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111.
A theory of extremes is developed for chaotic dynamical systems and illustrated on representative models of fully developed chaos and intermitent chaos. The cumulative distribution and its associated density for the largest value occurring in a data set, for monotonically increasing (or decreasing) sequences, and for local maxima are evaluated both analytically and numerically. Substantial differences from the classical statistical theory of extremes are found, arising from the deterministic origin of the underlying dynamics. 相似文献
112.
Wolfram Koepf 《The Ramanujan Journal》2007,13(1-3):103-129
The Bieberbach conjecture about the coefficients of univalent functions of the unit disk was formulated by Ludwig Bieberbach
in 1916 [4]. The conjecture states that the coefficients of univalent functions are majorized by those of the Koebe function
which maps the unit disk onto a radially slit plane.
The Bieberbach conjecture was quite a difficult problem, and it was surprisingly proved by Louis de Branges in 1984 [5] when
some experts were rather trying to disprove it. It turned out that an inequality of Askey and Gasper [2] about certain hypergeometric
functions played a crucial role in de Branges’ proof.
In this article I describe the historical development of the conjecture and the main ideas that led to the proof. The proof
of Lenard Weinstein (1991) [72] follows, and it is shown how the two proofs are interrelated.
Both proofs depend on polynomial systems that are directly related with the Koebe function. At this point algorithms of computer
algebra come into the play, and computer demonstrations are given that show how important parts of the proofs can be automated.
This article is dedicated to Dick Askey on occasion of his seventieth birthday.
2000 Mathematics Subject Classification Primary—30C50, 30C35, 30C45, 30C80, 33C20, 33C45, 33F10, 68W30 相似文献
113.
A sufficient and then a necessary condition are given for a function to be an extreme point of the unit ball of the Banach space of continuous functions, under the supremum norm, from a compact Hausdorff topological space into a Banach space equipped with its weak topology . Strongly extreme points of the unit ball of are characterized as the norm-one functions that are uniformly strongly extreme point valued on a dense subset of . It is shown that a variety of stronger types of extreme points (e.g. denting points) never exist in the unit ball of . Lastly, some naturally arising and previously known extreme points of the unit ball of are shown to actually be strongly exposed points.
114.
Rinya Takahashi Masaaki Sibuya 《Annals of the Institute of Statistical Mathematics》2001,53(3):647-660
This is a continuing paper of the authors (1998, Ann. Inst. Statist. Math., 50, 361–377). In the Wicksell corpuscle problem, the maximum size of random spheres in a volume part is to be predicted from the sectional circular distribution of spheres cut by a plane. The size of the spheres is assumed to follow the three-parameter generalized gamma distribution. Prediction methods based on the moment estimation are proposed and their performances are evaluated by simulation. For a practically probable case, one of these prediction methods is as good as a method previously proposed by the authors where the two shape parameters are assumed to be known. 相似文献
115.
Jiann-wien Hsu 《Physica A》2009,388(24):4991-4998
We study the survival of extreme opinions in various processes of consensus formation. All the opinions are treated equally and subjected to the same rules of changing. We investigate three typical models to reach a consensus in each case: (A) personal influence, (B) influence from surroundings, and (C) influence to surroundings. Starting with uniformly distributed random opinions, our calculated results show that the extreme opinions can survive in both models (A) and (B), but not in model (C). We obtain a conclusion that both personal influence and passive adaptation to the environment are not sufficient enough to eradicate all the extreme opinions. Only the active persuasion to change the surroundings eliminates the extreme opinions completely. 相似文献
116.
《复变函数与椭圆型方程》2012,57(3):229-237
Sharp distortion theorems for close-to-convex functions which satisfy Re ?'(z) > γ are proved using extreme points. 相似文献
117.
Ramin Okhrati 《Applied Mathematical Finance》2019,26(2):101-130
We investigate hedging the risk of delayed data in certain defaultable securities through the local risk minimization approach. From a financial point of view, this indicates that in addition to the risk of default, investors also face incomplete accounting data. In our analysis, the delay is modelled by a random time change, and different levels of information, including the full market’s, management’s, and investors’ information, are distinguished. We obtain semi-explicit solutions for pseudo locally risk minimizing hedging strategies from the perspective of investors where the results are presented according to the solutions of partial differential equations. In obtaining the main results of this paper, we apply a filtration expansion theorem that determines the canonical decomposition of stopped special semimartingales in an enlarged filtration of investors’ information. 相似文献
118.
《Optimization》2012,61(2):91-108
Optimal control problems with nonlinear equations usually do not have a solution, i.e. an optimal control. Nevertheless, if the cost functional is uniformly concave with respect to the state, the solution may exist. Using the Balder's technique based on a Youngmeasure relaxation, Bauer's external principle and investigation of extreme Young measures; the existence is demonstrated here for optimal control processes described by nonlinear integral equations 相似文献
119.
The mean excess plot is a tool widely used in the study of risk, insurance and extreme values. One use is in validating a generalized Pareto model for the excess distribution. This paper investigates some theoretical and practical aspects of the use of the mean excess plot. 相似文献
120.
We compute the normals to faces of b2,2-orbihedra and apply the results to Operator Interpolation Theory. 相似文献