isometric dilations for infinite sequences of noncommuting operators this paper develops a dilation theory for t n l an infinite sequence of noncommuting operators on a hilbert space when the matrix t1 t2 is a contraction a wold decomposition for an infinite sequence of isometries with orthogonal final spaces and a minimal isometric dilation for tn i are obtained some theorems on the geometric structure of the space of the minimal isometric dilation and some consequences are given this results are used to extend the sz nagy foia lifting theorem to this noncommutative setting this paper is a continuation of 5 and develops a dilation theory for an infinite sequence tn n of noncommuting operators on a hilbert space when en 1 tn tn i i is the identity on s many of the results and techniques in dilation theory for one operator 8 and also for two operators 3 4 are extended to this setting first we extend wold decomposition 8 4 to the case of an infinite sequence vn i of isometries with orthogonal final spaces in 2 we obtain a minimal isometric dilation for tn 1 by extending the schaffer construction in 6 4 using these results we give some theorems on the geometric structure of the space of the minimal isometric dilation finally we give some sufficient conditions on a sequence t7 n to be simultaneously quasi similar to a sequence rn n i of isometries on a hilbert space x with en rnrn n ix in 3 we use the above mentioned theorems to obtain the sz nagy foia5 lifting theorem 7 8 1 4 in our setting in a subsequent paper we will use the results of this paper for studying the characteristic function associated to a sequence tn lo 1 with ez 1 t t i throughout this paper a stands for the set 1 2 k k e n or the set n 1 2 received by the editors september 1 1987 1980 mathematics subject classification 1985 revision primary 47a20 secondary 47a45

models for n tuples of noncommuting operators abstract this paper proves versions of the rota model theorem the de branges rovnyak model theorem and the coisometric extension theorem for n tuples of not necessarily commuting operators this generalizes the work of a e frazho j funct anal 48 1982 1 11 for pairs of operators the methods involve applying the single operator results to matrices of operators

complements to models for noncommuting operators abstract this paper develops a dilation theory for two noncommutative operators many of the results and techniques in dilation theory for one operator are extended to this setting this is done by extending the schaffer construction for one operator to the fock space setting a new wold decomposition for two isometrics with orthogonal range is obtained this wold decomposition and the schaffer construction is used to extend the sz nagy foias lifting theorem and the characteristic function theory to the noncommutative setting the characteristic function is operator valued and defined in a fock space

marginal consistency upper bounding partition functions over commutative semirings many inference tasks in pattern recognition and artificial intelligence lead to partition functions in which addition and multiplication are abstract binary operations forming a commutative semiring by generalizing max sum diffusion one of convergent message passing algorithms for approximate map inference in graphical models we propose an iterative algorithm to upper bound such partition functions over commutative semirings the iteration of the algorithm is remarkably simple change any two factors of the partition function such that their product remains the same and their overlapping marginals become equal in many commutative semirings repeating this iteration for different pairs of factors converges to a fixed point when the overlapping marginals of every pair of factors coincide we call this state marginal consistency during that an upper bound on the partition function monotonically decreases this abstract algorithm unifies several existing algorithms including max sum diffusion and basic costraint propagation or local consistency algorithms in constraint programming we further construct a hierarchy of marginal consistencies of increasingly higher levels and show than any such level can be enforced by adding identity factors of higher arity order finally we discuss instances of the framework for several semirings including the distributive lattice and the max sum and sum product semirings

predictor corrector iterative algorithms for solving generalized mixed variational like inequalities the concept of partially relaxed h strong monotonicity of set valued mappings is introduced by applying the auxiliary variational inequality technique some new predictor corrector iterative algorithms for solving generalized mixed variational like inequalities are suggested and analyzed the convergence of the algorithms only need the continuity and the partially relaxed h strongly monotonicity of set valued mappings the algorithm and convergence result are new and generalize some known results in literatures

the generalized distributive law we discuss a general message passing algorithm which we call the generalized distributive law gdl the gdl is a synthesis of the work of many authors in information theory digital communications signal processing statistics and artificial intelligence it includes as special cases the baum welch algorithm the fast fourier transform fft on any finite abelian group the gallager tanner wiberg decoding algorithm viterbi s algorithm the bcjr algorithm pearl s belief propagation algorithm the shafer shenoy probability propagation algorithm and the turbo decoding algorithm although this algorithm is guaranteed to give exact answers only in certain cases the junction tree condition unfortunately not including the cases of gtw with cycles or turbo decoding there is much experimental evidence and a few theorems suggesting that it often works approximately even when it is not supposed to

generalized strongly nonlinear quasivariational inequalities abstract in this paper we prove an existence theorem of solutions and develop the algorithms of approximating solutions for a generalized strongly nonlinear variational inequality and a generalized strongly nonlinear complementarity problem an algorithm for finding the approximate solution of generalized strongly nonlinear quasivariational inequalities and generalized strongly nonlinear quasicomplementarity problems is also given as special cases these results include the corresponding results of fang and peterson noor siddiqi and ansari and ding

variable length lossy source code using a constrained random number generator a variable length lossy source code is introduced with a rate distortion pair close to the rate distortion function random numbers that satisfy a condition specified by a function and its value are used to construct a stochastic encoder the proof of the theorem is based on the balanced coloring property of an ensemble of functions since an ensemble of systematic sparse matrices has this property we can construct a tractable code for a memoryless source some algorithms for implementing the code are introduced and compared by simulation

standard noncommuting and commuting dilations of commuting tuples we introduce a notion called maximal commuting piece for tuples of hilbert space operators given a commuting tuple of operators forming a row contraction there are two commonly used dilations in multivariable operator theory first there is the minimal isometric dilation consisting of isometries with orthogonal ranges and hence it is a noncommuting tuple there is also a commuting dilation related with a standard commuting tuple on boson fock space we show that this commuting dilation is the maximal commuting piece of the minimal isometric dilation we use this result to classify all representations of the cuntz algebra o n coming from dilations of commuting tuples

an iterative method for generalized set valued nonlinear mixed quasi variational inequalities this paper presents an iterative method for solving the generalized nonlinear set valued mixed quasi variational inequality a problem class that was introduced by huang et al comp math appl 40 2 3 2000 205 215 the method incorporates step size controls that enable application to problems where certain set valued mappings do not always map to nonempty closed bounded sets

predictor corrector iterative algorithms for solving generalized mixed quasi variational like inclusion by applying the concept of partially relaxed h strong monotonicity of set valued mappings due to author and the auxiliary variational inequality technique some new predictor corrector iterative algorithms for solving generalized mixed quasi variational like inclusions are suggested and analyzed the convergence of the algorithms only need the continuity and the partially relaxed h strongly monotonicity of set valued mappings the algorithm and convergence result are new and generalize some recent known results in literatures

subalgebras of c algebras iii multivariable operator theory a d contraction is a d tuple t1 td of mutually commuting operators acting on a common hilbert space h such that t1 1 t2 2 td d 1 2 d for all 1 2 d h these are the higher dimensional counterparts of contractions we show that many of the operator theoretic aspects of function theory in the unit disk generalize to the unit ball bd in complex d space including von neumann s inequality and the model theory of contractions these results depend on properties of the d shift a distinguished d contraction which acts on a new h2 space associated with bd and which is the higher dimensional counterpart of the unilateral shift h 2 and the d shift are highly unique indeed by exploiting the noncommutative choquet boundary of the d shift relative to its generated c algebra we find that there is more uniqueness in dimension d 2 than there is in dimension one

algorithm of solutions for mixed implicit quasi variational inequalities with fuzzy mappings abstract in this paper by applying the auxiliary variational principle technique some existence theorems of solutions for a class of mixed implicit quasi variational inequalities with fuzzy mappings are proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria is also given as special cases of these results the open problem put forward by noor is answered positively our results are new and generalize a number of known results to mixed implicity quasi variational inequalities with fuzzy mappings

a new class of completely generalized quasi variational inclusions in banach spaces in this paper a new notion of j proximal mapping for a nonconvex lower semicontinuous subdifferentiable proper functional on banach space is introduced the existence and lipschitz continuity of j proximal mapping of a lower semicontinuous subdifferentiable proper functional are proved by applying the concept we introduce and study a new class of completely generalized quasi variational inclusions in reflexive banach spaces a novel and innovative iterative algorithm for finding the approximate solutions is suggested and analyzed the convergence criteria of the iterative sequences generated by the new iterative algorithm is also given these algorithm and existence result generalize many known results under hilbert space setting in recent literature to reflexive banach spaces

fuzzy nonlinear set valued variational inclusions the purpose of this paper is to study a new class of fuzzy nonlinear set valued variational inclusions in real banach spaces by using the fuzzy resolvent operator techniques for m accretive mappings we establish the equivalence between fuzzy nonlinear set valued variational inclusions and fuzzy resolvent operator equation problem applying this equivalence and nadler s theorem we suggest some iterative algorithms for solving fuzzy nonlinear set valued variational inclusions in real banach spaces by using the inequality of petryshyn the existence of solutions for these kinds of fuzzy nonlinear set valued variational inclusions without compactness is proved and convergence criteria of iterative sequences generated by the algorithm are also discussed

three step iterative algorithms for solving the system of generalized mixed quasi variational like inclusions in this paper we consider the system of generalized mixed quasi variational like inclusions in hilbert spaces we extend the auxiliary principle technique to develop a three step iterative algorithm for solving the system of generalized mixed quasi variational like inclusions under the assumptions of the continuity and partially relaxed h strong monotonicity of set valued mappings we establish the convergence for our algorithm our algorithm and its convergence results are new and generalize ding s predictor corrector iterative algorithms moreover our results unify some known results in the literature as well

a new look at the generalized distributive law in this paper we develop a measure theoretic version of the junction tree algorithm to compute desired marginals of a product function we reformulate the problem in a measure theoretic framework where the desired marginals are viewed as corresponding conditional expectations of a product of random variables we generalize the notions of independence and junction trees to collections of spl sigma fields on a space with a signed measure we provide an algorithm to find such a junction tree when one exists we also give a general procedure to augment the spl sigma fields to create independencies which we call lifting this procedure is the counterpart of the moralization and triangulation procedure in the conventional generalized distributive law gdl framework in order to guarantee the existence of a junction tree our procedure includes the conventional gdl procedure as a special case however it can take advantage of structures at the atomic level of the sample space to produce junction tree based algorithms for computing the desired marginals that are less complex than those gdl can discover as we argue through examples our formalism gives a new way by which one can hope to find low complexity algorithms for marginalization problems

a recursive approach to low complexity codes a method is described for constructing long error correcting codes from one or more shorter error correcting codes referred to as subcodes and a bipartite graph a graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes both the encoders and decoders proposed are shown to take advantage of the code s explicit decomposition into subcodes to decompose and simplify the associated computational processes bounds on the performance of two specific decoding algorithms are established and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed the proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver e g reliability information without greatly increasing the number of computations required it is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst error correction abilities the construction principles

free holomorphic functions on the unit ball of b h n abstract in this paper we continue the study of free holomorphic functions on the noncommutative ball b h n 1 x 1 x n b h n x 1 x 1 x n x n 1 2 1 where b h is the algebra of all bounded linear operators on a hilbert space h and n 1 2 or n several classical results from complex analysis have free analogues in our noncommutative setting we prove a maximum principle a naimark type representation theorem and a vitali convergence theorem for free holomorphic functions with operator valued coefficients we introduce the class of free holomorphic functions with the radial infimum property and study it in connection with factorizations and noncommutative generalizations of some classical inequalities obtained by schwarz and harnack the borel caratheodory theorem is extended to our noncommutative setting using a noncommutative generalization of schwarz s lemma and basic facts concerning the free holomorphic automorphisms of the noncommutative ball b h n 1 we obtain an analogue of julia s lemma for free holomorphic functions f b h n 1 b h m 1 we also obtain pick julia theorems for free holomorphic functions with operator valued coefficients we provide a noncommutative generalization of a classical inequality due to lindelof which turns out to be sharper then the noncommutative von neumann inequality finally we introduce a pseudohyperbolic metric on b h n 1 which is invariant under the action of the free holomorphic automorphism group of b h n 1 and turns out to be a noncommutative extension of the pseudohyperbolic distance on b n the open unit ball of c n in this setting we obtain a schwarz pick type lemma we also provide commutative versions of these results for operator valued multipliers of the drury arveson space

curvature invariant for hilbert modules over free semigroup algebras abstract we introduce a notion of relative curvature resp euler characteristic for finite rank contractive hilbert modules over c f n the complex free semigroup algebra generated by the free semigroup f n on n generators asymptotic formulas and basic properties for both the curvature and the euler characteristic are established in particular it is shown that the standard relative curvature invariant resp euler characteristic of a hilbert module h is a nonnegative number less than or equal to the rank of h and it depends only on the properties of the completely positive map t x ni 1 tixt i where t1 tn is the row contraction of not necessarily commuting operators uniquely determined by the c f n module structure of h moreover we prove that for every t 0 there is a hilbert module h such that curv h h t the module structure defined by the left creation operators on the full fock space f2 hn on n generators occupies the position of the rank one free module in the algebraic theory we obtain a complete description of the closed submodules resp quotients of the free hilbert module f2 hn and calculate their curvature invariant it is shown that the curvature is a complete invariant for the finite rank submodules of the free hilbert module f2 hn k where k is a finite dimensional hilbert space a noncommutative version of the gauss bonnet chern theorem from riemannian geometry is obtained for graded hilbert modules over c f n in particular it is proved that the curvature and euler characteristic coincide for certain classes of pure hilbert modules our investigation is based on noncommutative poisson transforms noncommutative dilation theory and harmonic analysis on fock spaces

algorithms of solutions for completely generalized mixed implicit quasi variational inclusions in this paper by applying resolvent operator technique an existence theorem of solutions for a class of completely generalized mixed implicit quasi variational inclusions involving relaxed lipschitz generalized pseudo contractive and relaxed monotone set valued mappings is proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria is also given these results of existence algorithm and convergence are new and unify and generalize some corresponding results in recent literatures

abstract dynamic programming models under commutativity conditions the unifying purpose of the abstract dynamic programming models is to find sufficient conditions on the recursive definition of the objective function that guarantee the validity of the dynamic programming iteration this paper presents backward forward and backward forward models that weaken previous sufficient conditions and that include but are not restricted to optimization problems the backward forward model is devoted to the simultaneous solution of a collection of interrelated sequential problems based on the independent computation of a cost to arrive function and a cost to go function several extremization and nonextremization problems illustrate the applicability of the proposed models

auxiliary principle for generalized mixed variational like inequalities abstract in this paper we use the auxiliary principle technique to prove the existence of a solution of some new classes of variational inequalities which are called the generalized mixed variational like inequalities this technique is used to analyze an iterative algorithm several special cases which can be obtained from our main result are also discussed

strongly nonlinear quasivariational inequalities abstract in this paper we develop the algorithms for finding the approximate solution of a strongly nonlinear quasivariational inequality and a strongly nonlinear quasicomplementarity problem and we include as special cases known results in this area we also observe that these two problems are equivalent if the convex set involved in the formulation of these problem is a convex cone

tree expectation propagation for ml decoding of ldpc codes over the bec we propose a decoding algorithm for ldpc codes that achieves the maximum likelihood ml solution over the binary erasure channel bec in this channel the tree structured expectation propagation tep decoder improves the peeling decoder pd by processing check nodes of degree one and two however it does not achieve the ml solution as the tree structure of the tep allows only for approximate inference in this paper we provide the procedure to construct the structure needed for exact inference this algorithm denoted as generalized tree structured expectation propagation gtep modifies the code graph by recursively eliminating any check node and merging this information in the remaining graph the gtep decoder upon completion either provides the unique ml solution or a tree graph in which the number of parent nodes indicates the multiplicity of the ml solution we also explain the algorithm as a gaussian elimination method relating the gtep to other ml solutions compared to previous approaches it presents an equivalent complexity it exhibits a simpler graphical message passing procedure and most interesting the algorithm can be generalized to other channels

models for noncommuting operators abstract this paper develops a model theory for a pair of noncommuting operators using backward shift operators on a fock space rota s theorem is generalized i e it is shown that any two bounded operators on a hilbert space are simultaneously similar to part of a pair of backward shift operators on a fock space these shift operators and the fock space framework are also used to develop a dilation theory for two noncommuting operators

on random variational inclusions with random fuzzy mappings and random relaxed cocoercive mappings in this paper we introduce and study the random variational inclusions with random fuzzy and random relaxed cocoercive mappings we define an iterative algorithm for finding the approximate solutions of this class of variational inclusions and establish the convergence of iterative sequences generated by proposed algorithm our results improve and generalize many known corresponding results

an iterative method for generalized nonlinear set valued mixed quasi variational inequalities with h monotone mappings generalized nonlinear set valued mixed quasi variational inequalities with maximal monotone mappings have been studied in the literature since the maximal monotone operators are known as special cases of the h monotone operators we generalize the study for these inequality problems with h monotone mappings in this paper precisely we establish the existence of solutions for the generalized nonlinear set valued mixed quasi variational inequality problem with h monotone mappings an iterative method for finding their approximate solutions are proposed furthermore a new convergence criteria for this iterative method is imposed

perturbed ishikawa type iterative algorithm for generalized quasivariational inclusions in this paper a perturbed ishikawa type iterative algorithm of solving a new class of generalized nonlinear implicit quasivariational inclusions are suggested and analysed first an existence theorem of solutions for generalized nonlinear implicit quasivariational inclusion is proved under suitable assumptions then the convergence of the perturbed ishikawa type iterative sequences generated by the new algorithm is proved as special cases some known results are also discussed

iterative algorithms for solving generalized nonlinear mixed variational inequalities a new concept of g partially relaxed strong monotonicity of mappings is introduced by applying the auxiliary variational inequality technique some new predictor corrector iterative algorithms for solving generalized nonlinear mixed variational inequalities are suggested and analyzed the convergence of the algorithms only need the continuity and the g partially relaxed strongly monotonicity of mappings these algorithms and convergence result are new and generalize some known results in literature

hash property and coding theorems for sparse matrices and maximum likelihood coding the aim of this paper is to prove the achievability of rate regions for several coding problems by using sparse matrices with logarithmic column degree and maximum likelihood ml coding these problems are the gel fand pinsker problem the wyner ziv problem and the one helps one problem source coding with partial side information at the decoder to this end the notion of a hash property for an ensemble of functions is introduced and it is proved that an ensemble of q ary sparse matrices satisfies the hash property based on this property it is proved that the rate of codes using sparse matrices and ml coding can achieve the optimal rate

fft based bp decoding of general ldpc codes over abelian groups we introduce a wide class of low density parity check ldpc codes large enough to include ldpc codes over finite fields rings or groups as well as some nonlinear codes a belief propagation decoding procedure with the same complexity as for the decoding of ldpc codes over finite fields is also presented moreover an encoding procedure is developed

nonnegative ranks decompositions and factorizations of nonnegative matrices the nonnegative rank of a nonnegative matrix is the smallest number of nonnegative rank one matrices into which the matrix can be decomposed additively such decompositions are useful in diverse scientific disciplines we obtain characterizations and bounds and show that the nonnegative rank can be computed exactly over the reals by a finite algorithm

generalized complementarity problems for fuzzy mappings in this paper we introduce a new class of generalized complementarity problems for the fuzzy mappings and construct a new iterative algorithm we also discuss the existence of solutions for the generalized complementarity problems and the convergence of iterative sequence

on the bcjr trellis for linear block codes in this semi tutorial paper we will investigate the computational complexity of an abstract version of the viterbi algorithm on a trellis and show that if the trellis has e edges the complexity of the viterbi algorithm is spl theta e this result suggests that the best trellis representation for a given linear block code is the one with the fewest edges we will then show that among all trellises that represent a given code the original trellis introduced by bahl cocke jelinek and raviv in 1974 and later rediscovered by wolf 1978 massey 1978 and forney 1988 uniquely minimizes the edge count as well as several other figures of merit following forney and kschischang and sorokine 1995 we will also discuss trellis oriented or minimal span generator matrices which facilitate the calculation of the size of the bcjr trellis as well as the actual construction of it

variational inequalities for fuzzy mappings ii in this paper we establish the equivalence between the variational inequalities for fuzzy mappings and the wiener hopf equations for fuzzy mappings we use this equivalence to suggest a number of new iterative algorithms for solving the variational inequalities for fuzzy mappings we also study the convergence criteria of these iterative algorithms the auxiliary principle technique is used to study the existence of a solution of the variational inequality for fuzzy mappings and to suggest a novel and innovative iterative algorithm for computing the approximate solution the results proved in this paper represent an improvement of previously known results

correctness of local probability propagation in graphical models with loops graphical models such as bayesian networks and markov networks represent joint distributions over a set of variables by means of a graph when the graph is singly connected local propagation rules of the sort proposed by pearl 1988 are guaranteed to converge to the correct posterior probabilities recently a number of researchers have empirically demonstrated good performance of these same local propagation schemes on graphs with loops but a theoretical understanding of this performance has yet to be achieved for graphical models with a single loop we derive an analytical relationship between the probabilities computed using local propagation and the correct marginals using this relationship we show a category of graphical models with loops for which local propagation gives rise to provably optimal maximum a posteriori assignments although the computed marginals will be incorrect we also show how nodes can use local information in the messages they receive in order to correct their computed marginals we discuss how these results can be extended to graphical models with multiple loops and show simulation results suggesting that some properties of propagation on single loop graphs may hold for a larger class of graphs specifically we discuss the implication of our results for understanding a class of recently proposed error correcting codes known as turbo codes

estimation and marginalization using the kikuchi approximation methods in this letter we examine a general method of approximation known as the kikuchi approximation method for finding the marginals of a product distribution as well as the corresponding partition function the kikuchi approximation method defines a certain constrained optimization problem called the kikuchi problem and treats its stationary points as approximations to the desired marginals we show how to associate a graph to any kikuchi problem and describe a class of local message passing algorithms along the edges of any such graph which attempt to find the solutions to the problem implementation of these algorithms on graphs with fewer edges requires fewer operations in each iteration we therefore characterize minimal graphs for a kikuchi problem which are those with the minimum number of edges we show with empirical results that these simpler algorithms often offer significant savings in computational complexity without suffering a loss in the convergence rate we give conditions for the convexity of a given kikuchi problem and the exactness of the approximations in terms of the loops of the minimal graph more precisely we show that if the minimal graph is cycle free then the kikuchi approximation method is exact and the converse is also true generically together with the fact that in the cycle free case the iterative algorithms are equivalent to the well known belief propagation algorithm our results imply that generically the kikuchi approximation method can be exact if and only if traditional junction tree methods could also solve the problem exactly

parametric completely generalized mixed implicit quasi variational inclusions involving h maximal monotone mappings a new class of parametric completely generalized mixed implicit quasi variational inclusions involving h maximal monotone mappings is introduced by applying resolvent operator technique of h maximal monotone mapping and the property of fixed point set of set valued contractive mappings the behavior and sensitivity analysis of the solution set of the parametric completely generalized mixed implicit quasi variational inclusions involving h maximal monotone mappings are studied the continuity and lipschitz continuity of the solution set with respect to the parameter are proved under suitable assumptions our approach and results are new and improve unify and extend previous many known results in this field

a new class of generalized nonlinear implicit quasivariational inclusions with fuzzy mappings in this paper we introduce and study a new class of generalized nonlinear implicit quasivariational inclusions with fuzzy mappings an existence theorem of solutions is proved without compactness assumptions a new iterative algorithm is suggested and analysed the convergence of iterative sequences generated by the new algorithm are also given as special cases some known results are also discussed

iterative algorithm for generalized quasi variational like inclusions with fuzzy mappings in banach spaces in this paper we introduce and study a class of generalized quasi variational like inclusions with fuzzy mappings in real banach spaces and show its equivalence with a class of relations using this equivalence we suggest and analyze an iterative algorithm for finding the approximate solution of this class of inclusions further we prove the existence of solution of this class of inclusions and discuss the convergence criteria of iterative sequences generated by the iterative algorithm

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

general algorithm of solutions for nonlinear variational inequalities in banach space abstract in this paper we shall study a class of general nonlinear variational inequalities in reflexive banach spaces by applying a minimax inequality obtained by the author some existence uniqueness theorems of solutions for the general nonlinear variational inequalities are proved next by applying the auxiliary problem technique we suggest an innovative iterative algorithm to compute the approximate solutions of the general nonlinear variational inequality finally the convergence criteria is also discussed

poisson transforms on some c algebras generated by isometries abstract a noncommutative poisson transform associated to a certain class of sequences of operators on hilbert spaces with property p is defined on some universal c algebras resp nonselfadjoint algebras generated by isometries its properties are described and used to study these universal algebras and their representations as consequences we obtain a functional calculus isometric resp unitary dilations and commutant lifting theorem for the class of sequences of operators with property p our geometrical approach leads also to new and elementary proofs as well as extensions of some classical results

existence results of a perturbed variational inequality with a fuzzy mapping abstract this paper is devoted to the existence of a perturbed variational inequality with a fuzzy mapping in a finite dimensional space we introduce two perturbation methods for a fuzzy mapping in one method it is perturbed by a nonlinear mapping and in the other it is perturbed by a vector under suitable coercivity conditions we show that the perturbed variational inequality with a fuzzy mapping has a solution when perturbed by both of the methods mentioned above the main results presented in this paper generalize and improve some known results

an analysis of belief propagation on the turbo decoding graph with gaussian densities motivated by its success in decoding turbo codes we provide an analysis of the belief propagation algorithm on the turbo decoding graph with gaussian densities in this context we are able to show that under certain conditions the algorithm converges and that somewhat surprisingly though the density generated by belief propagation may differ significantly from the desired posterior density the means of these two densities coincide since computation of posterior distributions is tractable when densities are gaussian use of belief propagation in such a setting may appear unwarranted indeed our primary motivation for studying belief propagation in this context stems from a desire to enhance our understanding of the algorithm s dynamics in a non gaussian setting and to gain insights into its excellent performance in turbo codes nevertheless even when the densities are gaussian belief propagation may sometimes provide a more efficient alternative to traditional inference methods