existence of bounded positive solutions of semilinear elliptic equations abstract in this paper by using fixed point theory under quite general conditions on the nonlinear term we obtain an existence result on bounded positive solutions of certain semilinear elliptic equations in r n n 3

recursion operators and non local symmetries a new formulation of recursion operators is presented which eliminates diffi culties associated with integro differential operators this interpretation treats recursion operators and their inverses on an equal footing efficient techniques for constructing non local symmetries of differential equations result

existence of unbounded positive solutions of quasilinear elliptic equations in two dimensional exterior domains in this paper by using the fixed point theory we obtain a new existence result for bounded positive solutions of the quasilinear elliptic equations in two dimensional exterior domains

periodic solutions of the lienard equation with one sided growth restrictions in this article we are concerned with the problem of the existence of periodic solutions to the periodically forced scalar lienard equation x f x x g x e t d dt 1 where f g e r r are continuous functions and e is periodic we are looking for solutions of 1 having the same period of the forcing term e throughout the paper we assume without loss of generality see e g 22 36 p 693 that

a fast bit vector algorithm for approximate string matching based on dynamic programming the approximate string matching problem is to find all locations at which a query of length m matches a substring of a text of length n with k or fewer differences simple and practical bit vector algorithms have been designed for this problem most notably the one used in agrep these algorithms compute a bit representation of the current state set of the k difference automaton for the query and asymptotically run in either o nm w or o nm log s w time where w is the word size of the machine e g 32 or 64 in practice and s is the size of the pattern alphabet here we present an algorithm of comparable simplicity that requires only o nm w time by virtue of computing a bit representation of the relocatable dynamic programming matrix for the problem thus the algorithm s performance is independent of k and it is found to be more efficient than the previous results for many choices of k and small m moreover because the algorithm is not dependent on k it can be used to rapidly compute blocks of the dynamic programming matrix as in the 4 russians algorithm of wu et al 1996 this gives rise to an o kn w expected time algorithm for the case where m may be arbitrarily large in practice this new algorithm that computes a region of the dynamic progr amming d p matrx w entries at a time using the basic algorithm as a subroutine is significantly faster than our previous 4 russians algorithm that computes the same region 4 or 5 entries at a time using table lookup this performance improvement yields a code that is either superior or competitive with all existing algorithms except for some filtration algorithms that are superior when k m is sufficiently small

blow up phenomena of second order nonlinear differential equations abstract this paper studies the blow up phenomena of the second order nonlinear differential equation x f t x x under appropriate conditions it is shown that some solutions of the equation blow up in finite time

study the stability of solutions of functional differential equations via fixed points in this paper we study the stability properties of solutions of a class of functional differential equations with variable delay by using the fixed point theory under an exponentially weighted metric we obtain some interesting sufficient conditions ensuring that the zero solution of the equations is stable and asymptotically stable

abundant lump type solutions of the jimbo miwa equation in 3 1 dimensions abstract based on the hirota bilinear form of the 3 1 dimensional jimbo miwa equation ten classes of its lump type solutions are generated via maple symbolic computations whose analyticity can be easily achieved by taking special choices of the involved parameters those solutions supplement the existing lump type solutions presented previously in the literature

approximate all pairs suffix prefix overlaps finding approximate overlaps is the first phase of many sequence assembly methods given a set of strings of total length n and an error rate e the goal is to find for all pairs of strings their suffix prefix matches overlaps that are within edit distance email protected email protected email protected where is the length of the overlap we propose a new solution for this problem based on backward backtracking lam et al 2008 and suffix filters karkkainen and na 2008 our technique uses nh k o email protected rlogr bits of space where h k is the k th order entropy and s the alphabet size in practice it is more scalable in terms of space and comparable in terms of time than q gram filters rasmussen et al 2006 our method is also easy to parallelize and scales up to millions of dna reads

the continuation of solutions for certain nonlinear differential equations and its applications we give some sufficient conditions for the continuation of solutions for some nonlinear differential equations as an application we obtain a new criterion for the oscillation of solutions of the lienard equation

fast and compact regular expression matching we study 4 problems in string matching namely regular expression matching approximate regular expression matching string edit distance and subsequence indexing on a standard word ram model of computation that allows logarithmic sized words to be manipulated in constant time we show how to improve the space and or remove a dependency on the alphabet size for each problem using either an improved tabulation technique of an existing algorithm or by combining known algorithms in a new way

a geometric approach to periodically forced dynamical systems in presence of a separatrix we consider the periodic boundary value problem for the non autonomous scalar second order equation x f x x e t with e a continuous and t periodic forcing term using a continuation theorem adapted from capietto et al trans amer math soc 329 1992 41 72 we propose some new conditions for the existence of t periodic solutions to the forced equation in terms of the dynamical properties of the trajectories of the associated autonomous equation x f x x 0 special emphasis will be addressed to the study of the case in which the presence of an unbounded separatrix for the autonomous system in the phase plane allows to obtain a priori bounds for the t periodic solutions of the homotopic equation x f x x e t

on the boundedness of the solutions of the nonlinear oscillating equation abstract we consider the nonlinear oscillating equation x f x h x x g x k x 0 without the common conditions a f x 0 for all x r b xg x 0 for all x 0 and give a set of necessary and sufficient conditions for the boundedness of all solutions of this equation and their derivatives

on the generalized lienard equation without the signum condition abstract we consider the generalized lienard equation x x h x x g x k x 0 without the signum condition xg x 0 for all x 0 and give a necessary and sufficient condition for the boundedness of all solutions of this equation and their derivatives

non auto baclund transformation nonlocal symmetry and cre solvability for the bogoyavlenskii kadomtsev petviashvili equation abstract in this paper we study the bogoyavlenskii kadomtsev petviashvili bkp equation by using the truncated painleve method and consistent riccati expansion cre through the truncated painleve method its nonlocal symmetry and non auto backlund transformation are presented the nonlocal symmetry is localized to a local lie point group via a prolonged system moreover with the help of the cre method we prove that the bkp equation is cre solvable finally the kink lump wave interaction solution of bkp equation is explicitly given by using the trilinear form the interaction between kink wave and lump wave is investigated and exhibited mathematically and graphically

boundedness and convergence of solutions of a second order nonlinear differential system abstract consider the second order nonlinear differential system x 1 a x h y f x y a x g x e t where a is a positive and continuous function on r h f and g are continuous functions on r and e t is a continuous function on i 0 we obtain sufficient and necessary conditions for all solutions to be bounded and to converge to zero our results can be applied to the well known equation x f 1 x x f 2 x x 2 g x e t which substantially extends and improves important results in the literature

a new filtration method and a hybrid strategy for approximate string matching in this paper we propose a new filtration algorithm as well as a hybrid filtration strategy to efficiently solve the approximate string matching problem also called k differences problem which aims to find all the positions i s in a given text such that there exists a substring of the text ending at position i whose edit distance from a given pattern is less than or equal to a given error bound k our experimental results on simulated datasets of dna sequences show that our filtration algorithm has better performance on the efficiency to filter out those positions of the text at which the pattern does not occur approximately moreover our hybrid filtration strategy further improves the performance efficiency of our filtration algorithm greatly when the ratio of the error bound and the pattern size is about 0 2

from cascade decompositions to bit vector algorithms a vector algorithm is an algorithm that applies a bounded number of vector operations to an input vcctor regardless of the length of the input in this paper we describe the links between the existence of vector algorithms and the cascade decompositions of counter free automata we show that any computation that can be carried out with a counter free automaton can be recast as a vector algorithm moreover we show that for a class of automata that is closely related to algorithms in bio computing the complexity of the resulting algorithms is linear in the number of transitions of the original automaton

boundedness of solutions for a class of retarded lienard equation consider the retarded lienard equation x f1 x x f2 x x2 gx t h e t where h is a nonnegative constant f1 f2 and g are continuous functions on r and e t is a continuous function on r 0 we obtain some new sufficient conditions as well as some new necessary and sufficient conditions for all solutions and their derivatives to be bounded which substantially extend and improve some important results in the literature

an improved algorithm for approximate string matching given a text string a pattern string and an integer k a new algorithm for finding all occurrences of the pattern string in the text string with at most k differences is presented both its theoretical and practical variants improve upon the known algorithms

qualitative analysis of the phase portrait for a class of planar vector fields via the comparison method abstract the phase portrait of the second order differential equation x l 0 n f l x x l 0 is studied some results concerning existence non existence and uniqueness of limit cycles are presented in particular a generalization of the classical massera uniqueness result is proved

bilinear backlund transformations kink periodic solitary wave and lump wave solutions of the bogoyavlenskii kadomtsev petviashvili equation abstract this paper investigates the bogoyavlenskii kadomtsev petviashvili equation by using the binary bell polynomials method and differential constraint technique several kinds of more general bilinear representations and baklund transformations are presented at the same time multiple wave solutions including the kink periodic solitary wave and bright dark lump wave solutions are constructed the resonant interactions between two kink solitary waves are investigated and exhibited mathematically and graphically lump wave solutions a kind of rational function localized in all directions of the space are obtained by the taylor expansion of the kink periodic solitary wave also we discuss the dynamical behavior of the lump wave solutions and their structures

boundedness theorems by two liapunov functions on considere le systeme d equations differentielles dx dt f t x y dy dt g t x y avec x r n y r m et f g des fonctions continues sur r r n r m on demontre un theoreme qui donne des criteres pour que des solutions soient uniformement bornees en se servant de deux fonctions de lyapunov et du theoreme de comparaison

on the boundedness of solution of the generalized lie nard equation without the signum condition on presente des criteres de limitation pour l equation de lienard generalisee x f x x g x 0 ou un systeme equivalent x y f x y g x ou f g r r sont continues et f x 0 x f d

n soliton solutions to a dimensional integrable equation we give explicitly n soliton solutions of a 2c 1 dimensional equation xtc xxxz 4cxxzcxxz 2c 1 x zzz 4 d 0 this equation is obtained by unifying two directional generalizations of the potential kdv equation the closed ring with the potential kp equation and the calogero bogoyavlenskij schiff equation this equation is also a reduction of the kp hierarchy we also find the miura transformation which yields the same ring of the corresponding modified equations the study of higher dimensional integrable systems is one of the central themes in integrable systems a typical example of a higher dimensional integrable system is obtained by modifying the lax operators of a basic equation the potential kdv p kdv equation in this paper the lax pair of the p kdv equation have the form l x t d 2 xcx x t 1 t x t d l x t 3 2

parameter limit method and its application in the 4 1 dimensional fokas equation abstract a new hirota s bilinear form of the 4 1 dimensional fokas equation is obtained by an appropriate wave transformation applying the parameter limit method introduced in this paper we obtain two homoclinic solutions and a rogue wave solution of 4 1 dimensional fokas equation besides we also discuss the interaction between rogue wave solution and different forms of stripe solitons one stripe soliton and double stripe solitons and investigate the annihilation and emergence of rogue waves finally the parametric reasons of soliton fusion and fission are discussed furthermore the fusion and fission phenomena of soliton are simulated by three dimensional plots

global stability analysis for stochastic coupled systems on networks this paper considers the global stability problem for some stochastic coupled systems on networks scsns we provide a systematic method for constructing a global lyapunov function for these scsns by using graph theory and the lyapunov second method consequently a new global stability principle which has a close relation to the topology property of the network is given as an application to the results we employ the principle to two well known coupled systems in physical and ecology and then some easy verified sufficient conditions which guarantee the global stability are obtained