端单调线性泛函的存在性(英文)

讨论了偏序线性空间的代数对偶空间上的端单调线性泛函的延拓性．进一步,还推导出端单调线性泛函的存在性定理．     

One Problem of Extremal Functional Interpolation and the Favard Constants

Doklady Mathematics - For an extremal functional interpolation problem first considered by Yu.N. Subbotin, the explicit form of the extremal interpolation constants is calculated in terms of the...     

一类极值问题

本文讨论了一类极值并刻划了它的解的特征.该极值问题为:给定d_i(x₀,…,x_n),i = 0,…,n,要确定y₀<…y_n 使得     

A Massera Type Criterion for Linear Functional Differential Equations with Advance and Delay

In this note, a Massera type criterion for the existence of periodic solutions for linear functional differential equations with advance and delay is established. Because of the presence of an advanced argument, the definition of the fundamental solution operator seems unknown. Hence a method different from the usual one is employed. Applications to periodic problems for nonlinear equations are also given.     

Extremal Metrics for Quadratic Functional of Scalar Curvature on Closed 3-Manifolds

In this paper, we first show the global existence of the three-dimensionalCalabi flow on any closed 3-manifold with an arbitrary background metric g ₀. Second, we show the asymptotic convergence of a subsequence ofsolutions of the Calabi flow on a closed 3-manifold with Yamabe constant Q < 0 or Q = 0 and Q > 0, up to conformal transformations. With itsapplication, we prove the existence of extremal metrics for quadraticfunctional of scalar curvature on a closed 3-manifold which is served asan extension of the Yamabe problem on closed manifolds. Moreover, theexistence of extremal metrics on complete noncompact 3-manifolds willdiscuss elsewhere.     

A Nonstandard Compactness Criterion

A general definition of consequence relation is given, and a criterion for compactness based on a nonstandard construction is demonstrated.     

Extremal continua: A class of non-separating subcontinua

The notion of a terminal continuum, as defined by D.E. Bennett and J.B. Fugate, is used to introduce extremal continua, a class of non-separating subcontinua of a continuum. An extremal continuum can be characterized as a proper subcontinuum Y of a metric continuum X with the property that Y contains a point of irreducibility of each irreducible subcontinuum of X that meets Y. If Y is an extremal subcontinuum of X, then Y does not separate any subcontinuum of X containing Y; moreover, if Y is a proper subcontinuum of X and Y does not cut any subcontinuum of X containing Y, then Y is extremal in X.     

Existence of New Extremal Doubly-Even Codes and Extremal Singly-Even Codes

Recently the author and Kimura have considered a construction of doubly-even codes from a given doubly-even code. In this note, we show that the restricutoion of doubly-even can be removed in the above construction. As an application, at least 137 inequivalent extremal doubly-even [56,28,12] codes and at least 1000 inequivalent extremal doubly-even [40,20,8] codes are constructed from known self-dual codes. The existence of new extremal singly-even codes is also described.     

Extremal Valued Fields

It is shown that every finite-dimensional skew field whose center is an extremal valued field is defect free. We construct an example of an algebraically complete valued field such that a finite-dimensional skew field over it has a non-trivial defect, that is, there exist algebraically complete valued fields that are not extremal.     

Extremal convex sets

Letf be an extended real valued function on the classK ⁿ of closed convex subsets of euclideann-dimensional space. A setK∈K ⁿ is said to bef-maximal if the conditionsK′∈K ⁿ ,K?K′,K≠K′ implyf(K)<f(K′), andf-minimal ifK′∈K ⁿ,K′∈K,K′≠K impliesf(K′)<f(K). In the cases whenf is the circumradius or inradius allf-maximal andf-minimal sets are determined. Under a certain regularity assumption a corresponding result is obtained for the minimal width. Moreover, a general existence theorem is established and a result concerning the existence of extremal sets with respect to packing and covering densities is proved.     

A Class of Extremal Functions and Trigonometric Polynomials

In this paper we present two classes of extremal approximating functions. These functions have the property that they are entire, have finite exponential type, and provide excellent approximations along the real line for a specific set of functions. One class of functions provides majorants and minorants, while the other class minimizes theL¹-norm on the real line. As applications we construct extremal trigonometric polynomials and obtain an inequality involving almost periodic trigonometric polynomials.     

Extremal symplectic lattices

We study the Jacobians of the genus 3 Picard and Fermat curves with respect to the problem of maximizing the minimum non-zero norm. We use criteria for symplectic lattices related to the criteria of perfect and eutactic for classical lattices. We show that the Picard curve is a local maximum, but the Fermat curve is not.     

Extremal integral representations

Let X be a closed bounded convex subset with the Radon-Nikodym property of a Banach space. For tight Borel probability measures μ, v on X, define μ ? v iff there is a dilation T on X such that T(μ) = v. Then, for every x?X, there is a measure μ on X which is maximal in the partial order ? and which has barycenter x. If X is separable, then μ(ex X) = 1 for all maximal measures μ. In general, a maximal measure need not be “on” ex X in this strong sense. If X is weakly compact, then a maximal measure is “on” ex X in the looser sense that μ(B) = 1 for all weak Baire sets B ? ex X.     

Extremal uncrowded hypergraphs

Let G be a (k + 1)-graph (a hypergraph with each hyperedge of size k + 1) with n vertices and average degreee t. Assume k ? t ? n. If G is uncrowded (contains no cycle of size 2, 3, or 4) then there exists and independent set of size $\text{c}{}_{\mathrm{k}}\text{(}\text{n}\text{t}\text{)(}\text{ln}\text{t)}{}^{\mathrm{<mtext>1</mtext><mtext>k</mtext>}}$.     

Extremal interval graphs

An interval graph is said to be extremal if it achieves, among all interval graphs having the same number of vertices and the same clique number, the maximum possible number of edges. We give an intrinsic characterization of extremal interval graphs and derive recurrence relations for the numbers of such graphs. © 1993 John Wiley & Sons, Inc.