a new analytical and numerical treatment for singular two point boundary value problems via the adomian decomposition method based on the adomian decomposition method a new analytical and numerical treatment is introduced in this research to investigate linear and non linear singular two point bvps the effectiveness of the proposed approach is verified by several linear and non linear examples

high speed low complexity systolic designs of novel iterative division algorithms in gf 2 sup m we extend the binary algorithm invented by stein and propose novel iterative division algorithms over gf 2 sup m for systolic vlsi realization while algorithm ebg is a basic prototype with guaranteed convergence in at most 2m 1 iterations its variants algorithms ebd and ebdf are designed for reduced complexity and fixed critical path delay respectively we show that algorithms ebd and ebdf can be mapped to parallel in parallel out systolic circuits with low area time complexities of o m sup 2 loglogm and o m sup 2 respectively compared to the systolic designs based on the extended euclid s algorithm our circuits exhibit significant speed and area advantages

on boundary value problems for singular second order functional differential equations abstract positive solutions to the boundary value problem y f x y w x 0 y x y x x a x 0 y x y x x 1 x b are obtained by applying the schauder fixed point theorem where w x is a continuous function defined on 0 1 and f x y is a function defined on 0 1 0 which satisfies certain restrictions and may have singularity at y 0 the result corrects and improves an existence theorem due to erbe and kong j comput appl math 53 1994 377 388

singular nonlinear boundary value problems for second order ordinary differential equations abstract the boundary value problem y f x y 0 y 0 y 0 0 y 1 y 1 0 is studied under conditions which are modeled on the problem y a x y p 0y 0 y 1 0 or y 0 y 1 0 which occurs in a number of applications the technical arguments involve properties of solutions i e concavity and the use of iterative techniques a new fixed point theorem for cones for decreasing mappings is proved and used it is of interest in its own right since most such theorems are for monotone increasing mappings

singularly perturbed ordinary differential equations with dynamic limits coupled slow and fast motions generated by ordinary differential equations are examined the qualitative limit behaviour of the trajectories as the small parameter tends to zero is sought after invariant measures of the parametrised fast flow are employed to describe the limit behaviour rather than algebraic equations which are used in the standard reduced order approach in the case of a unique invariant measure for each parameter the limit of the slow motion is governed by a chattering type equation without the uniqueness the limit of the slow motion solves a differential inclusion the fast flow in turn converges in a statistical sense to the direct integral respectively the set valued direct integral of the invariant measures

bit serial systolic divider and multiplier for finite fields gf 2 sup m a systolic structure for bit serial division over the field gf 2 sup m is developed consideration is given to avoid global data communications and dependency of the time step duration on m this is important for applications where the value of m is large the divider requires only three basic processors and one simple control signal and its circuit and time complexities are proportional to m sup 2 and m respectively it does not depend on the irreducible polynomial and can be expanded easily moreover with m additional simple processors a bit serial systolic multiplier is developed which uses part of the divider structure this is advantageous from the implementation point of view as both the divider and multiplier can be fabricated on a single chip resulting in a reduction of area

positive solutions and eigenvalue intervals of nonlocal boundary value problems with delays abstract the paper is concerned with the delay differential equation u b t f u t 0 satisfying u t 0 for t 0 and u 1 g 0 1 u t d t where 0 1 u t d t denotes the riemann stieltjes integral by applying the fixed point theorem in cones we show the relationship between the asymptotic behaviors of the quotient f u u at zero and infinity and the open intervals eigenvalue intervals of the parameter such that the problem has zero one and two positive solution s if g t t by using a property of the riemann stieltjes integral the above nonlocal boundary value problem educes a three point boundary value problem with delay for which some similar results are established

systolic array implementation of euclid s algorithm for inversion and division in gf 2 sup m this paper presents two new systolic arrays to realize euclid s algorithm for computing inverses and divisions in finite fields gf 2 sup m with the standard basis representation one of these two schemes is parallel in parallel out and the other is serial in serial out the former employs o m sup 2 area complexity to provide the maximum throughput in the sense of producing one result every clock cycle while the latter achieves a throughput of one result per m clock cycles using o m log m area complexity both of the proposed architectures are highly regular and thus well suited to vlsi implementation as compared to existing related systolic architectures with the same throughput performance the proposed parallel in parallel out scheme reduces the hardware complexity and thus the area time product by a factor of o m and the proposed serial in serial out scheme by a factor of o m log sub 2 m

smooth linearization of hyperbolic fixed points without resonance conditions a well known theorem of hartman grobman says that a c1 diffeomorphism f rn rn with a hyperbolic fixed point at 0 can be conjugated to the linear diffeomorphism l df 0 at least in a neighbourhood of 0 in this paper we will show that if is c2 then is differentiably conjugate to l at 0 moreover the conjugacy is holder outside 0 no resonance conditions will be required

positive solutions of second order two delay differential systems with twin parameter abstract the paper is concerned with the existence of positive solutions for a second order two delay differential systems with twin parameter firstly we present some sufficient conditions with the twin parameter belonging to an open rectangular region eigenvalue region to ensure the existence of positive solutions for the differential systems with singularity secondly we deal with the superlinear semipositone problem of the differential systems and establish the existence of positive solutions for the systems the proofs are based on a fixed point theorem in cones

gf 2 sup m multiplication and division over the dual basis in this paper an algorithm for gf 2 sup m multiplication division is presented and a new more generalized definition of duality is proposed from these the bit serial berlekamp multiplier is derived and shown to be a specific case of a more general class of multipliers furthermore it is shown that hardware efficient bit parallel dual basis multipliers can also be designed these multipliers have a regular structure are easily extended to different gf 2 sup m and hence suitable for vlsi implementations as in the bit serial case these bit parallel multipliers can also be hardwired to carry out constant multiplication these constant multipliers have reduced hardware requirements and are also simple to design in addition the multiplication division algorithm also allows a bit serial systolic finite field divider to be designed this divider is modular independent of the defining irreducible polynomial for the field easily expanded to different gf 2 sup m and its longest delay path is independent of m

positive solutions to a type of multi point boundary value problem with delay and one dimensional p laplacian abstract this paper deals with a type of multi point boundary value problem with delay and one dimensional p laplacian by using guo krasnosel skii fixed point theorem and generalization of the leggett williams fixed point theorem due to avery and peterson we obtain that bvp 1 1 has at least one positive solution or three positive solutions

efficient bit serial multiplication and the discrete time wiener hopf equation over finite fields discrete time wiener hopf equations dtwhes over finite fields are considered it is shown that solving the dtwhe is equivalent to performing division over finite fields the proof provides a new interpretation of the relationship between bit serial multiplication and dtwhes the interpretation enables bit serial multiplication over gf 2 sup m to be understood more easily as an example bit serial multiplication methods for multiplying any two elements that can be done without performing any transformation or with only a simple transformation of the bases are presented

smooth linearization near a fixed point in this paper we extend a theorem of sternberg and bi leckii we study a vector field or a diffeomorphism in the vicinity of a hyperbolic fixed point we assume that the eigenvalues of the linear part a at the fixed point satisfy qth order algebraic inequalities where q 2 2 then there is ck linearization in the vicinity of the fixed point where k is the q smoothness of a we give an explicit and simple algorithm for com puting k an illustrative example from celestial mechanics is included which shows that our main theorem is an improvement over previously known theories we also show that if the vector field or diffeomorphism depends smoothly on a parameter then the linearizing conjugation de pends smoothly on the parameter

vlsi architectures for computing multiplications and inverses in gf 2 m finite field arithmetic logic is central in the implementation of reed solomon coders and in some cryptographic algorithms there is a need for good multiplication and inversion algorithms that can be easily realized on vlsi chips massey and omura 1 recently developed a new multiplication algorithm for galois fields based on a normal basis representation in this paper a pipeline structure is developed to realize the massey omura multiplier in the finite field gf 2m with the simple squaring property of the normal basis representation used together with this multiplier a pipeline architecture is also developed for computing inverse elements in gf 2m the designs developed for the massey omura multiplier and the computation of inverse elements are regular simple expandable and therefore naturally suitable for vlsi implementation

boundary value problems for singular second order functional differential equations abstract we consider general linear boundary value problems for equations of the form y f x y x 0 0 x x is continuous and f x y has a singularity at y 0 the results improve and extend earlier results for the case x x due to taliaferro 1979 and gatica 1989

systolic vlsi arrays for polynomial gcd computation the problem of finding a greatest common divisor gcd of any two nonzero polynomials is fundamental to algebraic and symbolic computations as well as to the decoder implementation for a variety of error correcting codes this paper describes new systolic arrays that can lead to efricient vlsi solutions to both the gcd problem and the extended gcd problem

on computing multiplicative inverses in gf 2 sup m the design of a modular standard basis inversion for galois fields gf 2 sup m based on euclid s algorithm for computing the greatest common divisor of two polynomials is presented the asymptotic complexity is linear with m both in computation time and area requirement thus resulting in an at complexity of o m sup 2 this is a significant improvement over the best previous proposal which achieves at complexity of only o m sup 3

positive solutions and eigenvalue regions of two delay singular systems with a twin parameter abstract the paper is concerned with a two delay singular differential system with a twin parameter applying fixed point index theory we show the relationship between the asymptotic behaviors of nonlinearities at zero and infinity and the open regions eigenvalue regions of parameters which are correlated with delays such that the system has zero one and two positive solution s

a fast algorithm for multiplicative inversion in gf 2 sup m using normal basis a fast algorithm for multiplicative inversion in gf 2 sup m using normal basis is proposed it is an improvement on those proposed by itoh and tsujii and by chang et al which are based on fermat s theorem and require o logm multiplications the number of multiplications is reduced by decomposing m 1 into several factors and a small remainder

distributional convergence in planar dynamics and singular perturbations abstract motivated by applications to singular perturbations the paper examines convergence rates of distributions induced by solutions of ordinary differential equations in the plane the solutions may converge either to a limit cycle or to a heteroclinic cycle the limit distributions form invariant measures on the limit set the customary gauges of topological distances may not apply to such cases and do not suit the applications the paper employs the prohorov distance between probability measures it is found that the rate of convergence to a limit cycle and to an equilibrium are different than the rate in the case of heteroclinic cycle the latter may exhibit two paces depending on a relation among the eigenvalues of the hyperbolic equilibria the limit invariant measures are also exhibited the motivation is stemmed from singularly perturbed systems with non stationary fast dynamics and averaging the resulting rates of convergence are displayed for a planar singularly perturbed system and for a general system of a slow flow coupled with a planar fast dynamics

nonlinear superlinear singular and nonsingular second order boundary value problems abstract many new existence theorems are presented for singular and nonsingular second order boundary value problems singularities at y 0 t 0 and t 1 will be discussed