Fast algorithms for greedy triangulation

We present the first quadratic-time algorithm for the greedy triangulation of a finite planar point set, and the first linear-time algorithm for the greedy triangulation of a convex polygon.     

40CrNiMoA齿轮激光表面强化及抗疲劳性分析

对40CrNiMo齿轮进行了激光表面强化处理,用SEM和TEM对处理试样显微组织进行了分析,测试并分析了其显微硬度,并进行了抗疲劳性现场试验,结果表明:40CrNiMo激光淬火后其组织由淬硬层、过渡区和基体组成,淬硬层组织为细小的板条马氏体和针状马氏体,层深约1.5mm,过渡区为马氏体和索氏体混合组织,基体为回火索氏体。淬硬层表面硬度比常规淬火硬度有所提高。40CrNiMo激光淬火齿轮比20Cr2Ni4渗碳淬火齿轮疲劳强度提高约10%。     

Complex quadrics and spectral geometry

Some characterizations of complex quadrics in terms of the spectrum are given.     

Decaying states of perturbed wave equations

We study the solutions of perturbed wave equations that represent free wave motion outside some ball. When there are no trapped rays, it is shown that every solution whose total energy decays to zero must be smooth. This extends results of Rauch to the even-dimensional case and to systems having more than one sound speed. In these results, obstacles are not considered. We show that, even allowing obstacles, waves with compact spatial support cannot decay, assuming a unique continuation hypothesis. An example with obstacle is given where nonsmooth, compactly supported, decaying waves exist.     

Monotonieeigenschaften des Steffensen-Verfahrens

Steffensen's method is slightly generalized by introducing a real parameter. In this way one can get different monotonicity properties, depending on the choice of this parameter. These monotonicity statements give the possibility of bracketing the solution of a given problem. In a special case they even ensure the convergence and the existence of a solution. Furthermore there are given sufficient conditions, which show that Steffensen's method converges at least as quickly as Newton's method. A numerical example shows the efficiency of the theorems and compares Steffensen's and Newton's method.

     

Efficiency and Cramér-Rao type lnequalities for convex loss functions

A general method for obtaining inequalities of Cramér-Rao type for convex loss functions is presented. It is shown under rather weak assumptions that there are at least as many such inequalities as best unbiased estimators. More precisely, it is shown that an estimator is efficient with respect to an inequality of Cramér-Rao type if and only if it is the best in the class of unbiased estimators. Moreover, theorems of Blyth and Roberts (“Proceedings Sixth Berkeley Symposium on Math. Statist. Prob.,”) and of Blyth (Ann. Statist.2, 464–473) are extended. We make an use of methods of convex analysis and properties of convex integral functionals on Orlicz spaces.     

Countably many simultaneous random changes of time scales

Simultaneous changes of time scales of the components of a vector Markov process are defined and developed. Measurability properties, Dynkin's lemma, and the strong Markov property are established for the transformed process.