periodic solutions with prescribed energy for singular conservative systems involving strong forces this paper establishes under appropriate conditions which are stated below the existence of periodic solutions of the equation ii t vv q t 0 1 1 where q t e rn n 1 2 and v i is the gradient of a real function i which has a singularity at the origin in the literature the problem of the existence of periodic solutions of 1 1 has been addressed following two different points of view i given t 0 find periodic solutions of 1 1 having t as period fixed period problem ii given h e r find periodic solutions of 1 1 such that for all t e r

periodic solutions and almost periodic solutions of a neutral multispecies logarithmic population model a neutral multispecies logarithmic population model is proposed in this paper by using the contraction mapping principle and constructing a suitable lyapunov functional a set of easily applicable criteria are established for the existence uniqueness and global attractivity of positive periodic solution positive almost periodic solution of the model

multiple brake orbits for some classes of singular hamiltonian systems from which one can easily construct a periodic solution of period 2t by reflecting q around t 0 t if q x e e 1 v x hj is homeomorphic to a ball then the existence of one brake orbit is a classical result of seifert 11 generalizations of that result as well as alternative proofs were given in 2 6 141 in the case in which the topology of sz is richer then the existence of multiple solutions has been proved by bolotin and kozlov in 7 see also 8 in this paper we are mainly concerned with the case in which the potential v has singularities inside 2 in the sense that v x co as x x e ai and the topology of q is nontrivial more precisely in section 2 we shall assume that sz has a certain number of holes k and that v behaves like lxi o1 with 0 cx 2 near x 0 and we shall show that 1 3 has at least k classical brake orbits let us point out that the main interest of this result lies in the fact that we are able to prove that the solutions we find are classical ones that is they do not collide with the singularity while most of the papers dealing with existence of fixed energy 9 or fixed period lo solutions for singular potentials only prove existence of generalized solutions that is solutions which can collide with the singularity existence of a noncollision periodic solution for a singular potential

positive periodic solutions for a neutral delay lotka volterra system abstract applying a fixed point theorem of strict set contraction some new criteria are established for the existence of positive periodic solutions for a class of neutral delay lotka volterra systems x i t x i t r i t j 1 n a i j t x j t j 1 n b i j t x j t i j t j 1 n c i j t x j t i j t i 1 2 n compared to known results our main generalization is that delays of the derivatives are not assumed to be constants and our results are more easily verifiable

periodic solutions of a predator prey system with stage structures for predator and prey abstract by using the continuation theorem of coincidence degree theory the existence of a positive periodic solution for the predator prey system with stage structures for predator and prey is established

on the cartan matrix of an artin algebra of global dimension two the purpose of this paper is to show that if n is an artin algebra of g obal dimension 81 dim 2 then the determinant of its cartan matrix equals i this generalizes previous results of donovan and freislich 2 igusa and todorov 4 and wilson 5 we recall that if n is an artin algebra for instance a finite dimensional algebra over a field there are finitely many nonisomorphic indecomposable projective rl modules p p p we denote by end p hom p p the length of hom p pi as an end p module then the h x n matrix c n j having knd cpi hom p p i as the i j th entry is called the cartan matrix of rl let d be now an artin algebra of finite representation typethat is having finitely many nonisomorphic indecomposable 4 modules let h u end tr hom m n be the matrix with integral entries where m n range through the set of the nonisomorphic indecomposable ii modules donovan and freislich 2 have shown that if 4 kg is a group algebra of finite representation type then det h 1 then using associated graded algebras wilson showed that det h 1 if a is a finite dimensional algebra of finite representation type over an algebraically closed field 5 io independently the same result was proved by igusa and todorov 4 without making any assumption on the ground field let p be the auslander algebra of n see 1 for further details that is r end m 0 mt m jod where m m are the nonisomorphic indecomposable n modules then it has been shown that h c t where c t denotes the cartan matrix of the auslander algebra r it is known that gl dim r 2 we recall that

existence of positive periodic solutions for neutral functional differential equations abstract applying a fixed point theorem of strict set contraction some new criteria are established for the existence of positive periodic solutions of the following neutral functional differential equation x t x t a t f t x t x t 1 t x t n t x t 1 t x t m t

periodic solutions of nonautonomous stage structured cooperative system abstract by using the continuation theorem of coincidence degree theory the existence of a positive periodic solution for the nonautonomous stage structured cooperative system is established

global existence of positive periodic solutions of periodic predator prey system with infinite delays abstract a set of easily verifiable sufficient conditions is derived for the global existence of periodic solutions with strictly positive components for a periodic predator prey system with infinite delays by using the method of coincidence degree

jordan holder theorems for derived categories of derived discrete algebras abstract for any positive integer n n derived simple derived discrete algebras are classified up to derived equivalence furthermore the jordan holder theorems for all kinds of derived categories of derived discrete algebras are obtained

positive periodic solutions for a class of nonlinear delay equations abstract applying the theory of topological degree sufficient and realistic conditions are obtained for the existence of positive periodic solutions of a class of neutral delays equation from those conditions an algebraic criterion of existence for a more general neutral lotka volterra equation with several delays is obtained which extends and improves the previous results in addition this method is of great interest in many applications such as biomathematics

periodic solution of neutral lotka volterra system with periodic delays abstract a nonautonomous n species lotka volterra system with neutral delays is investigated a set of verifiable sufficient conditions is derived for the existence of at least one strictly positive periodic solution of this lotka volterra system by applying an existence theorem and some analysis techniques where the assumptions of the existence theorem are different from that of gaines and mawhin s continuation theorem r e gaines j l mawhin coincidence degree and nonlinear differential equations springer verlag berlin 1977 and that of abstract continuation theory for k set contraction w petryshyn z yu existence theorem for periodic solutions of higher order nonlinear periodic boundary value problems nonlinear anal 6 1982 943 969 moreover a problem proposed by freedman and wu h i freedman j wu periodic solution of single species models with periodic delay siam j math anal 23 1992 689 701 is answered

periodic solutions in higher dimensional lotka volterra neutral competition systems with state dependent delays abstract positive periodic solutions for two dimensional neutral lotka volterra system with state dependent delays are considered by the theory of coincidence degree and some new techniques of computation applying this method for higher dimensional system we can also get more general conclusions and give many easy and verifiable conditions for some special cases of system by restricting its coefficients

periodic solutions of a class of singular hamiltonian systems soit r n 0 n n n 3 et soit v c 1 rx r on etudie l existence des solutions periodiques t u t avec une periode prescrite du systeme suivant de n equations differentielles d ordre 2 u v t u

positive periodic solution for a neutral delay competitive system in this paper we study the existence of positive periodic solutions for a class of neutral type competitive system with delay applying the continuation theorem of coincidence degree theory a general criteria on the existence of positive periodic solutions are established some the related results are generalized and improved it is shown that the arguments delays have no effect on the existence positive periodic solution of system

dynamics of species in a model with two predators and one prey abstract in this paper we study a predator prey model which has one prey and two predators with beddington deangelis functional responses firstly we establish a set of sufficient conditions for the permanence and extinction of species secondly the periodicity of positive solutions is studied thirdly by using liapunov functions and the continuation theorem in coincidence degree theory we show the global asymptotic stability of such solutions finally we give some numerical examples to illustrate the behavior of the model

on positive periodic solutions of a nonautonomous neutral delay n species competitive system abstract the purpose of this paper is to investigate a general neutral delay n species competitive nonautonomous system different from gaines and mawhin s continuation theorem r e gaines j l mawhin coincidence degree and nonlinear differential equations springer verlag berlin 1977 and abstract continuation theory for k set contraction w petryshyn z yu existence theorem for periodic solutions of higher order nonlinear periodic boundary value problems nonlinear anal 6 1982 943 969 r e gaines j l mawhin lecture notes in mathematics vol 586 springer verlag berlin 1977 a new existence theorem is introduced with the help of the theorem and some techniques a set of sufficient conditions are derived for the existence of at least one strictly positive componentwise periodic solution as an application we also examine some special cases which have been studied extensively in the literature some known results are improved and generalized

the variational contribution of the periodic orbits provided by the birkhoff lewis theorem with applications to convex hamiltonians and to three body type problems

periodic solutions for higher order neutraldifferential equations with several delays neutral differential equations arise in many practical problems and have importantapplications in physics and engineering this paper introduces fourier series method and inequality techniques to investigate periodic solutions for a class of higher order delayed neutral differential equations this method is different to some traditional methods such as critical point theory fixed point method and topological degree method which are applied to study periodic solution problem of neutral differential equations some new necessary and sufficient conditions are obtained ensuring the existence and uniqueness of periodic solutions in addition three examples are given to illustrate the theory

boundedness of solutions of a nonlinear nonautonomous neutral delay equation abstract sufficient conditions are obtained for the boundedness of solutions of the non linear nonautonomous neutral equation x t r t x t a t x t 1 c t x t 1 which arise in a food limited population model this partially answers a recent open question proposed by k gopalsamy and b g zhang

existence of periodic solutions in neutral state dependent delays equations and models sufficient conditions are obtained for the existence of positive periodic solutions of neutral equations with state dependent delays the proof is based on the theory of coincidence degree the existence results are applied to equations of population dynamics

on the cyclic homology of monomial relation algebras abstract a finite dimensional monomial relation algebra has finite global dimension if and only if the relative cyclic homology of its radical is equal to zero

periodic solution of a periodic neutral delay equation abstract sufficient conditions are obtained for the existence of a positive periodic solution of the periodic neutral delay equation t n t a t n j 1 b j t n t j j 1 n c j t t j which arise in a food limited population model

a minimax method for a class of hamiltonian systems with singular potentials abstract this paper presents a minimax method which gives existence and multiplicity results for time periodic solutions of a class of hamiltonian systems when a singular potential is present the singularity satisfies the strong force condition of gordon when milder singularities are permitted a notion of generalized t periodic solution is introduced and we get existence and multiplicity results for such solutions

topologically distinct collision free periodic solutions for the n center problem this work concerns the planar n center problem with homogeneous potential of degree alpha alpha in 1 2 the existence of infinitely many topologically distinct non collision periodic solutions with a prescribed energy is proved a notion of admissibility in the space of loops on the punctured plane is introduced so that in any admissible class and for any positive h the existence of a classical periodic solution with energy h for the n center problem with alpha in 1 2 is proven in case alpha 1 a slightly different result is shown it is the case that there is either a non collision periodic solution or a collision reflection solution the results hold for any position of the centres and it is possible to prescribe in advance the shape of the periodic solutions the proof combines the topological properties of the space of loops in the punctured plane with variational and geometrical arguments

the fixed energy problem for a class of nonconvex singular hamiltonian systems we consider a noncompact hypersurface h in r2n which is the energy level of a singular hamiltonian of strong force type under global geometric assumptions on h we prove that it carries a closed characteristic as a consequence of a result by hofer and viterbo on the weinstein conjecture in cotangent bundles of compact manifolds our theorem contains as particular cases earlier results on the fixed energy problem for singular lagrangian systems of strong force type

dynamical systems with effective like potentials on etudie l existence des solutions t periodiques pour des systemes hamiltoniens d ordre 2 de la forme x v x ou v r n 0 r est de classe c 2 et v x quand x 0

periodic solutions of prescribed energy for a class of hamiltonian systems with singular potentials abstract we study the existence of periodic solutions of prescribed energy for a class of hamiltonian systems with singular potentials we found periodic solutions lying between two prescribed spheres

the cartan map on categories of graded modules this paper presents a technique based on elementary k theory it relies on the fact that k for a category of graded modules can be viewed as a z t t l module for some variable t in this context we will deduce a great deal of information from an explicit computation of the coordinates of the matrix of the cartan homomorphism in section 1 we begin by recalling some definitions and results that we will use throughout this paper from these we then describe our basic machinery section 2 will provide some applications of this machine we note in particular the following uses nakayama 131 proposed that if a is a finite dimensional algebra of infinite dominant dimension then a is self injective auslander and reiten 4 noticed that the following stronger statement would imply the truth of nakayama s conjecture given a finite dimensional algebra a with minimal injective resolution 0 a e e se every indecomposable injective module is isomorphic to a summand of some ei here we prove this generalized nakayama conjecture for graded algebras another application of this technique shows that the determinant of the cartan map is one for graded algebras of finite global dimension this in turn is used to show that if b is any algebra not necessarily graded with only finitely many nonisomorphic indecomposable modules m 1 m then the matrix whose ijth coordinate is dim hom mi mj has determinant one finally we give an application to the rationality of power series let f be a field and let a be a finite dimensional f algebra we will assume everywhere that a is basic that is for every simple a module s end s f this assumption is primarily to simplify notation and the arguments given could be modified to handle algebras that are not basic we will use the notation mod a for the category of finitely generated left a modules let g be a full subcategory of mod 4 and let x 55 be the free 390 0021 8693 83 3 00

uniform persistence for a predator prey system with delays we consider a class of delayed predator prey system with holling type iii functional response the uniform persistence and the existence of positive periodic solutions will be studied by using new approaches our results improve some in the literature an example is given to illustrate the obtained results

a multiplication in cyclic homology we define a multiplication on the cyclic homology of a commutative cocommutative bialgebra h with superproduct in the case when h is a field of characteristic zero the cyclic homology becomes a polynomial algebra in one generator the loday quillen multiplication is trivial in that case in this paper we define an associative multiplication on the cyclic homology of certain commutative algebras h the definition is based on the cartesian product of sets instead of the shuffle product as in the case of lq and ga when h contains q our product is compatible with the hodge decomposition of hc h so it has the form hc n h hc j m h hc n m h the existence of this multiplication in the case h k is classical since it is just given by the tensor product of complex line bundle however its significance came to our attention in joint work with john klein as a consequence of our study of fiberwise morse theory on circle bundles ik and in other joint works with r penner and r hain by doing morse theory on circles john klein and i realized that there was a rationally nontrivial associative multiplication on the cyclic homology of the integral group ring on any cyclic group and that it had important consequences for pseudoisotopy theory this will be explained in a later paper in this paper we show that this multiplication in cyclic homotopy is defined first in the case when the algebra is h km k m where m is the underlying additive group of a ring then in the case when h is a hopf algebra with superproduct in the sense of gaucher ga and finally in the more general case of any algebra example 12 4 in fact we do not need additive inverses in m nor do we need an antipode for h so we can take m to be a monoid and h to be a bialgebra when h k i e m 1 the cyclic homology becomes a divided power algebra which is of course isomorphic to a polynomial algebra in one generator if k is a field of characteristic zero we assume throughout the paper that k is a commutative ring with 1 and that all tensor products are taken over k this includes those tensor products which appear in the definition of cyclic homology we also use connes original definition that a cyclic object in a category c is a covariant functor c where is connes cyclic category since this is the same as a contravariant functor c an outline of the paper is as follows in the first section we give a topological definition of the multiplication in hc km the construction is so elementary that received by the editors april 14 1994 1991 mathematics subject classification primary 18g60 secondary 16w30 this research was supported by nsf grant no dms 90 02512 c 1999 american mathematical society

closed orbits of fixed energy for singular hamiltonian systems this paper deals with the existence of periodic solutions of q v q 0 such that 1 2 q 2 v q h where q r n h is a given number v c 2 r n 0 r has a singularity at x 0 and v denotes the gradient of v

sufficient conditions for the existence of positive periodic solutions of a class of neutral delay models by using the theory of coincidence degree the existence of positive periodic solutions is studied for the neutral model with periodic delaysn t n t a t email protected t n t email protected i 1 nb i t n email protected i t email protected i 1 nc i t n email protected i t our results extend and improve existing results and have further applications in population dynamics

periodicity on a class of neutral impulsive delay system we present some sufficient conditions for the existence of positive periodic solutions of a class of neutral impulsive delay differential system when our results applied to the differential system without impulse a known result in the literature is corrected moreover one example is given to illustrate the results obtained

positive periodic solutions of neutral lotka volterra system with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of neutral lotka volterra system with periodic delays and feedback control our results extend and improve existing results and have further applications in population dynamics

resolution quiver and cyclic homology criteria for nakayama algebras abstract if a nakayama algebra is not cyclic it has finite global dimension for a cyclic nakayama algebra there are many characterizations of when it has finite global dimension in 17 shen gave such a characterization using ringel s resolution quiver in 11 the second author with zacharia gave a cyclic homology characterization for when a monomial relation algebra has finite global dimension we show directly that these criteria are equivalent for all nakayama algebras our comparison result also reproves both characterizations in a separate paper we discuss an interesting example that came up in our attempt to generalize this comparison result to arbitrary monomial relation algebras 8

spatial chaotic structure of attractors of reaction diffusion systems the dynamics described by a system of reaction diffusion equations with a nonlinear potential exhibits complicated spatial patterns these patterns emerge from preservation of homotopy classes of solutions with bounded energies chaotically arranged stable patterns exist because of realizability of all elements of a fundamental homotopy group of a fixed degree this group corresponds to level sets of the potential the estimates of homotopy complexity of attractors are obtained in terms of geometric characteristics of the potential and other data of the problem

sufficient conditions for the existence positive periodic solutions of a class of neutral delay models with feedback control with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a neutral model with periodic delays and feedback controldndt n t a t email protected t n t email protected i 1nb i t n email protected i t email protected i 1nc i t n email protected i t email protected t u t email protected i 1nd i t u email protected i t dudt e t u t f t n t email protected i 1ng i t n email protected i t our results extend and improve existing results and have further applications in population dynamics

a note on periodic solutions of prescribed energy for singular hamiltonian systems abstract in this note we show under a less restrictive setting than previously that there exists a collision brake orbit of prescribed energy to a certain second order hamiltonian system

on the existence of positive periodic solutions for neutral functional differential equation with multiple deviating arguments by means of the abstract continuation theory for k contractions some criteria are established for the existence and nonexistence of positive periodic solutions of the following neutral functional differential equation dndt n t a t t n t j 1nbj t nt j t i 1mci t n t i t

positive periodic solutions of neutral lotka volterra system with periodic delays in this paper several sufficient conditions are investigated for the existence of positive periodic solutions of a general neutral lotka volterra system with unbounded delays by using the theory of coincidence degree our results extend and improve existing results and have further applications in population dynamics

analytical mini max methods for hamiltonian brake orbits of prescribed energy on considere des caracterisations explicites de solutions periodiques de systemes hamiltoniens autonomes d ordre 2 de la forme q v q q t r n ou le potentiel v satisfait les conditions suivantes v c 2 r n v x v o 0 v est strictement convexe sur r n

a proof of the strong no loop conjecture abstract the strong no loop conjecture states that a simple module of finite projective dimension over an artin algebra has no non zero self extension the main result of this paper establishes this well known conjecture for finite dimensional algebras over an algebraically closed field

existence and uniqueness of positive periodic solutions for a neutral logarithmic population model in this paper by using an abstract continuous theorem of k set contractive operator the criteria is established for the existence global attractivity of positive periodic solution of a neutral delay logarithmic population model with multiple delays the result improve the known ones in s p lu w g ge existence of positive periodic solutions for neutral logarithmic population model with multiple delays j comput appl math 166 2 2004 371 383

multiple closed orbits of fixed energy forn body type problems with gravitational potentials abstract using the equivariant ljusternik schnirelmann theory and the estimates of the upper bound and lower bound of the critical values for the variational functional we obtain results in general concerning multiple geometrically distinct periodic solutions of fixed energy for a class of planarn body type problems

periodic solutions of a class of neutral differential models with feedback control abstract sufficient conditions are obtained for the existence of positive periodic solutions of a class of neutral delay differential system with state dependent delays and feedback control by using the theory of topological degree and some new analytical techniques the analytical result obtained is not only of great interest in theory but also many applications such as biomathematics which extends substantially the existing relevant existence results in the literature as a demonstration applying the obtained analysis results to a real complex neutral lotka volterra population model the existence criterion for positive periodic solutions is easily obtained especially this method is more suitable to state dependent delay

periodic solutions of singular hamiltonian systems with prescribed energy abstract we study the existence of non collision periodic solutions for some class of singular hamiltonian systems in particular in the case that the weak force potential has a set of singular points which is a compact subset of r n we prove the existence of a non collision periodic solution for all positive prescribed energy