynomials

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

partial stabilisation of non homogeneous bilinear systems abstractin this work we study in a hilbert state space the partial stabilisation of non homogeneous bilinear systems using a bounded control necessary and sufficient conditions for weak and strong stabilisation are formulated in term of approximate observability like assumptions applications to parabolic and hyperbolic equations are presented

equivalent norms in polynomial spaces and applications abstract in this paper equivalence constants between various polynomial norms are calculated as an application we also obtain sharp values of the hardy littlewood constants for 2 homogeneous polynomials on l p 2 spaces 2 p we also provide lower estimates for the hardy littlewood constants for polynomials of higher degrees

exact semi internal control of an euler bernoulli equation this paper proves exact semi internal controllability of an euler bernoulli equation with variable coefficients the basic principle of the proof is the hilbert uniqueness method for this a multiplier technique and a unique continuation property have been used the proof of the unique continuation property is the main feature of this work

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