optimal control of systems possessing symmetries it is shown that a symmetry in an optimization problem induces a decomposition of the optimal feedback control law into factors one factor can be calculated algebraically and depends only on the symmetry the other factor corresponds to a lower dimensional optimization problem this gives a priori information about the structure of the optimal feedback control law and indicates a possibly more efficient method for optimizing such systems

fast base extension using a redundant modulus in rns a technique to extend the base of a residue number system rns based on the chinese remainder theorem crt and the use of a redundant modulus is proposed the technique obtains the residue s of a given number in the extended moduli without resorting to the traditional mixed radix conversion mrc algorithm the base extension can be achieved in log sub 2 n table lookup cycles where n is the number of moduli in the rns the superiority of the technique compared in terms of latency and hardware requirements to the traditional szabo tanaka method is demonstrated

on theory and fast algorithms for error correction in residue number system product codes the authors develop a coding theory approach to error control in residue number system product codes based on this coding theory framework computationally efficient algorithms are derived for correcting single errors double errors and multiple errors and simultaneously detecting multiple errors and additive overflow these algorithms have lower computational complexity than previously known algorithms by at least an order of magnitude in addition it is noted that all the literature published thus far deals almost exclusively with single error correction

the structure of nonlinear control systems possessing symmetries a concept of symmetry is defined for general nonlinear control systems it is shown under various technical conditions that nonlinear control systems with symmetries admit local and or global decompositions in terms of lower dimensional subsystems and feedback loops the structure of the individual subsystems is dependent on the structure of the symmetry group for example if the symmetry group is abelian one of the subsystems is a quadrature an additional feature of the decomposition is that the state space dimensions of the subsystems sum to the state space dimension of the original system

existence of positive solutions for first order discrete periodic boundary value problems with delay abstract let t 3 be a positive integer and t 0 1 2 t 1 we prove the existence of positive periodic solutions of the nonlinear discrete boundary value problem u t a t g u t u t b t f u t t t t u 0 u t our approach is based upon the global bifurcation techniques

single residue error correction in residue number systems we present a new method to correct single errors in an n residue number system through the use of r redundant moduli the method requires 2n r 2 recombinations of n residues in the worst case this is of lower complexity than any other known method

two periodic solutions of neutral difference systems depending on two parameters in this paper we establish existence multiplicity and nonexistence of periodic solutions for a class of first order neutral difference systems our approach is based on a fixed point theorem in cones as well as some analysis techniques

existence of multiple positive periodic solutions for functional differential equations abstract in our paper by employing krasnoselskii fixed point theorem we investigate the existence of multiple positive periodic solutions for functional differential equations x t a t x t x t f t x t where 0 is a parameter some easily verifiable sufficient criteria are established

existence of positive solutions for second order functional differential equations we afford a existence criterion of positive solutions of a boundary value problem concerning a second order functional differential equation by using the krasnoselskii fixed point theorem on cones in banach spaces moreover we also apply our results to establish several existence theorems of multiple positive solutions for some functional differential equations

positive periodic solutions of singular systems of first order ordinary differential equations the existence and multiplicity of positive periodic solutions for first non autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter the proof of our results is based on the krasnoselskii fixed point theorem in a cone

periodic solutions of first order functional differential equations with periodic deviations the paper is concerned with the functional differential equation u t a t g u h 1 t u t lb t f u h 2 t where l 0 a t b t h 1 t and h 2 t are periodic functions applying leggett williams fixed point theorem to the equation we show the explicit open intervals of l such that the equation has at least three nonnegative periodic solutions

positive periodic solution of second order neutral functional differential equations abstract in this paper we consider two types of second order neutral functional differential equations by choosing available operators and applying krasnoselskii s fixed point theorem we obtain sufficient conditions for the existence of periodic solutions to such equations

on the number of positive solutions of a nonlinear algebraic system abstract in this paper we study the nonlinear algebraic system of the form e x af x where 0 is a parameter x and f x denote the column vectors col x 1 x 2 x n and col f 1 x 1 f 2 x 2 f n x n respectively with fk r r k 1 2 n 1 n and n is a positive integer a aij n n is an n n matrix and all its entries are positive numbers many problems in various areas such as difference equations boundary value problems dynamical networks stochastic process numerical analysis etc can be converted to system e applying fixed point theorems we prove results on existence uniqueness multiplicity and nonexistence of positive solutions for e

the analysis of zero dynamics of nonlinear control systems with symmetries zero dynamics of nonlinear control systems with symmetries are studied in this paper it is shown that the zero dynamics of a symmetric system is also symmetric and admits a special form of cascade decomposition a local zero dynamics is always possible to be extended to the semiglobal case the relation between the zero dynamics and the quotient system is also discussed

positive periodic solutions of functional differential equations abstract we consider the existence multiplicity and nonexistence of positive periodic solutions for the periodic equation x t a t g x x t b t f x t t where a b c r 0 are periodic 0 a t dt 0 0 b t dt 0 f g c 0 0 and f u 0 for u 0 g x is bounded t is a continuous periodic function define f 0 lim u 0 f u u f lim u f u u i0 number of zeros in the set f 0 f and i number of infinities in the set f 0 f we show that the equation has i0 or i positive periodic solution s for sufficiently large or small 0 respectively

on the existence of positive solutions for semilinear elliptic equations in the annulus abstract we study the existence of positive radial solutions of u g x u 0 in annuli with dirichlet dirichlet neumann boundary conditions we prove that the problems have positive radial solutions on any annulus if is sublinear at 0 and

positive solutions to nonlinear first order pbvps with parameter on time scales abstract in this paper we consider the following nonlinear first order periodic boundary value problem with parameter on a time scale t x t p t x t f x t t 0 t t x 0 x t where 0 is a parameter for suitable 0 some existence multiplicity and nonexistence criteria of positive solutions are established by using well known results from the fixed point index

existence nonexistence and multiplicity of periodic solutions for a kind of functional differential equation with parameter abstract in this paper we study the existence multiplicity and nonexistence of positive periodic solutions for a kind of second order delay functional differential equation with parameter u t a t u t f t u t 0 t u t 1 t u t n t by employing the krasnoselskii fixed point theorem for a cone map where 0 is a parameter some new results are obtained as an application of our results we discuss an example

higher order functional differential systems with parameter dependence abstract in this paper we consider a class of high order functional differential systems depending on a parameter by using the fixed point index theory we prove that there exists a positive number separating 0 into two disjoint subintervals 1 and 2 such that the system has at least two positive periodic solutions for 1 one positive periodic solution for and no positive periodic solution for 2 our results extend and improve some results in the literature as an application an example is given to demonstrate our main results

on the number of positive solutions of nonlinear systems abstract we prove that appropriate combinations of superlinearity and sublinearity of f u with respect to at zero and infinity guarantee the existence multiplicity and nonexistence of positive solutions to boundary value problems for the n dimensional system u h t f u 0 0 is defined by u u 1 u n where u u 1 u n and covers the two important cases u u and u u p 2 u p 1 our methods employ fixed point theorems in a cone

existence theory for positive solutions to one dimensional p laplacian boundary value problems on time scales abstract in this paper we consider the one dimensional p laplacian boundary value problem on time scales p u t h t f u t 0 t a b u a b 0 u a 0 u b 0 where p u is p laplacian operator i e p u u p 2 u p 1 some new results are obtained for the existence of at least single twin or triple positive solutions of the above problem by using krasnosel skii s fixed point theorem new fixed point theorem due to avery and henderson and leggett williams fixed point theorem this is probably the first time the existence of positive solutions of one dimensional p laplacian boundary value problems on time scales has been studied

existence of positive periodic solutions for a class of functional differential equations in this article we investigate the existence of positive periodic solutions for a class of functional differential equations by using fixed point index theory we establish sufficient criteria that are easily verifiable and that generalize and improve related studies in the literature also we give some examples in bio mathematics to show that our main results are valid

symmetries and conservation laws for hamiltonian systems with inputs and outputs a generalization of noether s theorem the definition of symmetries and conservation laws for autonomous i e without external cases hamiltonian systems are generalized to hamiltonian systems with inputs and outputs it is shown that a symmetry implies the existence of a conservation law and vice versa thereby generalizing noether s theorem for autonomous hamiltonian systems

the existence of multiple positive periodic solutions for functional differential equations abstract the existence of multiple positive solutions for the integral equation x t t t g t s b s f s x s 1 s x s n s ds is studied by using fixed point index theory using these results we obtain new results on the existence of multiple positive periodic solutions for some first order periodic functional differential equations

periodicity and stability for a lotka volterra type competition system with feedback controls and deviating arguments abstract this paper deals with the general periodic lotka volterra type competition systems with feedback controls and deviating arguments by employing fixed point index theory on cone an explicit necessary and sufficient condition for the global existence of the positive periodic solution of the systems is proved by constructing a suitable lyapunov functional a set of easily verifiable sufficient conditions for the global asymptotic stability of the positive periodic solution of the systems is given

positive solutions for boundary value problems of functional differential equations abstract we study the existence of positive solutions of the second order boundary values problems of functional differential equations x t f t x t 0 0 t t x 0 x t a where f 0 t c r r is a continuous function c r c r 0 and a r the proof of our main result is based upon the fixed point theorem in cones

error detection and correction in communication channels using inverse gray rsns codes a novel number theoretic transform called inverse gray robust symmetrical number system igrsns is proposed for error control coding in this paper igrsns is obtained by modifying robust symmetrical number system rsns that was proposed earlier using inverse gray code property due to ambiguities present in each residue rsns has a short dynamic range dr compared to that in other number systems the short dr of rsns enables it to be effectively used for error detection without the addition of any redundant modulus as in redundant residue number system although rsns has a large redundant range its detection ability is not optimal due to the gray code property associated with it in an attempt to overcome this limitation we have proposed inverse gray coding to be combined with rsns in increasing its effectiveness in error detection the resulting igrsns thus inherits properties of both rsns and gray code analysis and simulations show that igrsns has a near optimal error detection ability the potential of igrsns for error correction is also investigated further a novel error correction algorithm using one redundant modulus is proposed simulations show that the proposed algorithm performs well under all cases of single bit errors

on static output feedback stabilization of systems with stable generalized zero dynamics in this note we define generalized zero dynamics introduce a generalized zero dynamics algorithm and give a sufficient condition which ensures stabilizability of linear systems with asymptotically stable generalized zero dynamics by static output feedback

periodic solutions for functional differential equations of mixed type in this paper we study the existence of periodic solutions for some functional differential equations of mixed type among the main results are the averaging principle and existence theorems for some equations with homogeneous nonlinearities we use here the coincidence degree theory of mawhin

periodic solutions for scalar functional differential equations suf ficient criteria are established f or the existence ofpositive periodic solutions ofscalar f tional differential equations which improve and generalize some related results in the literature the approach is based on the krasnoselskii s fixed point theorem numerical simulations are presented to support the analytical analysis 2005 elsevier ltd all rights reserved msc 34k13 92d25

on positive solutions for second order boundary value problems of functional differential equations in this paper by using krasnoselskii fixed point theorem we obtain sufficient conditions for the existence of at least one or two positive solutions of a second order boundary value problem for a class of nonlinear functional differential equations examples are also included to illustrate our results