aging of asymmetric dynamics on the random energy model we show aging of glauber type dynamics on the random energy model in the sense that we obtain the annealed scaling limits of the clock process and of the age process the latter encodes the gibbs weight of the configuration occupied by the dynamics both limits are expressed in terms of stable subordinators

double positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales a new double fixed point theorem is applied to investigate the existence of at least double positive solutions of three point boundary value problems for p laplacian dynamic equations on a time scale

multiple results of p laplacian dynamic equations on time scales in this paper a new fixed point theorem introduced by avery and peterson and another fixed point theorem are applied to boundary value problems for p laplacian dynamic equations on time scales by imposing some growth conditions on the nonlinearity f we establish the existence results of at least three positive solutions as an application some examples are included to illustrate the main results

existence and uniqueness of a nontrivial solution for a class of third order nonlinear p laplacian m point eigenvalue problems on time scales abstract in this paper we study the existence and uniqueness of a nontrivial solution for the following third order p laplacian m point eigenvalue problems on time scales p u f t u t u t 0 t 0 t u 0 u 0 0 u t i 1 m 2 a i u i u 0 0 where p s is p laplacian operator i e p s s p 2 s p 1 p 1 q 1 p 1 q 1 0 is a parameter 0 1 m 2 t we obtain several sufficient conditions of the existence and uniqueness of nontrivial solution of the above eigenvalue problems when is in some interval our approach is based on the leray schauder nonlinear alternative as an application some examples to demonstrate our results are given the conditions we used in the paper are different from those in z c hao l debnath on eigenvalue intervals and eigenfunctions of fourth order singular boundary value problems appl math lett 18 2005 543 553 d jiang r p agarwal a uniqueness and existence theorem for a singular third order boundary value problem on 0 1 appl math lett 15 2002 445 451 s h li positive solutions of nonlinear singular third order two point boundary value problem j math anal appl 323 2006 413 425 z liu j s ume d r anderson s m kang twin monotone positive solutions to a singular nonlinear third order differential equation j math anal appl 334 2007 299 313 q yao positive solutions to a special singular second order boundary value problem math comput model in press q yao successive iteration of positive solution for a discontinuous third order boundary value problem comput math appl 53 2007 741 749

first order dynamic inclusions on time scales abstract in this paper we study existence of solutions of first order dynamic inclusions on time scales with general boundary conditions both the derivative and derivative cases are considered examples are presented to illustrate that the derivative case needs more restrictive assumptions

multiple positive solutions for p laplacian m point boundary value problems on time scales let t be a time scale such that 0 email protected t a i 0 for i 1 m 2 let x i satisfy 0 x 1 x 2 x m 2 r t and i 1 m 2a i 1 we consider the following p laplacian m point boundary value problem on time scales f p u d t a t f t u t 0 email protected 0 t u 0 0 f p u d t email protected i 1m 2a email protected p u d x i where email protected c l d 0 t 0 and email protected c l d 0 t x 0 0 some new results are obtained for the existence of at least twin or triple positive solutions of the above problem by applying avery henderson and leggett williams fixed point theorems respectively in particular our criteria extend and improve some known results

higher order boundary value problems on time scales in this paper we study the existence of solutions for lidstone boundary value problems on time scale firstly by using schauder fixed point theorem in a cone we obtain the existence of solutions to a lidstone boundary value problem lbvp secondly existence result for this problem is also given by the monotone method finally by using krasnosel skii fixed point theorem it is proved that the lbvp has a positive solution

eigenvalue problem for p laplacian three point boundary value problems on time scales abstract let t be a time scale such that 0 t t 0 and 0 t we consider the following p laplacian three point boundary problem on time scales p u t h t f u t 0 t 0 t u 0 u 0 u u t 0 where p 1 0 h c ld 0 t 0 and f c 0 0 some sufficient conditions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are established in doing so the usual restriction that f 0 lim u 0 f u p u and f lim u f u p u exist is removed an example is also given to illustrate the main results

second order periodic boundary value problems on time scales in this paper we study the existence of solutions of periodic boundary value problem for second order nonlinear dynamic equations on time scales for this purpose we use two methods here first sign properties of the green s function are investigated and existence results of bounded solutions of nonlinear boundary value problems are established as a result of schauder fixed point theorem second the monotone method is discussed to assure the existence and uniqueness of solutions of such periodic boundary value problems on time scales

integrable equations on time scales integrable systems are usually given in terms of functions of continuous variables on r in terms of functions of discrete variables on z and recently in terms of functions of q variables on kq we formulate the gel fand dikii gd formalism on time scales by using the delta differentiation operator and find more general integrable nonlinear evolutionary equations in particular they yield integrable equations over integers difference equations and over q numbers q difference equations we formulate the gd formalism also in terms of shift operators for all regular discrete time scales we give a method allowing to construct the recursion operators for integrable systems on time scales finally we give a trace formula on time scales and then construct infinitely many conserved quantities casimirs of the integrable systems on time scales

calculus of variations on time scales with nabla derivatives abstract we prove a necessary optimality condition of the euler lagrange type for variational problems on time scales involving nabla derivatives of higher order the proof is done using a new and more general fundamental lemma of the calculus of variations on time scales

positive periodic solutions for nonlinear difference equations with periodic coefficients abstract we prove the existence of positive solutions of second order nonlinear difference equations on a finite discrete segment with periodic boundary conditions obtained results yield positive periodic solutions of the equation on the whole discrete axis provided that the coefficients are periodic

positive solutions to singular multi point dynamic eigenvalue problems with mixed derivatives abstract this paper considers a singular m point dynamic eigenvalue problem on time scales t p t u t f t u t t 0 1 t u 0 i 1 m 2 a i u i u 1 p 1 u 1 i 1 m 2 b i p i u i we allow f t w to be singular at w 0 and t 0 by constructing the green s function and studying its positivity eigenvalue intervals in which there exist positive solutions of the above problem are obtained by making use of the fixed point index theory

quenched localisation in the bouchaud trap model with slowly varying traps we consider the quenched localisation of the bouchaud trap model on the positive integers in the case that the trap distribution has a slowly varying tail at infinity our main result is that for each n in 2 3 ldots there exists a slowly varying tail such that quenched localisation occurs on exactly n sites as far as we are aware this is the first example of a model in which the exact number of localisation sites are able to be tuned according to the model parameters key intuition for this result is provided by an observation about the sum max ratio for sequences of independent and identically distributed random variables with a slowly varying distributional tail which is of independent interest

the r matrix approach to integrable systems on time scales a general unifying framework for integrable soliton like systems on time scales is introduced the r matrix formalism is applied to the algebra of differential operators in terms of which one can construct an infinite hierarchy of commuting vector fields the theory is illustrated by two infinite field integrable hierarchies on time scales which are differential counterparts of kp and mkp the difference counterparts of akns and kaup broer soliton systems are constructed as related finite field restrictions

the arcsine law as a universal aging scheme for trap models we give a general proof of aging for trap models using the arcsine law for stable subordinators this proof is based on abstract conditions on the potential theory of the underlying graph and on the randomness of the trapping landscape we apply this proof to aging for trap models on large two dimensional tori and for trap dynamics of the random energy model on a broad range of time scales c 2006 wiley periodicals inc

biased random walk on critical galton watson trees conditioned to survive we consider the biased random walk on a critical galton watson tree conditioned to survive and confirm that this model with trapping belongs to the same universality class as certain one dimensional trapping models with slowly varying tails indeed in each of these two settings we establish closely related functional limit theorems involving an extremal process and also demonstrate extremal aging occurs

higher order self adjoint boundary value problems on time scales in this study higher order self adjoint differential expressions on time scales and their associated self adjoint boundary conditions are discussed the symmetry property of the corresponding green s functions is shown together with specific formulas of green s functions for select time scales

hamiltonian systems on time scales linear and nonlinear hamiltonian systems are studied on time scales t we unify symplectic flow properties of discrete and continuous hamiltonian systems a chain rule which unifies discrete and continuous settings is presented for our so called alpha derivatives on generalized time scales this chain rule allows transformation of linear hamiltonian systems on time scales under simultaneous change of independent and dependent variables thus extending the change of dependent variables recently obtained by dosl and hilscher we also give the legendre transformation for nonlinear euler lagrange equations on time scales to hamiltonian systems on time scales

local energy statistics in disordered systems a proof of the local rem conjecture recently bauke and mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model here we give necessary conditions for this hypothesis to be true which we show to be satisfied in wide classes of examples short range spin glasses and mean field spin glasses of the sk type we also show that under certain conditions the conjecture holds even if energy levels that grow moderately with the volume of the system are considered

r matrix quantization of the elliptic ruijsenaars schneider model it is shown that the classical l operator algebra of the elliptic ruijsenaars schneider model can be realized as a subalgebra of the algebra of functions on the cotangent bundle over the centrally extended current group in two dimensions it is governed by two dynamic and bar r matrices satisfying a closed system of equations the corresponding quantum r and bar r matrices are found as solutions to quantum analogues of these equations we present the quantum l operator algebra and show that the system of equations for r and bar r arises as the compatibility condition for this algebra it turns out that the r matrix is twist equivalent to the felder elliptic rf matrix with bar r playing the role of the twist the simplest representation of the quantum l operator algebra corresponding to the elliptic ruijsenaars schneider model is obtained the connection of the quantum l operator algebra to the fundamental relation rb ll llrb with the belavin elliptic r matrix is established as a by product of our construction we find a new n parameter elliptic solution to the classical yang baxter equation

approximating crossed symmetric solutions of nonlinear dynamic equations via quasilinearization abstract crossed symmetric solutions of nonlinear boundary value dynamic problems play an important role in many applications in particular in adaptive algorithm designs this article is devoted to the continuation of our investigation on second order nonlinear companion dynamic boundary value problems on time scales monotonically convergent upper and lower solutions of the problems and their quasilinear approximations are investigated it is shown that under proper smoothness constraints the iterative sequences constructed not only converge to the analytic solutions of the desired companion problems monotonically but also preserve important crossed symmetry properties the quasilinearization offers an efficient way in the solution approximation computational examples are given to illustrate our results

the lax pairs for elliptic cn and bcn ruijsenaars schneider models and their spectral curves we study the elliptic c n and bcn ruijsenaars schneider models which are elliptic generalization of systems given in previous paper by the present authors chen j math phys 41 8132 2000 the lax pairs for these models are constructed by hamiltonian reduction technology we show that the spectral curves can be parametrized by the involutive integrals of motion for these models taking nonrelativistic limit and scaling limit we verify that they lead to the systems corresponding to calogero moser and toda types c 2001 american institute of physics

multiple positive solutions of some boundary value problems abstract we study the existence of multiple positive solutions of the equations u t u subject to linear boundary conditions we show that there are at least two positive solutions if t u is superlinear at one end point zero or infinity and sublinear at the other applications of these results are provided to yield multiple positive solutions of some elliptic boundary value problems on an annulus

stability criteria for set dynamic equations on time scales very recently a new theory known as set dynamic equations on time scales has been built in this paper notions of stability for the solutions of set dynamic equations on time scales using lyapunov like functions are considered criteria for the equistability equiasymptotic stability uniform and uniform asymptotic stability are developed

existence of solutions for a two point boundary value problem on time scales let t be a time scale let f 0 s 1 xr 2 r be continuous we study the existence of solutions for the nonlinear two point boundary value problems on time scalex t f t x t x t email protected 0 1 x 0 0 x s 1 0 we do not need any growth restrictions on f

triple positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales in this paper we present sufficient conditions for the existence of at least three positive solutions of three point boundary value problems for p laplacian dynamic equations on a time scale to show our main results we apply a new fixed point theorem due to avery and peterson three positive fixed points of nonlinear operators on ordered banach spaces comput math appl 42 2001 313 322

universality of the rem for dynamics of mean field spin glasses we consider a version of glauber dynamics for a p spin sherrington kirkpatrick model of a spin glass that can be seen as a time change of simple random walk on the n dimensional hypercube we show that for all p 3 and all inverse temperatures 0 there exists a constant p 0 such that for all exponential time scales exp n with p the properly rescaled clock process time change process converges to an stable subordinator where 2 1 moreover the dynamics exhibits aging at these time scales with a time time correlation function converging to the arcsine law of this stable subordinator in other words up to rescaling on these time scales that are shorter than the equilibration time of the system the dynamics of p spin models ages in the same way as the rem and by extension bouchaud s rem like trap model confirming the latter as a universal aging mechanism for a wide range of systems the sk model the case p 2 seems to belong to a different universality class

the existence of countably many positive solutions for nonlinear singular m point boundary value problems on the half line in this paper by introducing a new operator improving and generating a p laplace operator for some p 1 we study the existence of countably many positive solutions for nonlinear boundary value problems on the half line f u a t f u t 0 0r is the increasing homeomorphism and positive homomorphism and f 0 0 we show the sufficient conditions for the existence of countably many positive solutions by using the fixed point index theory and a new fixed point theorem in cones

three positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales abstract in this paper existence criteria of three positive solutions to the following boundary value problems for p laplacian dynamic equations on time scales p u t a t f u t 0 t 0 t t u 0 0 u t b 1 u 0 or u 0 b 0 u 0 u t 0 are established by using the well known leggett williams fixed point theorem an example is also given to illustrate the main results

quantum dynamical r matrices and quantum frobenius group we propose an algebraic scheme for quantizing the rational ruijsenaars schneider model in the r matrix formalism we introduce a special parametrization of the cotangent bundle over in new variables the standard symplectic structure is described by a classical frobenius r matrix and by a new dynamical matrix quantizing both of them we find the quantum l operator algebra and construct its particular representation corresponding to the rational ruijsenaars schneider system using the dual parametrization of the cotangent bundle we also derive the algebra for the l operator of the hyperbolic calogero moser system

on the existence of positive solutions for nonlinear differential equations with periodic boundary conditions we prove the existence of positive solutions of second order nonlinear differential equations on a finite interval with periodic boundary conditions and give upper and lower bounds for these positive solutions obtained results yield positive periodic solutions of the equation on the whole real axis provided that the coefficients are periodic

complete integrability of relativistic calogero moser systems and elliptic function identities poincare invariant generalizations of the galilei invariant calogero moser a particle systems are studied a quantization of the classical integrals s1 sn is presented such that the operators si9 sn mutually commute as a corollary it follows that si9 9sn poisson commute these results hinge on functional equations satisfied by the weierstrass and 0 functions a generalized cauchy identity involving the function leads to an n x n matrix l whose symmetric functions are proportional to sl5 9sn

universality and extremal aging for dynamics of spin glasses on subexponential time scales we consider random hopping time rht dynamics of the sherrington kirkpatrick sk model and p spin models of spin glasses for any of these models and for any inverse temperature 0 we prove that on time scales that are subexponential in the dimension the properly scaled clock process time change process of the dynamics converges to an extremal process moreover on these time scales the system exhibits aging like behavior which we call extremal aging in other words the dynamics of these models ages as the random energy model rem does hence by extension this confirms bouchaud s rem like trap model as a universal aging mechanism for a wide range of systems that for the first time includes the sk model 2011 wiley periodicals inc

glauber dynamics of the random energy model i metastable motion on the extreme states we investigate the long time behavior of the glauber dynamics for the random energy model below the critical temperature we give very precise estimates on the motion of the process to and between the states of extremal energies we show that when disregarding time the consecutive steps of the process on these states are governed by a markov chain that jumps uniformly on all possible states the mean times of these jumps are also computed very precisely and are seen to be asymptotically independent of the terminal point a first indicator of aging is the observation that the mean time of arrival in the set of states that have waiting times of order t is itself of order t the estimates proven in this paper will furnish crucial input for a follow up paper where aging is analysed in full detail

positive solutions for nonlinear three point boundary value problems on time scales abstract let t be a time scale such that 0 t t consider the following three point boundary value problem on time scales u t a t f t u t 0 t 0 t u 0 u 0 0 u u t where 0 0 0 t 0 t and d t 1 0 by using fixed point theorems in cones some new and general results are obtained for the existence of single and multiple positive solutions of the above problem in particular our criteria generalize and improve some known results

phase transition for the speed of the biased random walk on the supercritical percolation cluster we prove the sharpness of the phase transition for the speed in biased random walk on the supercritical percolation cluster on d that is for each d 2 and for any supercritical parameter p pc we prove the existence of a critical strength for the bias such that below this value the speed is positive and above the value it is zero we identify the value of the critical bias explicitly and in the subballistic regime we find the polynomial order of the distance moved by the particle each of these conclusions is obtained by investigating the geometry of the traps that are most effective at delaying the walk a key element in proving our results is to understand that on large scales the particle trajectory is essentially one dimensional we prove such a dynamic renormalization statement in a much stronger form than was previously known 2013 wiley periodicals inc

conserved quantities for hamiltonian systems on time scales abstract conserved quantities for hamiltonian systems on time scales with nabla derivatives and delta derivatives are presented first hamilton principle on time scales with nabla derivatives is established and hamilton canonical equation with nabla derivatives is obtained second noether identity and noether theorem for hamiltonian systems with nabla derivatives are achieved third hamilton canonical equation with delta derivatives noether identity and noether theorem for hamiltonian systems with delta derivatives are gotten through duality principle on the basis of the corresponding results with nabla derivatives fourth some special cases of noether identity and noether theorem are given and finally two examples are devoted to illustrate the methods and results

positive solutions to semi positone second order three point problems on time scales using a fixed point theorem of generalized cone expansion and compression we establish the existence of at least two positive solutions for the nonlinear semi positone three point boundary value problem on time scales u d t email protected t u t 0 u a 0 au h u t here email protected a t t where t is a time scale a 0 email protected a r t t a h a 0 belongs to a certain interval these results are new for difference equations as well as for general time scales an example is provided for differential difference and q difference equations

multi point boundary value problems on time scales at resonance abstract we study the nonlinear second order differential equation on a time scale u t f t u t u t e t t 0 1 t subject to the multi point boundary conditions u 0 0 u 1 i 1 m i u i and u 0 0 u 1 i 1 m i u i where t is a time scale such that 0 1 t i 0 1 t i 1 m and f is a continuous function satisfying a caratheodory type growth condition and e is a lebesgue integrable function our existence results are obtained by applying a coincidence degree theorem due to mawhin

higher even order convergence and coupled solutions for second order boundary value problems on time scales in this paper for a second order boundary value problem on time scales a method of generalized quasilinearization under coupled upper and lower solutions is discussed an attempt for the method is to establish sufficient conditions for generating monotone iterative schemes whose elements converge rapidly to the unique solution of the given problem furthermore the convergence is of order k k 2 which is even finally two examples are provided to illustrate our results

existence of weak solutions of two point boundary value problems for second order dynamic equations on time scales abstract in this paper by using critical point theory we establish the existence of weak solutions of the two point boundary value problem for a second order dynamic equation on an arbitrary time scale t so that the well known case of differential dynamic systems t r and the recently developed case of discrete dynamic systems t z are unified to the best of our knowledge this is the first time that boundary value problems of dynamic equations on time scales have been dealt with by using critical point theory

existence of positive solutions of nonlinear m point bvp for an increasing homeomorphism and positive homomorphism on time scales in this paper we will consider the following multipoint boundary value problem for the following second order dynamic equations on time scales f u d a t f t u t 0 t 0 t u 0 i 1m 2a iu x i f u d t i 1m 2b i f u d x i where f r r is an increasing homeomorphism and positive homomorphism and f 0 0 by using fixed point theorems we obtain an existence theorem of positive solutions for the above boundary value problem which includes and improve some related results in the relevant literature as an application an example to demonstrate our results is given

convergence to extremal processes in random environments and extremal ageing in sk models this paper extends recent results on ageing in mean field spin glasses on short time scales obtained by ben arous and gun commun pure appl math 65 77 127 2012 in law with respect to the environment to results that hold almost surely respectively in probability with respect to the environment it is based on the methods put forward in gayrard in aging in reversible dynamics of disordered systems ii emergence of the arcsine law in the random hopping time dynamics of the rem 2010 electron j probab 17 58 1 33 2012 and naturally complements bovier and gayrard in ann probab 2012

elliptic ruijsenaars schneider model via the poisson reduction of the affine heisenberg double it is shown that the elliptic ruijsenaars schneider model can be obtained from the affine heisenberg double by means of the poisson reduction procedure the dynamical r matrix naturally appears in the construction

positive solutions to boundary value problems with nonlinear boundary conditions abstract in this paper we consider the boundary value problem y t f t y t subject to the boundary conditions y a y and y 2 b 0 in this setting c rd a 2 b t r r is a continuous functional which represents a nonlinear nonlocal boundary condition by imposing sufficient structure on and the nonlinearity f we deduce the existence of at least one positive solution to this problem the novelty in our setting lies in the fact that may be strictly nonpositive for some y 0 our results are achieved by appealing to the krasnosel ski fixed point theorem we conclude with several examples illustrating our results and the generalizations that they afford

existence of solution and positive solution of bvp for nonlinear third order dynamic equation abstract in this paper we are concerned with the following third order two point boundary value problem on time scale t u t f t u t u t 0 t a b u a a u 2 b b u a c some existence criteria of solution and positive solution are established by using leray schauder fixed point theorem and our main conditions are local an example is also included to illustrate the importance of the results obtained

on green s functions and positive solutions for boundary value problems on time scales in this paper we offer a form of self adjoint differential equations on time scales so that the associated green s function is found symmetric in the usual sense for this purpose together with the delta derivative we employ the nabla derivative as well we introduce the concepts of lebesgue delta and nabla integrals on time scales next sign properties of the green s function are investigated and existence results for positive solutions of nonlinear boundary value problems are established upper and lower bounds for these positive solutions also are given

solutions for higher order dynamic equations on time scales let t be a time scale we study the existence of positive solutions for the nonlinear four point singular boundary value problem with higher order p laplacian dynamic equations on time scales by using the fixed point index theory the existence of positive solution and many positive solutions for nonlinear four point singular boundary value problem with p laplacian operator are obtained

existence of two solutions of m point boundary value problem for second order dynamic equations on time scales in this paper by means of a new twin fixed point theorem in a cone the existence of at least two positive solutions of m point boundary value problem for second order dynamic equations on time scales is considered

phase spaces and periodic solutions of set functional dynamic equations with infinite delay abstract very recently a new theory known as set dynamic equations on time scales has been built in this paper a phase space is built for set functional dynamic equations with infinite delay on time scales and sufficient criteria are established for the existence of periodic solutions of such equations which generalize and incorporate as special cases some known results for set differential equations and for set difference equations when the time scale is the real number set or the integer set respectively moreover for differential inclusions and difference inclusions if the variable under consideration is a single valued mapping our results show that one can unify the study of some continuous or discrete problems in the sense of set dynamic equations on general time scales

twin solutions of boundary value problems for differential equations on measure chains a new twin fixed point theorem is applied to obtain the existence of at least two positive solutions for the right focal boundary value problem on a measure chain t y t f y t 0 t 0 1 t y 0 y 1 0

positive solutions of nonlinear m point bvp for an increasing homeomorphism and homomorphism with sign changing nonlinearity on time scales in this paper several existence theorems of positive solutions are established for nonlinear m point boundary value problem for the following dynamic equations on time scales f u d a t f t u t 0 t 0 t f u d 0 i 1m 2a i f u d x i u t i 1m 2b iu x i where f r r is an increasing homeomorphism and homomorphism and f 0 0 the nonlinear term f may change sign as an application an example to demonstrate our results is given

the dn ruijsenaars schneider model the lax pair of the ruijsenaars schneider model with interaction potential of trigonometric type based on dn lie algebra is presented we give a general form for the lax pair and prove partial results for small n liouville integrability of the corresponding system follows a series of involutive hamiltonians generated by the characteristic polynomial of the lax matrix the rational case appears as a natural degeneration and the non relativistic limit exactly leads to the well known calogero moser system associated with dn lie algebra

the quasilinearization method for boundary value problems on time scales abstract in this paper we apply the method of quasilinearization to a family of boundary value problems for second order dynamic equations y q t y h t y on time scales the results include a variety of possible cases when h is either convex or a splitting of convex and concave parts and whether lower and upper solutions are of natural form or of natural coupled form

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

a new model in the calogero ruijsenaars family hamiltonian reduction is used to project a trivially integrable system on the heisenberg double of su n n to obtain a system of ruijsenaars type on a suitable quotient space this system possesses bcn symmetry and is shown to be equivalent to the standard three parameter bcn hyperbolic sutherland model in the cotangent bundle limit

self duality and scattering map for the hyperbolic van diejen systems with two coupling parameters with an appendix by s ruijsenaars in this paper we construct global action angle variables for a certain two parameter family of hyperbolic van diejen systems following ruijsenaars ideas on the translation invariant models the proposed action angle variables come from a thorough analysis of the commutation relation obeyed by the lax matrix whereas the proof of their canonicity is based on the study of the scattering theory as a consequence we show that the van diejen system of our interest is self dual with a factorized scattering map also in an appendix by s ruijsenaars a novel proof of the spectral asymptotics of certain exponential type matrix flows is presented this result is of crucial importance in our scattering theoretical analysis

elliptic ruijsenaars schneider model from the cotangent bundle over the two dimensional current group it is shown that the elliptic ruijsenaars schneider model can be obtained from the cotangent bundle over the two dimensional current group by means of the hamiltonian reduction procedure

on a disconjugacy criterion for second order dynamic equations on time scales in this paper a sufficient condition for disconjugacy of second order differential equations on time scales is given for this purpose a mean value result on time scales is employed

notes on the diamond α dynamic derivative on time scales abstract various dynamic derivative formulae have been proposed in the development of a time scales calculus with the goal of unifying continuous and discrete analysis recent discussions of combined dynamic derivatives in particular the derivative defined as a linear combination of the and the derivatives have promised improved approximation formulae for computational applications this paper presents an equivalent definition of the functions without reference to the existing and derivatives examines the status of the as a dynamic derivative and its properties relative to the and derivatives and compares data obtained using the various dynamic derivatives as approximation formulae in computational experiments a integral case is investigated

aging of the metropolis dynamics on the random energy model we study the metropolis dynamics of the simplest mean field spin glass model the random energy model we show that this dynamics exhibits aging by showing that the properly rescaled time change process between the metropolis dynamics and a suitably chosen fast markov chain converges in distribution to a stable subordinator the rescaling might depend on the realization of the environment but we show that its exponential growth rate is deterministic

multiple positive solutions for functional dynamic equations on time scales in this paper we study the following functional dynamic equation on time scales f u d t a t f u t u m t 0 email protected 0 t t u t email protected t email protected r 0 t u 0 b 0 u d 0 0 u d t 0 where f r r is an increasing homeomorphism and a positive homomorphism and f 0 0 by using the well known leggett williams fixed point theorem existence criteria for multiple positive solutions are established an example is also given to illustrate the main results

triple positive solutions of m point bvps for p laplacian dynamic equations on time scales abstract this paper is concerned with the existence of positive solutions of p laplacian dynamic equation p u t a 1 t f u t 0 subject to boundary conditions u 0 b 0 i 1 m 2 a i u i 0 u t 0 or u 0 0 u t b 1 i 1 m 2 b i u i 0 where p v v p 2 v with p 1 by using the five functionals fixed point theorem we prove that the boundary value problem has at least three positive solutions as an application an example is given to illustrate the result

the method of quasilinearization and dynamic equations on compact measure chains the method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand in this paper we show the method applies to a family of two point boundary value problems for a dynamic equation on a compact measure chain

glauber dynamics of the random energy model ii aging below the critical temperature we investigate the long time behavior of the glauber dynamics for the ran dom energy model below the critical temperature we establish that for a suitably chosen timescale that diverges with the size of the system one can prove that a natural auto correlation function exhibits aging moreover we show that the long time asymptotics of this function coincide with those of the so called rem like trap model proposed by bouchaud and dean our results rely on very precise estimates on the distribution of transition times of the process between different states of extremely low energy

sturm liouville eigenvalue problems on time scales for sturm liouville eigenvalue problems on time scales with separated boundary conditions we give an oscillation theorem and establish rayleigh s principle our results not only unifly the corresponding theories for differential and difference equations but are also new in the discrete case

higher order dynamic equations on measure chains wronskians disconjugacy and interpolating families of functions this paper introduces generalized zeros and hence disconjugacy of nth order linear dynamic equations which cover simultaneously as special cases among others both differential equations and difference equations we also define markov fekete and descartes interpolating systems of functions the main result of this paper states that disconjugacy is equivalent to the existence of any of the above interpolating systems of solutions and that it is also equivalent to a certain factorization representation of the operator the results in this paper unify the corresponding theories of disconjugacy for nth order linear ordinary differential equations and for nth order linear difference equations

several sufficient conditions of solvability for a nonlinear higher order three point boundary value problem on time scales abstract in this paper a nonlinear higher order three point boundary value problem on time scales is considered under certain growth conditions on the nonlinearity several sufficient conditions for the existence of nontrivial solution are obtained by using leray schauder nonlinear alternative as an application some examples to demonstrate our results are given

the non dynamical r matrix structure for the elliptic calogero moser model in this paper we construct a new lax operator for the elliptic calogero moser model with general from the classical dynamical twisting in which the corresponding r matrix is purely numerical non dynamic the non dynamical r matrix structure of this lax operator is obtained which is the elliptic symmetric r matrix

aging in metropolis dynamics of the rem a proof we consider metropolis dynamics of the random energy model we prove that the classical two time correlation function that allows one to establish aging converges almost surely to the arcsine law distribution function as predicted in the physics literature in the optimal domain of the time scale and temperature parameters where this result can be expected to hold to do this we link the two time correlation function to a certain continuous time clock process which after proper rescaling is proven to converge to a stable subordinator almost surely in the random environment and in the fine j 1 topology of skorohod this fine topology then enables us to deduce from the arcsine law for stable subordinators the asymptotic behavior of the two time correlation function that characterizes aging