pinecone/core-2020-05-10-deduplication huggingface dataset:
Chaotic Invariant Sets of High-Dimensional Hénon-Like Maps

AbstractHigh-dimensional Hénon-like maps have many applications in the research of spatial chaos and traveling waves of extended systems. Meanwhile, they are of great interest in their own right. The aim of this paper is, by applying the implicit function theorem, to show for high-dimensional Hénon-like maps the existence of chaotic invariant sets and the density of homoclinic points and heteroclinic points in them. Our method is motivated by Aubry's “anti-integrability” concept and is rather different from the traditional techniques such as horseshoes, transversal homoclinic points and heteroclinic cycles, and snap-back repellers
Existence of Solutions to u″+u+g(t,u,u′)=p(t),u(0)=u(π)=0

AbstractExistence and multiplicity results for the boundary value problem[formula]are presented. The proofs are based on the alternative method, a connectedness result, the contraction mapping principle, and a detailed analysis of the bifurcation equation utilizing, e.g., a generalization of the mean value theorem for integrals. We shall obtain results with g bounded or unbounded, having finite limits at ±∞ or without limits, thus extending some recent results in the literature. The proofs offer a constructive way to find the bounds for p̄ and to find numerically the number of solutions and the approximative solutions
Characterizations of Nonemptiness and Compactness of the Set of Weakly Efficient Solutions for Convex Vector Optimization and Applications

AbstractIn this paper, we give characterizations for the nonemptiness and compactness of the set of weakly efficient solutions of an unconstrained/constrained convex vector optimization problem with extended vector-valued functions in terms of the 0-coercivity of some scalar functions. Finally, we apply these results to discuss solution characterizations of a constrained convex vector optimization problem in terms of solutions of a sequence of unconstrained vector optimization problems which are constructed with a general nonlinear Lagrangian
A Characterization for an L(μ,K)-Topological Module to Admit Enough Canonical Module Homomorphisms

AbstractLet K be the scalar field of all real or complex numbers, let (Ω,A,μ) be a σ-finite measure space, and let L(μ,K) be the algebra of the μ-equivalence classes of all K-valued μ-measurable functions defined on (Ω,A,μ). L(μ,K) is a topological algebra over K when endowed with the topology of convergence locally in measure; topological modules over this topological algebra L(μ,K) (briefly, L(μ,K)-topological modules) are an extensive class of topological modules, which arise naturally in the course of the study of the theory of probabilistic normed spaces. The purpose of this paper is to show that an arbitrary regular L(μ,K)-topological module admits enough canonical module homomorphisms if and only if all of its quasi-free submodules of finite rank are complemented in the sense of topological modules
An Inversion Algorithm in Two-Dimensional Elasticity

AbstractIn this paper scattering problems for the rigid body and the cavity in two-dimensional linear elasticity are considered. In each case the corresponding far-field scattering amplitudes are presented and the Herglotz condition and Herglotz wavefunctions are introduced. A pair of integral equations are constructed in the far-field region. The properties of the Herglotz functions are used to derive solvability conditions and to built approximate far-field equations. A method for solving inverse scattering problems is proposed, and the support of the scattering obstacle is found by noting the unboundedness of the L2-norm of the Herglotz densities as an interior point approaches the boundary of the scattering object from inside the scatterer. Illustration of the unboundedness property on the boundary is carried out for rigid circular cylinders and cavities. Numerical results for rigid bodies are also given, showing the applicability of this method
Singularity Sets of Constant Principal Strain Deformations

AbstractWe show that if f is a mapping with constant principal strains (cps-mapping) of a planar domain of the form D\S, where D is itself a domain and S is a closed subset of D with linear measure 0, then f has an extension to a cps-mapping of D\S′, where S′⊂S has no accumulation points in D. The proof uses properties of cps-mappings attributable to the nonlinear hyperbolic nature of the underlying system of partial differential equations as well as results about their behavior in neighborhoods of isolated singularities previously established by the author
Set-Operational Properties of Semiatoms in Non-additive Measure Theory

AbstractThe semiatom is a basic concept in the non-additive measure theory, or the fuzzy measure theory, and has been used for applications of the theory (T. Murofushi et al., 1997, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems5, 563–585; and T. Murofushi and M. Sugeno, 2000, ibid.8, 385–415). This paper shows several properties of semiatoms on set operations: union, intersection, difference, symmetric difference, countable union, and countable intersection. Characteristic consequences are as follows: if S and T are semiatoms, and if S∩T is non-null, then S∪T and S∩T are semiatoms; moreover, if S\T and T\S are non-null, then S\T, T\S, S▵T also are semiatoms
Existence and Stability for Mathematical Models of Sedimentation–Consolidation Processes in Several Space Dimensions

AbstractIn this paper, we study several spatially multidimensional initial-boundary value problems modelling sedimentation–consolidation processes of a flocculated suspension. This solid–fluid mixture is considered as two superimposed continuous media differing in density and viscosity. The phenomenological foundation and derivation of the mathematical model are based on the previous work by R. Bürger et al. (2000, Z. Angew. Math. Mech. 80, 79–92). We study the full coupling of the conservation of mass equation and the conservation of linear momentum equation. For different types of regularization, we establish energy estimates. The dissipative nature of the whole system assures the existence as well as the stability (long time asymptotics) of a solution of the system (provided that the viscosities of the fluid are large enough). Moreover, the energy estimates might serve as the foundation for the design of numerical algorithms to simulate the system
Global Optimization of Nonlinear Sums of Ratios

AbstractThe nonlinear sum of ratios problem (P) has several important applications. However, it is also a difficult problem to solve, since it generally possesses many local optima that are not global optima. In this article we present and show the convergence of an algorithm for finding a global optimal solution to problem (P). The algorithm uses a branch and bound search procedure that globally solves problem (P) by concentrating primarily on solving an equivalent outcome space version of the problem. The algorithm can be implemented by using standard convex programming methods
Evaluate Fuzzy Riemann Integrals Using the Monte Carlo Method

AbstractTechniques for using the Monte Carlo method to evaluate fuzzy Riemann integrals and improper fuzzy Riemann integrals are proposed in this paper. Owing to the α-level set of the (improper) fuzzy Riemann integral being the closed interval whose end points are the classical (improper) Riemann integrals, it is possible to invoke the Monte Carlo method to approximate the end points of the α-level closed intervals. We develop the strong law of large numbers for fuzzy random variables in order to give the techniques proposed for evaluating the (improper) fuzzy Riemann integrals using the Monte Carlo approach more theoretical support. The membership function of the (improper) fuzzy Riemann integral can be transformed into mathematical programming problems. Therefore, we can obtain the membership value by solving the mathematical programming problems using the commercial optimizer
Reconstruction of a Radially Symmetric Potential from Two Spectral Sequences

AbstractWe consider the problem of determining a radially symmetric potential in the three-dimensional Schrödinger equation from eigenvalues associated with two different angular-momentum quantum numbers. This leads to a singular eigenvalue problem for which there are no known general uniqueness results for the most reasonable conjectures. We are able to give strong evidence for uniqueness in some cases and we discuss a computational solution method together with some supporting analysis. One application we have in mind is the determination of certain physical parameters in the standard model of the sun constructed from eigenvalue data
On(p,r)-Invexity-Type Nonlinear Programming Problems

AbstractMathematical programming problems involving (p,r)-invex functions with respect to η are considered. We introduce new classes of nonlinear programming problems, called KT-(p,r)-invex, WD-(p,r)-invex, and HC-(p,r)-invex problems (where p,r are some real numbers). It is shown that for these types of problems Kuhn–Tucker conditions are both necessary and sufficient for optimality. Furthermore, these (p,r)-invexity-type problems with r≠0 are not sufficient for Wolfe weak duality. In this way it was shown that the optimization problems possessing “some kind” of invexity need not be equivalent to the class of optimization problems for which Kuhn–Tucker necessary conditions for optimality are also sufficient and Wolfe weak duality holds
Mathematical Economics and Descriptive Set Theory

AbstractThe purpose of this paper is first to show that for any integer n≥2, there exist no Borel measurable necessary and sufficient conditions on n lower semi-continuous payoff functions defining a non-cooperative n-person game in strategic form which can assert the existence of non-cooperative Nash equilibria (in either pure or mixed strategies). Second we show that there exist no Borel measurable necessary and sufficient conditions on an exchange economy with preference relations that are represented by lower semi-continuous utility functions which can assert the existence of Walrasian equilibria. And third we show that there exist no Borel measurable necessary and sufficient conditions on a triple of a lower semi-continuous one-period return function, a compact-valued continuous constraint correspondence, and a discount factor defining a deterministic discrete infinite horizon macroeconomic model which can assert the existence of optimal plans starting at some point
Thermohaline Convection of Veronis and Stern Types Revisited

AbstractThe present paper prescribes upper limits for oscillatory motions of neutral or growing amplitude in thermohaline configurations of G. Veronis (1965, J. Mar. Res.23, 1) and M. E. Stern (1960, Tellus12, 172) types in such a way that it also results in sufficient conditions of stability for an initially top-heavy as well as an initially bottom-heavy configuration. Furthermore, the characterization theorem of Mihir B. Banerjee, J. R. Gupta, and Jyoti Prakash, (1993, J. Math. Anal. Appl.179, 327) for Veronis' thermohaline configuration follows as a consequence
Decomposability of Finite-Rank Operators in Commutative Subspace Lattice Algebras

AbstractIn this paper, we explore conditions for a finite-rank operator in a commutative subspace lattice (CSL) algebra to be decomposable (that is, it can be written as the sum of rank one operators in that algebra). We introduce correlation coefficients for rank two operators, the property (F), and correlation matrices for finite-rank operators, based on which we prove that a rank two operator is decomposable if and only if it has only finitely many correlation coefficients, and if a finite-rank operator has the property (F) (has only finitely many correlation matrices) then it is decomposable
Convergence Analysis for the Full-Upwind Finite Volume Solution of a Convection–Diffusion Problem

AbstractThe paper is devoted to the study of convergence properties for an often used cell-centered full-upwind Finite Volume Method (FVM) with Voronoi boxes. This FVM is applied to a convection–diffusion problem. The approach to proving convergence of the FVM is based on the construction of a nonconforming Petrov–Galerkin Finite Element Method (FEM), such that the system of linear equations coincides completely with that of the FVM. Thus, by proving convergence properties of the FEM we obtain similar ones for the FVM. For the error estimation of the FEM the second Strang lemma has to be modified
Periodic Solution for a Two-Species Nonautonomous Competition Lotka–Volterra Patch System with Time Delay

AbstractBy using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a two-species nonautonomous competition Lotka–Volterra patch system with time delay,x′1(t)=x1(t)[r1(t)−a1(t)x1(t)−b1(t)y(t)]+D1(t)[x2(t)−x1(t)],x′2(t)=x2(t)[r2(t)−a2(t)x2(t)]+D2(t)[x1(t)−x2(t)],y′(t)=y(t)r3(t)−a3(t)x1(t)−b3(t)y(t)−β(t)∫−τ0K(s)y(t+s)ds,is established, where ri(t),ai(t)(i=1,2,3),Di(t)(i=1,2),bi(t)(i=1,3), and β(t) are all positive periodic continuous functions with period w>0,τ is a nonnegative constant, and K(s) is a continuous nonnegative function on [−τ,0]
On Complex-Lamellar Motion of a Prim Gas

AbstractAn intrinsic formulation of Prim's canonical equations of gas dynamics is employed to establish a generalization of Crocco's theorem to complex-lamellar motion. This new result is then employed to establish the existence of a Heisenberg spin-type equation in such motion. The optimal coordinate systems in the generalized Lagrangian method which are known to exist only in complex-lamellar motion are then shown by intrinsic geometric methods to correspond to a marching direction along geodesics on generalized Bernoulli surfaces
The Contact Problem in Thermoviscoelastic Materials

AbstractWe stablish an existence result for the thermoviscoelastic degenerated contact problem. The nonlinear stress–strain relation we will consider here is given byσ=M∫L0|ux|2dxux−αθ+γuxt,where M is a function satisfying M∈C1(]0,∞[)∩C([0,∞[),M(s)≥C|s|p. Moreover, we show that the solution decays uniformly to zero. That is, denoting by E(t) the first-order energy associated to the equation, we show that there exist positive constants C satisfyingEt≤CE01+t−(p+2)/pwhere p is a positive number which depends on nonlinear terms of the system
On the Geometry of Cake Division

AbstractWe study partitions of a “cake” C among n players. Each player uses a countably additive non-atomic probability measure to evaluate the sizes of pieces of cake. If the players' measures are m1,m2,…,mn, then the “Individual Pieces Set,” which we studied before (2000, J. Math. Econom.33, 401–424), is the set {(m1(P1),m2(P2),…,mn(Pn)):〈P1,P2,…,Pn〉 is a partition of C}. We continue our study of this set here. Our motivating question is: What are the possible shapes of such sets? We give an exact characterization for n=2, establish some partial results for n=3, and close with open questions
Analysis of a Scale-Similarity Model of the Motion of Large Eddies in Turbulent Flows

AbstractIn turbulent flow, the normal procedure has been to seek means ū of the fluid velocity u rather than the velocity itself. If these means are defined by local spacial averaging with an averaging radius of δ the approach is known as large eddy simulation, and ū denotes the eddies of size 0(δ) and larger. One approach to the closure problem which arises from averaging the nonlinear term is use of a scale-similarity hypothesis. We consider one such scale-similarity model. For this model we show the solution w to the model for ū converging to u as the averaging radius δ→0. We also show that the error ‖ū−w‖ is bounded by the modeling error (perhaps better termed “modeling residual”), evaluated on the true solution u. This last bound suggests one path to validating the model in either computational or physical experiments
Thermal Effects in a Two-Dimensional Hybrid Elastic Structure

AbstractIn this paper we consider a two-dimensional hybrid thermo-elastic structure consisting of a thermo-elastic plate which has a beam attached to its free end. We show that the initial-boundary-value problem for the interactive system of partial differential equations which take account of the mechanical strains/stresses and the thermal stresses in the plate and the beam, can be associated with a uniformly bounded evolution operator. It turns out that the interplay of parabolic dynamics due to the thermal effects in the hybrid structure and the hyperbolic dynamics associated with the elasticity of the structure yields analyticity for the entire system. This result yields solvability for the problem under optimal initial freedom of the displacement, velocity, and temperature in the plate and the beam, while uniform stability is readily available
The Spectral Expansion for a Nonself-adjoint Hill Operator with a Locally Integrable Potential

AbstractWe construct the spectral expansion for the one-dimensional Schrödinger operatorL=−d2dx2+q(x),−∞<x<∞,in L2(−∞,∞), where q(x) is a 1-periodic, Lebesgue integrable on [0,1], and complex-valued potential. We obtain the asymptotic formulas for the eigenfunctions and eigenvalues of the operator Lt, for t≠0, π, generated by this operation in L2[0,1] and the t-periodic boundary conditions. Using it, we prove that the eigenfunctions and associated functions of Lt form a Riesz basis in L2[0,1] for t≠0, π. Then we find the spectral expansion for the operator L
Multiparameter Sturm–Liouville Problems with Eigenparameter Dependent Boundary Conditions

AbstractA system of ordinary differential equations,−y″j+qjyj=∑k=1nλkrjkyj,j=1,…,n,0.1with real valued and continuous coefficient functions qj,rjk is studied on [0,1] subject to boundary conditionsy′j0yj0=cotβjandbjyj1−djy′j1=eTjλcjy′j1−ajyj10.2for j=1,…,n. Here ET=[e1e2···en] is an arbitrary n×n matrix of real numbers and ωj=ajdj−bjcj≠0. A point λ=[λ1···λn]T∈Cn satisfying (0.1) and (0.2) is called an eigenvalue of the system. Results are given on the existence and location of the eigenvalues and completeness and oscillation of the eigenfunctions
Points of Weak-Norm Continuity in the Unit Ball of Banach Spaces

AbstractUsing the M-structure theory, we show that several classical function spaces and spaces of operators on them fail to have points of weak-norm continuity for the identity map on the unit ball. This gives a unified approach to several results in the literature that establish the failure of strong geometric structure in the unit ball of classical function spaces. Spaces covered by our result include the Bloch spaces, dual of the Bergman space L1a and spaces of operators on them, as well as the space C(T)/A, where A is the disc algebra on the unit circle T. For any unit vector f in an infinite-dimensional function algebra A we explicitly construct a sequence {fn} in the unit ball of A that converges weakly to f but not in the norm
Spectral Asymptotics for Schrödinger Operators with Periodic Point Interactions

AbstractSpectrum of the second-order differential operator with periodic point interactions in L2(R) is investigated. Classes of unitary equivalent operators of this type are described. Spectral asymptotics for the whole family of periodic operators are calculated. It is proven that the first several terms in the asymptotics determine the class of equivalent operators uniquely. It is proven that the spectrum of the operators with anomalous spectral asymptotics (when the ratio between the lengths of the bands and gaps tends to zero at infinity) can be approximated by standard periodic “weighted” operators with step-wise density functions. It is shown that this sequence of periodic weighted operators converges in the norm resolvent sense to the formal (generalized) resolvent of the periodic “Schrödinger operator” with certain energy-dependent boundary conditions. The operator acting in an extended Hilbert space such that its resolvent restricted to L2(R) coincides with the formal resolvent is constructed explicitly
Asymptotics of Solutions to the Boundary-Value Problem for the Korteweg–de Vries–Burgers Equation on a Half-Line

AbstractWe study the following initial–boundary value problem for the Korteweg–de Vries–Burgers equation,where α=0,1. We prove that if the initial data u0∈H0,ω∩H1,0, where Hs,k={f∈L2;‖f‖Hs,k=‖〈x〉k〈i∂x〉sf‖L2<∞}, ω∈(12,32), and the norm ‖u0‖H0,ω+‖u0‖H1,0 is sufficiently small, then there exists a unique solution u∈C([0,∞),H0,ϰ)∩C((0,∞),H1,ω) of the initial–boundary value problem (0.1), where ϰ∈(0,12). Moreover, if the initial data are such that x1+μu0(x)∈L1, μ=ω−12, then there exists a constant A such that the solution has the asymptoticsu(x,t)=AtΦαx2t,t+Ominxt,1t−1−for t→∞ uniformly with respect to x>0, where α=0,1, Φ0(q,t)=(q/π)e−q2, Φ1(q,t)=(1/2πt)(e−q2(2qt−1)+e−2q
A Mathematical Study for a Rotenberg Model

AbstractThis paper deals with a mathematical model in cell dynamics population originally proposed by M. Rotenberg (1983, J. Theoret. Biol.103, 181–199). Individual cells are distinguished by their degree of maturity and maturation velocity. Here, all biological rules are considered. We bring new techniques to the discussion of this model. We show that the model is well posed in the sense of the theory of semigroups, we study the positivity and irreducibility of the generated semigroups, and we calculate its essential type. The asymptotic behavior is obtained in uniform topology
Change in Network Revenue Due to Changes in Capacities of Links

AbstractA multirate, loss network is investigated. The intensities of the traffic carried on each link, and the link capacities, are assumed to be commensurately large. An asymptotic approximation to the change in network revenue, due to small changes in the capacities of the links, is derived. A significant advantage of this approximation is that it is not necessary to specify which links are overloaded, critically loaded, or underloaded. Moreover, it is shown how to asymptotically calculate the change in revenue in terms of quantities which are already known for the unchanged network. This result has been used to calculate linearized capacity costs in the joint resource allocation and routing design of virtual private networks
Remarks on Propagation of Singularities in Thermoelasticity

AbstractThe propagation of high order weak singularities for the system of homogeneous thermoelasticity in one space variable is studied by using paralinearization and a new decoupling technique introduced by the author (Microlocal analysis in nonlinear thermoelasticity, to appear). For the linear system, one shows that the nonsmooth initial data for the parabolic part lead to singularities in the hyperbolic part of solutions, even when the initial data for that part are identically zero. Both the Cauchy problem and the problem inside of a domain for the semilinear system are considered. It is shown that the propagation of high order singularities is essentially dominated by the hyperbolic operator in the system of thermoelasticity
Weighted Norm Inequalities for Pluriharmonic Conjugate Functions

AbstractWe define pluriharmonic conjugate functions on the unit ball of Cn. Then we show that for a weight there exist weighted norm inequalities for pluriharmonic conjugate functions on Lp if and only if the weight satisfies the Ap-condition. As an application, we prove the equivalence of the weighted norm inequalities for the Cauchy integral and the Ap-condition of the weight. Along the way, we show that there exist norm inequalities for pluriharmonic conjugate functions on BMO and on the nonisotropic Lipschitz spaces
Further Results on the Stability of Linear Systems with Multiple Delays

AbstractThis paper has two purposes. One is to establish new stability criteria for linear systems with multiple time-varying/constant delays, and the other is to point out the limitations of the author's previous results. The stability criteria, including delay-dependent and delay-independent ones, are derived by using both time-domain and frequency-domain techniques. All of the established stability criteria are given in the form of linear matrix inequality problems, including only one tuning parameter matrix P>0∈Rn×n