multiplier free iir filter realization using periodically time varying state space structure i structure and design a multiplier free realization for iir filters is proposed a given target iir filter is implemented in cascade or parallel form of biquad units each biquad unit is realized with a periodically time varying ptv state space system the system uses a higher order ptv state space ptv ss structure operating at an elevated signal rate to realize each biquad the coefficients of the ptv ss structure used in the realization are restricted to a few power of two values therefore such a structure can be implemented without any hardware multiplier a brief analysis of precision and round off error for the realization is presented examples show that the frequency response of the proposed realization matches very well with that of the target filter

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

asymptotic stability of two dimensional digital filters under quantization the stability of 2 d digital filters implemented with two s complement quantization is investigated the difference equation model is considered for the following cases i quantization after each product and ii quantization after a complete sum of products for both cases sufficient conditions are established for asymptotic stability the 2 d state space roesser s 1975 model is also considered under two s complement quantization and a sufficient condition is derived for its stability some examples are given to illustrate the results

extension of unbounded left hilbert algebras to partial algebras in this paper an unbounded generalization of left hilbert algebras by partial algebras is considered and the tomita takesaki theory is extended to partial o algebras while such a construction has been considered in previous papers a inoue publ rims kyoto univ 22 725 1986 23 673 1987 modular systems for algebras of unbounded operators preprint fukuoka univ 1990 the present one places emphasis on a rich class of unbounded operators and is more applicable to examples

an exhaustive search algorithm for checking limit cycle behavior of digital filters the presence of limit cycles that may arise in fixed point arithmetic implementation of a digital filter can significantly impair its performance this paper presents an algorithm to determine the presence absence of such limit cycles for generality the filter is taken to be in its state space formulation the algorithm is applicable independent of filter order type of quantization nonlinearity and whether the accumulator is single or double length it may be utilized to construct limit cycle free regions in filter coefficient space once a filter is determined to be limit cycle free a technique that provides a robustness region in coefficient space where all filters remain limit cycle free is also presented

robust wideband beamforming by the hybrid steepest descent method this paper uses the hybrid steepest descent method hsdm to design robust smart antennas several design criteria as well as robustness are mathematically described by a finite collection of closed convex sets in a real euclidean space desirable beamformers are defined as points of the generalized convex feasible set which is well defined even in the case of inconsistent design criteria a quadratic cost function is formed by the correlations of the incoming data and the hsdm constructs a point sequence that strongly converges to the unique minimizer of the cost function over the generalized convex feasible set numerical examples validate the proposed design

a computer aided test for the absence of limit cycles in fixed point digital filters the problem of determining the existence of limit cycles in direct form digital filters with quantization nonlinearities is considered a method based on an exhaustive search is introduced it is applicable to all direct form digital filters regardless of the type of quantization arithmetic the number of quantizers and the order of the filter the equivalence between the concept of global asymptotic stability and the exclusion of limit cycles is proved for linearly stable finite wordlength digital filters the robustness of this test with respect to coefficient perturbation in the digital filter is presented the computational aspects of the algorithm are also discussed the algorithm is shown to be capable of always determining the global asymptotic stability of the tested realization

low roundoff noise and normal realizations of fixed point iir digital filters explicit design and performance equations are given in terms of the parameters of the desired transfer function h z for two classes of realizations these realizations offer the digital circuit designer an alternative to the usual designs based on direct forms in addition to low roundoff noise these new realizations offer other desirable properties such as low coefficient sensitivities and freedom from overflow oscillations numerical results are presented which detail the design process and verify the theory

unbounded partial hilbert algebras a notion of an unbounded partial hilbert algebra is introduced and some properties and examples of such an algebra are furnished noncommutative versions of arens l spaces over partial hilbert algebras are formulated and shown to be unbounded partial hilbert algebras moreover necessary and sufficient conditions for the l spaces to be pure unbounded partial hilbert algebras are established

almost mean field ising model an algebraic approach we study the thermodynamic limit of the algebraic dynamics for an almost mean field ising model which is a slight generalization of the ising model in the mean field approximation we prove that there exists a family of relevant states on which the algebraic dynamics t can be defined this t defines a group of automorphisms of the algebra obtained by completing the standard spin algebra with respect to the quasiuniform topology defined by our states

strong convergence of an iterative method for nonexpansive and accretive operators abstract let x be a banach space and a an m accretive operator with a zero consider the iterative method that generates the sequence x n by the algorithm x n 1 n u 1 n j r n x n where n and r n are two sequences satisfying certain conditions and j r denotes the resolvent i r a 1 for r 0 strong convergence of the algorithm x n is proved assuming x either has a weakly continuous duality map or is uniformly smooth

approximation of a zero point of accretive operator in banach spaces abstract this paper introduces a composite iteration scheme for approximating a zero point of accretive operator in the framework of uniformly smooth banach spaces and the reflexive banach space which has a weak continuous duality map respectively strong convergence of the composite iteration scheme x n defined by y n n x n 1 n j r n x n x n 1 n u 1 n y n where j r n is the resolvent of m accretive operator a and u c is an arbitrary but fixed element in c and sequences n in 0 1 n in 0 1 is established under certain appropriate assumptions on the sequences n n and r n that x n defined by the above iteration scheme converges to a zero point of a is proved the results improve and extend results of t h kim h k xu and some others

quasi algebras and multiplication of distributions a self adjoint operatorainl2 defines in a natural way a space of test functions sa and a corresponding space of distributions s a these are considered as quasi algebras and the problem of multiplying distributions is studied in terms of multiplication operators defined on a rigged hilbert space

a use of conjugate gradient direction for the convex optimization problem over the fixed point set of a nonexpansive mapping in this paper we discuss the convex optimization problem over the fixed point set of a nonexpansive mapping the main objective of the paper is to accelerate the hybrid steepest descent method for the problem to this goal we present a new iterative scheme that utilizes the conjugate gradient direction its convergence to the solution is guaranteed under certain assumptions in order to demonstrate the effectiveness performance and convergence of our proposed algorithm we present numerical comparisons of the algorithm with the existing algorithm

viscosity approximation methods for nonexpansive mappings abstract viscosity approximation methods for nonexpansive mappings are studied consider a nonexpansive self mapping t of a closed convex subset c of a banach space x suppose that the set fix t of fixed points of t is nonempty for a contraction f on c and t 0 1 let x t c be the unique fixed point of the contraction x tf x 1 t tx consider also the iteration process x n where x 0 c is arbitrary and x n 1 n f x n 1 n tx n for n 1 where n 0 1 if x is either hilbert or uniformly smooth then it is shown that x t and under certain appropriate conditions on n x n converge strongly to a fixed point of t which solves some variational inequality

spatiality of derivations of partial o algebras the notion of derivation on an algebra of unbounded operators is extended to partial o algebras and the corresponding notion of spatiality is investigated special emphasis is given to derivations associated to one parameter groups of automorphisms and to derivations of partial gw algebras

elimination of limit cycles due to two s complement quantization in normal form digital filters normal form digital filters are attractive due to their desirable properties when implemented in finite wordlength arithmetic these filters are free from all overflow limit cycles and quantization limit cycles when magnitude truncation is used however when two s complement truncation tct quantization is used limit cycles can still exist in this paper it is shown that when block structures are used normal form digital filters can be made free of limit cycles due to tct quantization it is shown that this can be done with a small block size an algorithm is also presented to find the minimum block size required for a given filter some examples are given to illustrate the results

locally convex quasi algebras with sufficiently many representations the main aim of this paper is the investigation of conditions under which a locally convex quasi algebra a a0 attains sufficiently many tw continuous representations in l d h to separate its points having achieved this a usual notion of bounded elements on a rises on the other hand a natural order exists on a a0 related to the topology that also leads to a kind of bounded elements which we call order bounded what is important is that under certain conditions the latter notion of boundedness coincides with the usual one several nice properties of order bounded elements are extracted that enrich the structure of locally convex quasi algebras

two s complement quantization in two dimensional state space digital filters two dimensional 2 d state space digital filters are investigated for stability with and without quantization a sufficient condition is obtained for the stability of the linear fornasini marchesini 1976 state space model the same model is then studied for stability when implemented using two s complement truncation quantization and a sufficient condition for asymptotic stability of the nonlinear filter is obtained in the process a theorem is proved which gives a sufficient condition for the stability of a one dimensional 1 d state space digital filter under the same type of quantization

some remarks on the gelfand naimark segal representations of topological algebras after an appropriate restatement of the gelfand naimark segal construction for topological algebras we prove that there exists an isomorphism among the set cycl a of weakly continuous strongly cyclic representations of a barreled dual separable algebra with unit a the space hilba a of the hilbert spaces that are continuously embedded in a and are invariant under the dual left regular action of a and the set of the corresponding reproducing kernels we show that these isomorphisms are cone morphisms and we prove many interesting results that follow from this fact we discuss how these results can be used to describe cyclic representations on more general inner product spaces

algorithms for zeros of two accretive operators for solving convex minimization problems and its application to image restoration problems abstract in this paper a new viscosity iterative method minimization algorithm for image restoration algorithm is proposed based on a new viscosity iteration the algorithm for finding the common zeros of two accretive operators in the framework of uniformly smooth banach spaces moreover the strong convergence theorems for the iterative algorithms and an example is proposed which shows the validity of main theorem are proved the results of this paper are improved and extended of the corresponding ones announced by many others and we also applied our result to solve a convex minimization problem and g teaux differentiable e p s and variational inequality experiment results show that the proposed algorithms outperform some other methods finally we give the numerical experiments to show the efficiency and advantage of the proposed methods and we also used our proposed algorithm for applying to solve the image deblurring and image recovery problems

standard partial o algebras the main purpose of this paper is to extend the powers result 19 for the standardness and the schmudgen result 23 for standard extensions of commutative o algebras to formally commutative partial o algebras

algebraic dynamics in o algebras a perturbative approach in this paper the problem of recovering an algebraic dynamics in a perturbative approach is discussed the mathematical environment in which the physical problem is considered is that of algebras of unbounded operators endowed with the quasiuniform topology after some remarks on the domain of the perturbation conditions are given for the dynamics to exist as the limit of a net of regularized linear maps

a hybrid viscosity algorithm via modify the hybrid steepest descent method for solving the split variational inclusion in image reconstruction and fixed point problems abstract in this paper we introduce and study a new viscosity approximation method by modify the hybrid steepest descent method for finding a common solution of split variational inclusion problem and fixed point problem of a countable family of nonexpansive mappings under suitable conditions we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of the split variational inclusion problem and fixed point problem for a countable family of nonexpansive mappings which is the unique solution of the variational inequality problem the results present in this paper are the supplement extension and generalization of the previously known results in this area numerical results demonstrate the performance and convergence of our result that the algorithm converges to a solution to a concrete split variational inclusion problem and fixed point problem

stability of distributed 3 d systems implemented on grid sensor networks using the givone roesser and the fornasini marchesini state space models for m d systems a method for distributed information processing in rectangular grid based wireless sensor networks is presented it can be used for distributed implementation of any general linear system on a grid sensor network nonlinearities caused by finite precision number representation schemes used for in node computations and inter node communication are modeled stability of the system is analyzed with special consideration given to the influence of inter node communication on system dynamics a necessary and sufficient condition for global asymptotic stability under finite precision arithmetic is established simulation results are presented to illustrate the theoretical results

applications of topological algebras of unbounded operators in this paper we discuss some physical applications of topological algebras of unbounded operators the first example is a simple system of free bosons then we consider other models related to this one finally we discuss the time evolution of two interacting models of matter and bosons we show that for all these systems it is possible to build up a common mathematical framework where the existence of the thermodynamical limit of the algebraic dynamics can be conveniently analyzed

viscosity approximation methods for fixed points problems the aim of this work is to propose viscosity approximation methods which amounts to selecting a particular fixed point of a given nonexpansive self mapping

partial algebras of matrices and operators the set m of infinite matrices and the set q of squarable matrices are considered as partial algebras the connection between q and two partial algebras of closed operators is studied conditions for a matrix representation in von neumann s sense of a family of closed operators are given

completely positive conjugate bilinear maps on partial algebras the set of invariant completely positive conjugate bilinear maps on an arbitrary unital partial algebra is introduced and characterized by considering a natural order structure on this set all order intervals in it having the zero map as minorant are characterized and a certain extremal problem is solved in particular a radon nikodym theorem for members of the set is deduced finally an extension theorem for completely positive but not necessarily invariant conjugate bilinear maps on unital partial algebras is obtained

biweights on partial algebras representations of algebras are generally obtained by the familiar gelfand naimark segal gns construction starting from a positive linear functional or even a quasi weight that is a functional that may take infinite values in previous works we have extended this construction to the case of a partial algebra using invariant positive sesquilinear forms which play the same role as positive linear functionals for algebras in this paper we extend the construction further by introducing and studying systematically the notion of biweight on a partial algebra in particular we characterize through the associated gns representation the so called approximately admissible biweights i e limits of biweights with a bounded gns representation c 2000 academic press

partial algebras and volterra convolution of distribution kernels the set of distribution kernels is considered as a partial algebra when the multiplication of two kernels is defined as their volterra convolution the partial algebra of distribution kernels corresponding to a certain partial algebra of closable operators in l2 is studied

homomorphisms and derivations in proper jcq triples we investigate homomorphisms in proper jcq triples and derivations on proper jcq triples associated with the 3 variable jensen functional equation begin array rcl 2f left frac x y z 2 right f x f y f z end array which was introduced and investigated by park cho and han we moreover prove the hyers ulam rassias stability of homomorphisms in proper jcq triples and of derivations on proper jcq triples this is applied to investigate isomorphisms between proper jcq triples

two s complement quantization in periodic digital filters the stability of periodically shift variant psv filters are studied when implemented with two s complement truncation tct quantization block form and standard nonblock form implementations are considered and two sufficient conditions are established for stability as a special case second order coupled form psv filters are then investigated under tct quantization stability regions are established within the parameter space for block implementations examples are given to illustrate the results

stability of digital filters implemented with two s complement truncation quantization the stability of digital filters implemented with two s complement truncation quantization is investigated both the direct form and normal form realizations are considered and regions in the parameter plane are obtained where the filters are globally asymptotically stable regions within the stability triangle of a direct form digital filter are also studied where limit cycles of period one and two are possible the results are illustrated with several examples

tensor products of normed and banach quasi algebras abstract quasi algebras form an essential class of partial algebras which are algebras of unbounded operators in this work we aim to construct tensor products of normed respectively banach quasi algebras and study their capacity to preserve some important properties of their tensor factors like for instance semisimplicity and full representability

o algebras and quantum dynamics some existence results we discuss the possibility of defining an algebraic dynamics within the settings of o algebras compared to our previous results on this subject the main improvement here is that we are not assuming the existence of some hamiltonian for the full physical system we will show that under suitable conditions the dynamics can still be defined via some limiting procedure starting from a given regularized sequence

new methods and structures in the theory of the multi mode dicke laser model we base a treatment of the dissipative multi mode version of dicke laser model on the theory of completely positive dynamical semigroups and quantum markov processes this leads to new results at both the mathematical and physical levels on the physical side it provides a generalization of the hepp lieb model that admits both chaotic and polychromatic laser radiation on the mathematical side it extends the theory of dynamical semigroups to a regime where the generators are perturbed by unbounded derivations