pinecone/core-2020-05-10-deduplication huggingface dataset:
An Abstract Extremal Principle with Applications to Welfare Economics

AbstractIn this paper we introduce general prenormal and normal structures in Banach spaces that cover conventional concepts of normals to arbitrary closed sets under minimal requirements. Based on these structures, we establish new abstract versions of the extremal principle in variational analysis, which plays a fundamental role in many applications. The main applications of this paper concern necessary conditions for Pareto optimality in nonconvex models of welfare economics. We obtain new results in this direction that extend approximate and exact versions of the generalized second welfare theorem for Pareto, weak Pareto, and strong Pareto optimal allocations
Hierarchical Production Control in a Stochastic N-Machine Flowshop with Long-Run Average Cost

AbstractThis paper presents an asymptotic analysis of stochastic manufacturing systems consisting of machines in tandem subject to breakdown and repair and facing a constant demand, as the rates of change of the machine states approach infinity. This situation gives rise to a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. The long-run average cost for the original problem converges to the long-run average cost of the limiting problem. A method of “shrinking” and “entire lifting” is introduced in order to construct the near optimal controls for the original problem by using near optimal controls of the limiting problem. The convergence rate of the long-run average cost for the original problem to that of the limiting problem is established. This helps in providing an error estimate for the constructed open-loop asymptotic optimal control
Diffusion in Poro-Elastic Media

AbstractExistence, uniqueness, and regularity theory is developed for a general initial-boundary-value problem for a system of partial differential equations which describes the Biot consolidation model in poro-elasticity as well as a coupled quasi-static problem in thermoelasticity. Additional effects of secondary consolidation and pore fluid exposure on the boundary are included. This quasi-static system is resolved as an application of the theory of linear degenerate evolution equations in Hilbert space, and this leads to a precise description of the dynamics of the system
Some Families of Generating Functions Associated with the Stirling Numbers of the Second Kind

AbstractThe object of this paper is to present a systematic introduction to (and several interesting applications of) a general result on generating functions (associated with the Stirling numbers of the second kind) for a fairly wide variety of special functions and polynomials in one, two, and more variables. The main results given below are shown to apply not only to the classical orthogonal polynomials including, for example, the Jacobi polynomials (which contain, as their special cases, the Gegenbauer or ultraspherical polynomials, the Legendre or spherical polynomials, and the Chebyshev polynomials of the first and second kinds) and the Laguerre polynomials, and to their various extensions and generalizations studied in recent years, but indeed also to a class of generalized hypergeometric functions, the Lauricella polynomials in several variables, and the familiar Lagrange polynomials which arise in certain problems in statistics. Relevant connections of some of these families of generating functions with various known results are also indicated
Fundamental Principles of Lagrangian Dynamics: Mechanical Systems with Non-ideal, Holonomic, and Nonholonomic Constraints

AbstractThis paper deals with the foundations of analytical dynamics. It obtains the explicit equations of motion for mechanical systems that are subjected to non-ideal holonomic and nonholonomic equality constraints. It provides an easy incorporation of such non-ideal constraints into the framework of Lagrangian dynamics. It bases its approach on a fundamental principle that includes non-ideal constraints and that reduces to D'Alembert's Principle in the special case when all the constraints become ideal. Based on this, the problem of determining the equations of motion for the constrained system is reformulated as a constrained minimization problem. This yields a new fundamental minimum principle of analytical dynamics that reduces to Gauss's Principle when the constraints become ideal. The solution of this minimization problem then yields the explicit equations of motion for systems with non-ideal constraints. An illustrative example showing the use of this general equation for a system with sliding Coulomb friction is given
A Riemann–Hilbert Approach to the Laplace Equation

AbstractLet q(x,y) satisfy the Laplace equation in an arbitrary convex polygon. By performing the spectral analysis of the equation μz−ikμ=qx−iqy,z=x+iy, which involves solving a scalar Riemann–Hilbert (RH) problem, we construct an integral representation in the complex k-plane of q(x,y) in terms of a function ρ(k). It has been recently shown that the function ρ(k) can be expressed in terms of the given boundary conditions by solving a matrix RH problem. Here we show that this method is also useful for solving problems in a non-convex polygon.We also recall that for simple polygons it is possible to bypass the above integral representation and to solve the Laplace equation by formulating a RH problem in the complex z-plane
Low Frequency Longitudinal Vibrations of an Elastic Bar Made of a Dynamic Material and Excited at One End

AbstractThe dynamic materials, particularly the spatio-temporal composites, have been investigated in a number of recent publications. In the present paper, we examine a dynamic performance of an elastic bar with material parameters specified as an activated (moving at uniform velocity V) periodic pattern of segments occupied by ordinary materials 1 and 2, with density ρ and stiffness k specified as (ρ1,k1) and (ρ2,k2), respectively. We particularly consider the low frequency wave propagation arising when the period d of the material pattern is much less than the wavelength λ of a dynamic disturbance. The bar is excited at its left end by a signal g(t)
Global Existence and Stability of Solutions of Matrix Riccati Equations

AbstractWe consider a matrix Riccati equation containing two parameters c and α. The quantity c denotes the average total number of particles emerging from a collision, which is assumed to be conservative (i.e., 0<c≤1), and α(0≤α<1) is an angular shift. Let S={(c,α):0<c≤1 and 0≤α<1}. Stability analysis for two steady-state solutions Xmin and Xmax are provided. In particular, we prove that Xmin is locally asymptotically stable for S−{(1,0)}, while Xmax is unstable for S−{(1,0)}. For c=1 and α=0, Xmin=Xmax is neutral stable. We also show that such equations have a global positive solution for (c,α)∈S, provided that the initial value is small and positive
Measures on the Lattice of Closed Inner Ideals in a Spin Triple

AbstractTwo elements J and K of the complete lattice I(A) of weak*-closed inner ideals in a JBW*-triple A are said to be centrally orthogonal if there exists a weak*-closed ideal I in A such that A2(J)⊆A2(I) and A2(K)⊆A0(I), and are said to be rigidly collinear when A2(J)⊆A1(K) and A2(K)⊆A1(J), where, for j equal to 0, 1, or 2, Aj(I), Aj(J), and Aj(K), are the components in the generalized Peirce decomposition of A relative to the weak*-closed inner ideals I, J, and K, respectively. A measure m on I(A) is a mapping from I(A) to C such that, if J and K are either centrally orthogonal or rigidly collinear, thenmJ∨K=mJ+mK.A complex Hilbert space A endowed with a conjugation possesses a triple product and norm with respect to which it forms a JBW*-triple, known as a spin triple. In this paper the structure of the complete lattice I(A) of closed inner ideals in a spin triple A and the measures on it are investigated. It is shown that, if the dimension of A is greater than 5, then there are no non-zero measures on I(A). When the dimension of A is 5, non-zero measures exist and, up to multiplication by a constant, a unique measure exists that is invariant under automorphisms of A. When the dimension of A is 4, then A is triple isomorphic to the W*-algebra of 2×2 complex matrices. In this case results of Bunce and Wright are used to show that there is an uncountable number of measures on I(A). The situation when the dimension of A is less than 4 is also described
Statistical Cluster Points and Turnpike Theorem in Nonconvex Problems

AbstractIn this paper we develop the method suggested by S. Pehlivan and M. A. Mamedov (“Statistical Cluster Points and Turnpike,” submitted), where it was proved that under some conditions optimal paths have the same unique stationary limit point–stationary cluster point. This notion was introduced by J. A. Fridy (1993, Proc. Amer. Math. Soc.118, 1187–1192) and it turns out to be a very useful and interesting tool in turnpike theory. The purpose of this paper is to avoid the convexity conditions. Here the turnpike theorem is proved under conditions that are quite different from those of Pehlivan and Mamedov and may be satisfied for the mappings with nonconvex images and for nonconcave functions in the definition of functionals
Necessary and Sufficient Conditions for Oscillation of Second Order Neutral Differential Equations

AbstractConsider the second order nonlinear neutral differential equation with delays: (E) d2/dt2[y(t)−py(t−τ)]+q(t)f(y(t−σ))=0, for t∈[0,∞), where q(t),f(x) are continuous functions, q(t)≥0, yf(y)>0 if y≠0, and 0<p<1, τ>0, σ>0. When f(y) satisfies either the superlinear or sublinear conditions which include the special case f(y)=y|y|γ−1 of γ>1 and 0<γ<1, respectively, we give necessary and sufficient conditions for the oscillation of all continuable solutions of (E). When p=τ=σ=0 in (E), these results reduce to the well known theorems of Atkinson and Belohorec in the special case when f(y)=y|y|γ−1, γ≠1
The Derivative of Minkowski's ?(x) Function

AbstractMinkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it enables us to prove that its derivative, when it exists in a wide sense, can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k̄=5.31972, and ?′(x) exists, then ?′(x)=0. In the same way, if the same average is less than ḵ=2log2Φ, where Φ is the golden ratio, then ?′(x)=∞. Finally some results are presented concerning metric properties of continued fractions and alternated dyadic expansions
On the Controllability of the Lotka–McKendrick Model of Population Dynamics

AbstractIn this work we consider the problem of exact controllability of the linear Lotka–McKendrick model of population dynamics. We establish an observability inequality and show that any initial condition can be steered into any quasi steady state by a distributed control, except for a small interval of ages near zero. In contrast with that we observe that the boundary control is more efficient in the sense that it controls the entire population. The biological implication of our conclusions is that a closed population is more efficiently controlled through birth control as opposed to migration and eradication. In particular, this supports the “trap-alter-release” method for controlling a population of stray cats as opposed to the “trap and kill” method
On Summing Multipliers and Applications

AbstractA scalar sequence (αi) is said to be a p-summing multiplier of a Banach space E, if ∑∞i=1‖αixi‖p<∞ for all weakly p-summable sequences in E. We study some important properties of the space mp(E) of all p-summing multipliers of E, consider applications to E-valued operators on the sequence space lp, and extend this work to general “summing multipliers.” The case p=1 shows close resemblance to the work of B. Marchena and C. Piñeiro (Quaestiones Math., to appear), where the results originated from the authors' interest in sequences in the ranges of vector measures
Asymptotic Synchronization in Lattices of Coupled Three-Dimension Nonlinear Chaotic Equations

AbstractIn this paper we study the asymptotic synchronization in coupled system of three-dimension nonlinear chaotic equations with various boundary conditions. We couple the nearest neighbors of each variable of equations in a squared n×n lattice. A general mathematical framework for analyzing asymptotic synchronization is given. We prove that the asymptotic synchronization occurs provided that the coupled system is pointwise dissipativeness and the coupling coefficients are sufficiently large. As an illustration of the application, particular attention is paid to the asymptotic synchronization of coupled Lorenz equations with Dirichlet, Neumann, and periodic boundary conditions, respectively. The relationship between dynamics and boundary conditions is discussed. A specific Lyapunov function is constructed to establish the pointwise dissipativeness of coupled Lorenz equations
Monotonic Averages of Convex Functions

AbstractWe investigate the monotonicity of various averages of the values of a convex (or concave) function at n equally spaced points. For a convex function, averages without end points increase with n, while averages with end points decrease. Averages including one end point are treated as a special case of upper and lower Riemann sums, which are shown to decrease and increase, respectively. Corresponding results for mid-point Riemann sums and the trapezium estimate require convexity or concavity of the derivative as well as the function. Special cases include some known results and some new ones, unifying them in a more systematic theory. Further applications include results on series and power majorization
On a Recursive Approximation of Singularly Perturbed Parabolic Equations

AbstractThe asymptotic analysis of IBVPs for the singularly perturbed parabolic PDE ∂tu+∂xu=ε∂xxu in the limit ε→0 motivates investigations of certain recursively defined approximative series (“ping-pong expansions”). The recursion formulae rely on operators assigning to a boundary condition at the left or the right boundary a solution of the parabolic PDE. Sufficient conditions for uniform convergence of ping-pong expansions are derived and a detailed analysis for the model problem ∂tu+∂xu=ε∂xxu is given
A Generalization for Fourier Transforms of a Theorem due to Marcinkiewicz

AbstractIt is shown that the maximal operator of the Marcinkiewicz means of a tempered distribution is bounded from Hp(R2) to Lp(R2) for all p0<p≤∞ and, consequently, is of weak type (1,1), where p0<1. As a consequence we obtain a generalization for Fourier transforms of a summability result due to Marcinkiewicz and Zhizhiashvili, more exactly, the Marcinkiewicz means of a function f∈L1(R2) converge a.e. to the function in question. Moreover, we prove that the Marcinkiewicz means are uniformly bounded on the spaces Hp(R2) and so they converge in the norm (p0<p<∞). Similar results for the Riesz transforms are also given
Discrete Cocompact Subgroups of the Four-Dimensional Nilpotent Connected Lie Group and Their Group C*-Algebras

AbstractLet G4 be the unique, connected, simply connected, four-dimensional, nilpotent Lie group. In this paper, the discrete cocompact subgroups H of G4 are classified and shown to be in 1–1 correspondence with triples (p1,p2,p3)∈Z3 that satisfy p2,p3>0 and a certain restriction on p1. The K-groups of the group C*-algebra C*(H) are computed and shown to involve all three parameters. Furthermore, for each such subgroup H, the set of faithful simple quotients (i.e., those generated by a faithful representation of H) of the group C*-algebra C*(H) is shown to be independent of p1 and p3 and to be in 1–1 correspondence with the irrational θ's in [0,1/2). The other infinite-dimensional simple quotients of C*(H) (those generated by a representation of H that is not faithful) are shown to be isomorphic to matrix algebras over irrational rotation algebras
An Asymptotic Property of Schachermayer's Space under Renorming

AbstractLet X be a Banach space with closed unit ball B. Given k∈N, X is said to be k-β, respectively, (k+1)-nearly uniformly convex ((k+1)-NUC), if for every ϵ>0 there exists δ, 0<δ<1, so that for every x∈B and every ϵ-separated sequence (xn)⊆B there are indices (ni)ki=1, respectively, (ni)k+1i=1, such that (1/(k+1))||x+∑ki=1xni||≤1−δ, respectively, (1/(k+1))||∑k+1i=1xni||≤1−δ. It is shown that a Banach space constructed by Schachermayer is 2-β, but is not isomorphic to any 2-NUC Banach space. Modifying this example, we also show that there is a 2-NUC Banach space which cannot be equivalently renormed to be 1-β
Attracting Mappings in Banach and Hyperbolic Spaces

AbstractIn this paper we study spaces of mappings A:K→K satisfying Ax=x for all x∈F, where K is a closed convex subset of a hyperbolic complete metric space and F is a closed convex subset of K. These spaces are equipped with natural complete uniform structures. We study the convergence of powers of (F)-attracting mappings as well as the convergence of infinite products of uniformly (F)-attracting sequences and show that if there exists an (F)-attracting mapping, then a generic mapping is also (F)-attracting. We also consider a finite sequence of subsets Fi⊂K, i=1,…,n, with a nonempty intersection F and a certain regularity property and show that if each mapping Ai is (Fi)-attracting, i=1,…,n, then their product and convex combinations are (F)-attracting
A Variational Principle for the Kramers Equation with Unbounded External Forces

AbstractA time discrete variational principle is developed for the Cauchy problem of the Kramers equation with unbounded external force fields. The variational scheme is based on the idea of maximizing a relative entropy with respect to the Kantorovich functional associated with a certain cost function. Convergence of the scheme is established. Consequently, global existence of weak solutions of the Kramers equation with a broad class of unbounded force fields and initial data is obtained. Our results also show that, in some senses, the Kramers dynamics follows, at each instant of time, the direction of a steepest descent of a free energy functional with respect to the Kantorovich functional
Stability Criteria for Linear Time-Invariant Systems with Multiple Delays

AbstractTwo new asymptotic stability criteria for linear time-invariant systems with multiple delays are established by using a quadratic inequality lemma together with frequency-domain techniques. One criterion is for delay-dependent α-stability and another is for delay-independent asymptotic stability. Each of them has only one tuning parameter matrix P>0 as the Lyapunov-type stability criteria for the corresponding linear time-invariant systems without delays do. Both of the established stability criteria are given in the form of LMI problems and hence are very easy to use in applications. In addition, it is remarked that the established delay-independent asymptotic stability criterion with one tuning parameter matrix P>0 improves and simplifies the existing criterion with more than one tuning parameter matrix in the literature
Defuzzification Filters and Applications to Power System Stabilization Problems

AbstractDefuzzification is a very important step in fuzzy systems applications. There are a number of different defuzzification methods reported in the literature. In this paper, the concept of defuzzification filters in a control system setting is first discussed and a methodology for designing such filters considered. As will be seen, the design of such filters requires the knowledge of the plant model and its inverse. A reference control signal is computed and then is used to generate the actual defuzzified control signal which will be applied to control the plant. The application of the defuzzification filter is made by introducing the filter into a power system in which a neuro-fuzzy self-learning controller was applied to stabilize the system but success could not always be guaranteed. With the defuzzification filter, however, the system is always stabilized. Simulation results are presented
A Generalization of Bernstein–Kantorovič Operators

AbstractIn this paper, we use a probabilistic setting to introduce a double sequence (L〈k〉n) of linear polynomial operators which includes, as particular cases, the classical Bernstein operators, the Kantorovič operators, and the operators recently introduced by Cao. For these operators, we discuss several approximation properties. In particular, we deal with the convergence properties according to the way in which the different parameters vary, and the preservation of global smoothness and classes of functions determined by concave moduli of continuity. A remarkable feature of our approach is that if f is differentiable, the approximation properties of both L〈k〉nf and its derivatives can be discussed simultaneously. Throughout the paper, probabilistic methods play an important role
Relatively Strictly Singular Perturbations, Essential Spectra, and Application to Transport Operators

AbstractThe stability of essential spectra of a closed, densely defined linear operator A on Lp-spaces, 1≤p≤∞, when A is subjected to a perturbation by a bounded strictly singular operator was discussed in a previous paper by K. Latrach and A. Jeribi (1998, J. Math. Anal. Appl.225, 461–485). In the present paper we prove the invariance of the Gustafson–Weidmann, Wolf, Schechter, and Browder essential spectra of A under relatively strictly singular (not necessarily bounded) perturbations on these spaces. Further, a precise characterization of the Schechter essential spectrum is given. We show that these results are also valid on C(Ξ) where Ξ is a compact Hausdorff space. The results are applied to the one-dimensional transport equations with anisotropic scattering and abstract boundary conditions
Exceptional Properties of Second and Third Order Ordinary Differential Equations of Maximal Symmetry

AbstractThe Riccati transformation is used in the reduction of order of second and third order ordinary differential equations of maximal symmetry. The sl(2,R) subalgebra is preserved under this transformation. The Riccati transformation is itself associated with the symmetry that is annihilated in the reduction of order. The solution symmetries and the intrinsically contact symmetries become nonlocal symmetries under the Riccati transformation. We investigate the fate and origins of the contact symmetries arising from the Riccati transformation. The exceptional properties of the second and third order equations of maximal symmetry are indicated. In the context of generalised symmetries we express the solution symmetries, contact symmetries, and the sl(2,R) elements in terms of a Jacobian. We show that a basis for the solution set of equations of maximal symmetry is given in terms of the solution set of a second order ordinary differential equation
Local Compactness in Fuzzy Convergence Spaces

AbstractTwo notions of local precompactness in the realm of fuzzy convergence spaces are investigated. It is shown that the property of local precompactness possesses a “good extension.” Moreover, for each given fuzzy convergence space, there exists a coarsest locally precompact space which is finer than the original space. Continuity between fuzzy spaces is preserved between the associated locally precompact spaces. Invariance of regularity with respect to taking locally precompact modifications is discussed
The Pointwise Densities of the Cantor Measure

AbstractLet C be the classical middle-third Cantor set and let μC be the Cantor measure. Set s=log2/log3. We will determine by an explicit formula for every point x∈C the upper and lower s-densities Θ*s(μC,x), Θ∗s(μC,x) of the Cantor measure at the point x, in terms of the 3-adic expansion of x. We show that there exists a countable set F⊂C such that 9(Θ*s(μC,x))−1/s+(Θ∗s(μC,x))−1/s=16 holds for x∈C\F. Furthermore, for μC almost all x, Θ*s(μC,X)−2·4−s and Θ∗s(μC,x)=4−s. As an application, we will show that the s-dimensional packing measure of the middle-third Cantor set C is 4s