Analyticity on families of circles

It is known that iff is a continuous function on the complex plane which extends holomorphically from each circle surrounding the origin, thef is not necessarily holomorphic. In the paper we prove that if, in addition,f extends holomorphically from each circle belonging to an open family of circles which do not surround the origin, thef is holomorphic.     

Analyticity and Singularity Sets

The problem of approximating singularity sets by analytic varieties has been considered by several authors. The present work deals with singularity sets projecting over a finitely connected domain. The results obtained in these cases allow us to prove the existence of a Riemann surface in a neighborhood of a two-sheeted singularity set.     

Analyticity of solutions of semi-linear equations with double characteristics

We prove the analyticity and Gevrey regularity of solutions of elliptic degenerate semi-linear differential equations principle part of which is a linear operator with double characteristics considered first by Gilioli and Treves. A new elementary proof for hypoellipticity in the weak sense is given.     

Analyticity on circles for rational and real-analytic functions of two real variables

Conditions for rational and real-analytic functions of two real variables to be holomorphic are given in terms of holomorphic extendibility from families of circles. The first author was supported by the Israel Science Foundation, grant No. 279/02-1. The second author was partially supported by a grant from the Slovenian Ministry of Science and Technology. Both authors were supported by the Ministry of Science of Israel and the Ministry of Science and Technology of Slovenia, in the framework of the Program of Exchange by scientists.     

磁流体方程的时间解析半径

本文考查了二维周期边界条件下的磁流体方程 ,证明了当初值位于全局吸引子上和定常解足够接近时 ,解在t=0的时间解析半径可以任意大     

Analyticity and the Analysis Relation

Quine famously argued that analyticity is indefinable, since there is no good account of analyticity in terms of synonymy, and intensions are of no help since there are no intensions. Yet if there are intensions, the question still remains as to the right account of analyticity in terms of them. On the assumption that intensions must be admitted, the present paper considers two such accounts. The first analyzes analyticity in terms of concept identity, and the second analyzes analyticity in terms of the analysis relation. The first fails in light of possible counterexamples. The second is defended, both by considering test cases of intuitively clear analyticities, and by developing the account in light of possible counterexamples.

Analyticity of a thermoelastic plate with variable coefficients

A thermoelastic plate with variable coefficients in the absence of dissipative boundary mechanisms is considered. Using C₀-semigroup theory and some techniques in partial differential equations, it is shown that the corresponding C₀-semigroup is analytic and hence the exponential stability of the system is concluded.     

Topological relations between separating circles

The family of separating circles of two finite sets in the plane consists of all the circles that enclose the first set but exclude the second set. We prove some theoretical results on distances between families of circles, and properties about enclosure and intersection. Most of these results state that a property that involves one or more infinite families of circles can be verified by examining a finite subcollection of circles. As a result enclosure and intersection can be decided, and distances can be computed with simple geometric algorithms. Furthermore, the circles of the finite subcollections correspond to the vertices of a polytope in the parameter space of separating circles. A polytope of separating circle parameters is well-known computational geometry, but we prove some new properties and we introduce the concept of an elementary circular separation as a concise way to define such a polytope.     

On small circles containing zeros and ones of analytic functions

Gol'dberg considered the class of functions with unequal positive numbers of zeros and ones inside the unit disc. The maximum modulus of zeros and ones in this class is bounded from below by a universal constant. This constant determines the limits of certain controller designs as well as covering regions of certain composites with schlicht functions. Considering lower bounds in a zero-free region of the extremal function the best known estimates of this constant are improved.     

Analyticity and exponential stability of semigroups for the elastic systems with structural damping in Banach spaces

In this paper, we consider a second order evolution equation in a Banach space, which can model an elastic system with structural damping. New forms of the corresponding first order evolution equation are introduced, and their well-posed property is proved by means of the operator semigroup theory. We give sufficient conditions for analyticity and exponential stability of the associated semigroups.     

Comultiplications on free groups and wedges of circles

By means of the fundamental group functor, a co-H-space structure or a co-H-group structure on a wedge of circles is seen to be equivalent to a comultiplication or a cogroup structure on a free group . We consider individual comultiplications on and their properties such as associativity, coloop structure, existence of inverses, etc. as well as the set of all comultiplications of . For a comultiplication of we define a subset of quasi-diagonal elements which is basic to our investigation of associativity. The subset can be determined algorithmically and contains the set of diagonal elements . We show that is a basis for the largest subgroup of on which is associative and that is a free factor of . We also give necessary and sufficient conditions for a comultiplication on to be a coloop in terms of the Fox derivatives of with respect to a basis of . In addition, we consider inverses of a comultiplication, the collection of cohomomorphisms between two free groups with comultiplication and the action of the group on the set of comultiplications of . We give many examples to illustrate these notions. We conclude by translating these results from comultiplications on free groups to co-H-space structures on wedges of circles.

     

Apollonius circles and irreducibility criteria for polynomials

We prove the irreducibility of integer polynomials $f\left(X\right)$ whose roots lie inside an Apollonius circle associated to two points on the real axis with integer abscissae $a$ and $b$, with ratio of the distances to these points depending on the canonical decomposition of $f\left(a\right)$ and $f\left(b\right)$. In particular, we obtain irreducibility criteria for the case where $f\left(a\right)$ and $f\left(b\right)$ have few prime factors, and $f$ is either an Eneström–Kakeya polynomial, or has a large leading coefficient. Analogous results are also provided for multivariate polynomials over arbitrary fields, in a non-Archimedean setting.     

An extension of Lewis's Lemma,renormalization of harmonic and analytic functions,and normal families

An extension of a lemma due to J. Lewis is established and is used to give rapid proofs of some classical theorems in complex function theory such as Montel's theorem and Miranda's theorem. Another application of Lewis's Lemma yields a general normality criterion for families of harmonic and holomorphic functions. This criterion permits a quick proof of Bloch's classical covering theorem for holomorphic functions (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Linear models for the approximate solution of the problem of packing equal circles into a given domain

The linear models for the approximate solution of the problem of packing the maximum number of equal circles of the given radius into a given closed bounded domain G are proposed. We construct a grid in G; the nodes of this grid form a finite set of points T, and it is assumed that the centers of circles to be packed can be placed only at the points of T. The packing problems of equal circles with the centers at the points of T are reduced to 0–1 linear programming problems. A heuristic algorithm for solving the packing problems based on linear models is proposed. This algorithm makes it possible to solve packing problems for arbitrary connected closed bounded domains independently of their shape in a unified manner. Numerical results demonstrating the effectiveness of this approach are presented.     

Characterization of totally umbilic hypersurfaces in a space form by circles

In this paper we characterize totally umbilic hypersurfaces in a space form by a property of the extrinsic shape of circles on hypersurfaces. This characterization corresponds to characterizations of isoparametric hypersurfaces in a space form by properties of the extrinsic shape of geodesics due to Kimura-Maeda.The first author was partially supported by Grant-in-Aid for Scientific Research (C) No. 14540075, Ministry of Education, Science, Sports and Culture. The second author was partially supported by Grant-in-Aid for Scientific Research (C) No. 14540080, Ministry of Education, Science, Sports and Culture.     

The support points of several classes of analytic functions with fixed coefficients

Let B denote the set of functions ?(z) that are analytic in the unit disk D and satisfy |?(z)|?1(|z|<1). Let P denote the set of functions p(z) that are analytic in D and satisfy p(0)=1 and Rep(z)>0(|z|<1). Let T denote the set of functions f(z) that are analytic in D, normalized by f(0)=0 and f^′(0)=1 and satisfy that f(z) is real if and only if z is real (|z|<1). In this article we investigate the support points of the subclasses of B, P and T of functions with fixed coefficients.     

k-Moments of distances between centers of Ford circles

In this paper, we investigate a problem on the distribution of Ford circles, which concerns moments of distances between centers of these circles that lie above a given horizontal line.