boundary layer analysis in the semiclassical limit of a quantum drift diffusion model abstract we study a singularly perturbed elliptic second order system in one space variable as it appears in a stationary quantum drift diffusion model of a semiconductor we prove the existence of solutions and their uniqueness as minimizers of a certain functional and determine rigorously the principal part of an asymptotic expansion of a boundary layer of those solutions we prove analytical estimates of the remainder terms of this asymptotic expansion and confirm by means of numerical simulations that these remainder estimates are sharp

centers and isochronous centers for generalized quintic systems in this paper we classify the centers and the isochronous centers of certain polynomial differential systems in r 2 of degree d 5 odd that in complex notation are z i z z z d 5 2 a z 5 b z 4 z c z 3 z 2 d z 2 z 3 e z z 4 f z 5 where z x i y r and a b c d e f c note that if d 5 we obtain the class of polynomial differential systems in the form of a linear system with homogeneous polynomial nonlinearities of degree 5 due to the huge computations required for computing the necessary and sufficient conditions for the characterization of the centers and isochronous centers our study uses algorithms of computational algebra based on the grobner basis theory and on modular arithmetics

cahn hilliard and thin film equations with nonlinear mobility as gradient flows in weighted wasserstein metrics abstract in this paper we establish a novel approach to proving existence of non negative weak solutions for degenerate parabolic equations of fourth order like the cahn hilliard and certain thin film equations the considered evolution equations are in the form of a gradient flow for a perturbed dirichlet energy with respect to a wasserstein like transport metric and weak solutions are obtained as curves of maximal slope our main assumption is that the mobility of the particles is a concave function of their spatial density a qualitative difference of our approach to previous ones is that essential properties of the solution non negativity conservation of the total mass and dissipation of the energy are automatically guaranteed by the construction from minimizing movements in the energy landscape

the thermal equilibrium solution of a generic bipolar quantum hydrodynamic model the thermal equilibrium state of a bipolar isothermic quantum fluid confined to a bounded domain d 1 2 or d 3 is entirely described by the particle densities n p minimizing the energy where g 1 2 are strictly convex real valued functions it is shown that this variational problem has a unique minimizer in and some regularity results are proven the semi classical limit is carried out recovering the minimizer of the limiting functional the subsequent zero space charge limit leads to extensions of the classical boundary conditions due to the lack of regularity the asymptotics can not be settled on sobolev embedding arguments the limit is carried out by means of a compactness by convexity principle

elliptic operators with unbounded drift coefficients and neumann boundary condition abstract we study the realization an of the operator a 1 2 du d in l 2 with neumann boundary condition where is a possibly unbounded convex open set in r n u is a convex unbounded function du x is the element with minimal norm in the subdifferential of u at x and dx c exp 2u x dx is a probability measure infinitesimally invariant for a we show that an is a dissipative self adjoint operator in l 2 log sobolev and poincare inequalities allow then to study smoothing properties and asymptotic behavior of the semigroup generated by an

the power spectral density of maximum entropy charge constrained sequences a limit on the absolute value of the running digital sum of a sequence is known as the charge constraint such a limit imposes a spectral null at dc the maximum entropy distribution of a charge constrained sequence is presented a closed form expression for the power spectral density of maximum entropy charge constrained sequences is given and plotted

bifurcation analysis of a generalized gause model with prey harvesting and a generalized holling response function of type iii abstract in this paper we study a generalized gause model with prey harvesting and a generalized holling response function of type iii p x m x 2 a x 2 b x 1 the goal of our study is to give the bifurcation diagram of the model for this we need to study saddle node bifurcations hopf bifurcation of codimension 1 and 2 heteroclinic bifurcation and nilpotent saddle bifurcation of codimension 2 and 3 the nilpotent saddle of codimension 3 is the organizing center for the bifurcation diagram the hopf bifurcation is studied by means of a generalized lienard system and for b 0 we discuss the potential integrability of the system the nilpotent point of multiplicity 3 occurs with an invariant line and can have a codimension up to 4 but because it occurs with an invariant line the effective highest codimension is 3 we develop normal forms in which the invariant line is preserved for studying of the nilpotent saddle bifurcation for b 0 the reversibility of the nilpotent saddle is discussed we study the type of the heteroclinic loop and its cyclicity the phase portraits of the bifurcations diagram partially conjectured via the results obtained allow us to give a biological interpretation of the behavior of the two species

weak solutions to the stationary quantum drift diffusion model abstract the existence of weak solutions to the stationary quantum drift diffusion equations for semiconductor devices is investigated the proof is based on minimization procedure of non linear functional and schauder fixed point theorem furthermore the semiclassical limit e 0 from the quantum drift diffusion model to the classical drift diffusion model is discussed

implementation of a new algorithm of computation of the poincare liapunov constants in the last years many papers giving different methods to compute the poincare liapunov constants have been published in appl math warsaw 28 2002 17 a new method to compute recursively all the poincare liapunov constants as a function of the coefficients of the system for an arbitrary analytic system which has a perturbed linear center at the origin was given and thus a theoretical answer to the classical center problem was given the method also computes the coefficients of the poincare series as a function of the same coefficients we describe its implementation in two different ways by means of a computer algebra system and an algorithm in any computer language if this second alternative is used later it is necessary to translate the results so that they can be manipulated with a computer algebra system we describe also how the availability of symbolic manipulation procedures has recently led to a significant progress in the resolution of the different problems related with the poincare liapunov constants as they are the central problems like the small amplitude limit cycles

the number of limit cycles of certain polynomial differential equations two dimensional differential systems are considered where p and q are polynomials the question of interest is the maximum possible numberof limit cycles of such systems in terms of the degree of p and q an algorithm is described for determining a so called focal basis this can be implemented on a computer estimates can then be obtained for the number of small amplitude limit cycles the technique is applied to certain cubic systems a class of examples with exactly five small amplitude limit cycles is constructed quadratic systems are also considered

on the bipolar multidimensional quantum euler poisson system the thermal equilibrium solution and semiclassical limit abstract in this paper we establish the existence of a unique thermal equilibrium solution of the bipolar multidimensional quantum euler poisson system over the whole space r 3 and obtain the relevant semiclassical limit and a combined planck debye length limit through using energy estimating methods and a fixed point theory

on singular limits of mean field equations mean field equations arise as steady state versions of convection diffusion systems where the convective field is determined by solution of a poisson equation whose right hand side is affine in the solutions of the convection diffusion equations in this paper we consider the repulsive coupling case for a system of two convection diffusion equations for general diffusivities we prove the existence of a unique solution of the mean field equation by a variational analysis of a saddle point problem usually without coercivity also we analyze the small debye length limit and prove convergence to either the so called charge neutral case or to a double obstacle problem for the limiting potential depending on the data

existence of solutions for a class of fourth order cross diffusion systems of gradient flow type abstract this article is concerned with the existence and the long time behavior of weak solutions to certain coupled systems of fourth order degenerate parabolic equations of gradient flow type the underlying metric is a wasserstein like transportation distance for vector valued functions with nonlinear mobilities in each component under the hypothesis of flat convexity of the driving free energy functional weak solutions are constructed by means of the variational minimizing movement scheme for metric gradient flows the essential regularity estimates are derived by variational methods

from a large deviations principle to the wasserstein gradient flow a new micro macro passage we study the connection between a system of many independent brownian particles on one hand and the deterministic diffusion equation on the other for a fixed time step h 0 a large deviations rate functional j h characterizes the behaviour of the particle system at t h in terms of the initial distribution at t 0 for the diffusion equation a single step in the time discretized entropy wasserstein gradient flow is characterized by the minimization of a functional k h we establish a new connection between these systems by proving that j h and k h are equal up to second order in h as h 0 this result gives a microscopic explanation of the origin of the entropy wasserstein gradient flow formulation of the diffusion equation simultaneously the limit passage presented here gives a physically natural description of the underlying particle system by describing it as an entropic gradient flow

entropy stable and entropy dissipative approximations of a fourth order quantum diffusion equation structure preserving numerical schemes for a nonlinear parabolic fourth order equation modeling the electron transport in quantum semiconductors with periodic boundary conditions are analyzed first a two step backward differentiation formula bdf semi discretization in time is investigated the scheme preserves the nonnegativity of the solution is entropy stable and dissipates a modified entropy functional the existence of a weak semi discrete solution and in a particular case its temporal second order convergence to the continuous solution is proved the proofs employ an algebraic relation which implies the g stability of the two step bdf second an implicit euler and q q step bdf discrete variational derivative method are considered this scheme which exploits the variational structure of the equation dissipates the discrete fisher information or energy numerical experiments show that the discrete relative entropies and fisher information decay even exponentially fast to zero

expressions for renyi and shannon entropies for bivariate distributions exact forms of renyi and shannon entropies are determined for 27 continuous bivariate distributions including the kotz type distribution truncated normal distribution distributions with normal and centered normal conditionals natural exponential distribution freund s exponential distribution marshall and olkin s exponential distribution exponential mixture distribution arnold and strauss s exponential distribution mckay s gamma distribution distribution with gamma conditionals gamma exponential distribution dirichlet distribution inverted beta distribution distribution with beta conditionals beta stacy distribution cuadras and auge s distribution farlie gumbel morgenstern distribution logistic distribution pearson type vii distribution pearson type ii distribution distribution with cauchy conditionals bilateral pareto distribution muliere and scarsini s pareto distribution distribution with pareto conditionals and the distribution with gumbel conditionals we believe that the results presented here will serve as an important reference for scientists and engineers in many areas

parallelization of the lyapunov constants and cyclicity for centers of planar polynomial vector fields christopher in 2006 proved that under some assumptions the linear parts of the lyapunov constants with respect to the parameters give the cyclicity of an elementary center this paper is devote to establish a new approach namely parallelization to compute the linear parts of the lyapunov constants more concretely it is showed that parallelization computes these linear parts in a shorter quantity of time than other traditional mechanisms to show the power of this approach we study the cyclicity of the holomorphic center iz z 2 z 3 z n under general polynomial perturbations of degree n for n 13 we also exhibit that from the point of view of computation among the hamiltonian time reversible and darboux centers the holomorphic center is the best candidate to obtain high cyclicity examples of any degree for n 4 5 13 we prove that the cyclicity of the holomorphic center is at least n 2 n 2 this result give the highest lower bound for m 6 m 7 m 13 among the existing results where m n is the maximum number of limit cycles bifurcating from an elementary monodromic singularity of polynomial systems of degree n as a direct corollary we also obtain the highest lower bound for the hilbert numbers h 6 40 h 8 70 and h 10 108 because until now the best result was h 6 39 h 8 67 and h 10 100

existence and positivity of solutions of a fourth order nonlinear pde describing interface fluctuations we study the partial differential equation which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system in that application x lies in r but here we study primarily the periodic case x e s we establish existence uniqueness and regularity of solutions locally in time for positive initial data in h s and prove the existence of several families of lyapunov functions for the evolution from the latter we establish a sharp connection between existence globally in time and positivity preservation if o t is a maximal half open interval of existence for a positive solution of the equation with t 1 16r2 then t 03 and lim m w r exists and is constant we discuss also some explicit solutions and propose a generalization to higher dimensions 0 1994 john wiley

large time behavior of solution to the three dimensional quantum bipolar drift diffusion model from semiconductors abstract in this study we consider the three dimensional quantum bipolar drift diffusion model arising from the semiconductor device simulation which consists of the coupled nonlinear fourth order parabolic equation and poisson equation based on the results of the self similar stability for the one dimensional quantum bipolar drift diffusion equation we show the stability of planar self similar wave for the three dimensional quantum bipolar drift diffusion model using the energy methods we present the global existence of smooth solutions for the initial value problem of the three dimensional quantum bipolar drift diffusion equation when the initial data are close to the planar self similar wave we also show that in large time the solution of the three dimensional quantum bipolar drift diffusion equations tends to the planar self similar wave at an algebraic time decay rate

a method for characterizing nilpotent centers to characterize when a nilpotent singular point of an analytic differential system is a center is of particular interest first for the problem of distinguishing between a focus and a center and after for studying the bifurcation of limit cycles from it or from its period annulus we give an effective algorithm in the search of necessary conditions for detecting nilpotent centers based in recent developments moreover we survey the last results on this problem and illustrate our approach by means of examples

polynomial first integrals via the poincare series in appl math 28 2001 17 a method to compute the poincare liapunov constants for an arbitrary analytic differential system which has a linear center at the origin in function of the coefficients of the system was given this method also computes the coefficients of the poincare series in function of the same coefficients in this work we use this method to determine polynomial differential systems which have a polynomial first integral

free boundaries in optimal transport and monge ampere obstacle problems given compactly supported 0 f g 2 l 1 r n the problem of trans porting a fraction m min kfkl1 kgkl1 of the mass of f onto g as cheaply as possible is considered where cost per unit mass transported is given by a cost function c typically quadratic c x y x y 2 2 this question is shown to be equivalent to a double obstacle problem for the monge ampere equation for which sucient conditions are given to guarantee uniqueness of the solution such as f vanishing on sptg in the quadratic case the part of f to be transported increases monotonically with m and if sptf and sptg are separated by a hyperplane h then this part will separated from the balance of f by a semiconcave lipschitz graph over the hyperplane if f f and g g are bounded away from zero and infinity on separated strictly convex domains r n for the quadratic cost this graph is shown to be a c 1 loc hypersurface in whose normal coincides with the direction transported the optimal map between f and g is shown to be holder continuous up to this free bound ary and to those parts of the fixed boundary which map to locally convex parts of the path connected target region

existence and stability for fokker planck equations with log concave reference measure we study markov processes associated with stochastic differential equations whose non linearities are gradients of convex functionals we prove a general result of existence of such markov processes and a priori estimates on the transition probabilities the main result is the following stability property if the associated invariant measures converge weakly then the markov processes converge in law the proofs are based on the interpretation of a fokker planck equation as the steepest descent flow of the relative entropy functional in the space of probability measures endowed with the wasserstein distance

limit cycle bifurcations from a non degenerate center in this work we discuss the computational problems which appear in the computation of the poincare liapunov constants and the determination of their functionally independent number moreover we calculate the minimum number of bautin ideal generators which give the number of small limit cycles under certain hypothesis about the generators in particular we consider polynomial systems of the form x y pn x y y x qn x y where pn and qn are a homogeneous polynomial of degree n we use center bifurcation rather than multiple hopf bifurcations used a previous work 19 to estimate the cyclicity of a unique singular point of focus center type for n 4 5 6 7 and compare with the results given by the conjecture presented in 18

algorithmic derivation of centre conditions the conditions for a critical point of a polynomial differential system to be a centre are of particular significance because of the frequency with which they are required in applications we demonstrate how computer algebra can be effectively employed in the search for necessary and sufficient conditions for critical points of such systems to be centres we survey recent developments and illustrate our approach by means of examples

the stationary current voltage characteristics of the quantum drift diffusion model this paper is concerned with numerical algorithms for the bipolar quantum drift diffusion model for the thermal equilibrium case a quasi gradient method minimizing the energy functional is introduced and strong convergence is proved the computation of current voltage characteristics is performed by means of an extended gummel iteration it is shown that the involved fixed point mapping is a contraction for small applied voltages in this case the model equations are uniquely solvable and convergence of the proposed iteration scheme follows numerical simulations of a one dimensional resonant tunneling diode are presented the computed current voltage characteristics are in good qualitative agreement with experimental measurements the appearance of negative differential resistances is verified for the first time in a quantum drift diffusion model

an information based learning approach to dual control dual control aims to concurrently learn and control an unknown system however actively learning the system conflicts directly with any given control objective for it will disturb the system during exploration this paper presents a receding horizon approach to dual control where a multiobjective optimization problem is solved repeatedly and subject to constraints representing system dynamics balancing a standard finite horizon control objective a knowledge gain objective is defined to explicitly quantify the information acquired when learning the system dynamics measures from information theory such as entropy based uncertainty fisher information and relative entropy are studied and used to quantify the knowledge gained as a result of the control actions the resulting iterative framework is applied to markov decision processes and discrete time nonlinear systems thus the broad applicability and usefulness of the presented approach is demonstrated in diverse problem settings the framework is illustrated with multiple numerical examples

an analytic numerical method for computation of the liapunov and period constants derived from their algebraic structure we consider the problem of computing the liapunov and the period constants for a smooth differential equation with a nondegenerate critical point first we investigate the structure of both constants when they are regarded as polynomials on the coefficients of the differential equation second we take advantage of this structure to derive a method to obtain the explicit expression of the above mentioned constants although this method is based on the use of the runge kutta fehlberg methods of orders 7 and 8 and the use of richardson s extrapolation it provides the real expression for these constants

formulas for renyi information and related measures for univariate distributions in a recent paper song j stat plan infer 93 2001 51 considered renyi information of order and established its connection to the loglikelihood from this relation an intrinsic distribution measure was proposed and analytic expressions of this measure and renyi information were derived for some standard continuous distributions in this paper we derive analytical formulas for renyi and shannon entropies as well as for song s measure for 26 flexible families of univariate continuous distributions we believe that the results presented here will serve as an important reference for scientists and engineers in many areas

existence and asymptotic behavior of multi dimensional quantum hydrodynamic model for semiconductors this paper is devoted to the study of the existence and the time asymptotic of multi dimensional quantum hydrodynamic equations for the electron particle density the current density and the electrostatic potential in spatial periodic domain the equations are formally analogous to classical hydrodynamics but differ in the momentum equation which is forced by an additional nonlinear dispersion term due to the quantum bohm potential and are used in the modelling of quantum effects on semiconductor devices we prove the local in time existence of the solutions in the case of the general nonconvex pressure density relation and large and regular initial data furthermore we propose a subsonic type stability condition related to one of the classical hydrodynamical equations when this condition is satisfied the local in time solutions exist globally in time and converge time exponentially toward the corresponding steady state since for this problem classical methods like for instance the friedrichs theory for symmetric hyperbolic systems cannot be used we investigate via an iterative procedure an extended system which incorporates the one under investigation as a special case in particular the dispersive terms appear in the form of a fourth order wave type equation

a second order equation for schrodinger bridges with applications to the hot gas experiment and entropic transportation cost the schrodinger problem is obtained by replacing the mean square distance with the relative entropy in the monge kantorovich problem it was first addressed by schrodinger as the problem of describing the most likely evolution of a large number of brownian particles conditioned to reach an unexpected configuration its optimal value the entropic transportation cost and its optimal solution the schrodinger bridge stand as the natural probabilistic counterparts to the transportation cost and displacement interpolation moreover they provide a natural way of lifting from the point to the measure setting the concept of brownian bridge in this article we prove that the schrodinger bridge solves a second order equation in the riemannian structure of optimal transport roughly speaking the equation says that its acceleration is the gradient of the fisher information using this result we obtain a fine quantitative description of the dynamics and a new functional inequality for the entropic transportation cost that generalize talagrand s transportation inequality finally we study the convexity of the fisher information along schrodigner bridges under the hypothesis that the associated reciprocal characteristic is convex the techniques developed in this article are also well suited to study the feynman kac penalisations of brownian motion

long time behavior for a nonlinear fourth order parabolic equation we study the asymptotic behavior of solutions of the initial boundary value problem with periodic boundary conditions for a fourth order nonlinear degenerate diffusion equation with a logarithmic nonlinearity for strictly positive and suitably small initial data we show that a positive solution exponentially approaches its mean as time tends to infinity these results are derived by analyzing the equation verified by the logarithm of the solution

bifurcations of limit cycles in complex networks of hamiltonian systems and lloyd s conjecture abstract this paper is motivated by hilbert s sixteenth problem concerning the number and distribution of limit cycles in planar polynomial vector fields we propose an original method inspired by the complex systems framework in order to construct a family of hamiltonian systems admitting non degenerate centers located on the vertices of a planar network we introduce two novel polynomial perturbations adapted to those systems with the aim to produce a high number of limit cycles the first one is oriented along the gradient of the unperturbed system and the second one is again constructed with a complex systems approach using the melnikov integral we reach in a small number of particular cases the lower bound of cubical order for the hilbert number h n conjectured by lloyd in 1988

best asymptotic normality of the kernel density entropy estimator for smooth densities in the random sampling setting we estimate the entropy of a probability density distribution by the entropy of a kernel density estimator using the double exponential kernel under mild smoothness and moment conditions we show that the entropy of the kernel density estimator equals a sum of independent and identically distributed i i d random variables plus a perturbation which is asymptotically negligible compared to the parametric rate n sup 1 2 an essential part in the proof is obtained by exhibiting almost sure bounds for the kullback leibler divergence between the kernel density estimator and its expected value the basic technical tools are doob s submartingale inequality and convexity jensen s inequality

on the effects of the bohm potential on a macroscopic system of self interacting particles abstract we consider a nonstationary macroscopic system of self interacting particles with an additional potential the so called bohm potential we study the existence of nonnegative global solutions to the system of equations and allude to the differences to results obtained for classical models the problem is considered on a bounded domain up to three spatial dimensions subject to initial and neumann boundary conditions for the particle density and the dirichlet boundary condition for the self interacting potential moreover the initial datum is only assumed to be nonnegative and to satisfy a weak integrability condition

the wasserstein gradient flow of the fisher information and the quantum drift diffusion equation we prove the global existence of non negative variational solutions to the drift diffusion evolution equation partial t u div left u mathrm d left 2 frac delta sqrt u sqrt u f right right 0 under variational boundary condition despite the lack of a maximum principle for fourth order equations non negative solutions can be obtained as a limit of a variational approximation scheme by exploiting the particular structure of this equation which is the gradient flow of the perturbed fisher information functional fancyscript f f u frac 12 int left mathrm d log u right 2 u dx int fu dx with respect to the kantorovich rubinstein wasserstein distance between probability measures we also study long time behavior of the solutions proving their exponential decay to the equilibrium state g e v characterized by delta v frac12 left mathrm d v right 2 f quad int rm e v dx int u 0 dx when the potential v is uniformly convex in this case the functional fancyscript f f coincides with the relative fisher information fancyscript f f u frac12 fancyscript i u g int left mathrm d log u g right 2u dx

some limit analysis in a one dimensional stationary quantum hydrodynamic model for semiconductors in this paper we study the steady state hydrodynamic equations for isothermal states including the quantum bohn potential the one dimensional equations for the electron current density and the particle density are coupled self consistently to the poisson equation for the electric potential the quantum correction can be interpreted as a dispersive regularization of the classical hydrodynamic equations in a bounded interval supplemented by the proper boundary conditions we investigate the zero electron mass limit the zero relaxation time limit the debye length quasi neutral limit and some combined limits respectively for each limit we show the strong convergence of the sequence of solutions and give the associated convergence rate

a method of constructing cycles without contact around a weak focus has a weak focus then limit cycles can be made to appear in its neighborhood by varying slightly the right sides 11 frommer 2 bautin 3 chin et al 4 and tung 5 are examples of excellent expositions of poincare s idea it is necessary to go from numerical examples to general theory in the first part of this paper we present a method of constructing cycles without contact around a weak focus which makes clear poincart s idea used in the above work 2 51 in the second part another method to analyze global phase portraits is used quadratic systems with at least four limit cycles are produced by means of both the above methods this contradicts the results of petrovskii and landis 6

convergent finite element discretizations of the density gradient equation for quantum semiconductors we study nonlinear finite element discretizations for the density gradient equation in the quantum drift diffusion model in particular we give a finite element description of the so called nonlinear scheme introduced by ancona we prove the existence of discrete solutions and provide a consistency and convergence analysis which yields the optimal order of convergence for both discretizations the performance of both schemes is compared numerically in particular with respect to the influence of approximate vacuum boundary conditions

high frequency limit of non autonomous gradient flows of functionals with time periodic forcing we study the high frequency limit of non autonomous gradient flows in metric spaces of energy functionals comprising an explicitly time dependent perturbation term which might oscillate in a rapid way on grounds of the existence results by ferreira and guevara 2015 on non autonomous gradient flows which we also extend to a broader range of energy functionals we prove that the associated solution curves converge to a solution of the time averaged evolution equation in the limit of infinite frequency under additional assumptions on the energy we obtain an explicit rate of convergence furthermore we specifically investigate nonlinear drift diffusion equations with time dependent drift which formally are gradient flows with respect to the l2 wasserstein distance we prove that a family of weak solutions obtained as a limit of the minimizing movements scheme exhibits the above mentioned behavior in the high frequency limit

minimum number of ideal generators for a linear center perturbed by homogeneous polynomials abstract using the algorithm presented in j gine x santallusia on the poincare liapunov constants and the poincare series appl math warsaw 28 1 2001 17 30 the poincare liapunov constants are calculated for polynomial systems of the form x y p n x y y x q n x y where p n and q n are homogeneous polynomials of degree n the objective of this work is to calculate the minimum number of ideal generators i e the number of functionally independent poincare liapunov constants through the study of the highest fine focus order for n 4 and n 5 and compare it with the results that give the conjecture presented in j gine on the number of algebraically independent poincare liapunov constants appl math comput 188 2 2007 1870 1877 moreover the computational problems which appear in the computation of the poincare liapunov constants and the determination of the number of functionally independent ones are also discussed

a strengthened central limit theorem for smooth densities abstract we consider the central limit theorem for the probability density function n x of the standardized sum of independent and identically distributed random variables with finite variance and regular probability density function by showing boundedness of different convex functionals along the sequence fn we prove convergence in various norms to the normal density

bohmian measures and their classical limit abstract we consider a class of phase space measures which naturally arise in the bohmian interpretation of quantum mechanics we study the classical limit of these so called bohmian measures in dependence on the scale of oscillations and concentrations of the sequence of wave functions under consideration the obtained results are consequently compared to those derived via semi classical wigner measures to this end we shall also give a connection to the theory of young measures and prove several new results on wigner measures themselves our analysis gives new insight on oscillation and concentration effects in the semi classical regime

nonlinear mobility continuity equations and generalized displacement convexity we consider the geometry of the space of borel measures endowed with a distance that is defined by generalizing the dynamical formulation of the wasserstein distance to concave nonlinear mobilities we investigate the energy landscape of internal potential and interaction energies for the internal energy we give an explicit sufficient condition for geodesic convexity which generalizes the condition of mccann we take an eulerian approach that does not require global information on the geodesics as by product we obtain existence stability and contraction results for the semigroup obtained by solving the homogeneous neumann boundary value problem for a nonlinear diffusion equation in a convex bounded domain for the potential energy and the interaction energy we present a non rigorous argument indicating that they are not displacement semiconvex

conditions for the existence of a center for the kukles homogeneous systems abstract in this work we study necessary and sufficient conditions for the existence of centers in two families of linear centers with homogeneous quartic and quintic nonlinearities systems of this class are called kukles homogeneous systems systems of this type were studied for the first time by kukles who studied a linear center with cubic nonhomogeneous nonlinearities

ordering univariate distributions by entropy and variance this paper examines the role of variance and entropy in ordering distributions and random prospects there is no universal relation between entropy and variance orderings of distributions but we place their relationship in the context of a stronger ordering relation known as dispersion ordering further some conditions are identified under which variance and entropy order similarly when continuous variables are transformed we also analyze parametric changes which do not disturb the agreement between these rankings the results are conveniently tabulated in terms of distribution parameters

a family of fourth order q logarithmic equations we prove the existence of global in time weak nonnegative solutions to a family of nonlinear fourth order evolution equations parametrized by a real parameter q 0 1 which includes the well known thin film q 1 2 and the derrida lebowitz speer spohn dlss equation q 1 subject to periodic boundary conditions in one spatial dimension in contrast to the gradient flow approach in 25 our method relies on dissipation property of the corresponding entropy functionals tsallis entropies resulting in required a priori estimates and extends the existence result from 25 to a wider range of the family members namely to 0 q 1 2 generalized beckner type functional inequalities yield an exponential decay rate of relative entropies which in further implies the exponential stability in the l1 norm of the constant steady state finally we provide illustrative numerical examples supporting the analytical results

on the number of algebraically independent poincare liapunov constants abstract in this paper an upper bound for the number of algebraically independent poincare liapunov constants in a certain basis for planar polynomial differential systems is given finally it is conjectured that an upper bound for the number of functionally independent poincare liapunov quantities would be m 2 3 m 7 where m is the degree of the polynomial differential system moreover the computational problems which appear in the computation of the poincare liapunov constants and in the determination of the center cases are also discussed

initial time layer problem for quantum drift diffusion model we study the initial time layer problem to the quantum drift diffusion model the limit of vanishing debye length is established by entropy method and compactness argument as a byproduct the global weak solution is also obtained for this model

centers for a class of generalized quintic polynomial differential systems abstract we characterize the centers of the planar polynomial differential systems of degree d 5 odd that in complex notation writes as z iz z z d 5 2 az 5 bz 4 z cz 3 z 2 dz 2 z 3 ez z 4 f z 5 where a b c d e f c and either a re e 0 or a im e 0 or re a e 0 or im a e 0

on the structure of poincare lyapunov constants for the weak focus of polynomial vector fields in this paper generalized poincare lyapunov constants vi i 1 2 are defined and an explicit formula is given for the lyapunov functions it is shown that vi is determined modulo v1 vi 1 this is used for the investigation and creation of limit cycles

a measure of total variability for the multivariate t distribution with applications to finance general expressions for the entropy of the multivariate t and cauchy distributions are derived as well as their sample moments generated functions cumulant functions means and variances the asymptotic distribution of the multivariate t entropy is also obtained a real life application for index returns of four different countries is considered and the analysis of their multivariate variability is analyzed by means of the entropy

a convexity principle for interacting gases a new set of inequalities is introduced based on a novel but natural interpolation between borel probability measures on r d using these estimates in lieu of convexity or rearrangement inequalities the existence and uniqueness problems are solved for a family of attracting gas models in these models the gas interacts with itself through a force which increases with distance and is governed by an equation of state p p relating pressure to density p d 1 d is assumed non decreasing for a d dimensional gas by showing that the internal and potential energies for the system are convex functions of the interpolation parameter an energy minimizing stateunique up to translationis proven to exist the concavity established for t pd q as a function of t 0 1 generalizes the brunnminkowski inequality from sets to measures 1997 academic press

limit cycles of polynomial differential systems with homogeneous nonlinearities of degree 4 via the averaging method by using the averaging method we study the limit cycles for a class of quartic polynomial differential systems as well as their global shape in the plane more specifically we analyze the global shape of limit cycles bifurcating from a hopf bifurcation and also from periodic orbits with linear center x y y x the perturbation of these systems is made inside the class of quartic polynomial differential systems without quadratic and cubic terms

long time asymptotics for strong solutions of the thin film equation in this paper we investigate the large time behavior of strong solutions to the one dimensional fourth order degenerate parabolic equation u t u u xxx x modeling the evolution of the interface of a spreading droplet for nonnegative initial values u 0 x h 1 both compactly supported or of finite second moment we prove explicit and universal algebraic decay in the l 1 norm of the strong solution u x t towards the unique among source type solutions strong source type solution of the equation with the same mass the method we use is based on the study of the time decay of the entropy introduced in 13 for the porous medium equation and uses analogies between the thin film equation and the porous medium equation

uniform convergence of an exponentially fitted scheme for the quantum drift diffusion model we analyze an exponentially fitted finite element scheme for the unipolar quantum drift diffusion model in one dimensional space the existence of discrete solutions is shown under very mild assumptions and convergence of a subsequence is proved by compactness arguments the scheme is constructed in such a way that it reduces in the semiclassical limit to the well known scharfetter gummel discretization for the classical drift diffusion model we derive uniform error bounds which allow for the semiclassical limit on the discrete level numerical tests underlining the analytical results are presented

entropy expressions and their estimators for multivariate distributions entropy expressions for several continuous multivariate distributions are derived point estimation of entropy for the multinormal distribution and for the distribution of order statistics from d g weinman s ph d dissertation ariz state univ tempe az 1966 exponential distribution is considered the asymptotic distribution of the uniformly minimum variance unbiased estimator for multinormal entropy is obtained simulation results on convergence of the means and variances of these estimators are provided

information in generalized method of moments estimation and entropy based moment selection abstract in this paper we make five contributions to the literature on information and entropy in generalized method of moments gmm estimation first we introduce the concept of the long run canonical correlations lrccs between the true score vector and the moment function f v t 0 and show that they provide a metric for the information contained in the population moment condition e f v t 0 0 second we show that the entropy of the limiting distribution of the gmm estimator can be written in terms of these lrccs third motivated by the above results we introduce an information criterion based on this entropy that can be used as a basis for moment selection fourth we introduce the concept of nearly redundant moment conditions and use it to explore the connection between redundancy and weak identification fifth we analyse the behaviour of the aforementioned entropy based moment selection method in two scenarios of interest these scenarios are i nonlinear dynamic models where the parameter vector is identified by all the combinations of moment conditions considered ii linear static models where the parameter vector may be weakly identified for some of the combinations considered the first of these contributions rests on a generalized information equality that is proved in the paper and may be of interest in its own right

an extension of the derrida lebowitz speer spohn equation we show how the derivation of the derrida lebowitz speer spohn equation can be prolonged to obtain a new equation generalizing the models obtained in the paper by these authors we then investigate its properties from both an analytical and numerical perspective specifically a numerical method is presented to approximate solutions of the prolonged equation using this method we investigate the relationship between the solutions of the prolonged equation and the tracy widom goe distribution

higher order limit cycle bifurcations from non degenerate centers abstract the computational problems which appear in the computation of the poincare liapunov constants and the determination of their functionally independent number has led in recent works to consider only the lowest terms of these constants in this work we improve the results obtained in this direction for polynomials systems of the form x y p n x y y x q n x y where p n and q n are a homogeneous polynomial of degree n we use center bifurcation to estimate the cyclicity of a unique singular point of focus center type for different values of n and compare with the results given by the conjecture presented in 15

polar factorization and monotone rearrangement of vector valued functions given a probability space x p and a bounded domain r in rd equipped with the lebesgue measure 1 i normalized so that 10 i i it is shown under additional technical assumptions on x and q that for every vector valued function u e lp x p rd there is a unique polar factorization u v s where is a convex function defined on r and s is a measure preserving mapping from x p into q i i provided that u is nondegenerate in the sense that p u e 0 for each lebesgue negligible subset e of rd through this result the concepts of polar factorization of real matrices helmholtz decomposition of vector fields and nondecreasing rearrangements of real valued functions are unified the monge amgre equation is involved in the polar factorization and the proof relies on the study of an appropriate monge kantorovich problem

the geometry of optimal transportation introduction 113 1 summary of main results 120 2 background on optimal measures 126 part i strictly convex costs 133 3 existence and uniqueness of optimal maps 133 4 characterization of the optimal map 137 part ii costs which are strictly concave as a function of d i s t a n c e 141 5 the role of optimal maps 141 6 uniqueness of optimal solutions 144 part iii appendices 148 a legendre transforms and conjugate costs 148 b examples of c concave potentials 152 c regularity of c concave potentials 154 references 159