the expansion of functions under transformation and its application to optimization abstract this paper proposes the expansion of functions under transformation which represents infinite kinds of extensions of taylor s expansion based on this duffin s condensation formula is developed as a condensation formula of high order furthermore a theorem of efficiently solving mathematical programming by using the expansion of functions is proposed according to the condensation formula of high order two kinds of second order primal algorithms are proposed for solving generalized geometric programming with rapid and stable convergence which could be applied to a wide range of structural optimization problems finally an efficient fully stressed design method under the function transformation is proposed using these expansions of functions

matrix regular operator spaces the concept of the regular or riesz norm on ordered real banach spaces is generalized to matrix ordered complex operator spaces in a way that respects the matricial structure of the operator space a norm on an ordered real banach spaceeis regular if 1 x y ximplies that y x and 2 y 1 implies the existence ofx esuch that x 1 and x y x a matrix ordered operator space is called matrix regular if at each matrix level the restriction of the norm to the self adjoint elements is a regular norm in such a space elements at each matrix level can be written as linear combinations of four positive elements the concept of the matrix ordered operator space is made specific in such a way as to be a natural generalization of ordered real and complex banach spaces for the case wherevis a matrix ordered operator space a natural cone is defined on the operator spacex hv hx with hindicating the haagerup tensor product so as to make it a matrix ordered operator space exploiting the advantages gained by takingxto be the column hilbert spacehc an equivalence is established between the matrix regularity of a space and that of its operator dual this concept of matrix regularity also provides for more accessible proofs of the christensen sinclair multilinear representation and multilinear decomposition theorems

every completely polynomially bounded operator is similar to a contraction it is proved that a bounded operator on a hilbert space is similar to a contraction if and only if it is completely polynomially bounded this gives a partial answer to problem 6 of halmos bull amer math soc 76 1970 877 933 the set of completely bounded maps between c algebras is studied to obtain some structure representation and extension theorems for this class of maps these allow a characterization of the completely bounded representations on a hilbert space of any subalgebra of a c algebra to be obtained the result in the title follows by applying this characterization to the disk algebra

global optimization of signomial geometric programming using linear relaxation various local optimization approaches have been developed for solving signomial geometric programming sgp problems but up to now less work has been devoted to solving global optimization of sgp due to the inherent difficulty this paper considers the global minimum of sgp that arise in various practice problems by utilizing an exponential variable transformation and tangential hypersurfaces and convex envelop approximations a linear relaxation of sgp is then obtained thus initial nonconvex nonlinear problem sgp is reduced to a sequence of linear programming problems through the successive refinement of a linear relaxation of feasible region of the objective function the proposed algorithm is convergent to the global minimum of sgp by means of the subsequent solutions of a series of linear programming problems test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve global minimum of sgp on a microcomputer

a characterization of operator algebras abstract an operator algebra is a uniformly closed algebra of bounded operators on a hilbert space in this paper we give a characterization of unital operator algebras in terms of their matricial norm structure more precisely if a is an l matricially normed space and also an algebra with a completely contractive multiplication and an identity of norm 1 then there is a completely isometric isomorphism of a onto a unital operator algebra indeed the multiplication on a need not be assumed to be associative for this conclusion to follow examples are given to show that the condition on the identity is necessary it follows from the above that the quotient of an operator algebra by a closed two sided ideal with the natural matricial structure is again an operator algebra up to complete isometric isomorphism

a new hybrid method for solving global optimization problem abstract in this paper we present a new hybrid method called the sasp method the purpose of this method is the hybridization of the simulated annealing sa with the descent method where we estimate the gradient using simultaneous perturbation firstly the new hybrid method finds a local minimum using the descent method then sa is executed in order to escape from the currently discovered local minimum to a better one from which the descent method restarts a new local search and so on until convergence the new hybrid method can be widely applied to a class of global optimization problems for continuous functions with constraints experiments on 30 benchmark functions including high dimensional functions show that the new method is able to find near optimal solutions efficiently in addition its performance as a viable optimization method is demonstrated by comparing it with other existing algorithms numerical results improve the robustness and efficiency of the method presented

multiplication free approximate algorithms for compressed domain linear operations on images we propose a method for devising approximate multiplication free algorithms for compressed domain linear operations on images e g downsampling translation filtering etc we demonstrate that the approximate algorithms give output images that are perceptually nearly equivalent to those of the exact processing while the computational complexity is significantly reduced

factorization of completely bounded maps through reflexive operator spaces with applications to weak almost periodicity abstract let m be a hopf von neumann algebra so that m is a completely contractive banach algebra we investigate whether the product of two elements of m that are both weakly almost periodic functionals on m is again weakly almost periodic for that purpose we establish the following factorization result if m and n are injective von neumann algebras and if x y m n correspond to weakly compact operators from m to n factoring through reflexive operator spaces x and y respectively then the operator corresponding to xy factors through the haagerup tensor product x h y provided that x h y is reflexive as a consequence for instance for any hopf von neumann algebra m with m injective the product of a weakly almost periodic element of m with a completely almost periodic one is again weakly almost periodic

a nonisolated optimal solution for special reverse convex programming problems in this paper an efficient algorithm is proposed for globally solving special reverse convex programming problems with more than one reverse convex constraints the proposed algorithm provides a nonisolated global optimal solution which is also stable under small perturbations of the constraints and it turns out that such an optimal solution is adequately guaranteed to be feasible and to be close to the actual optimal solution convergence of the algorithm is shown and the numerical experiment is given to illustrate the feasibility of the presented algorithm

operator space tensor products and inductive limits abstract we investigate whether the tensor product of operator spaces which includes the operator space projective haagerup and schur tensor products and the tensor product of operator systems commute with inductive limits in the sense that if x n n is an inductive system of operator spaces or operator systems with an inductive limit x and if y is any operator space or operator system then whether x n y n id becomes an inductive system and if so whether the inductive limit of this system is same as x y where denotes the tensor product of operator spaces or operator systems we also discuss about the bidual of such an inductive limit and obtain embeddings lim x n y lim x n y under certain restrictions

modules over operator algebras and the maximal c dilation abstract we continue our study of the general theory of possibly nonselfadjoint algebras of operators on a hilbert space and modules over such algebras developing a little more technology to connect nonselfadjoint operator algebra with the c algebraic framework more particularly we make use of the universal or maximal c algebra generated by an operator algebra and c dilations this technology is quite general however it was developed to solve some problems arising in the theory of morita equivalence of operator algebras and as a result most of the applications given here and in a companion paper are to that subject other applications given here are to extension problems for module maps and characterizations of c algebras

frequency domain motion estimation using a complex lapped transform a frequency domain algorithm for motion estimation based on overlapped transforms of the image data is developed as an alternative to block matching methods the complex lapped transform clt is first defined by extending the lapped orthogonal transform lot to have complex basis functions the clt basis functions decay smoothly to zero at their end points and overlap by 2 1 when a data sequence is transformed a method for estimating cross correlation functions in the clt domain is developed this forms the basis of a motion estimation algorithm that calculates vectors for overlapping windowed regions of data the overlapping data window used has no block edge discontinuities and results in smoother motion fields furthermore when motion compensation is performed using similar overlapping regions the algorithm gives comparable or smaller prediction errors than standard models using exhaustive search block matching and computational load is lower for larger displacement ranges and block sizes

transform domain filtering based on pipelining structure the concept of transform domain filtering tdf is defined and a pipelining structure is proposed as a means to implement it tdf refers to filtering applied directly to transform domain data the proposed structure consists of product blocks and an array of m adders where m is the transform block length the tdf output data can be obtained by summing the outputs of each product block the product block in the proposed structure performs the product operation between an m m matrix and an m vector which can be effectively implemented by using a distributed arithmetic structure of a systolic array structure the proposed structure is simple with localized interconnections and is therefore suitable for vlsi implementations

lovasz theta type norms and operator systems abstract to each graph on n vertices there is an associated subspace of the n n matrices called the operator system of the graph we prove that two graphs are isomorphic if and only if their corresponding operator systems are unitally completely order isomorphic this means that the study of graphs is equivalent to the study of these special operator systems up to the natural notion of isomorphism in their category we define new graph theory parameters via this identification certain quotient norms that arise from studying the operator system of a graph give rise to a new family of parameters of a graph we then show basic properties about these parameters and write down explicitly how to compute them via a semidefinite program and discuss their similarities to the lovasz theta function finally we explore a particular parameter in this family and establish a sandwich theorem that holds for some graphs

fast dct domain filtering using the dct and the dst a method for efficient spatial domain filtering directly in the discrete cosine transform dct domain is developed and proposed it consists of using the discrete sine transform dst and the dct for transform domain processing on the in jpeg basis of the previously derived convolution multiplication properties of discrete trigonometric transforms the proposed scheme requires neither zero padding of the input data nor kernel symmetry it is demonstrated that in typical applications the proposed algorithm is significantly more efficient than the conventional filtered spatial domain and earlier proposed dct domain methods the proposed method is applicable to any dct based image compression standard such as jpeg mpeg and h 261

a new rectangle branch and pruning approach for generalized geometric programming generalized geometric programming ggp problem occurs frequently in engineering design and management in this paper a branch and pruning global optimization algorithm is proposed for ggp by utilizing some transformations a linear relaxation of the problem ggp is obtained based on the linear lower bound functions of objective and constraint functions inside some hyperrectangle region then a new pruning technique is given to accelerate the convergence of the given algorithm and this pruning technique offers the possibility to cut away a large part of the current investigated region in which there no exist global optimum solution the proposed algorithm which connects branch and bound method with the pruning technique successfully is convergent to the global minimum according to the successive refinement of the linear relaxation of feasible region of the objective function and the solutions of a series of linear relaxation problems and finally numerical experiment is given to illustrate the feasibility and efficiency of the proposed algorithm

an operator space approach to condition c abstract we show that there exists a natural embedding from the tensor product v w of the biduals of operator spaces v and w into the bidual v w of the injective tensor product of v and w which is separately weak continuous from this we define condition c for operator spaces

self duality for the haagerup tensor product and hilbert space factorizations d blecher and v paulsen showed that the haagerup tensor product v h w for operator spaces v and w preserves inclusions it is proved to also preserve complete quotient maps and to be self dual in the sense that it induces the haagerup norm on the algebraic tensor product v w the full operator dual space v h w is computed it coincides with the natural operator space gg2 v w of maps v w which have completely bounded factorizations through hilbert spaces with vectors identified with row matrices more generally one has the natural complete isometry gg2 v h w x gg2 v gg2 w x given hilbert spaces h and k with vectors regarded as column matrices it is shown that one may identify the operator spaces b h k and cb h k

bilinear ideals in operator spaces abstract we introduce a concept of bilinear ideal of jointly completely bounded mappings between operator spaces in particular we study the bilinear ideals n of completely nuclear i of completely integral and e of completely extendible bilinear mappings we also consider the multiplicatively bounded bilinear mappings mb and its symmetrization smb we prove some basic properties of them one of which is the fact that i is naturally identified with the ideal of linear completely integral mappings on the injective operator space tensor product

on generalized geometric programming problems with non positive variables generalized geometric programming ggp problems occur frequently in engineering design and management some exponential based decomposition methods have been developed for solving global optimization of ggp problems however the use of logarithmic exponential transformations restricts these methods to handle the problems with strictly positive variables this paper proposes a technique for treating non positive variables with integer powers in ggp problems by means of variable transformation the ggp problem with non positive variables can be equivalently solved with another one having positive variables in addition we present some computationally efficient convexification rules for signomial terms to enhance the efficiency of the optimization approach numerical examples are presented to demonstrate the usefulness of the proposed method in ggp problems with non positive variables

a global optimization algorithm using linear relaxation various local optimization approaches have been developed for solving the non convex quadratically constrained quadratic programs qp but up to now less work has been devoted to solving global optimization of qp problem due to the inherent difficulty this paper considers the global minimum of qp that arise in various practice problems by utilizing the inherent property of the quadratic function an approximations a linear relaxation of qp is then obtained thus initial qp is reduced to a sequence of linear programming problems through the successive refinement of a linear relaxation of feasible region of the objective function the proposed algorithm is convergent to the global minimum of qp by means of the subsequent solutions of a series of linear programming problems test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve the global minimum of qp on a microcomputer

tensor products of operator systems abstract the purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems after giving an axiomatic definition of tensor products in this category we examine in detail several particular examples of tensor products including a minimal maximal maximal commuting maximal injective and some asymmetric tensor products we characterize these tensor products in terms of their universal properties and give descriptions of their positive cones we also characterize the corresponding tensor products of operator spaces induced by a certain canonical inclusion of an operator space into an operator system we examine notions of nuclearity for our tensor products which on the category of c algebras reduce to the classical notion we exhibit an operator system s which is not completely order isomorphic to a c algebra yet has the property that for every c algebra a the minimal and maximal tensor product of s and a are equal

tensor products of operator spaces abstract in this paper we lay the foundations for a systematic study of tensor products of subspaces of c algebras to accomplish this various notions of duality are introduced and employed elementary proofs of the complete injectivity of the haagerup norm and of the extension theorem for completely bounded maps are given pisier s gamma norms are examined and found to be special cases of the haagerup norm we identify the greatest operator space cross norm and show that the spatial tensor norm is the least operator space cross norm in an appropriate sense indeed most of the elementary theory of banach space tensor norms generalizes to the category of operator spaces

diagonalizing properties of the discrete cosine transforms since its introduction in 1974 by ahmed et al the discrete cosine transform dct has become a significant tool in many areas of digital signal processing especially in signal compression there exist eight types of discrete cosine transforms dcts we obtain the eight types of dcts as the complete orthonormal set of eigenvectors generated by a general form of matrices in the same way as the discrete fourier transform dft can be obtained as the eigenvectors of an arbitrary circulant matrix these matrices can be decomposed as the sum of a symmetric toeplitz matrix plus a hankel or close to hankel matrix scaled by some constant factors we also show that all the previously proposed generating matrices for the dcts are simply particular cases of these general matrix forms using these matrices we obtain for each dct a class of stationary processes verifying certain conditions with respect to which the corresponding dct has a good asymptotic behavior in the sense that it approaches karhunen loeve transform performance as the block size n tends to infinity as a particular result we prove that the eight types of dcts are asymptotically optimal for all finite order markov processes we finally study the decorrelating power of the dcts obtaining expressions that show the decorrelating behavior of each dct with respect to any stationary processes

accelerating method of global optimization for signomial geometric programming abstract signomial geometric programming sgp has been an interesting problem for many authors recently many methods have been provided for finding locally optimal solutions of sgp but little progress has been made for global optimization of sgp in this paper we propose a new accelerating method for global optimization algorithm of sgp using a suitable deleting technique this technique offers a possibility to cut away a large part of the currently investigated region in which the globally optimal solution of sgp does not exist and can be seen as an accelerating device for global optimization algorithm of sgp problem compared with the method of shen and zhang global optimization of signomial geometric programming using linear relaxation appl math comput 150 2004 99 114 numerical results show that the computational efficiency is improved obviously by using this new technique in the number of iterations the required saving list length and the execution time of the algorithm

representations of completely bounded multilinear operators a deli ion of a completely bounded multilinear operator from one c algebra into another is introduced each completely bounded multilinear operator from a algebra into the algebra of bounded linear operators on a hilbert space is shown to be representable in terms of representations of the c algebra and interlacing operators this result extends wittstock s theorem that decomposes a completely bounded linear operator from a c algebra into an injective c algebra into completely positive linear operators 0 1987 academic press inc stinespring s theorem gives a useful representation for a completely positive linear operator from a c algebra into the algebra bl h for continuous linear operators on a hilbert space h 12 11 using this representation with wittstock s theorem that decomposes a completely bounded linear operator as a finite linear combination of completely positive linear operators 14 lo one obtains a representation of a completely bounded linear operator from a c algebra into bl h our main result is a representation theorem for completely bounded multilinear operators from a c algebra into bl h which generalizes this representation of completely bounded linear operators corollaries give multilinear generalizations of several results known for completely bounded linear operators we shall briefly describe the type of representations to be 151

global optimization for sum of generalized fractional functions this paper considers the solution of generalized fractional programming gfp problem which contains various variants such as a sum or product of a finite number of ratios of linear functions polynomial fractional programming generalized geometric programming etc over a polytope for such problems we present an efficient unified method in this method by utilizing a transformation and a two part linearization method a sequence of linear programming relaxations of the initial nonconvex programming problem are derived which are embedded in a branch and bound algorithm numerical results are given to show the feasibility and effectiveness of the proposed algorithm

symmetric convolution and the discrete sine and cosine transforms this paper discusses the use of symmetric convolution and the discrete sine and cosine transforms dsts and dcts for general digital signal processing the operation of symmetric convolution is a formalized approach to convolving symmetrically extended sequences the result is the same as that obtained by taking an inverse discrete trigonometric transform dtt of the product of the forward dtts of those two sequences there are 16 members in the family of dtts each provides a representation for a corresponding distinct type of symmetric periodic sequence the author defines symmetric convolution relates the dsts and dcts to symmetric periodic sequences and then use these principles to develop simple but powerful convolution multiplication properties for the entire family of dsts and dcts symmetric convolution can be used for discrete linear filtering when the filter is symmetric or antisymmetric the filtering will be efficient because fast algorithms exist for all versions of the dtts conventional linear convolution is possible if one first zero pad the input data symmetric convolution and its fast implementation using dtts are now an alternative to circular convolution and the dft

representations of function algebras abstract operator spaces and banach space geometry let g be the closed unit ball of some norm on cn and let a g be the closure of the polynomials in the sup norm we prove that if n 5 then there is a contractive representation of a g as operators on a hilbert space which is not completely contractive our technique involves introducing a numerical invariant x for a normed space x which measures the difference between the minimal operator space structure which can be assigned to x min x and the maximal structure max x we estimate x using banach space techniques we also prove that if x is any infinite dimensional subspace of the space of continuous functions on a compact hausdorff space then there exists a bounded linear map on x which is not completely bounded

a global optimization using linear relaxation for generalized geometric programming many local optimal solution methods have been developed for solving generalized geometric programming ggp but up to now less work has been devoted to solving global optimization of ggp problem due to the inherent difficulty this paper considers the global minimum of ggp problems by utilizing an exponential variable transformation and the inherent property of the exponential function and some other techniques the initial nonlinear and nonconvex ggp problem is reduced to a sequence of linear programming problems the proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve the global minimum of ggp on a microcomputer

extensions of locally compact quantum groups and the bicrossed product construction abstract in the framework of locally compact quantum groups we study cocycle actions we develop the cocycle bicrossed product construction starting from a matched pair of locally compact quantum groups we define exact sequences and establish a one to one correspondence between cocycle bicrossed products and cleft extensions in this way we obtain new examples of locally compact quantum groups

range division and contraction algorithm for a class of global optimization problems abstract this article presents a range division and contraction algorithm for a class of global optimization problems in the algorithm the original problem is first converted into an equivalent monotonic optimization problem whose objective function is just a simple univariate by exploiting the particularity of this monotonicity the variable bound in a particular node is then tightened and the bounds on the constraints are calculated to remove the region which doesn t contain optimal solutions the proposed method can reach an approximate solution within an acceptable error in which such solution is adequately guaranteed to be feasible and to be close to the actual global optimal solution several numerical examples are given to illustrate the feasibility and efficiency of the present algorithm

interpolation of operator spaces abstract we develop the real interpolation theory for operator spaces we show that the main theorems in the classical real interpolation theory for banach spaces hold in our operator space setting these include the equivalence duality and reiteration theorems as an application of the duality theorem we prove that the real interpolation operator space of parameters 1 2 2 between an operator space and its antidual is completely isomorphic to an operator hilbert space oh i discovered recently by g pisier we also present an outline of a general interpolation theory in the category of operator spaces in particular we construct the operator space version of the orbit and coorbit functors and extend to operator spaces the classical aronzsajn gagliardo theorem our development complements some recent works of pisier

global optimization for sum of geometric fractional functions this paper presents an efficient branch and bound algorithm for globally solving sum of geometric fractional functions under geometric constraints which arise in various practical problems by using an equivalent transformation and a new linear relaxation technique a linear relaxation programming problem of the equivalent problem is obtained the proposed algorithm is convergent to the global optimal solution by means of the subsequent solutions of a series of linear programming problems numerical results are reported to show the feasibility of our algorithm

global optimization of generalized linear fractional programming with nonlinear constraints this paper presents a branch and bound algorithm for globally solving a wide class of generalized linear fractional programming problems glfp this class includes such problems as minimizing a sum or error for product of a finite number of ratios of linear functions linear multiplicative programming polynomial programming etc over nonconvex feasible region first a problem q is derived which is equivalent to problem glfp in the algorithm lower bounds are derived by solving a sequence of linear relaxation programming problems which is based on the construction of the linear lower bounding functions for the objective function and constraint functions of problem q over the feasible region convergent property of the presented algorithm is proved and numerical results are given to show the feasibility of the proposed algorithm

amenability of hopf von neumann algebras and kac algebras abstract let m be a hopf von neumann algebra the operator predualm ofmis a completely contractive banach algebra with multiplicationm m m m we call m operator amenableif the completely contractive banach algebram isoperator amenable i e for every operatorm bimodulev every completely bounded derivation fromm into the dualm bimodulev is inner there is a weaker notion of amenability introduced by d voiculescu we say that a hopf von neumann algebra m isvoiculescu amenableif there exists a left invariant mean onm we show that if a hopf von neumann algebra m is operator amenable then it is voiculescu amenable for kac algebras there is astrong voiculescu amenability we show that for discrete kac algebras these amenabilities are all equivalent in fact if we letk m be a discrete kac algebra and letk m be its compact dual kac algebra then the following are equivalent 1 kis operator amenable 2 kis voiculescu amenable 3 the von neumann algebramis hyperfinite 4 kis strong voiculescu amenable 5 kis operator amenable 6 m has a bounded approximate identity

a new bound and reduce approach of nonconvex quadratic programming problems abstract for the nonconvex quadratic programming problem a new linear programming relaxation bound and reduce algorithm is proposed and its convergence is proved in this algorithm a new hyper rectangle partition technique and a new linear programming relaxation tactics are used at the same time the hyper rectangular reduction method is used to raise its convergent speed the numerical results demonstrate the effectiveness and feasibility of the proposed algorithm

a polynomially bounded operator on hilbert space which is not similar to a contraction let e 0 we prove that there exists an operator te e2 2 such that for any polynomial p we have iip te ii not similar to a contraction i e there does not exist an invertible operator s f2 e f2 such that jis 1tesii tributed to halmos after his well known 1970 paper ten problems in hilbert space we also give some related finite dimensional estimates department of mathematics texas a m university college station texas 77843 universite paris vi equipe d7analyse case 186 75252 paris cedex 05 france e mail address gipqccr jussieu fr this content downloaded from 157 55 39 104 on sun 19 jun 2016 06 52 47 utc all use subject to http about jstor org terms

a factorization problem for normal completely bounded mappings abstract given an operator space x and a von neumann algebra a we consider a contractive mapping q a eh x eh a ncb x a formally defined by q aj xjk bk xjk ajbk from the extended haagerup tensor product a eh x eh a into the space of w continuous completely bounded maps from x into a we characterize elements of the range space im q by a factorization property involving decomposable operators and investigate various properties of that space in the case when x b is the predual of a von neumann algebra b im q is included in the space dec b a of decomposable operators from b into a regarding q as having values in that space we show that q is a quotient map onto its range then we prove that dec b a is a normal dual operator a bimodule and that im q dec b a is a strong operator a bimodule

multilinear maps and tensor norms on operator systems abstract we extend work of christensen and sinclair on completely bounded multilinear forms to the case of subspaces of c algebras and obtain a representation theorem and a hahn banach extension theorem for such maps in the second part of the paper the haagerup norms on tensor products are investigated and we obtain new characterizations of these quantities

ein operatorwertiger hahn banach satz abstract we generalize arveson s extension theorem for completely positive mappings 1 to a hahn banach principle for matricial sublinear functionals with values in an injective c algebra or an ideal in b h we characterize injective w algebras by a matricial order condition we illustrate the matricial hahn banach principle by three applications 1 let a b b be unital c algebras b a subalgebra of a and b b injective if a b is a completely bounded self adjoint b bihomomorphism then it can be expressed as the difference of two completely positive b bihomomorphism 2 let m be a w algebra containing 1 h on a hilbert space h if m is finite and hyperfinite there exists an invariant expectation mapping p of b h onto m p is an extension of the center trace 3 combes 7 proved that a lower semicontinuous scalar weight on a c algebra is the upper envelope of bounded positive functionals we generalize this result to unbounded completely positive mappings with values in an injective w algebra

adaptive cosine transform coding of images in perceptual domain an adaptive cosine transform coding scheme for color images which incorporates human visual properties into the coding scheme is described it employs adaptive quantization to exploit the statistical nature of the coefficients and adaptive block distortion equalization to reduce the block edge structures inherent in block transform coding schemes results show that the subjective quality of the reconstructed images at a bit rate of 0 4 bit pixel or a compression ratio of 60 1 is very good

a direct computation of dct coefficients for a signal block taken from two adjacent blocks a direct computational algorithm for obtaining the dct discrete cosine transform coefficients of a signal block taken from two adjacent blocks is proposed this algorithm reduces the number of both multiplications and additions subtractions compared to the traditional method which requires inverse transforms of two received coefficient blocks followed by a forward transform the proposed algorithm is efficient and useful for speech coding and image processing especially for real time applications

the predual of the space of decomposable maps from a c algebra into a von neumann algebra abstract for a c algebra a and a von neumann algebra r we describe the predual of space d a r of decomposable maps from a into r equipped with decomposable norm this predual is found to be the matrix regular operator space structure on a r with a certain universal property its matrix norms are the largest and its positive cones on each matrix level are the smallest among all possible matrix regular operator space structures on a r under the two natural restrictions 1 x y x y for x m k a y m l r and 2 v w is positive if v m k a and w m l r

subspaces of c algebras abstract basic properties of matricially normed spaces are considered and a simple matrix norm characterization of the subspaces of c algebras is given the latter result is used to study the haagerup tensor products and quotients of such subspaces