共查询到20条相似文献,搜索用时 15 毫秒
1.
Jong-Do Park 《复变函数与椭圆型方程》2016,61(9):1267-1289
In this paper, we give an algorithmic method of constructing inner product formulas which contain weighted inner products of holomorphic functions on the unit ball. This result covers all inner product formulas which have been proved before. As an application, we prove Zhu’s characterization theorem by an elementary method. Finally, by using one-to-one correspondence between inner product formulas and lattices with circles, we prove all inner product formulas again without any complicated computation. 相似文献
2.
The article examines the general features of convergence of two-step iterative methods with a linearly convergent outer process.
Three specifications of the inner process are considered. In the first specification, the inner process iterations end when
the specified accuracy is reached. In the second specification, the inner process iterations end when a specified relative
error is reached. In the third specification, the inner process is an iterative method with a superlinear rate of convergence. 相似文献
3.
§1. IntroductionandNarratationoftheTheoremIffunctionfisanalyticindomainDandf′(z)≠0atpointz,wedefinetheschwarzianderivativeoffasSf(z)=(f″(z)f′(z))′-12(f″(z)f′(z))2.(1.1) Foralocallyunivalentholomorphicfunction,itsSchwarzianderivativeisclear.Atpoles,t… 相似文献
4.
Tao CHENG~ 《中国科学A辑(英文版)》2007,50(7):987-996
In this paper,the inner radius of univalency of hyperbolic domains by pre-Schwarzian derivative is studied,and some general formulas for the lower bound of the inner radius are established. As their applications,the lower bounds of inner radiuses for angular domains and strongly starlike domains are obtained. 相似文献
5.
Jizhu Nan & Xuemin Yu 《数学研究通讯:英文版》2015,31(4):345-350
In this paper, we discuss a kind of Hermitian inner product — symplectic inner product, which is different from the original inner product — Euclidean inner product. According to the definition of symplectic inner product, the codes under the symplectic inner product have better properties than those under the general Hermitian inner product. Here we present the necessary and sufficient condition for judging whether a linear code C over Fp with a generator matrix in the standard form is a symplectic self-dual code. In addition, we give a method for constructing a new symplectic self-dual codes over Fp, which is simpler than others. 相似文献
6.
Chuan Kuan Yuan 《数学学报(英文版)》1992,8(3):236-242
For infinite discrete groups, Effros introduced the notion of inner amenability which gives a new classification of discrete
groups. The inner amenability is a considerably weaker condition than amenability, but closely related to the quite deep property
Γ of groups. In this paper the author investigates the structures of inner amenable groups by theoretical set theory. A sequence
of characterizations of inner amenable groups is given here by developing the well-known Folner's conditions for amenable
locally compact groups.
This work is partly supported by the National Science Foundation of China. 相似文献
7.
Amélia Fonseca 《Linear and Multilinear Algebra》2013,61(3-4):191-196
We show that a well-known polarization formula for Hermitian inner products on complex vector spaces generalizes to the case of inner products on Clifford modules. This observation allows us to conclude that norm-preserving linear maps of Clifford modules necessarily preserve the inner product. These results hold for modules over the quaternious as a special case. 相似文献
8.
Alexander Mitsos Panayiotis Lemonidis Paul I. Barton 《Journal of Global Optimization》2008,42(4):475-513
A bounding algorithm for the global solution of nonlinear bilevel programs involving nonconvex functions in both the inner
and outer programs is presented. The algorithm is rigorous and terminates finitely to a point that satisfies ε-optimality in the inner and outer programs. For the lower bounding problem, a relaxed program, containing the constraints
of the inner and outer programs augmented by a parametric upper bound to the parametric optimal solution function of the inner
program, is solved to global optimality. The optional upper bounding problem is based on probing the solution obtained by
the lower bounding procedure. For the case that the inner program satisfies a constraint qualification, an algorithmic heuristic
for tighter lower bounds is presented based on the KKT necessary conditions of the inner program. The algorithm is extended
to include branching, which is not required for convergence but has potential advantages. Two branching heuristics are described
and analyzed. Convergence proofs are provided and numerical results for original test problems and for literature examples
are presented. 相似文献
9.
This paper deals with a modified nonlinear inexact Uzawa (MNIU) method for solving the stabilized saddle point problem. The modified Uzawa method is an inexact inner-outer iteration with a variable relaxation parameter and has been discussed in the literature for uniform inner accuracy. This paper focuses on the general case when the accuracy of inner iteration can be variable and the convergence of MNIU with variable inner accuracy, based on a simple energy norm. Sufficient conditions for the convergence of MNIU are proposed. The convergence analysis not only greatly improves the existing convergence results for uniform inner accuracy in the literature, but also extends the convergence to the variable inner accuracy that has not been touched in literature. Numerical experiments are given to show the efficiency of the MNIU algorithm. 相似文献
10.
在特征不是2的正交空间中,相关文献给出了Witt定理.华罗庚把它推广到体上的一些内积空间.把域上内积空间中的Witt定理推广到奇异内积空间,并给出相应的证明. 相似文献
11.
随机结构空间理论初探 总被引:6,自引:3,他引:3
苏永福 《应用泛函分析学报》2002,4(2):152-157
提出了随机结构空间的概念,引出了随机拓扑空间、随机度量空间、随机赋范空间、随机内积空间、随机关系等随机数学结构的概念,初步研究了随机度量空间、随机赋范空间、随机内积空间的基本构造以及与概率度量空间、概率赋范空间、概率内积空间的关系。 相似文献
12.
所有真子环都同构的结合环,称为内同构环,任两不同的子环都不同构的结合环,称为内异环.本文目的是给出内同构环与内异环的一些结构定理,从而基本上解决了Szasz F.A.提出的问题81:怎样的结合环,它的不同子环总不同构? 相似文献
13.
Stephanie Halbeisen 《manuscripta mathematica》2000,103(2):169-182
The tangent cones of an inner metric Alexandrov space with finite Hausdorff dimension and a lower curvature bound are always inner metric spaces with nonnegative curvature. In this paper we construct an infinite-dimensional inner metric Alexandrov
space of nonnegative curvature which has in one point a tangent cone whose metric is not an inner metric.
Received: 20 October 1999 / Revised version: 8 May 2000 相似文献
14.
本文首先定义了内积函数,这个概念推广了内积的定义.然后定义了Hilbert空间(H,〈·,·〉)上由严格正算子A诱导的范数,这个范数与由〈·,·〉诱导的范数是等价的.进一步,证明了所有的内积函数与线性有界的严格正算子全体之间存在一一对应关系. 相似文献
15.
The functional principal components analysis (PCA) involves new considerations on the mechanism of measuring distances (the norm). Some properties arising in functional framework (e.g., smoothing) could be taken into account through an inner product in the data space. But this proposed inner product could make, for example, interpretational or (and) computational abilities worse. The results obtained in this paper establish equivalences between the PCA with the proposed inner product and certain PCA with a given well-suited inner product. These results have been proved in the theoretical framework given by Hilbert valued random variables, in which multivariate and functional PCAs appear jointly as particular cases. 相似文献
16.
该文利用Brick Wall方法,计算轴对称Einstein Maxwell Dilaton Axion 黑洞背景下标量场的自由能和熵.结果表明,当黑洞具有内外视界时,所得熵不仅与外视界面积有关,而且也是内视界面积的函数.当内视界面积于零时,可回到已知结论.并且表明,用内外视界位置参量表达的熵,在黑洞辐射温度趋于绝对零度时,黑洞的熵也趋于零,它满足能斯特定理,可视为黑洞的普朗克绝对熵. 相似文献
17.
Pamela Gorkin Leonardo Laroco Raymond Mortini Rudolf Rupp 《Results in Mathematics》1994,25(3-4):252-269
According to K. Stephenson [12] an inner function I is called prime if, for any given composition I = u o υ with inner functions u and υ, at least one of them is a Möbius transform. Only a few examples of prime inner function. 相似文献
18.
Two approaches that solve the mixed-integer nonlinear bilevel programming problem to global optimality are introduced. The first addresses problems mixed-integer nonlinear in outer variables and C2-nonlinear in inner variables. The second adresses problems with general mixed-integer nonlinear functions in outer level. Inner level functions may be mixed-integer nonlinear in outer variables, linear, polynomial, or multilinear in inner integer variables, and linear in inner continuous variables. This second approach is based on reformulating the mixed-integer inner problem as continuous via its vertex polyheral convex hull representation and solving the resulting nonlinear bilevel optimization problem by a novel deterministic global optimization framework. Computational studies illustrate proposed approaches. 相似文献
19.
Frank Uhlig 《Linear and Multilinear Algebra》1982,11(2):179-181
Using the convexity of the 2-dirnensionai field of values we reprove the well-known result that an inner product that is semibounded on the neutral set of an indefinite inner product of arbitrary dimension is so on the whole space. With this field of values approach we can also remedy some errors in the literature on indefinite inner product spaces. 相似文献
20.
Vincent Darrigrand Andrei Dumitrasc Carola Kruse Ulrich Rüde 《Numerical Linear Algebra with Applications》2023,30(5):e2484
We study an inexact inner–outer generalized Golub–Kahan algorithm for the solution of saddle-point problems with a two-times-two block structure. In each outer iteration, an inner system has to be solved which in theory has to be done exactly. Whenever the system is getting large, an inner exact solver is, however, no longer efficient or even feasible and iterative methods must be used. We focus this article on a numerical study showing the influence of the accuracy of an inner iterative solution on the accuracy of the solution of the block system. Emphasis is further given on reducing the computational cost, which is defined as the total number of inner iterations. We develop relaxation techniques intended to dynamically change the inner tolerance for each outer iteration to further minimize the total number of inner iterations. We illustrate our findings on a Stokes problem and validate them on a mixed formulation of the Poisson problem. 相似文献