moments of the position of the maximum for gue characteristic polynomials and for log correlated gaussian processes we study three instances of log correlated processes on the interval the logarithm of the gaussian unitary ensemble gue characteristic polynomial the gaussian log correlated potential in presence of edge charges and the fractional brownian motion with hurst index h rightarrow 0 fbm0 in previous collaborations we obtained the probability distribution function pdf of the value of the global minimum equivalently maximum for the first two processes using the freezing duality conjecture fdc here we study the pdf of the position of the maximum x m through its moments using replica this requires calculating moments of the density of eigenvalues in the beta jacobi ensemble using jack polynomials we obtain an exact and explicit expression for both positive and negative integer moments for arbitrary beta 0 and positive integer n in terms of sums over partitions for positive moments this expression agrees with a very recent independent derivation by mezzadri and reynolds we check our results against a contour integral formula derived recently by borodin and gorin presented in the appendix 1 from these authors the duality necessary for the fdc to work is proved and on our expressions found to correspond to exchange of partitions with their dual performing the limit n rightarrow 0 and to negative dyson index beta rightarrow 2 we obtain the moments of x m and give explicit expressions for the lowest ones numerical checks for the gue polynomials performed independently by n simm indicate encouraging agreement some results are also obtained for moments in laguerre hermite gaussian as well as circular and related ensembles the correlations of the position and the value of the field at the minimum are also analyzed

modified r matrix and separation of variables for the modified korteweg de vries mkdv hierarchy abstract in this article it is first given that a lax representation in terms of 2 2 matrices for the completeey integrable finite dimensional hamiltonian system cifhs h produced through the nonlinearization procedure for the mkdv hierarchy and then an associated non dynamical modified r matrix is constructed by making use of this r matrix and matrix trace equality a set of finite dimensional involutive functions fm m 0 1 f0 h which guarantees the integrability of hamiltonian systems h and the lax representations in terms of 2 2 matrices for the whole hamiltonian hierarchies fm m 0 1 are obtained moreover the involutive solutions of the mkdv hierarchy are given finally it is found that the hamiltonian jacobi equation for the hamiltonian system h can be separable under a group of new coordinates introduced by the 2 2 lax matrix

the c1 property of carrying simplices for a class of competitive systems of odes abstract in this paper we consider a class of dissipative competitive systems of odes on the nonneptive orthant c we assume among others that the system restricted to any face of c is weakly persistent it is proved that the carrying simplex is a c1 manifold with corners in the proof we analyze the asymptotic behavior of the linearization of the original system

limit cycles for competitor competitor mutualist lotka volterra systems abstract it is known that a limit cycle or periodic coexistence can occur in a competitor competitor mutualist lotka volterra system x 1 x 1 r 1 a 11 x 1 a 12 x 2 a 13 x 3 x 2 x 2 r 2 a 21 x 1 a 22 x 2 a 23 x 3 x 3 x 3 r 3 a 31 x 1 a 32 x 2 a 33 x 3 where r i a i j are positive real constants x liang j jiang the dynamical behavior of type k competitive kolmogorov systems and its applications to 3 dimensional type k competitive lotka volterra systems nonlinearity 16 2003 785 801 in this paper we shall construct an example with at least two limit cycles and furthermore we will show that the number of periodic orbits and hence a fortiori of limit cycles is finite it is also shown that contrary to three dimensional competitive lotka volterra systems nontrivial periodic coexistence does occur even if none of the three species can resist invasion from either of the others in this case new amenable conditions are given on the coefficients under which the system has no nontrivial periodic orbits these conditions imply that the positive equilibrium if it exists is globally asymptotically stable

full counting statistics of chaotic cavities from classical action correlations we present a trajectory based semiclassical calculation of the full counting statistics of quantum transport through chaotic cavities in the regime of many open channels our method to obtain the mth moment of the density of transmission eigenvalues requires two correlated sets of m classical trajectories therefore generalizing previous works on conductance and shot noise the semiclassical results agree for all values of m with the corresponding predictions from random matrix theory

carrying simplices in nonautonomous and random competitive kolmogorov systems abstract the purpose of this paper is to investigate the asymptotic behavior of positive solutions of nonautonomous and random competitive kolmogorov systems via the skew product flows approach it is shown that there exists an unordered carrying simplex which attracts all nontrivial positive orbits of the skew product flow associated with a nonautonomous random competitive kolmogorov system

a hypergeometric generating function approach to charge counting statistics in ballistic chaotic cavities we apply the method of multivariate hypergeometric generating function to study cumulants of the charge counting statistics ccs of a ballistic chaotic cavity coupled ideally to two electron reservoirs via perfect conducting leads with an arbitrary number of scattering channels the underlying chaotic dynamics causes each cumulant of ccs denoted charge transfer cumulant ctc to behave like a random variable which we describe via exact calculations of its statistical moments and cumulants besides reproducing several known results of the literature for the first few statistical cumulants of conductance and shot noise power which are the first and second ctc respectively we obtain new exact results for the first four statistical cumulants of the third and fourth ctc all analytical results are supported by numerical simulations of the circular ensembles

the trace identity a powerful tool for constructing the hamiltonian structure of integrable systems a new approach to hamiltonian structures of integrable systems is proposed by making use of a trace identity for a variety of isospectral problems that can be unified to one model x u it is shown that both the related hierarchy of evolution equations and the hamiltonian structure can be obtained from the same solution of the equation vx u v

convergence to equilibrium on invariant d hypersurfaces for strongly increasing discrete time semigroups abstract convergence to equilibrium for every positive semi orbit of strongly increasing discrete time semigroups on strongly ordered spaces is proved the domain of the semigroup is assumed to be slightly more general than a closed order interval in a strongly ordered banach space which is continuously imbedded into a banach lattice the semigroup is assumed to be order compact and every positive semi orbit is assumed to be order bounded the crucial hypothesis is the ljapunov stability of all equilibria it is also proved that the set of equilibria is a simply ordered arc the key tools are invariant d hypersurfaces

transmission eigenvalue densities and moments in chaotic cavities from random matrix theory we point out that the transmission eigenvalue density and higher order correlation functions in chaotic cavities for an arbitrary number of incoming and outgoing leads n1 n 2 are analytically known from the jacobi ensemble of random matrix theory using this result and a simple linear statistic we give an exact and non perturbative expression for moments of the form m for m n1 n2 1 and 2 thus improving the existing results in the literature secondly we offer an independent derivation of the average density and higher order correlation function for 2 4 which does not make use of the orthogonal polynomials technique this result may be relevant for an efficient numerical implementation avoiding determinants pacs numbers 73 23 b 73 50 td 05 45 mt 73 63 kv

on invariant hypersurfaces of strongly monotone maps forck k 1 strongly monotone discrete time dynamical systems we present simple criteria which ensure that nonmonotone invariant manifolds areck

combinatorial theory of the semiclassical evaluation of transport moments i equivalence with the random matrix approach to study electronic transport through chaotic quantum dots there are two main theoretical approachs one involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging the other treats the transport in the semiclassical approximation and studies correlations among sets of classical trajectories there are established evaluation procedures within the semiclassical evaluation that for several linear and non linear transport moments to which they were applied have always resulted in the agreement with random matrix predictions we prove that this agreement is universal any semiclassical evaluation within the accepted procedures is equivalent to the evaluation within random matrix theory the equivalence is shown by developing a combinatorial interpretation of the trajectory sets as ribbon graphs maps with certain properties and exhibiting systematic cancellations among their contributions remaining trajectory sets can be identified with primitive palindromic factorisations whose number gives the coefficients in the corresponding expansion of the moments of random matrices the equivalence is proved for systems with and without time reversal symmetry

periodic solutions of the kdv equation in this paper we construct a large family of special solutions of the kdv equation which are periodic in x and almost periodic in t these solutions lie on n dimensional tori very likely they are dense among all solutions the special solutions are characterized variationally they minimize fn u subject to the constraints fj u aj j 1 n 1 here fj denote the remarkable sequence of conserved functionals discovered by kruskal and zabusky the above minimum problem was originally suggested by them in exploring the manifold of solutions of this minimum problem we make essential use of gardner s discovery that these functionals are in involution with respect to a suitable poisson bracket gardner greene kruskal and miura have shown that the eigenvalues of the schrodinger operator are conserved functionals if the potential is a function of t and satisfies the kdv equation in section 6 a new set of conserved quantities is constructed which serve as a link between the eigenvalues of the schrodinger operator and the fj another result in section 6 is a slight sharpening of an earlier result of the author and j moser for the special solutions constructed above all but 2n 1 eigenvalues of the schrodinger operator are double the simplest class of special solutions n 1 are cnoidal waves in an appendix m hyman describes the results of computing numerically the next simplest case n 2 these calculations show that the shape of these solutions recurs exactly after a finite time in a shifted position the theory verifies this fact

neumann type integrable reduction for nonlinear evolution equations in 1 1 and 2 1 dimensions a family of new neumann type systems is given in view of the nonlinearization technique realizing the variable separation of the modified jaulent miodek hierarchy and a new coupled modified kadomtsev petviashvili equation on the symplectic submanifold tsn 1 by two casimir functions and a special solution of the lenard eigenvalue equation we deduce the lax moser matrix of the neumann type systems that yields integrals of motion and the constrained hamiltonians whose vector fields are tangent to tsn 1 based on the dirac poisson bracket and a lax equation on tsn 1 a new systematic way is proposed to prove the liouville integrability of a family of neumann type systems synchronously the dirac poisson bracket and the generating function are used to reveal the explicit relation between infinite dimensional integrable systems and neumann type systems and then we point out that compatible solutions of neumann type systems yield the finite parametric solutions of 1 1 and 2 1 dimensional integrable nonlinear

quasi periodic solutions for some 2 1 dimensional integrable models generated by the jaulent miodek hierarchy some 2 1 dimensional integrable models including the modified kadomtsev petviashvili equation generated by the jaulent miodek hierarchy are investigated with the help of the jaulent miodek eigenvalue problem these 2 1 dimensional integrable models are separated into compatible hamiltonian systems of ordinary differential equations using the generating function flow method the involutivity and the functional independence of the integrals are proved the abel jacobi coordinates are introduced from which the quasi periodic solutions for these 2 1 dimensional integrable models are derived by resorting to the riemann theta functions pacs number 0230j

lax representation r matrix method and separation of variables for the neumann type restricted flow the r matrix method and the method of separation of variables for restricted flows with neumann constraints are considered restricted jaulent miodek flows are taken as illustrative examples lax representations are obtained from the adjoint representation of the corresponding soliton hierarchy the r matrix formula based on this lax representation is derived and the separation of variables for the hamilton jacobi equation are performed

nonlinear random matrix statistics symmetric functions and hyperdeterminants nonlinear statistics i e statistics of permanents on the eigenvalues of invariant random matrix models are considered for the three dyson s symmetry classes 1 2 4 general formulas in terms of hyperdeterminants are found for 2 for specific cases and all s more computationally efficient results are obtained based on symmetric functions expansions as an application we consider the case of quantum transport in chaotic cavities extending results from savin et al 2008 phys rev b 77 125332

statistics of quantum transport in weakly nonideal chaotic cavities we consider statistics of electronic transport in chaotic cavities where time reversal symmetry is broken and one of the leads is weakly nonideal that is it contains tunnel barriers characterized by tunneling probabilities i using symmetric function expansions and a generalized selberg integral we develop a systematic perturbation theory in 1 i valid for an arbitrary number of channels and obtain explicit formulas up to second order for the average and variance of the conductance and for the average shot noise higher moments of the conductance are considered to leading order

c neumann and bargmann systems associated with the coupled kdv soliton hierarchy under two different constraints between the potentials and the eigenfunctions the eigenvalue problem associated with the coupled kdv hierarchy is nonlinearised to be a completely integrable c neumann system on the tangent bundle of sphere tsn 1 with the hamiltonian h 1 2 lambda q p 1 2 q q p p 1 2 q p 2 1 2 q p lambda p p and a completely integrable bargmann system r2n dpdq h with the hamiltonian h 1 2 lambda q p 1 2 p p q p 1 2 q q respectively the involutive solutions of the coupled kdv equation associated with the two systems are given

smoothness of the carrying simplex for discrete time competitive dynamical systems a characterization of neat embedding abstract the paper is concerned with the question of smoothness of the carrying simplex s for a discrete time dissipative competitive dynamical system we give a necessary and sufficient criterion for s being a c 1 submanifold with corners neatly embedded in the nonnegative orthant formulated in terms of inequalities between lyapunov exponents for ergodic measures supported on the boundary of the orthant this completes one thread of investigation occasioned by a question posed by m w hirsch in 1988 besides amenable conditions are presented to guarantee the c r r 1 smoothness of s in the time periodic competitive kolmogorov systems of odes examples are also presented one in which s is of class c 1 but not neatly embedded the other in which s is not of class c 1

stability and convergence in strongly monotone dynamical systems soit x un systeme dynamique x est un espace topologique et le flot t t r est une famille d applications continues de sous ensembles ouverts de x dans x on decrit qualitativement le comportement asymptotique quand t des trajectoires t t x pour les etats initiaux x dans le cas de systemes ayant un principe de comparaison fort

the finite band solution of the jaulent miodek equation a method to construct the finite band solution to the soliton equation is presented we take the jaulent miodek equation as an example with the use of the nonlinearization of lax pair the jaulent miodek equation is decomposed into two finite dimensional integrable systems whose properties are studied from the view of an r matrix then through solving these finite dimensional integrable systems the finite band solution of the jaulent miodek equation is obtained

large n expansions for the laguerre and jacobi β ensembles from the loop equations the ensembles of random matrix theory with classical weights have many special properties one is that the loop equations specifying the resolvent and corresponding multipoint correlators permit a derivation at the general order of the correlator via aomoto s method from the theory of the selberg integral we use aomoto s method to derive the full hierarchy of loop equations for laguerre and jacobi ensembles and use these to systematically construct the explicit form of the 1 n expansion at low orders this allows us to give the explicit form of corrections to the global density and allows various moments to be computed complementing results available in the literature motivated by problems in quantum transport

new integrable hierarchy its parametric solutions cuspons one peak solitons and m w shape peak solitons in this paper we propose a new completely integrable hierarchy particularly in the hierarchy we draw two new soliton equations 1 mt 12 1 m2 xxx 12 1 m2 x 2 mt mx u2 ux2 2m2ux 0 m u uxx the first one is the second positive member in the hierarchy while the second one is the second negative member in the hierarchy both equations can be derived from the two dimensional euler equation by using the approximation procedure all equations in the hierarchy are proven to have bi hamiltonian operators and lax pairs through solving a crucial matrix equation moreover we develop parametric solutions of the entire hierarchy through constructing two kinds of constraints one is for all negative members of the hierarchy on a symplectic submanifold and the other is for all positive members in the standard symplectic space the most interesting things are both equations possess new type of peaked solitons continuous and piecewise smooth w m shape peak soliton solutions in addition we find new cusp solit

quantum conductance problems and the jacobi ensemble in one dimensional transport problems the scattering matrix s is decomposed into a block structure corresponding to reflection and transmission matrices at the two ends for s a random unitary matrix the singular value probability distribution function of these blocks is calculated the same is done when s is constrained to be symmetric or to be self dual quaternion real as is relevant in the presence of particular time reversal symmetries the latter results are shown to be very similar to those obtained under the unphysical assumption that s has real elements or has real quaternion elements respectively three methods are used metric forms a variant of the ingham seigel matrix integral and a theorem specifying the jacobi random matrix ensemble in terms of wishart distributed matrices

linearization and invariant manifolds on the carrying simplex for competitive maps abstract a result due to m w hirsch states that most competitive maps admit a carrying simplex i e an invariant hypersurface of codimension one which attracts all nontrivial orbits the common approach in the study of these maps is to focus on the dynamical behavior on the carrying simplex however this manifold is normally non smooth therefore not every tool coming from differential geometry can be applied in this paper we prove that the restriction of the map to the carrying simplex in a neighborhood of an interior fixed point is topologically conjugate to the restriction of the map to its pseudo unstable manifold by an invariant foliation this implies that the linearization techniques are applicable for studying the local dynamics of the interior fixed points on the carrying simplex we further construct the stable and unstable manifolds on the carrying simplex our results give partial responses to hirsch s problem regarding the smoothness of the carrying simplex we discuss some applications in classical models of population dynamics

factorisation of energy dependent schrodinger operators miura maps and modified systems we consider the energy dependent schrodinger operator mathbb l sum limits i 0 n lambda i varepsilon i partial 2 u i which we have previously shown to be associated with multi hamiltonian structures 2 in this paper we use an unusual form of the lax approach to derive by asingle construction the time evolutions of the eigenfunctions of mathbb l the associated hamiltonian operators and the hamiltonian functionals we then generalise the well known factorisation of standard lax operators to the case of energy dependent operators the simple product of linear factors is replaced by a dependent quadratic form we thus generalise the resulting construction of miura maps and modified equations we show that for some of our systems there exists a sequence ofn such modifications therth modification possessing n r 1 hamiltonian structures