pinecone/core-2020-05-10-deduplication huggingface dataset:
Interval Oscillation Criteria Related to Integral Averaging Technique for Certain Nonlinear Differential Equations

AbstractWe present new interval oscillation criteria related to integral averaging technique for certain classes of second order nonlinear differential equations that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t0,∞), rather than on the whole half-line. Our results are sharper than some previous results and handle the cases which are not covered by known criteria. In particular, several examples that dwell upon the sharp conditions of our results are also included
Cores of Cooperative Games, Superdifferentials of Functions, and the Minkowski Difference of Sets

AbstractLet v be a cooperative (TU) game and v=v1−v2 be a decomposition of v as a difference of two convex games v1 and v2. Then the core C(v) of the game v has a similar decomposition C(v)=C(v1)⊖C(v2), where ⊖ denotes the Minkowski difference. We prove such a decomposition as a consequence of two claims: the core of a game is equal to the superdifferential of its continuation, known as the Choquet integral, and the superdifferential of a difference of two concave functions equals the Minkowski difference of corresponding superdifferentials
Minimal Representation of Convex Regions Defined by Analytic Functions

AbstractIn this paper we are concerned with characterizing minimal representation of feasible regions defined by both linear and convex analytic constraints. We say that a representation is minimal if every other representation has either more analytic (nonlinear) constraints, or has the same number of analytic constraints and at least as many linear constraints. We prove necessary and sufficient conditions for the representation to be minimal. These are expressed in terms of the redundant constraints, pseudo-analytic constraints, and implicit equality constraints. In order to prove the minimal representation theorem, we present results on the facets of the convex regions defined by analytic constraints. Finally, we outline the steps of the procedure that could be used to determine a minimal representation
The Group of L-Fuzzy Homeomorphisms and the Group of Permutations of the Ground Set

AbstractIn this paper we study some relations between the group of L-fuzzy homeomorphisms of an L-fuzzy topological space X and the group of permutations of the ground set X. In contrast with the results in general topology, it is proved that the subgroups generated by cycles and proper normal subgroups can be represented as groups of L-fuzzy homeomorphisms for some L-fuzzy topology on X. The relation between the group of L-fuzzy homeomorphisms and the group of homeomorphisms of the associated topology is also discussed
The Spectrum of Analytic Mappings of Bounded Type

AbstractA Banach space E is said to be (symmetrically) regular if every continuous (symmetric) linear mapping from E to E′ is weakly compact. For a complex Banach space E and a complex Banach algebra F, let Hb(E,F) denote the algebra of holomorphic mappings from E to F which are bounded on bounded sets. We endow Hb(E,F) with the usual Fréchet topology. M(Hb(E,F),F) denotes the set of all non-null continuous homomorphisms from Hb(E,F) to F. A subset of GEF on which the extension of Zalduendo is multiplicative is presented and it is shown that, in general, the sets GEF and M(Hb(E,F),F) do not coincide. We prove that if E is symmetrically regular and every continuous linear mapping from E to F is weakly compact then there exists an analytic structure on M(Hb(E,F),F)
A Linearization for a Class of λ-Nonlinear Boundary Eigenvalue Problems

AbstractIn this paper a new linearization of boundary eigenvalue problems for systems ỹ′+Ã0ỹ=λÃ1ỹ of n first order differential equations with λ-polynomial boundary conditions is proposed. The linearized problem is again a boundary eigenvalue problem for a system y′+A0y=λA1y of first order differential equations of dimension n+n̂ where n̂ is the total polynomial degree of the boundary conditions. As a particular case, we consider systems of first order differential equations induced by nth order differential equations Nη=λPη, and we give an application to the Orr–Sommerfeld equation with λ-quadratic boundary conditions
Essential Spectrum of a Self-Adjoint Operator on an Abstract Hilbert Space of Fock Type and Applications to Quantum Field Hamiltonians

AbstractWe establish general theorems on locating the essential spectrum of a self-adjoint operator of the form A⊗I+I⊗dΓ(S)+HI on the tensor product H⊗Fb(K) of a Hilbert space H and the abstract Boson Fock space Fb(K) over a Hilbert space K, where A is a self-adjoint operator on H bounded from below, dΓ(S) is the second quantization of a nonnegative self-adjoint operator S on K, and HI is a symmetric operator on H⊗Fb(K). We then apply the theorems to the generalized spin-boson model by A. Arai and M. Hirokawa (1997, J. Funct. Anal.151, 455–503) and a general class of models of quantum particles coupled to a Bose field including the Pauli–Fierz model in nonrelativistic quantum electrodynamics
Evolution of Positive Solution Curves in Semipositone Problems with Concave Nonlinearities

AbstractWe study the existence, multiplicity, and stability of positive solutions to−u″x=λfuxfor x∈−1,1,u−1=0=u1,where λ>0 and f: [0,∞)→R is monotonically increasing and concave with f(0)<0 (semipositone). We establish that f should be appropriately concave (by establishing conditions on f) to allow multiple positive solutions. For any λ>0, we obtain the exact number of positive solutions as a function of f(t)/t. We follow several families of nonlinearities f for which f′(∞)≔limt→∞f′(t)>0 and study how the positive solution curves to the above problem evolve. Also, we give examples where our results apply. This work extends the work of A. Castro and R. Shivaji (1988, Proc. Roy. Soc. Edinburgh Sect. A108, 291–302) and S.-H. Wang (1994, Proc. Roy. Soc. Edinburgh124, No. 3, 507–515) by obtaining sharper results and also gives a complete study of positive solutions for concave semipositone nonlinearities
On the Summation of Series Involving Bessel or Struve Functions

AbstractThe subject called “summation of series” can be viewed in two different ways. From one point of view, it means numerical summation which involves acceleration of convergence, and from the other, it represents a variety of summation formulas which are considered important, but which are often not useful. The aim of this paper is to produce a compromise between the two opposite approaches when series of Bessel or Struve functions are considered. The proposed method leads to series of Riemann zeta and related functions which converge much faster than the originals. In the most significant cases, closed-form formulas were obtained
A-Properness and Fixed Point Theorems for Sums of Dissipative and Ball-Condensing Maps

AbstractWe obtain new results on A-properness of sums of dissipative and ball-condensing maps in π1-Banach spaces. The maps involved need not be self-maps, and the dissipative maps are not required to satisfy any extra range conditions. Moreover, the domains of the maps may be closed subsets. It is known that, in general, it is difficult to prove A-properness at all points of the whole space for a map defined on a closed subset. An open question on A-properness of a k-contraction defined on a ball in a general π1-Banach space, raised by Petryshyn in 1975 and 1993, has not been completely solved so far. Our result will give a partial answer to the open question. New fixed point theorems for sums of the above maps and range results for dissipative maps are derived. An application to eigenvalue problems for homogeneous integral equations is provided
Weak Property (Y0) and Regularity of Inductive Limits

AbstractAn inductive limit (E,t)=ind(En,tn) is regular if and only if it satisfies the weak property (Y0); i.e., each weakly unconditionally Cauchy series in (E,t) is contained and is a weakly unconditionally Cauchy series in some (En,tn). In particular, an (LF)-space (E,t)=ind(En,tn) is regular if and only if every weakly unconditionally Cauchy series ∑kxk is a C-series; i.e., for any scalar sequence (ξk)∈c0, the series ∑kξkxk is convergent. Furthermore, for inductive limits of Fréchet spaces containing no copy of c0, a number of characteristic conditions of regularity are given
Integrability of Lie Equations and Pseudogroups

AbstractIn this paper the theory of jets based on Weil's near points is applied to Lie equations and pseudogroups. Linear systems of partial differential equations are interpreted, in a canonical way, as distributions on the fibre bundles of invertible jets invariant under translations. We prove the two fundamental theorems for Lie equations and generalize the results of Rodrigues; a geometric correspondence between linear and nonlinear Lie equations is given, and the symbols of a linear Lie equation and its prolongations are canonically identified with the symbols of their attached nonlinear equations. From this fact we deduce that a linear Lie equation verifies the conditions of Goldsmichmidt's criterion on formal integrability if and only if its attached nonlinear Lie equation satisfies them locally. Finally, we define the Cartan 1-form on the fibre bundle of invertible jets and give a global form to the equivalence between the Lie and Cartan definitions of continuous groups
Extinction in Finite Time of Solutions to Degenerate Parabolic Equations with Nonlinear Boundary Conditions

AbstractThis work concerns a nonlinear diffusion–absorption equation with nonlinear boundary flux. The main topic of interest is the problem of finite time extinction, i.e., the solutions vanish after a finite time. The sufficient and necessary conditions for occurrence of extinction are established. It is shown that extinction is caused by either strong absorption in the interior of the domain or fast diffusion combined with strong absorption through the boundary of the domain. Extinction results are also obtained for the mixed boundary value problem. In contrast to the nonlinear Neumann problem, the absorption on the boundary is no longer important, i.e., the occurrence of extinction in this case is completely determined by the effects of diffusion and interior absorption
A Generalization of Ekeland's ϵ-Variational Principle and Its Borwein–Preiss Smooth Variant

AbstractWe give a generalization of Ekeland's ϵ-Variational Principle and of its Borwein–Preiss smooth variant, replacing the distance and the norm by a “gauge-type” lower semi-continuous function. As an application of this generalization, we show that if on a Banach space X there exists a Lipschitz β-smooth “bump function,” then every continuous convex function on an open subset U of X is densely β-differentiable in U. This generalizes the Borwein–Preiss theorem on the differentiability of convex functions
Multiple Objective Nonatomic Markov Decision Processes with Total Reward Criteria

AbstractWe consider a Markov decision process with an uncountable state space and multiple rewards. For each policy, its performance is evaluated by a vector of total expected rewards. Under the standard continuity assumptions and the additional assumption that all initial and transition probabilities are nonatomic, we prove that the set of performance vectors for all policies is equal to the set of performance vectors for (nonrandomized) Markov policies. This result implies the existence of optimal (nonrandomized) Markov policies for nonatomic constrained Markov decision processes with total rewards. We provide two examples of applications of our results to constrained multiple objective problems in inventory control and finance
Relative Oscillation–Non-Oscillation Criteria for Perturbed Periodic Dirac Systems

AbstractUnder minimal hypotheses, sufficient criteria for a perturbed Dirac system to be relatively oscillatory or non-oscillatory at ∞ with respect to a reference equation with periodic coefficients are proved my means of an asymptotic analysis of generalized Prüfer angles. As illustrated by an example, they help decide whether the number of eigenvalues in gaps of the essential spectrum is finite or infinite. The critical perturbations naturally occur in the partial-wave analysis of spherically symmetric Dirac operators
A Dynamic Model with Friction and Adhesion with Applications to Rocks

AbstractDynamic frictional contact with adhesion of a viscoelastic body and a foundation is formulated as a hemivariational inequality. This may model the dynamics of rock layers. The normal stress–displacement relation on the contact boundary is nonmonotone and nonconvex because of the adhesion process. A sequence of regularized problems is considered, the necessary a priori estimates are obtained, and the existence of a weak solution for the hemivariational inequality is established by passing to the limit as the regularization parameter vanishes
Conditions for Global Attractivity of n-Patches Predator–Prey Dispersion-Delay Models

AbstractIn this paper, a nonautonomous predator–prey dispersion model with functional response and continuous time delay is studied, where all parameters are time dependent. In this system, which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. It is proved the system is uniformly persistent under any dispersion rate effect. Furthermore, the sufficient conditions are established for global attractivity of a periodic solution of the system
Diffraction Problems and Inversion of Infinite Structured Matrices

AbstractMany model diffraction problems, generated by the Helmholtz equation, can be reduced to solving the infinite systems of linear algebraic equations SX=F. It proves that often the operators S in these problems satisfy some operator identities of the form AS−SB=Π1Π*2, where A and B are diagonal matrices and matrices Π1 and Π2 have a finite number of columns. By the rigorous regularization and simultaneous application of the operator identity method one can justify and significantly improve the procedure for solving such systems. The case of the diffraction in the planar waveguide with a cross-sectional jump, absolutely soft upper boundary, and absolutely hard lower boundary is thoroughly considered in the paper as an example. In this case S is an infinite matrix, acting as an unbounded operator. The reflection and transmission coefficients are expressed explicitly via the action of S−1 on two fixed columns, and the ways of obtaining S−1 on these columns are investigated
Trace Representation of Weights on Algebras of Unbounded Operators

AbstractThe purpose of this paper is to study when a weight ϕ on an O*-algebra M on a dense subspace D in a Hilbert space H is a trace weighted by a positive self-adjoint operator, that is, when there exists a positive self-adjoint operator Ω such that ϕ(X†X)=tr(X†*Ω)*X†*Ω whenever ϕ(X†X)<∞. We show that if M is QMP-solvable (that is, every strongly positive linear functional on M is a trace weighted by a positive trace class operator), then every sequentially monotonously regular weight ϕ on the positive cone M+≡{X∈M;X≥0} (ϕ=supnfn for some increasing sequence {fn} of strongly positive linear functionals on M) with the property that {X†ξ; ξ∈D, X∈M, and ϕ(X†X)<∞} is total in H is a trace weighted by a positive self-adjoint operator. More general results are obtained for an O*-algebra M containing the algebra F(D) generated by the set of all symmetric finite rank operators A satisfying AD⊂D. We also show that if ϕ is a weight on M+ and there exists an element N of M+ such that ϕ(N2)<∞ and N−1 is a bounded compact operator on H, then there exists a positive trace class operator T on H such that ϕ(X†X)=tr(T1/2X†)*T1/2X† whenever ϕ(X†N2X)<∞
Holomorphic Idempotents and Retracts in the Unit Ball of a Commutative C*-Algebra with Identity

AbstractLet A be a commutative C*-algebra with identity and open unit ball B. We study holomorphic functions F: B→B that are idempotent under composition and establish necessary and sufficient conditions for a set R⊆B to be the image of B under such an idempotent function. (In other words, R is a holomorphic retract of B.) In order to achieve this result, a representation for linear idempotents of the algebra must be attained. The linear part of a holomorphic idempotent taking 0 to 0 is idempotent itself, and thus the linear representation can be used to prove several identities relating the linear and holomorphic idempotents, giving the main result
A Selection Principle for Mappings of Bounded Variation

AbstractE. Helly's selection principle states that an infinite bounded family of real functions on the closed interval, which is bounded in variation, contains a pointwise convergent sequence whose limit is a function of bounded variation. We extend this theorem to metric space valued mappings of bounded variation. Then we apply the extended Helly selection principle to obtain the existence of regular selections of (non-convex) set-valued mappings: any set-valued mapping from an interval of the real line into nonempty compact subsets of a metric space, which is of bounded variation with respect to the Hausdorff metric, admits a selection of bounded variation. Also, we show that a compact-valued set-valued mapping which is Lipschitzian, absolutely continuous, or of bounded Riesz Φ-variation admits a selection which is Lipschitzian, absolutely continuous, or of bounded Riesz Φ-variation, respectively
Dichotomic Behavior of Linear Difference Systems with Advanced Argument

AbstractIn this paper, the difference equation with advanced argument y(n+1)=A(n)y(n)+B(n)y(g(n)) is considered. The sequence of advances {g(n)} satisfies 1≤g(n)−n≤N, where N is a fixed number. The matrices A(n) are invertible, whereas, in general, matrices B(n) are not. In this paper the notion of an ordinary dichotomy for a linear equation with advance is given. This construction relies on a variation of constants formula obtained for the nonhomogeneous equation y(n+1)=A(n)y(n)+B(n)y(g(n))+f(n) and on the notion of admissibility of a pair of functional spaces. It is proven that these ordinary dichotomies are not destroyed by l1-perturbations. A theorem of existence of ordinary dichotomies is given
Higher Order Dynamic Equations on Measure Chains: Wronskians, Disconjugacy, and Interpolating Families of Functions

AbstractThis paper introduces generalized zeros and hence disconjugacy of nth order linear dynamic equations, which cover simultaneously as special cases (among others) both differential equations and difference equations. We also define Markov, Fekete, and Descartes interpolating systems of functions. The main result of this paper states that disconjugacy is equivalent to the existence of any of the above interpolating systems of solutions and that it is also equivalent to a certain factorization representation of the operator. The results in this paper unify the corresponding theories of disconjugacy for nth order linear ordinary differential equations and for nth order linear difference equations
Infinitely Many Solutions for a Floquet-Type BVP with Superlinearity Indefinite in Sign

AbstractBy the application of a technique developed by G. J. Butler we find infinitely many solutions of the BVP[formula]where q:[0,ω]→R is allowed to change sign, g:R→R is superlinear and g(x)x>0 for all x≠0, and Λ:R2→R2 is a continuous, positively homogeneous, and nondegenerate map. At first we apply the main result to obtain solutions with a prescribed large number of zeros when Λ is the rotation of a fixed angle λ; second, we find infinitely many subharmonic solutions of any order and, again, solutions with a prescribed large number of zeros for the periodic problem associated to the equation ẍ+cẋ+q(t)g(x)=0, with q and g as above and c∈R
Analytical Results for a BVP Describing Radial Stagnation Flow with Transpiration

AbstractWe investigate the boundary value problem (BVP) resulting from an exact reduction of the Navier–Stokes equations for radial stagnation flow impinging on a porous cylinder with uniform transpiration. Existence of a solution is proven for all values of the Reynolds number and for both suction and blowing. The results are obtained using a topological shooting argument which varies a parameter related to the axial shear stress. This formulation permits a derivation of useful bounds on the axial shear stress in a straightforward manner. For a certain parameter range, uniqueness results are also obtained
Oscillation Criteria for Second Order Nonlinear Differential Equations Involving General Means

AbstractConsider the second order nonlinear differential equation (E) y″+a(t)f(y)=0 where a(t)∈C[0,∞), f(y)∈C1(−∞,∞), f′(y)≥0, and yf(y)>0 for y≠0. Furthermore, f(y) also satisfies either a superlinear or a sublinear condition, which covers the nonlinear function f(y)=y|y|γ−1 with γ>1 and 0<γ<1, respectively, commonly known as the Emden–Fowler case. Here the coefficient function a(t) is allowed to be negative for arbitrarily large values of t. Kamenev type oscillation criteria involving integral averages for the linear equations (L) y″+a(t)y=0 are extended to the nonlinear equation (E) by using more general means. The results extend similar results on general means by Philos for the linear equation (L) and also results based upon Kamenev's integral averaging method concerning the nonlinear equation (E)
Regularity and Stability for the Scattering Map of a Linearized Inverse Medium Problem

AbstractThe main goal of this paper is to study the linearization of an inverse medium problem. Regularity and stability results are established for the near-field scattering map (or scattering matrix) which maps the scatterer to the scattered field. Properties on continuity and Fréchet differentiability of the scattering map are examined. A lower bound of the linearized scattering map is obtained, which in particular characterizes the stability properties. These results are useful in the analysis of the nonlinear inverse scattering problem
Outer Automorphisms of the Generic Dynamics Factor

AbstractLet A be the generic dynamics factor. Since A is a quotient of the Borel*-envelope of the Fermion algebra it is hyperfinite. Let OutA=AutA/InnA be the outer automorphism group of A. Among other more general results it is shown that every countable group can be isomorphically embedded in OutA; there exist continuum many elements of OutA corresponding to aperiodic outer automorphisms; for each natural number p≥2 there exist continuum many elements of OutA corresponding to periodic automorphisms of order p
A Representation of Properly Relaxed Controls with Two Delays

AbstractThe search of a proper relaxation procedure (in the sense that relaxed minimizers can be approximated with ordinary controls) for optimal control problems involving delays in the control variables has been the main topic of several recent papers. Three models of relaxation, which we call the weak, strong, and D procedures, have been proposed and, in all cases, the existence of minimizers has been established. It has been proved that the D-model is a proper relaxation procedure, but determining the set of D-relaxed controls for specific problems is very difficult and perhaps even a hopeless task. Thus there is a need to find more concrete characterizations of the closure of the space of ordinary delayed controls. In the event of commensurate delays this is solved through the strong model: the space of strongly relaxed controls coincides with the space of D-relaxed controls. For the noncommensurate case, the problem of how to characterize D-relaxed controls has remained unsolved and, although a natural candidate had been the space of weakly relaxed controls, now we know that for either commensurate or noncommensurate delays it may fail to be proper. In this paper we are finally able to characterize D-relaxed controls for two noncommensurate delays by the introduction of a new model of relaxation, the P-model, which turns out to be a space strictly contained in that of weakly relaxed controls