on a class of functionals invariant under a zn action abstract this document considers a system of ordinary differential equations of the form q v sub q t q f t where f and v are periodic in t v is periodic in the components of q q sub 1 q sub m and the mean value of f vanishes by showing that a corresponding functional is invariant under a natural z sub n action a simple variational argument yields at least n 1 distinct periodic solutions of more general versions of are also treated as is a class of neumann problems for semilinear elliptic partial differential equations

three periodic solutions for perturbed second order hamiltonian systems in this paper we study the existence of three distinct solutions for the following problem u a t u f t u g t u a e in 0 t u t u 0 u t u 0 0 where r t is a real positive number a 0 t rn n is a continuous map from the interval 0 t to the set of n order symmetric matrices we propose sufficient conditions only on the potential f more precisely we assume that g satisfies only a usual growth condition which allows us to use a variational approach

morse theory and asymptotic linear hamiltonian system on considere l existence de solutions 2 periodiques des systemes hamiltoniens asymptotiquement quadratiques jz h z t ou j 0 i i 0 i in la matrice identite de n n

analytic surgery of the zeta function in this paper we study the asymptotic behavior in the sense of meromorphic functions of the zeta function of a laplace type operator on a closed manifold when the underlying manifold is stretched in the direction normal to a dividing hypersurface separating the manifold into two manifolds with infinite cylindrical ends we also study the related problem on a manifold with boundary as the manifold is stretched in the direction normal to its boundary forming a manifold with an infinite cylindrical end such singular deformations fall under the category of analytic surgery developed originally by hassell comm anal geom 6 255 289 1998 hassell et al comm anal geom 3 115 222 1995 and mazzeo and melrose geom funct anal 5 14 75 1995 in the context of eta invariants and determinants

non autonomous second order hamiltonian systems abstract we study the existence of periodic solutions for a second order non autonomous dynamical system containing variable kinetic energy terms our assumptions balance the interaction between the kinetic energy and the potential energy with neither one dominating the other we study sublinear problems and the existence of non constant solutions

infinitely many nontrivial periodic solutions for damped vibration problems with asymptotically linear terms in this paper we study a class of damped vibration problem with asymptotically quadratic terms at infinity we obtain infinitely many nontrivial periodic solutions by variational method to the best of our knowledge there is no published result focusing on this class of damped vibration problem with asymptotically quadratic terms at infinity

meyer vietoris type formula for determinants of elliptic differential operators abstract for a closed codimension one submanifold of a compact manifold m let m be the manifold with boundary obtained by cutting m along let a be an elliptic differential operator on m and b and c be two complementary boundary conditions on if a b is an elliptic boundary valued problem on m then one defines an elliptic pseudodifferential operator r of neumann type on and prove the following factorization formula for the regularized determinants det a det a b k det r with k a local quantity depending only on the jets of the symbols of a b and c along the particular case when m has dimension 2 a is the laplace beltrami operator and b resp c is the dirichlet resp neumann boundary condition is considered

periodic solutions of classical hamiltonian systems without palais smale condition abstract in this paper we study the existence of periodic solutions for classical hamiltonian systems without the palais smale condition we prove that the information of the potential function contained in a finite domain is sufficient for the existence of periodic solutions moreover we establish the existence of infinitely many periodic solutions without any symmetric condition on the potential function v

multiple solutions of perturbed superquadratic second order hamiltonian systems abstract in this paper the author proves the existence of infinitely many distinct t periodic solutions of the perturbed second order hamiltonian systems q v q f t under the condition that v is c and superquadratic via minimax methods we also obtain similar results for general nonautonomous second order hamiltonian systems and perturbed lagrangian systems keywords invariance asymmetry a priori growth estimates multiple periodic solutions

the relations of go and stop wave to car accidents in a cellular automaton with velocity dependent randomization abstract in this paper we numerically study the probability p ac of the occurrence of traffic accidents in the nagel schreckenberg ns model with velocity dependent randomization vdr numerical results show that there is a critical density over which car accidents occur but below which no car accidents happen different from the accident probability in the ns model the accident probability in the vdr model monotonously decreases with increase of car density above the critical density the value of the accident probability is only determined by the stochastic noise and the number of cars on road in the stochastic vdr model with the speed limit v max 1 no critical density exists and car accidents happen in the whole density region the braking probabilities of standing cars and moving cars have different influences on the accident probability a mean field theory reveals that the accident probability is proportional to the mean density of go and stop wave per time step theoretical analyses give excellent agreement with numerical results in the vdr model

zeta regularized determinants for conic manifolds we study relative zeta regularized determinants of laplace type operators on compact conic manifolds we establish gluing formulae for relative zeta regularized determinants for arbitrary self adjoint extensions of the laplace beltrami operator we express the relative determinants for these as a ratio of the determinants of certain finite matrices for the self adjoint extensions corresponding to dirichlet and neumann conditions the formula is particularly simple and elegant

precise constants in bosonization formulas on riemann surfaces i a computation of the constant appearing in the spin 1 bosonization formula is given this constant relates faltings delta invariant to the zeta regularized determinant of the laplace operator with respect to the arakelov metric

a new proof of weyl s formula on the asymptotic distribution of eigenvalues one of the more perplexing problems of finite particle quantum mechanics is to find the appropriate quantum mechanical description of a given classical mechanical system unfortunately from the mathematical point of view this problem is not terribly well posed suppose the classical system in question is represented by a symplectic manifold x and a classical observable p x r suppose also for simplicity that this system is a confined system in the sense that the sets p 1 are all compact let h be a hilbert space and let p be a self adjoint operator on h representing a quantum observable without specifying anything further about p for instance its relation to other observables there is practically no way of ascertaining whether p is an appropriate quantum counterpart of p at first glance the only requirements this appears to impose on p are that the spectrum of p be discrete and that the number of eigenvalues n a less than 1 be finite for all 1 this is the analogue of the condtion that p 1 be compact by examining the statistical properties of a large aggregate of classical systems each a copy of x p one can in fact say a little bit more about the relation p to p by comparing classical and quantum partition functions one can show that for iz large

on the determinant of elliptic differential and finite difference operators in vector bundles over s 1 for an elliptic differential operatora overs 1 a sum limits k 0 n a k x d k witha k x in end r and as a principal angle the regularized determinant det a is computed in terms of the monodromy mapp a associated toa and some invariant expressed in terms ofa n anda n 1 a similar formula holds for finite difference operators a number of applications and implications are given in particular we present a formula for the signature ofa whena is self adjoint and show that the determinant ofa is the limit of a sequence of computable expressions involving determinants of difference approximation ofa

the existence of periodic solutions of non autonomous second order hamiltonian systems abstract the purpose of this paper is to study the existence of periodic solutions for a class of non autonomous second order hamiltonian systems some new existence theorems are obtained by using the least action principle and the saddle point theorem

the burghelea friedlander kappeler gluing formula for zeta determinants on a warped product manifold and a product manifold the burghelea friedlander kappeler bfk gluing formula for the regularized zeta determinants of laplacians contains a constant which is expressed by the constant term in the asymptotic expansion of the regularized zeta determinants of a one parameter family of the dirichlet to neumann operators when the dimension of a cutting hypersurface is odd or the metric is a product one near a cutting hypersurface this constant is well known in this paper we discuss this constant in two cases one is when a warped product metric is given near a cutting hypersurface and the other is when a manifold is a product manifold especially in the first case we use the result of fucci and kirsten commun math phys 317 635 665 2013 in which the regularized zeta determinant of the laplacian defined on a warped product manifold is computed

infinitely many periodic solutions for second order hamiltonian systems in this paper we study the existence of infinitely many periodic solutions for second order hamiltonian systems u uv t u 0 where v t u is either asymptotically quadratic or superquadratic as u

on the gluing problem for the spectral invariants of dirac operators abstract in this paper we solve the gluing problem for the determinant of a dirac laplacian to do so we develop a new approach to solve such problems which relies heavily on the theory of elliptic boundary problems the analysis of the resolvent of the dirac operator and the introduction of an auxiliary model problem moreover as a byproduct of our approach we obtain a new gluing formula for the eta invariant au gratis

on the periodic nonlinearity and the multiplicity of solutions abstract this document studies the multiplicity of solutions for semilinear elliptic systems as well as hamiltonian systems in which the nonlinear terms are periodic in certain variables the cuplength for cohomology rings of the torus is used our results generalize and unify several recent works by conley zehnder rabinowitz mawhin willem pucci serrin etc in particular the resonance problems and indefinite problems are studied keywords critical point neumann problem periodic solution

on the spectrum of the laplace operator of metric graphs attached at a vertex spectral determinant approach we consider a metric graph made of two graphs and attached at one point we derive a formula relating the spectral determinant of the laplace operator in terms of the spectral determinants of the two subgraphs the result is generalized to describe the attachment of n graphs the formulae are also valid for the spectral determinant of the schrodinger operator

periodic solutions of non autonomous second order systems with a p laplacian abstract in this paper we investigate non autonomous second order systems with a p laplacian and obtain existence results for periodic solutions with the dual least action principle

spectral determinants on mandelstam diagrams we study the regularized determinant of the laplacian as a functional on the space of mandelstam diagrams noncompact translation surfaces glued from finite and semi infinite cylinders a mandelstam diagram can be considered as a compact riemann surface equipped with a conformal flat singular metric omega 2 where omega is a meromorphic one form with simple poles such that all its periods are pure imaginary and all its residues are real the main result is an explicit formula for the determinant of the laplacian in terms of the basic objects on the underlying riemann surface the prime form theta functions the canonical meromorphic bidifferential and the divisor of the meromorphic form omega as an important intermediate result we prove a decomposition formula of the type of burghelea friedlander kappeler for the determinant of the laplacian for flat surfaces with cylindrical ends and conical singularities

boundary effects on car accidents in a cellular automaton model in this paper we numerically study the probability pac of occurrence of car accidents in the nagel schreckenberg ns model with open boundary condition in the deterministic ns model numerical results show that there exists a critical value of extinction rate above which no car accidents occur and below which the probability pac is independent of the speed limit vmax and the injection rate but only determined by the extinction rate in the non deterministic ns model the probability pac is a non monotonic function of in the region of low value while it is independent of in the region of high value the stochastic braking not only reduces the occurrence of car accidents but splits degenerate effects of vmax on the probability pac theoretical analyses give an agreement with numerical results in the deterministic ns model and in the non deterministic ns model with vmax 1 in the case of low value region qualitative differences between open and periodic systems in the relations of pac to the bulk density imply that various correlations may exist between the two systems

on the asymptotics of determinant of laplacian at the principal boundary of the principal stratum of the moduli space of abelian differentials let x be a translation surface of genus g 1 with 2g 2 conical points of angle 4 and let be two homologous saddle connections of length s joining two conical points of x and bounding two surfaces s and s with boundaries s and s gluing the opposite sides of the boundary of each surface s s one gets two closed translation surfaces x x of genera g g g g g let and be the friedrichs extensions of the laplacians corresponding to the flat conical metrics on x x and x respectively we study the asymptotical behavior of the modified i e with zero modes excluded zeta regularized determinant det as and shrink we find the asymptotics

periodic solutions for some nonautonomous second order hamiltonian systems the existence and multiplicity of periodic solutions are obtained for nonautonomous second order hamiltonian systems by the minimax methods in critical point theory

burghelea friedlander kappeler s gluing formula for the zeta determinant and its applications to the adiabatic decompositions of the zeta determinant and the analytic torsion the gluing formula of the zeta determinant of a laplacian given by burghelea friedlander and kappeler contains an unknown constant in this paper we compute this constant to complete the formula under an assumption that the product structure is given near the boundary as applications of this result we prove the adiabatic decomposition theorems of the zeta determinant of a laplacian with respect to the dirichlet and neumann boundary conditions and of the analytic torsion with respect to the absolute and relative boundary conditions

statistical mechanical approach to fukui ishibashi traffic flow models we consider cellular automaton models for one dimensional traffic flow problems starting with a microscopic relation for the updating rule describing the occupancy on each site of the road a macroscopic evolution relation for the average speed of cars can be obtained by carrying out statistical averages mean field equations are obtained by considering the asymptotic form of the evolution relation this gives the average car speed in the long time limit as a function of the car density the evolution relation is a nonlinear mapping between the average speeds at two consecutive time steps the mean field results can be obtained by studying the attractors of the mapping the approach is applied to study the model recently proposed by fukui and ishibashi our calculations show that for models in which the maximum speed of each car is m a decoupling scheme retaining correlations up to m 1 sites can be applied to the calculation of spatial correlations involving more than m 1 sites exact results are obtained using our approach for models without random delay for models with random delay results are in good agreement with simulation results

periodic solutions of non autonomous second order systems we obtain an existence theorem of periodic solutions of non autonomous second order systems with classical theorems of variational calculus

a generalized saddle point theorem abstract the well known saddle point theorem is extended to the case of functions defined on a product space x v where x is a banach space and v is a compact manifold under some linking conditions the existence of at least cuplength v 1 critical points is proved the abstract theorems are applied to the existence problems of periodic solutions of hamiltonian systems with periodic nonlinearity and or resonance

refined analytic torsion given an acyclic representation alpha of the fundamental group of a compact oriented odd dimensional manifold which is close enough to an acyclic unitary representation we define a refinement t alpha of the ray singer torsion associated to alpha which can be viewed as the analytic counterpart of the refined combinatorial torsion introduced by turaev t alpha is equal to the graded determinant of the odd signature operator up to a correction term the metric anomaly needed to make it independent of the choice of the riemannian metric t alpha is a holomorphic function on the space of such representations of the fundamental group when alpha is a unitary representation the absolute value of t alpha is equal to the ray singer torsion and the phase of t alpha is proportional to the eta invariant of the odd signature operator the fact that the ray singer torsion and the eta invariant can be combined into one holomorphic function allows one to use methods of complex analysis to study both invariants in particular using these methods we compute the quotient of the refined analytic torsion and turaev s refinement of the combinatorial torsion generalizing in this way the classical cheeger m uller theorem as an application we extend and improve a result of farber about the relationship between the farber turaev absolute torsion and the eta invariant as part of our construction of t alpha we prove several new results about determinants and eta invariants of non self adjoint elliptic operators

determinants of laplacians and isopolar metrics on surfaces of infinite area we construct a determinant of the laplacian for infinite area surfaces which are hyperbolic near infinity and without cusps in the case of a convex co compact hyperbolic metric the determinant can be related to the selberg zeta function and thus shown to be an entire function of order two with zeros at the eigenvalues and resonances of the laplacian in the hyperbolic near infinity case the determinant is analyzed through the zeta regularized relative determinant for a conformal metric perturbation we establish that this relative determinant is a ratio of entire functions of order two with divisor corresponding to eigenvalues and resonances of the perturbed and unperturbed metrics these results are applied to the problem of compactness in the smooth topology for the class of metrics with a given set of eigenvalues and resonances

discrete stochastic models for traffic flow we investigate a probabilistic cellular automaton model which has been introduced recently this model describes single lane traffic flow on a ring and generalizes the asymmetric exclusion process models we study the equilibrium properties and calculate the so called fundamental diagrams flow versus density for parallel dynamics this is done numerically by computer simulations of the model and by means of an improved mean field approximation which takes into account short range correlations for cars with a maximum velocity of 1 the simplest nontrivial approximation gives the exact result for higher velocities the analytical results obtained by iterated application of the approximation scheme are in excellent agreement with the numerical simulations

ζ determinants of laplacians with neumann and dirichlet boundary conditions in this paper we derive a formula for the ratio of the determinants of the laplacian with neumann and dirichlet boundary conditions over a noncompact manifold with an infinite cylindrical end and a compact boundary in terms of the determinant of the dirichlet to neumann map

exact results for car accidents in a traffic model within the framework of a recent model for car accidents on single lane highway traffic we study analytically the probability of the occurrence of car accidents exact results are obtained various scaling behaviours are observed the linear dependence of the occurrence of car accidents on density is understood as the dominance of a single velocity in the distribution

periodic solutions for a class of nonautonomous subquadratic second order hamiltonian systems some existence theorems are obtained for periodic solutions of a class of unbounded nonautonomous nonconvex subquadratic second order hamiltonian systems by using the minimax methods in critical point theory

on variational methods for a class of damped vibration problems abstract in the present paper the following damped vibration problems 1 1 u t q t u t a t u t f t u t a e t 0 t u 0 u t u 0 e q t u t 0 and 1 1 u t q t u t a t u t f t u t a e t 0 t u 0 u t u 0 e q t u t 0 are studied where t 0 0 q l 1 0 t r q t 0 t q s d s a t a i j t is a symmetric n n matrix valued function defined in 0 t with a i j l 0 t for all i j 1 2 n and there exists a positive constant such that a t 2 for all r n and a e t 0 t the variational principles are given and an existence theorem and three multiplicity theorems of periodic solutions are obtained

spectral functions special functions and the selberg zeta function the functional determinant of an eigenvalue sequence as defined by zeta regularization can be simply evaluated by quadratures we apply this procedure to the selberg trace formula for a compact riemann surface to find a factorization of the selberg zeta function into two functional determinants respectively related to the laplacian on the compact surface itself and on the sphere we also apply our formalism to various explicit eigenvalue sequences reproducing in a simpler way classical results about the gamma function and the barnesg function concerning the latter our method explains its connection to the selberg zeta function and evaluates the related glaisher kinkelin constanta

periodic solutions of nonautonomous second order hamiltonian systems with even typed potentials abstract some existence and multiplicity theorems are obtained for periodic solutions of nonautonomous second order hamiltonian systems with even typed potentials by the least action principle and the minimax methods in critical point theory

some critical point theorems and their applications to periodic solution for second order hamiltonian systems abstract some critical point theorems without the compactness assumptions are obtained by the reduction method the perturbation argument and the least action principle as applications some existence results of periodic solutions are obtained for nonautonomous second order hamiltonian systems which unify and generalize some recent corresponding results

functional determinants and geometry in this paper we study the zeta function determinant in the context of elliptic boundary value problems our main technique is to relate the determinant of an operator or a ratio of determinants to the boundary values of the solutions of the operator this has the advantage of restricting attention to the solutions of the operator which do not depend on the boundary conditions and can often be written down explicitly rather than the eigenvalues which are usually difficult to work with in addition the problem is reduced to a calculation over the boundary of the manifold which is a closed manifold of dimension one less than the original manifold this has special significance in the case that the manifold is a finite interval in this case the boundary is a pair of points and the determinant of an ordinary differential operator is expressed in terms of the determinant of a finite matrix

critical metrics for the determinant of the laplacian in odd dimensions let m be a closed compact n dimensional manifold with n odd we calculate the first and second variations of the zeta regularized determinants det a and det l as the metric on m varies where a denotes the laplacian on functions and l denotes the conformal laplacian we see that the behavior of these functionals depends on the dimension indeed every critical metric for 1 n 1 2det a or 1 n 1 21 det l has finite index consequently there are no local maxima if n 4rm 1 and no local minima if n 4m 3 we show that the standard 3 sphere is a local maximum for det a while the standard 4m 3 sphere with m 1 2 is a saddle point by contrast for all odd n the standard n sphere is a local extremal for det l an important tool in our work is the canonical trace on odd class operators in odd dimensions this trace is related to the determinant by the formula det q tr log q and we prove some basic results on how to calculate this trace

periodic solutions for nonautonomous second order systems with bounded nonlinearity some existence and multiplicity theorems are obtained for periodic solutions of nonautonomous second order systems with bounded nonlinearity by the minimax methods

traffic accidents in a cellular automaton model with a speed limit zone in this paper we numerically study the probability pac of the occurrence of car accidents in the nagel schreckenberg ns model with a speed limit zone numerical results show that the probability for car accidents to occur pac is determined by the maximum speed v max of the speed limit zone but is independent of the length lv of the speed limit zone in the deterministic ns model however in the nondeterministic ns model the probability of the occurrence of car accidents pac is determined not only by the maximum speed v max but also the length lv the probability pac increases accordingly with the increase of the maximum speed of the speed limit zone but decreases with the increase of the length of the speed limit zone in the low density region however in the case of v max 1 the probability pac increases with the increase of the length in the low density region but decreases in the interval between the low density and high density regions the speed limit zone also causes an inhomogeneous distribution of car accidents over the whole road theoretical analyses give an agreement with numerical results in the nondeterministic ns model with v max 1 and vmax 5

periodic solutions of second order differential inclusions systems with p laplacian some existence results are obtained for periodic solutions of nonautonomous second order differential inclusions systems with p laplacian

saddle point characterization and multiplicity of periodic solutions of non autonomous second order systems abstract in the present paper the non autonomous second order systems 1 1 u t f t u t a e t 0 t u 0 u t u 0 u t 0 and 1 2 u t t u t f t u t a e t 0 t u 0 u t u 0 u t 0 are studied and a existence result of periodic solutions with saddle point character and two new multiplicity results are obtained

nontrivial periodic solutions for asymptotically linear resonant difference problem in this paper the existence of nontrivial periodic solution for second order asymptotically linear difference equation at resonance is obtained the methods used here are based on combining the minimax methods and the morse theory especially the observation on the critical groups

complex valued ray singer torsion abstract in the spirit of ray and singer we define a complex valued analytic torsion using non selfadjoint laplacians we establish an anomaly formula which permits to turn this into a topological invariant conjecturally this analytically defined invariant computes the complex valued reidemeister torsion including its phase we establish this conjecture in some non trivial situations

multiple periodic solutions for hamiltonian systems with not coercive potential under an appropriate oscillating behavior of the nonlinear term the existence of infinitely many periodic solutions for a class of second order hamiltonian systems is established moreover the existence of two non trivial periodic solutions for hamiltonian systems with not coercive potential is obtained and the existence of three periodic solutions for hamiltonian systems with coercive potential is pointed out the approach is based on critical point theorems

moduli spaces of meromorphic functions and determinant of laplacian the hurwitz space is the moduli space of pairs x f where x is a compact riemann surface and f is a meromorphic function on x we study the laplace operator delta df 2 of the flat singular riemannian manifold x df 2 we define a regularized determinant for delta df 2 and study it as a functional on the hurwitz space we prove that this functional is related to a system of pde which admits explicit integration this leads to an explicit expression for the determinant of the laplace operator in terms of the basic objects on the underlying riemann surface the prime form theta functions the canonical meromorphic bidifferential and the divisor of the meromorphic differential df the proof has several parts that can be of independent interest as an important intermediate result we prove a decomposition formula of the type of burghelea friedlander kappeler for the determinant of the laplace operator on flat surfaces with conical singularities and euclidean or conical ends we introduce and study the s matrix s lambda of a surface with conical singularities as a function of the spectral parameter lambda and relate its behavior at lambda 0 with the schiffer projective connection on the riemann surface x we also prove variational formulas for eigenvalues of the laplace operator of a compact surface with conical singularities when the latter move

periodic solutions of non autonomous second order systems with γ quasisubadditive potential abstract the existence of periodic solutions to non autonomous second order systems with quasisubadditive potential is proved with classical theorems of variational calculus

variations on a theme of jost and pais abstract we explore the extent to which a variant of a celebrated formula due to jost and pais which reduces the fredholm perturbation determinant associated with the schrodinger operator on a half line to a simple wronski determinant of appropriate distributional solutions of the underlying schrodinger equation generalizes to higher dimensions in this multi dimensional extension the half line is replaced by an open set r n n n n 2 where has a compact nonempty boundary satisfying certain regularity conditions our variant involves ratios of perturbation determinants corresponding to dirichlet and neumann boundary conditions on and invokes the corresponding dirichlet to neumann map as a result we succeed in reducing a certain ratio of modified fredholm perturbation determinants associated with operators in l 2 d n x n n to modified fredholm determinants associated with operators in l 2 d n 1 n 2 applications involving the birman schwinger principle and eigenvalue counting functions are discussed