commutant structure of u n 1 u transformations in this paper we have found irreducible representations irreps of the algebra of partially transposed permutation operators on the last subsystem we give here the direct method of irreps construction for an arbitrary number of subsystems n and local dimension d our method is inspired by the representation theory of the symmetric group s n the theory of brauer algebras and walled brauer algebras

irreducible representations of brauer algebras irreducible representations of brauer algebras are constructed by using the induced representation and the linear equation method as examples some matrix representations of brauer algebras df n with f or 5 are presented

on the blocks of the walled brauer algebra we determine the blocks of the walled brauer algebra in characteristic zero these can be described in terms of orbits of the action of a weyl group of type a on a certain set of weights in positive characteristic we give a linkage principle in terms of orbits of the corresponding affine weyl group we also classify the semisimple walled brauer algebras in all characteristics

strong convergence of modified mann iterations abstract the mann iterations for nonexpansive mappings have only weak convergence even in a hilbert space we propose two modifications of the mann iterations in a uniformly smooth banach space one for nonexpansive mappings and the other for the resolvent of accretive operators the two modified mann iterations are proved to have strong convergence

convergence theorems of fixed points for κ strict pseudo contractions in hilbert spaces abstract let c be a closed convex subset of a real hilbert space h and assume that t c h is a strict pseudo contraction such that f t x c x t x 0 consider the normal mann s iterative algorithm given by x 1 c x n 1 n x n 1 n p c s x n n 1 where s c h is defined by s x x 1 t x p c is the metric projection of h onto c and n n 1 for all n 1 it is proved that if the control parameter sequence n is chosen so that n 1 and n 1 n 1 n then x n converges weakly to a fixed point of t in order to get a strong convergence theorem we modify the normal mann s iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in c the results presented in this article respectively improve and extend the recent results of marino and xu g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert spaces j math anal appl 329 2007 336 349 from strictly pseudo contractive self mappings to nonself mappings and of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 from nonexpansive mappings to strict pseudo contractions

weak and strong convergence theorems for strict pseudo contractions in hilbert spaces abstract let c be a closed convex subset of a real hilbert space h and assume that t is a strict pseudo contraction on c with a fixed point for some 0 1 given an initial guess x 0 c and given also a real sequence n in 0 1 the mann s algorithm generates a sequence x n by the formula x n 1 n x n 1 n t x n n 0 it is proved that if the control sequence n is chosen so that n 1 and n 0 n 1 n then x n converges weakly to a fixed point of t however this convergence is in general not strong we then modify mann s algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence this result extends a recent result of nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 from nonexpansive mappings to strict pseudo contractions

distillation of entanglement by projection on permutationally invariant subspaces we consider distillation of entanglement from two qubit states which are mixtures of two pure entangled states and one pure product state which is orthogonal to them we distill entanglement from such states by projecting n copies of the state on a permutationally invariant subspace and then applying one way hashing protocol we find analytical expressions for the rate of the protocol and show that for wide range of parameters this protocol achieves higher rates than previous ones we also generalize this method to higher dimensional systems to get analytical expression for two qubit case we faced a mathematical problem of diagonalizing a family of matrices enjoying some symmetries w r t the symmetric group we have solved this problem in two ways i directly by the use of schur weyl decomposition and young symmetrizers and ii showing that the problem is equivalent to a problem of diagonalizing adjacency matrices in a particular instance of a so called algebraic association scheme

on the decomposition of tensor products of the representations of the classical groups by means of the universal characters on definit les caracteres universels d une representation rationnelle de gl n c et on donne les formules de decomposition des produits tensoriels entre eux en termes de coefficients de littlewood richardson on demontre les formules de decomposition du produit tensoriel de deux representations irreductibles de sp 2n c et de so n c

strong convergence of krasnoselskii and mann s type sequences for one parameter nonexpansive semigroups without bochner integrals abstract in this paper we prove krasnoselskii and mann s type convergence theorems for nonexpansive semigroups without using bochner integral and without assuming the strict convexity of banach spaces one of our main results is the following let c be a compact convex subset of a banach space e and let t t t 0 be a one parameter strongly continuous semigroup of nonexpansive mappings on c let t n be a sequence in 0 satisfying lim inf n t n lim sup n t n and lim n t n 1 t n 0 let 0 1 define a sequence x n in c by x 1 c and x n 1 t t n x n 1 x n for n n then x n converges strongly to a common fixed point of t t t 0

convergence theorems of common fixed points for a finite family of lipschitz pseudocontractions in banach spaces abstract in this paper we continue to study weak convergence problems for the implicit iteration process for a finite family of lipschitzian continuous pseudocontractions in general banach spaces the results presented in this paper improve and extend the corresponding ones of xu and ori h k xu r g ori an implicit iteration process for nonexpansive mappings numer funct anal optim 22 2001 767 773 osilike m o osilike implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps j math anal appl 294 2004 73 81 chen et al r chen y s song h y zhou convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings j math anal appl 314 2006 701 709 and others

strong convergence theorems for finitely many nonexpansive mappings and applications abstract let e be a uniformly convex banach space which satisfies opial s condition or whose norm is frechet differentiable recently takahashi and shimoji w takahashi k shimoji convergence theorems for nonexpansive mappings and feasibility problems math comput modelling 32 2000 1463 1471 introduced an iterative scheme given by finitely many nonexpansive mappings in e and proved weak convergence theorems which are connected with the problem of image recovery in this paper we introduce a new iterative scheme which includes their iterative scheme as a special case under the assumption that e is a reflexive banach space whose norm is uniformly g teaux differentiable and which has a weakly continuous duality mapping we prove strong convergence theorems which are connected with the problem of image recovery using the established results we consider the problem of finding a common fixed point of finitely many nonexpansive mappings

unsupervised segmentation of textured images abstract in this paper a new unsupervised segmentation algorithm for textured images is developed the proposed algorithm utilizes the characteristic of the markov random fields mrf for modeling the contextual information embedded in image formation textured images are regarded as realizations of the stationary gaussian mrf on a two dimensional square lattice and are modeled by the conditional autoregressive car equations with a second order noncausal neighborhood a hypothesis test over two radially masked areas is involved in our algorithm to detect the location of boundaries the hypothesis assumes that these two areas belong to the same class of textures and car model parameters are estimated in a minimum mean square error mmse sense the hypothesis is tested by the analysis of variance anova like technique and if it is rejected a measure of dissimilarity is accumulated on the rejected area this approach produces potential edge maps from these maps the boundaries among various textures can be detected without microedges the performance of the proposed algorithm is demonstrated by some experiments using real textures as well as synthetic ones the experiments show that the proposed algorithm can produce satisfactory segmentation without any a priori information

structure and properties of the algebra of partially transposed permutation operators we consider the structure of algebra of operators acting in n fold tensor product space which are partially transposed on the last term using purely algebraical methods we show that this algebra is semi simple and then considering its regular representation we derive basic properties of the algebra in particular we describe all irreducible representations of the algebra of partially transposed operators and derive expressions for matrix elements of the representations it appears that there are two kinds of irreducible representations of the algebra the first one is strictly connected with the representations of the group s n 1 induced by irreducible representations of the group s n 2 the second kind is structurally connected with irreducible representations of the group s n 1

feature detection via linear contrast techniques abstract a new technique for the detection of grey level features embedded in noise is developed using the linear contrast methodology within the context of the analysis of variance anova the feature to be detected is first partitioned into a set of disjoint homogeneous regions based on the one way model under anova each region is assigned a weight factor called an elementary contrast a test statistic which is simply a linear combination of the elementary contrasts is generated and the feature detection problem is reduced to a hypothesis test with a confidence level the technique introduced here is particularly useful in real time processing due to the computation of only one sum of squares in the alternative space the problem of using additional test features is addressed by introducing orthogonal contrast functions the procedure proved to be computationally efficient and very reliable in noisy environments

two dimensional object detection in correlated noise abstract in this paper a procedure for the detection of two dimensional objects embedded in correlated noise is presented the procedure developed here is an extension of the dependent noise model of the recent work by chang and kurz object detection and experimental designs comput vision graphics image process 40 147 168 1987 the model for the dependent data is based on the two way analysis under the analysis of variance anova with fixed effects and known correlation matrix the detection is based on the test of homogeneity and heterogeneity properties of target and background arrays and the combination of both the global array for each data array f statistics are calculated and tested against tabulated thresholds for the case of objects with large size a reduced algorithm in the form of a contrast test statistic is proposed results of computer simulations carried out to evaluate the new algorithms are presented

a composite iterative algorithm for common fixed points for a finite family of nonexpansive mappings and applications this paper is concerned with a new composite iteration approximating to common fixed points for a finite family of nonexpansive mappings in banach spaces which have a uniformly gateaux differentiable norm utilizing the iterative algorithm we obtain the strong convergence theorems for a finite family of nonexpansive mappings furthermore the problem of image recovery is considered in the above result our results extend and improve the corresponding results

strong convergence theorems of modified ishikawa iterative process with errors for an infinite family of strict pseudo contractions abstract in this paper we study modified ishikawa iterative process with errors to have strong convergence for an infinite family of strict pseudo contractions in the framework of q uniformly smooth banach spaces our results improve and extend the recent ones announced by many others

tensor product representations of general linear groups and their connections with brauer algebras abstract for the complex general linear group g gl r c we investigate the tensor product module t p v q v of p copies of its natural representation v c r and q copies of the dual spare v of v we describe the maximal vectors of t and from that obtain an explicit decomposition of t into its irreducible g summands knowledge of the maximal vectors allows us to determine the centralizer algebra c of all transformations on t commuting with the action of g to construct the irreducible c representations and to identify c with a certain subalgebra b r p q of the brauer algebra b r p q

the approximation of fixed points of compositions of nonexpansive mappings in hilbert space determining fixed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences an algorithm for finding common fixed points of nonexpansive mappings in hilbert space essentially due to halpern is analyzed the main theorem extends wittmann s recent work and partially generalizes a result by lions algorithms of this kind have been applied to the convex feasibility problem

image enhancement using the modified icm method a generalized version of the iterative conditional modes icm method for image enhancement is developed the proposed algorithm utilizes the characteristic of markov random fields mrf in modeling the contextual information embedded in image formation to cope with real images a new local mrf model with a second order neighborhood is introduced this model extracts contextual information not only from the intensity levels but also from the relative position of neighboring cliques also an outlier rejection method is presented in this method the rejection depends on each candidate s contribution to the local variance to cope with a mixed noise case a hypothesis test is implemented as part of the restoration procedure the proposed algorithm performs signal adaptive nonlinear and recursive filtering in comparing the performance of the new procedure with several well known order statistic filters the superiority of the proposed algorithm is demonstrated both in the mean square error mse and the mean absolute error mae senses in addition the new algorithm preserves the details of the images well it should be noted that the blurring effect is not considered

on the implicit iterative process for strictly pseudo contractive mappings in banach spaces in this paper we consider a composite implicit iterative process for an infinite family of strictly pseudo contractive mappings strong convergence theorems are established in an arbitrary real banach space the results presented in this paper improve and extend the recent ones announced by many others

strong convergence theorems for an infinite family of nonexpansive mappings in banach spaces in an infinite dimensional hilbert space the normal mann s iteration algorithm has only weak convergence in general even for nonexpansive mappings in order to get a strong convergence result we modify the normal mann s iterative process for an infinite family of nonexpansive mappings in the framework of banach spaces our results improve and extend the recent results announced by many others

representations of the brauer algebra and littlewood s restriction rules let g be either sp v or o v using an action of the brauer algebra we describe the subspace t k v m v m of tensors of valence k as an induced representation as an application we recover a special case of littlewood s restriction rule affording the decomposition of an irreducible gl v module when restricted to g moreover we get an explicit realization of the irreducible representations of the brauer algebra m schur duality tells us that the algebra of operators generated by sp v and the above quotient of the brauer algebra are mutual central izer and establishes a bijective correspondence between the representations of either of these algebras the sp v module v m splits as v m m 2 k 0 t k v m the subspace t k v m being the sum of the sp v isotypic components of v m which appear for the first time in tensor power m 2k more directly if pq v m v m 2 is the extension operator which inserts in the positions p q the canonical element of the skew form t k v m is the vector space generated by k fold extensions of the traceless tensors in v m 2k i e

suppression of salt and pepper noise based on youden designs abstract this paper presents a new class of algorithms based on youden designs to detect and restore edges present in an image imbedded by mixture or salt and pepper noise the mixture noise consists of a uncorrelated or correlated noisy background plus uncorrelated impulsive noise the objective is to restore pixels affected by the impulsive part of the mixture noise the approach is to consider that these pixels have lost their true value and their estimate is obtained via the normal equation that yields the least sum of square error lsse this procedure is known in the literature as the missing value approach problem the estimates are introduced into the image data and an anova technique based on youden design is carried out we introduce youden designs which are special symmetric balanced incomplete block sbib designs the pertinent statistical tests and estimates of the factor effects we derive the estimate of the missing value for the uncorrelated noise environment as well as for the correlated one the high level of performance of these algorithms can be evaluated visually via the input output images and objectively via the input output signal to noise ratio snr

strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in this paper we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in hilbert spaces by the hybrid method in the mathematical programming

the weyl approach to the representation theory of reflection equation algebra the present paper deals with the representation theory of reflection equation algebra connected to a hecke type r matrix up to some reasonable additional conditions the r matrix is arbitrary not necessary originating from quantum groups we suggest a universal method for constructing finite dimensional irreducible representations in the framework of the weyl approach well known in the representation theory of classical lie groups and algebras with this method a series of irreducible modules is constructed the modules are parametrized by young diagrams the spectrum of central elements sk trqlk is calculated in the single row and single column representations a rule for the decomposition of the tensor product of modules into a direct sum of irreducible components is also suggested

edge detection in correlated noise using latin square masks abstract in this paper new classes of algorithms are developed for processing of two dimensional image data imbedded in correlated noise the algorithms are based on modifications of standard analysis of variance anova techniques involving latin square ls technique and ensuring their proper operation in dependent noise the ls technique enables us to analyse three effects including the gray level or diagonal effect instead of two based on the same data for two way designs though the theoretical development leading to the actual image processing procedure is laborious and complicated the actual procedure is simple robust and useful in real time applications the efficiency of all algorithms for processing image data corrupted by statistically dependent noise is verified by extensive monte carlo simulations

gradings on walled brauer algebras and khovanov s arc algebra abstract we introduce some z graded versions of the walled brauer algebra b r s working over a field of characteristic zero this allows us to prove that b r s is morita equivalent to an idempotent truncation of a certain infinite dimensional version of khovanov s arc algebra we deduce that the walled brauer algebra is koszul whenever 0

convergence theorems for λ strict pseudo contractions in 2 uniformly smooth banach spaces abstract in this paper we discuss some properties of iterates generated by a strict pseudo contraction or a finite family of strict pseudo contractions in a real 2 uniformly smooth banach space the results presented in this paper are interesting extensions and improvements upon those known ones of marino and xu g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert spaces j math anal appl 324 2007 336 349 in order to get a strong convergence theorem we modify the normal mann s iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in c this result extends a recent result of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 both from nonexpansive mappings to strict pseudo contractions and from hilbert spaces to 2 uniformly smooth banach spaces

weak multiplicativity for random quantum channels it is known that random quantum channels exhibit significant violations of multiplicativity of maximum output p norms for any p 1 in this work we show that a weaker variant of multiplicativity nevertheless holds for these channels for any constant p 1 given a random quantum channel mathcal n i e a channel whose stinespring representation corresponds to a random subspace s we show that with high probability the maximum output p norm of mathcal n otimes n decays exponentially with n the proof is based on relaxing the maximum output norm of mathcal n to the operator norm of the partial transpose of the projector onto s then calculating upper bounds on this quantity using ideas from random matrix theory

inequalities in banach spaces with applications well known that many problems in a hilbert space h are solved by applying the following identity ilax 1 a yi12 a412 1 llyl12 a 1 mx yl12 1 1 for all x y in h and 0 5 i 5 1 therefore one natural method to solve problems in a banach space xis to establish equalities and usually inequalities in xanalogous to 1 1 this is in fact shown by some authors recent work see for example reich l poffald and reich 2 lim 3 lim et af 4 prus and smarzewski 5 smarzewski 6 and reich 21 the purpose of this paper is to continue carrying out investigations in this line more precisely in section 3 we establish some inequalities analogous to 1 l in either uniformly convex or uniformly smooth banach spaces as corollaries we obtain new characteristics of p uniform convexity and q uniform smoothness of a banach space x via the functionals i lip and ii llq respectively we give in section 4 applications of the inequalities obtained in section 3 to fixed points of uniformly lipschitzian mappings and to best approximation theory

iterative approaches to finding nearest common fixed points of nonexpansive mappings in hilbert spaces abstract the iteration scheme xn 1 n 1y 1 n 1 tn 1xn is first considered for infinitely many nonexpansive maps t1 t2 t3 in a hilbert space a result of shimizu and takahashi j math anal appl 211 1997 71 is generalized and it is shown that the sequence of iterates converges to py where p is some projection for this same iteration scheme with finitely many maps t1 t2 tn a complementary result to a result of bauschke j math anal appl 202 1996 150 is proved by introducing a new condition on the sequence of parameters n this condition improves lions condition c r acad sci paris ser a b 284 1977 1357 the iterates converge to py where p is the projection onto the intersection of the fixed point sets of the tis

contrast techniques for line detection in a correlated noise environment a new class of line detectors based on the theory of linear contrasts is developed by incorporating the f statistic and the shape test the new algorithm detects and locates line features simultaneously and thereby increases the detection power substantially many classes of detectors including the step edge detector naturally becomes subclasses of the proposed detector mathematical analysis indicates that the new algorithm that accounts for noise dependence performs better than its counterpart that neglects the dependence of noise a symmetrical balanced incomplete blocks sbib design is introduced to model real world images in terms of a treatment group that is associated with preexistent conspicuous features such as lines edges etc and an incomplete treatment group that is randomized to accommodate image textures the new algorithm in conjunction with the sbib design is applied in the four main directions perpendicularly to the line under investigation it is robust simple efficient and amenable to real time applications all pertinent statistics for the implementation of the procedure are estimated from data extensive computer simulations demonstrate the performance of the proposed detector