the webster scalar curvature flow on cr sphere part ii abstract this is the first of two papers in which we prove some properties of the webster scalar curvature flow more precisely we establish the long time existence l p convergence and the blow up analysis for the solution of the flow as a by product we prove the convergence of the cr yamabe flow on the cr sphere the results in this paper will be used to prove a result of prescribing webster scalar curvature on the cr sphere which is the main result of the second paper

a note on barotropic compressible quantum navier stokes equations abstract the global in time existence of weak solutions to the barotropic compressible quantum navier stokes equations has been proved very recently by jungel 2009 1 if the viscosity constant is smaller than the scaled plank constant this paper extends the results to the case that the viscosity constant equals the scaled plank constant by using a new estimate on the square root of the solution apparently not available in 1 the semiclassical limit for the viscous quantum euler equations which are equivalent to the barotropic compressible quantum navier stokes equations can be performed then the results of this paper are obtained easily

monotonicity and uniqueness of traveling waves for a reaction diffusion model with a quiescent stage abstract this paper is concerned with the monotonicity and uniqueness of traveling waves for a reaction diffusion model with quiescent stage we first obtain the exponential decay rate of wave profiles and then we show that any profile is strictly monotone by using the strong comparison principle furthermore we prove the uniqueness up to translation of all traveling waves including even the waves with minimal speed

a divide and conquer algorithm on the double dimensional inverse eigenvalue problem for jacobi matrices abstract this paper proposes a divide and conquer algorithm for reconstructing a 2 n th order jacobi matrix j 2 n with a given n th order leading principal submatrix j n and with all eigenvalues of j 2 n this algorithm needs to compute the eigenvalues of the n th order jacobi matrix j n 1 2 n and the first components of the unit eigenvectors of j n 1 2 n where j n 1 2 n j n 1 2 n n e 1 e 1 t the method needs not to reconstruct the leading principal submatrix j n and can avoid computing the coefficients of the characteristic polynomial for getting the eigenvalues of j n

canonical perturbation expansions to large order from classical hypervirial and hellmann feynman theorems the classical hypervirial and hellmann feynman theorems are used to formulate a perturbation theory without fourier series that can be used to generate canonical series expansions for the energies of perturbed periodic orbits for separable classical hamiltonians as in the case where these theorems are used to generate quantum mechanical rayleigh schrodinger perturbation series the method is very efficient and may be used to generate expansions to large order either numerically or in algebraic form here the method is applied to one dimensional anharmonic oscillators and radial kepler problems in all cases the classical series for energies and expectation values are seen to correspond to the expansions associated with their quantum mechanical counterparts through an appropriate action preserving classical limit as discussed by turchetti graffi and paul this action fixing is inherent in the classical hellmann feynman theorem applied to periodic orbits

existence of triple positive solutions to a class of p laplacian boundary value problems abstract by using leggett williams fixed point theorem a class of p laplacian boundary value problem is studied sufficient conditions for the existence of triple positive solutions are established

triple positive solutions and dependence on higher order derivatives abstract in this paper we consider the lidstone boundary value problem y 2 m t f y t y 2 j t y 2 m 1 t 0 t 1 y 2 i 0 0 y 2 i 1 0 i m 1 where 1 m f 0 growth conditions are imposed on f and inequalities involving an associated green s function are employed which enable us to apply the leggett williams fixed point theorem to cones in ordered banach spaces this in turn yields the existence of at least three positive symmetric concave solutions the emphasis here is that f depends on higher order derivatives

invasion by an inferior or superior competitor a diffusive competition model with a free boundary in a heterogeneous environment in this study we consider the population dynamics of an invasive species and a resident species which are modeled as a diffusive competition process in a radially symmetric setting with a free boundary we assume that the resident species undergoes diffusion and growth in r n while the invasive species initially exists in a finite ball but invades the environment with a spreading front evolving according to a free boundary when the invasive species is inferior we show that if the resident species is already well established initially then the invader can never invade deep into the underlying habitat thus it dies out before its invading front reaches a certain finite limiting position when the invasive species is superior a spreading vanishing dichotomy holds and sharp criteria for spreading and vanishing with d 1 mu and u 0 as variable factors are obtained where d 1 mu and u 0 are the dispersal rate expansion capacity and initial number of invaders respectively in particular we obtain some rough estimates of the asymptotic spreading speed when spreading occurs c 2014 elsevier inc all rights reserved

the hvt technique and the treatment of two basic inequalities the quantum mechanical hypervirial theorems hvt technique is used in treating two basic inequalities relating the ground state mean square radius of the orbit of a particle in a central potential and its kinetic energy respectively to the spacing of the two lowest energy levels e for quite a wide class of those potentials the parameters of which also lead to a sufficiently small dimensionless quantity s the difference between the two sides of each inequality is of order s3 and higher while e is of order s and higher and thus it is expected in general to be quite small

integration of subdifferentials of nonconvex functions in nonsmooth analysis and optimization subgradients come in many different flavors e g approximate dini proximal clarke generalized see 2 5 6 12 14 191 these subgradients are important and valuable tools however many questions remain unsolved concerning the exact link between the function and its subgradients for instance can two functions not differing by an additive constant have the same subgradients in this paper we study the fundamental problem of determining functions that can be recovered up to an additive constant from the knowledge of their subgradients this integration problem is not very well understood and very few functions or classes of functions are known to be recoverable from their subgradients in section 4 we show that if the basic constraint qualification holds at r then the composition of a closed i e lowersemicontinuous proper convex function with a twice continuously differentiable mapping is determined up to an additive constant by its generalized subgradients actually in this case all above mentioned subgradients are the same beside the obvious theoretical interest of this integration problem it is our hope or perhaps our long term goal that once this problem is better understood we can then tackle the question of uniqueness of solutions to generalized differential equations involving subgradients in place of partial derivatives an example of such an equation that well deserves study is the extended hamilton jacobi equation used in optimal control see clarke 2 let us also mention that a problem similar to the integration problem is the one of determining the set valued mappings that are in fact subgradient set valued mappings uniqueness is not mandatory for a contribution to this problem see janin 8 before we look at some of the known cases where the function can be recovered from its subgradients let us look at some negative examples it is clear that not every function can be recovered up to an additive constant from its subgradients we only need to look at the following two functions 0 x50 0 x10 f x 1 x o g x 2 x o

the perturbed three dimensional oscillator a renormalized version of inner product and hypervirial theories is used to calculate the energy eigenvalues for four states of a perturbed three dimensional oscillator and to obtain the rayleigh schrodinger energy perturbation series

a note on the schrodinger equation for the potential a exp x2 l l 1 x2 the bound states energies and eigenfunctions of the schrodinger equation with a radial gaussian potential are obtained using a perturbational and also a variational treatment on a conveniently chosen basis of transformed jacobi functions the accuracy of the results is fairly good

elliptic equations with bmo coefficients in reifenberg domains the inhomogeneous dirichlet problems concerning divergence form elliptic equations are studied optimal regularity requirements on the coefficients and domains for the w1 p theory 1 p are obtained the principal coefficients are supposed to be in the john nirenberg space with small bmo seminorms the domain is a reifenberg domain these conditions for the w1 p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domains in fact these domains might have fractal dimensions 2004 wiley periodicals inc

the energy levels of the schrodinger equation for various types of potentials using a renormalized method a perturbative method is used to compute energy levels for many different forms of potentials results of high accuracy are produced for various eigenstates

prox regular sets and epigraphs in uniformly convex banach spaces various regularities and other properties we continue the study of prox regular sets that we began in a previous work in the setting of uniformly convex banach spaces endowed with a norm both uniformly smooth and uniformly convex e g l p w m p spaces we prove normal and tangential regularity properties for these sets and in particular the equality between mordukhovich and proximal normal cones we also compare in this setting the proximal normal cone with different holderian normal cones depending on the power types s q of moduli of smoothness and convexity of the norm in the case of sets that are epigraphs of functions we show that j primal lower regular functions have prox regular epigraphs and we compare these functions with poliquin s primal lower nice functions depending on the power types s q of the moduli the preservation of prox regularity of the intersection of finitely many sets and of the inverse image is obtained under a calmness assumption a conical derivative formula for the metric projection mapping of prox regular sets is also established among other results of the paper it is proved that the attouch wets convergence preserves the uniform r prox regularity property and that the metric projection mapping is in some sense continuous with respect to this convergence for such sets

prox regular functions in hilbert spaces this paper studies the prox regularity concept for functions in the general context of hilbert space in particular a subdifferential characterization is established as well as several other properties it is also shown that the moreau envelopes of such functions are continuously differentiable

a jacobi matrix inverse eigenvalue problem with mixed data abstract in this paper the inverse eigenvalue problem of reconstructing a jacobi matrix from part of its eigenvalues and its leading principal submatrix is considered the necessary and sufficient conditions for the existence and uniqueness of the solution are derived furthermore a numerical algorithm and some numerical examples are given

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

a diffusive logistic model with a free boundary in time periodic environment abstract we study the diffusive logistic equation with a free boundary in time periodic environment such a model may be used to describe the spreading of a new or invasive species with the free boundary representing the expanding front for time independent environment in the cases of one space dimension and higher space dimensions with radial symmetry this free boundary problem has been studied in du and lin 2010 12 du and guo 2011 9 in both cases a spreading vanishing dichotomy was established and when spreading occurs the asymptotic spreading speed was determined in this paper we show that the spreading vanishing dichotomy is retained in time periodic environment and we also determine the spreading speed the former is achieved by further developing the earlier techniques and the latter is proved by introducing new ideas and methods

periodic solutions for second order systems with not uniformly coercive potential abstract the existence and multiplicity of periodic solutions are obtained for the nonautonomous second order systems with locally coercive potential that is f t x as x for a e t in some positive measure subset of 0 t by using an analogy of egorov s theorem the properties of subadditive functions the least action principle and a three critical point theorem proposed by brezis and nirenberg

relativistic effects on information measures for hydrogen like atoms position and momentum information measures are evaluated for the ground state of the relativistic hydrogen like atoms consequences of the fact that the radial momentum operator is not self adjoint are explicitly studied exhibiting fundamental shortcomings of the conventional uncertainty measures in terms of the radial position and momentum variances the shannon and renyi entropies the fisher information measure as well as several related information measures are considered as viable alternatives detailed results on the onset of relativistic effects for low nuclear charges and on the extreme relativistic limit are presented the relativistic position density decays exponentially at large r but is singular at the origin correspondingly the momentum density decays as an inverse power of p both features yield divergent renyi entropies away from a finite vicinity of the shannon entropy while the position space information measures can be evaluated analytically for both the nonrelativistic and the relativistic hydrogen atom this is not the case for the relativistic momentum space some of the results allow interesting insight into the significance of recently evaluated dirac fock vs hartree fock complexity measures for many electron neutral atoms

state of the art location on networks a survey part ii exploiting tree network structure the discussion of the fundamental p center and p median problems in part i of this paper provides the basis for the work surveyed in part ii part ii deals with the minimax and minisum location problems with mutual communication location problems involving multiple objectives the distance constraints problem and problems involving the location of paths in addition convexity issues in network location problems are discussed virtually all of this work exploits network structure specifically it is based on the assumption that the network is a tree the conclusion section gives a brief discussion of the state of the art and of current trends in network location research

further properties of steady state solutions to the navier stokes problem past a three dimensional obstacle we show that the weak formulation of the steady state navier stokes problem in the exterior of a three dimensional compact set closure of a bounded domain corresponding to a nonzero velocity at infinity and subjected to a given body force is equivalent to a nonlinear equation in appropriate banach spaces we thus show that the relevant nonlinear operator enjoys a number of fundamental properties that allow us to derive many significant results for the original problem in particular we prove that the manifold constituted by the pairs u with the nondimensional speed at infinity reynolds number and u weak solution corresponding to and to a given body force f is for generic f a c one dimensional manifold and that for almost any the number of solutions is finite we also show that for any given f in the appropriate function space and any given 0 the corresponding solutions can be controlled by their specification only in a suitable neighborhood i of the boundary the size

characteristic inequalities of uniformly convex and uniformly smooth banach spaces abstract let x be a real banach space with dual x and moduli of convexity and smoothness x e and x respectively for 1 p denotes the duality mapping from x into 2 x with gauge function t p 1 and j p denotes an arbitrary selection for j p let a r 0 0 t is strictly increasing and there exists c 0 such that t c x t 2 and f r 0 0 t is convex nondecreasing and there exists k 0 such that k x it is proved that x is uniformly convex if and only if there is a a such that x y p x p p j p x y x y x y x and x is uniformly smooth if and only if there is a f such that x y p x p p j p x y x y x y x where for given function f f x y is defined by f x y p 0 1 x ty x p t f t y x ty x dt these inequalities which have various applications can be regarded as general banach space versions of the well known polarization identity occurring in hilbert spaces

a new algorithm on the inverse eigenvalue problem for double dimensional jacobi matrices abstract in this paper we investigate some properties of eigenvalues and eigenvectors of jacobi matrices we propose a new algorithm for reconstructing a 2 n th order jacobi matrix j 2 n with a given nth order leading principal submatrix j n and with all eigenvalues of j 2 n this algorithm needs to compute the eigenvalues of the nth order tailing principal submatrix j n 1 2 n and the first components of the unit eigenvectors of j n 1 2 n our method needs not to reconstruct j n and can avoid computing the coefficients of the characteristic polynomial for getting the eigenvalues of j n 1 2 n we also present some numerical results

periodic solutions of a class of non autonomous second order systems some existence theorems are obtained by the least action principle for periodic solutions of nonautonomous second order systems with a potential which is the sum of a subconvex function and a subquadratic function

chemically reacting mixtures in terms of degenerated parabolic setting the paper analyzes basic mathematical questions for a model of chemically reacting mixtures we derive a model of several finite component compressible gas taking rigorously into account the thermodynamical regime mathematical description of the model leads to a degenerate parabolic equation with hyperbolic deviation the thermodynamics implies that the diffusion terms are non symmetric not positively defined and cross diffusion effects must be strongly marked the mathematical goal is to establish the existence of weak solutions globally in time for arbitrary number of reacting species a key point is an entropy like estimate showing possible renormalization of the system

the eigenvalues of the schrodinger equation for spherically symmetric states for various types of potentials in two three and n dimensions by using perturbative and non perturbative methods the energy levels of the schrodinger equation involving various model potentials in two three and n dimensional space are calculated by using perturbative and non perturbative methods the methods have been used effectively to calculate the energy eigenvalues even for high state numbers and large values of the perturbation parameters

scaling properties of composite information measures and shape complexity for hydrogenic atoms in parallel magnetic and electric fields abstract the scaling properties of various composite information theoretic measures shannon and renyi entropy sums fisher and onicescu information products tsallis entropy ratio fisher shannon product and shape complexity are studied in position and momentum spaces for the non relativistic hydrogenic atoms in the presence of parallel magnetic and electric fields such measures are found to be invariant at the fixed values of the scaling parameters given by s 1 b 3 4 0 2 z 2 m 2 e 3 and s 2 f 4 4 0 3 z 3 e 5 m 2 numerical results which support the validity of the scaling properties are shown by choosing the representative example of the position space shape complexity physical significance of the resulting scaling behavior is discussed

differential properties of the moreau envelope in a vector space endowed with a uniformly g teaux differentiable norm it is proved that the moreau envelope enjoys many remarkable differential properties and that its subdifferential can be completely described through a certain approximate proximal mapping this description shows in particular that the moreau envelope is essentially directionally smooth new differential properties are derived for the distance function associated with a closed set moreover the analysis when applied to the investigation of the convexity of tchebyshev sets allows us to recover several known results in the literature and to provide some new ones

inverse eigenvalue problem of jacobi matrix with mixed data in this paper the inverse eigenvalue problem of reconstructing a jacobi matrix from its eigenvalues its leading principal submatrix and part of the eigenvalues of its submatrix is considered the necessary and sufficient conditions for the existence and uniqueness of the solution are derived furthermore a numerical algorithm and some numerical examples are given

symmetric positive solutions of nonlinear boundary value problems abstract we study the nonlinear boundary value problem u 2 m f t u u u 2 m 2 t 0 1 u 2 i 0 u 2 i 1 0 i 0 m 1 the existence of symmetric positive solutions of the above problem is discussed sufficient conditions are obtained for the problem to have one any finite number and a countably infinite number of such solutions our results extend some recent work in the literature on boundary value problems of ordinary differential equations we illustrate our results by two examples none of which can be handled using the existing results

brownian subordinators and fractional cauchy problems a brownian time process is a markov process subordinated to the absolute value of an independent one dimensional brownian motion its transition densities solve an initial value problem involving the square of the generator of the original markov process an apparently unrelated class of processes emerging as the scaling limits of continuous time random walks involves subordination to the inverse or hitting time process of a classical stable subordinator the resulting densities solve fractional cauchy problems an extension that involves fractional derivatives in time in this paper we will show a close and unexpected connection between these two classes of processes and consequently an equivalence between these two families of partial differential equations

the hvt technique and the uncertainty relation for central potentials the quantum mechanical hypervirial theorems hvt technique is used to treat the so called uncertainty relation for quite a general class of central potential wells including the reduced poeschl teller and the gaussian one it is shown that this technique is quite suitable in deriving an approximate analytic expression in the form of a truncated power series expansion for

local differentiability of distance functions recently clarke stern and wolenski characterized in a hilbert space the closed subsets c for which the distance function dc is continuously differentiable everywhere on an open tube of uniform thickness around c here a corresponding local theory is developed for the property of dc being continuously differentiable outside of c on some neighborhood of a point x c this is shown to be equivalent to the prox regularity of c at x which is a condition on normal vectors that is commonly fulfilled in variational analysis and has the advantage of being verifiable by calculation additional characterizations are provided in terms of dc being locally of class c 1 or such that dc 2 is convex around x for some 0 prox regularity of c at x corresponds further to the normal cone mapping nc having a hypomonotone truncation around x and leads to a formula for pc by way of nc the local theory also yields new insights on the global level of the clarke stern wolenski results and on a property of sets introduced by shapiro as well as on the concept of sets with positive reach considered by federer in the finite dimensional setting

hypervirial perturbation theory revisited a wide range of topics in the area of hypervirial perturbation theory hvpt is discussed it is shown that with the use of a few simple procedures hvpt is capable of high accuracy for many problems results from many previous works in the literature are found to be improvable by the careful use of hvpt with appropriate choice of the unperturbed potential and of the origin at which the energy expansion is carried out two multi well problems from the literature are analysed in detail to show the value of a combination of hvpt and finite difference methods

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

on the schrodinger equation for the interaction x2 λx2 1 gx2 by forming the 6 6 pade approximants to the energy perturbation series for the interaction x2 lambda x2 1 gx2 as obtained from the hypervirial relations the ground and the first three excited state energy levels are calculated for g or 2 the results of the present calculation are in good agreement with those of the variational calculations the authors also present another set of exact solutions to the schrodinger equation for the interaction x2 lambda x2 1 gx2