Completion of the mixed unit interval graphs hierarchy

We describe the missing class of the hierarchy of mixed unit interval graphs. This class is generated by the intersection graphs of families of unit intervals that are allowed to be closed, open, and left‐closed‐right‐open. (By symmetry, considering closed, open, and right‐closed‐left‐open unit intervals generates the same class.) We show that this class lies strictly between unit interval graphs and mixed unit interval graphs. We give a complete characterization of this new class, as well as quadratic‐time algorithms that recognize graphs from this class and produce a corresponding interval representation if one exists. We also show that the algorithm from Shuchat et al. [8] directly extends to provide a quadratic‐time algorithm to recognize the class of mixed unit interval graphs.     

On the facial structure of the unit ball in the dual space of a JB*-triple

It is shown that every proper weak* closed face of the closed unit ball E₁^*{E_1^*} in the dual space of a JB*-triple E coincides with set of all elements in the unit sphere of E* attaining their norm at a unique compact tripotent in E**. In particular every proper weak* closed face of the closed unit ball E₁^*{E_1^*} is weak*-semi-exposed. This result provides an affirmative answer to a conjecture posed over 20 years ago.     

Finite Blaschke product interpolation on the closed unit disc

We show how to construct all finite Blaschke product solutions and the minimal scaled Blaschke product solution to the Nevanlinna-Pick interpolation problem in the open unit disc by solving eigenvalue problems of the interpolation data. Based on a result of Jones and Ruscheweyh we note that there always exists a finite Blaschke product of degree at most n−1 that maps n distinct points in the closed unit disc, of which at least one is on the unit circle, into n arbitrary points in the closed unit disc, provided that the points inside the unit circle form a positive semi-definite Pick matrix of full rank. Finally, we discuss a numerical limiting procedure.     

Closed convex sets and their best simultaneous approximation properties with applications

We develop a theory of best simultaneous approximation for closed convex sets in a conditionally complete lattice Banach space X with a strong unit. We study best simultaneous approximation in X by elements of closed convex sets, and give necessary and sufficient conditions for the uniqueness of best simultaneous approximation. We give a characterization of simultaneous pseudo-Chebyshev and quasi-Chebyshev closed convex sets in X. Also, we present various characterizations of best simultaneous approximation of elements by closed convex sets in terms of the extremal points of the closed unit ball B _X* of X*.     

解析函数的加权代数中的闭理想问题

该文讨论了单位圆盘上解析函数的加权代数犃犘中的闭理想问题,并且利用加权系给出了一个闭理想成为犃犘中的补子空间的判断准则     

析函数的(FN)-代数中的闭理想问题

本文讨论了解析函数的(FN)-代数A0P中的闭理想问题,利用射影加权系给出了一个闭理想成为A0P中的补子空间的判别准则.     

Lipshitz maps from surfaces

We give a simple procedure to estimate the smallest Lipshitz constant of a degree 1 map from a Riemannian 2-sphere to the unit 2-sphere, up to a factor of 10. Using this procedure, we are able to prove several inequalities involving this Lipshitz constant. For instance, if the smallest Lipshitz constant is at least 1, then the Riemannian 2-sphere has Uryson 1-width less than 12 and contains a closed geodesic of length less than 160. Similarly, if a closed oriented Riemannian surface does not admit a degree 1 map to the unit 2-sphere with Lipshitz constant 1, then it contains a closed homologically non-trivial curve of length less than 4π. On the other hand, we give examples of high genus surfaces with arbitrarily large Uryson 1-width which do not admit a map of non-zero degree to the unit sphere with Lipshitz constant 1. Received: May 2004 Revision: December 2004 Accepted: December 2004     

Estimates of conjugate harmonic functions with given set of singularities and application

Analysis Mathematica - Let E be an arbitrary closed set on the unit circle ?? and u be a harmonic function on the unit disk ? satisfying |u(z)| ? (1 ?...     

Unit Interval Graphs of Open and Closed Intervals

We give two structural characterizations of the class of finite intersection graphs of the open and closed real intervals of unit length. This class is a proper superclass of the well‐known unit interval graphs.     

JB代数中的面结构

本文描述了含单元元的ＪＢ代数及其对偶空间的单位球和这些单位球的正部的闭面。     

Extremal problems for the central projection

We consider area minimizing problems for the image of a closed subset in the unit sphere under a projection from the center of the sphere to a tangent plane, the central projection. We show, for any closed subset in the sphere, the uniqueness of a tangent plane that minimizes the area, and then the minimality of the spherical discs among closed subsets with the same spherical area.     

A Characterization of Mixed Unit Interval Graphs

We give a complete characterization of mixed unit interval graphs, the intersection graphs of closed, open, and half‐open unit intervals of the real line. This is a proper superclass of the well‐known unit interval graphs. Our result solves a problem posed by Dourado, Le, Protti, Rautenbach, and Szwarcfiter (Mixed unit interval graphs, Discrete Math 312, 3357–3363 (2012)).     

Uniform Asymptotics for Second-Kind Ultraspherical Polynomials on the Unit Circle

The object under consideration is the system of orthonormal polynomials of the second kind which corresponds to ultraspherical weight function on the unit circle. We obtain a uniform asymptotic representation for such polynomials in the closed unit disk as well as two-sided bounds on the unit circle. October 24, 1996. Date revised: April 10, 1997.     

A topology on the union of the double arrow space and the integers

We construct a topology on the union of the double arrow space (Cantor set version) and the integers which is a hereditarily Lindelöf hereditarily separable 0-dimensional compact Hausdorff space but not the continuous image of a closed subspace of the product of the double arrow space and the closed unit interval (answering a question of Fremlin).     

$p$-双调和算子的第一特征值的等周上界和 Reilly 型不等式

在本文中,我们给出了嵌入到欧氏空间中的$n$维闭超曲面上$p$-双调和算子的第一特征值的一些等周上界.我们也给出了浸入到高维流形如欧氏空间,球面和射影空间中的闭子流形上$p$-双调和算子的第一特征值的一些Reilly-型不等式.     

Extreme points in polyhedral Banach spaces

We show that there exists a polyhedral Banach space X such that the closed unit ball of X is the closed convex hull of its extreme points. This solves a problem posed by J. Lindenstrauss in 1966.     

Double-saturated packing of unit disks

A set of closed unit disks in the Euclidean plane is said to be double-saturated packing if no two disks have inner points in common and any closed unit disk intersects at least two disks of the set. We prove that the density of a double saturated packing of unit disks is ≥ and the lower bound is attained by the family of disks inscribed into the faces of the regular triangular tiling. Partially supported by the Hungarian National Foundation for Scientific Research, grant number 1238.     

Power bounded operators and supercyclic vectors

By the well-known result of Brown, Chevreau and Pearcy, every Hilbert space contraction with spectrum containing the unit circle has a nontrivial closed invariant subspace. Equivalently, there is a nonzero vector which is not cyclic.

We show that each power bounded operator on a Hilbert space with spectral radius equal to one has a nonzero vector which is not supercyclic. Equivalently, the operator has a nontrivial closed invariant homogeneous subset. Moreover, the operator has a nontrivial closed invariant positive cone.

     

On an analog of periodic boundary value problems for the Poisson equation in the disk

We consider a periodic and an antiperiodic problem for the Poisson equation in the unit disk and prove their well-posedness. The possibility of separation of variables is justified. We construct the Green functions of these problems in closed form and obtain an integral representation of the solution. The problems are self-adjoint, and we construct all eigenvalues and eigenfunctions in closed form.     

单位圆内亚纯函数的Borel半径的分布

对于单位圆周上的任一非空闭集E,任意正数λ及任意实数μ（0≤μ≤λ）;构造了一个单位国内的λ级亚纯函数,以{（L（θ）|θ∈E｝为Borel半径集,并且｛L（θ）|θ|E｝都不是Julia半径,同时N（r,f）的级为θ.