reconstruction of jacobi matrices with mixed spectral data abstract we study the inverse problem of reconstructing a jacobi matrix from the partial information given on the matrix and on the set of eigenvalues and norming constants the first components of normalized eigenvectors necessary and sufficient conditions are provided for the existence of solution for the inverse problem numerical algorithms and numerical examples are also presented

periodic solutions for a class of non autonomous second order systems abstract the purpose of this paper is to study the existence of periodic solutions of non autonomous second order systems u t f t u t a e t 0 t u 0 u t u 0 u t 0 some new existence theorems are obtained by the least action principle

the proximal normal formula in banach space approximation by proximal normals to the clarke generalized subdifferential for a distance function generated by a nonempty closed set and the normal cone to the set generated by the proximal normals are important tools in nonsmooth analysis we give simple general versions of such formulae in infinite dimensional banach spaces which satisfy different geometrical conditions our first class of spaces with uniformly g teaux differentiable norm includes the hilbert space case and the formulae is attained through dense subsets our second class of reflexive kadec smooth spaces is the most general for which such formulae can be obtained for all nonempty closed sets in the space our technique also allows us to establish the existence of solutions for a class of optimization problems substantially extending similar work of ekeland and lebourg

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

second order eliptic and parabolic equations with b r2 v mo coefficients the solvability in sobolev spaces w 1 2 p is proved for nondivergence form second order parabolic equations for p 2 close to 2 the leading coefficients are assumed to be measurable in the time variable and two coordinates of space variables and almost vmo vanishing mean oscillation with respect to the other coordinates this implies the w 2 p solvability for the same p of nondivergence form elliptic equations with leading coefficients measurable in two coordinates and vmo in the others under slightly different assumptions we also obtain the solvability results when p 2

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

asymptotic speeds of spread and traveling waves for integral equations and delayed reaction diffusion models abstract the theory of asymptotic speeds of spread and monotone traveling waves is generalized to a large class of scalar nonlinear integral equations and is applied to some time delayed reaction and diffusion population models

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

a new class of incremental gradient methods for least squares problems the least mean squares lms method for linear least squares problems differs from the steepest descent method in that it processes data blocks one by one with intermediate adjustment of the parameter vector under optimization this mode of operation often leads to faster convergence when far from the eventual limit and to slower sublinear convergence when close to the optimal solution we embed both lms and steepest descent as well as other intermediate methods within a one parameter class of algorithms and we propose a hybrid class of methods that combine the faster early convergence rate of lms with the faster ultimate linear convergence rate of steepest descent these methods are well suited for neural network training problems with large data sets furthermore these methods allow the effective use of scaling based for example on diagonal or other approximations of the hessian matrix

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

the diffusive logistic model with a free boundary in heterogeneous environment abstract in this paper we study the population dynamics of an invasive species in heterogeneous environment which is modeled by a diffusive logistic equation with free boundary condition to understand the effect of the dispersal rate d and the parameter the ratio of the expansion speed of the free boundary and the population gradient at the expanding front on the dynamics of this model we divide the heterogeneous environment into two cases strong heterogeneous environment and weak heterogeneous environment by choosing d and as variable parameters we derive sufficient conditions for species spreading resp vanishing in the strong heterogeneous environment while in the weak heterogeneous environment we obtain sharp criteria for the spreading and vanishing moreover when spreading happens we give an estimate for the asymptotic spreading speed of the free boundary these theoretical results may have important implications for prediction and prevention of biological invasions

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

integration of subdifferentials of lower semicontinuous functions on banach spaces abstract this paper studies the lower semicontinuous functions on banach spaces whose subdifferentials are not disassociated from several conditions are given to ensure that two lower semicontinuous functions with the same subdifferential are equal up to an additive constant

optimal sobolev imbeddings involving rearrangement invariant quasinorms let m and n be positive integers with n 2 and 1 m n 1 we study rearrangement invariant quasinorms r and d on functions f 0 1 view the mathml source such that to each bounded domain in view the mathml sourcen with lebesgue measure there corresponds c c 0 for which one has the sobolev imbedding inequality r u t c d mu t u cm0 involving the nonincreasing rearrangements of u and a certain mth order gradient of u when m 1 we deal in fact with a closely related imbedding inequality of talenti in which d need not be rearrangement invariant r u t c d d dt x view the mathml sourcen u x u t u x dx u c10 in both cases we are especially interested in when the quasinorms are optimal in the sense that r cannot be replaced by an essentially larger quasinorm and d cannot be replaced by an essentially smaller one our results yield best possible refinements of such limiting sobolev inequalities as those of trudinger strichartz hansson brezis and wainger

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

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 diffusive logistic equation with a free boundary and sign changing coefficient abstract this short paper concerns a diffusive logistic equation with a free boundary and sign changing coefficient which is formulated to study the spread of an invasive species where the free boundary represents the expanding front a spreading vanishing dichotomy is derived namely the species either successfully spreads to the right half space as time t and survives persists in the new environment or it fails to establish itself and will extinct in the long run the sharp criteria for spreading and vanishing are also obtained when spreading happens we estimate the asymptotic spreading speed of the free boundary

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

spreading vanishing dichotomy in a diffusive logistic model with a free boundary ii abstract we study the diffusive logistic equation with a free boundary in higher space dimensions and heterogeneous 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 simplicity we assume that the environment and the solution are radially symmetric in the special case of one space dimension and homogeneous environment this free boundary problem was investigated in du and lin 2010 10 we prove that the spreading vanishing dichotomy established in du and lin 2010 10 still holds in the more general and ecologically realistic setting considered here moreover when spreading occurs we obtain best possible upper and lower bounds for the spreading speed of the expanding front when the environment is asymptotically homogeneous at infinity these two bounds coincide our results indicate that the asymptotic spreading speed determined by this model does not depend on the spatial dimension

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

bmo estimates for the p laplacian we prove bmo estimates of the inhomogeneous p laplace system given by div jruj p 2 ru divf we show that f 2 bmo impliesjruj p 2 ru2 bmo which is the limiting case of the nonlinear calder on zygmund theory this extends the work of dibenedetto and manfredi dm93 which was restricted to the super quadratic case p 2 to the full case 1 p 1 and even more general growth moreover we prove that a ru inherits the campanato and vmo regularity of f

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

asymptotic behaviour of a reaction diffusion model with a quiescent stage this paper is devoted to the investigation of the asymptotic behaviour for a reaction diffusion model with a quiescent stage we first establish the existence of the asymptotic speed of spread and show that it coincides with the minimal wave speed for monotone travelling waves then we obtain a threshold result on the global attractivity of either zero or positive steady state in the case where the spatial domain is bounded

fluctuations in a sis epidemic model with variable size population in an epidemiological model time spent in one compartment is often modeled by a delay in the model in general the presence of delay in differential equations can change the stability of an equilibrium to instability and causes the appearance of oscillatory solutions in this paper we consider a sis epidemiological model with demographic effects birth mortality and mortality caused by infection the delay is the period of infection we define the concept of oscillation in the sense that solutions of the model studied fluctuate around a steady state our goal is to show that in this model there are oscillating solutions for certain parameters values we determine a large set of initial data for which solutions of this model are slowly oscillating

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

partial extensions of attouch s theorem with applications to proto derivatives of subgradient mappings attouch s theorem which gives on a reflexive banach space the equivalence between the mosco epi convergence of a sequence of convex functions and the graph convergence of the associated sequence of subgradients has many important applications in convex optimization in particular generalized derivatives have been defined in terms of the epi convergence or graph convergence of certain difference quotient mappings and attouch s theorem has been used to relate these various generalized derivatives these relations can then be used to study the stability of the solution mapping associated with a parameterized family of optimization problems we prove in a hilbert space several partial extensions of attouch s theorem to functions more general than convex these functions are called primal lower nice furthermore we use our extensions to derive a relationship between the second order epi derivatives of primal lower nice functions and the proto derivative of their associated subgradient mappings

existence and multiplicity results for some nonlinear problems with singular phi laplacian using leray schauder degree theory we obtain various existence and multiplicity results for nonlinear boundary value problems phi u f t u u l u u 0 where l u u 0 denotes the dirichlet periodic or neumann boundary conditions on 0 t phi a a r is an increasing homeomorphism phi 0 0 the difichlet problem is always solvable for neumann or periodic boundary conditions we obtain in particular existence conditions for nonlinearities which satisfy some sign conditions upper and lower solutions theorems ambrosetti prodi type results we prove lazer solimini type results for singular nonlinearities and periodic boundary conditions c 2007 elsevier inc all rights reserved

green s function for a third order generalized right focal problem abstract we determine the green s function for the third order three point generalized right focal boundary value problem x t 0 t 1 t t 3 x t 1 x t 2 0 x t 3 x t 3 0 where 0 and determine conditions on the coefficients and boundary points to ensure its positivity then we use the krasnoselskii and leggett and williams fixed point theorems to prove the existence of solutions to the nonlinear problem x t f t x t t 1 t t 3 x t 1 x t 2 0 x t 3 x t 3 0 for certain constraints placed on nonnegative f

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

three positive fixed points of nonlinear operators on ordered banach spaces we generalize the fixed point theorem of leggett williams which is a theorem giving conditions that imply the existence of three fixed points of an operator defined on a cone in a banach space we then show how to apply our theorem to prove the existence of three positive solutions to a second order discrete boundary value problem 2001 elsevier science ltd all rights reserved

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

convergence and applications of a gossip based gauss newton algorithm the gauss newton algorithm is a popular and efficient centralized method for solving non linear least squares nlls problems in this paper a multi agent distributed version of this algorithm is proposed to solve general nlls problems in a network named gossip based gauss newton ggn algorithm furthermore we analyze and present sufficient conditions for its convergence and show numerically that the ggn algorithm achieves performance comparable to the centralized algorithm with graceful degradation in case of network failures more importantly the ggn algorithm provides significant performance gains compared to other distributed first order methods

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

nonhomogeneous boundary value problems for some nonlinear equations with singular phi laplacian using leray schauder degree theory we obtain various existence results for the quasilinear equation problems phi u f t u u submitted to nonhomogeneous dirichlet or nonlinear neumann steklov boundary conditions on 0 t when phi a a r is an increasing homeomorphism phi 0 0 we compare the results with the ones proved earlier in the homogeneous case c 2008 elsevier inc all rights reserved

existence multiplicity and dependence on a parameter for a periodic boundary value problem the authors consider the boundary value problem y 2 y g t f y 0 0 t 2 y 0 y 2 y 0 y 2

some existence results on periodic solutions of ordinary p laplacian systems some existence theorems are obtained for periodic solutions of ordinary p laplacian systems by the minimax methods in critical point theory

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

periodic solutions of nonlinear perturbations of phi laplacians with possibly bounded phi using leray schauder degree theory we obtain various existence and multiplicity results for nonlinear periodic boundary value problems of the form phi u f t u u u 0 u t 0 u 0 u t where phi r a a 0 r is a continuous function c 2007 elsevier ltd all rights reserved

2 solvability of the dirichlet problem for nondivergence elliptic equations with vmo coefficients we prove a well posedness result in the class w 2 p w 0 1 p for the dirichlet problem lu f a e in u 0 on we assume the coefficients of the elliptic nondivergence form equation that we study are in vmo l

a class of inverse eigenvalue problems for real symmetric banded matrices with odd bandwidth abstract in this paper we propose and discuss a class of inverse eigenvalue problems for real symmetric banded matrices with odd bandwidth for an odd 2 p 1 with a positive integer p the problem is to construct an n n real symmetric banded matrix with bandwidth 2 p 1 whose m m leading principal submatrix is a given m m real symmetric banded matrix with bandwidth 2 p 1 and spectrum is a given set of real numbers i i 1 n where the number of distinct real numbers of i i 1 n is 2k when m p k or 2 k 1 when p k m p k 1 where m n and k are positive integers and m n we point out that the well known double dimensional dd problem is a special case of our proposed inverse eigenvalue problems the necessary and sufficient condition for the solvability of the above inverse eigenvalue problem is derived and the target real symmetric banded matrix can be constructed by the block lanczos algorithms when the inverse eigenvalue problem is solvable several numerical examples show that our algorithms are feasible some concluding remarks are introduced

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

existence of multiple solutions for second order boundary value problems we give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y f x y y 0 x epsilon 0 1 y 0 0 y 1 in the special case f x y y f y greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions we give an example showing this latter result is sharp our results extend those of avery and of lakshmikantham et al

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

the impact of outliers and leverage points for technical efficiency measurement using high breakdown procedures given that most data used for production studies have not been accumulated for such purposes it is important that the quantitative tools for messy data which can affect the accuracy of computed technical efficiency measures be found in this study high breakdown robust methods are used in conjunction with a robust distance measure defined relative to the minimum volume ellipsoid estimator the standardized robust residuals from the high breakdown estimators and the robust distance measures are used to statistically and graphically depict both multivariate outliers and leverage points once these points are found their relationship to those observations that exhibit strong technically efficient or inefficient behavior scale inefficiency and or unusual production characteristics is analyzed for three linerboard manufacturing facilities additionally the impact of the outliers and leverage points on the estimated least squares coefficients which are used by the corrected ordinary least squares methodology to compute the full frontier technical efficiency measures is explored finally a sensitivity analysis of the impact of outliers and leverage points on the computed linear programming based technical efficiency measures is presented