Generic existence of Lipschitzian solutions of optimal control problems without convexity assumptions

The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions. In this paper we consider a large class of optimal control problems which is identified with a complete metric space of integrands without convexity assumptions and show that for a generic integrand the corresponding optimal control problem possesses a unique solution and this solution is Lipschitzian.     

Geometric modeling and validation of twist drills with a generic point profile

Traditionally, twist drills with a few specific point geometry, such as planar, conical, cylindrical, ellipsoidal or hyperboloidal, have been designed and adapted for specific applications. Using CAD, the point geometry can be given a generic definition which will enhance the freedom to design drills with different point profiles and optimize them for multiple objectives. Such a definition can also be used for several downstream applications. This paper presents a methodology to model the twist drills with generic point geometry using NURBS. To begin with, a detailed basic model for a fluted twist drill with sectional geometry made up of arcs and straight lines has been presented in terms of bi-parametric surface patches. The coordinates of cutting lips and chisel edge of the drill have been obtained as solution to a surface-curve intersection problem using optimization algorithm. Subsequently, the model has been generalized by employing NURBS to represent the curves whereby the cutting edges and angles can be altered simply by changing the control points or their respective weights. Using this methodology, the generic definitions of the conventional angles on the drill point have been derived and presented. The proposed model has been illustrated in MATLAB environment and validated experimentally for a conical and an arbitrary point geometry. The experiments show a good conformity with the theoretical evaluations.     

曲贝替定的合成研究进展

作为首个来源于海洋的抗肿瘤药物, 曲贝替定已经被多个国家批准用于进展期软组织肉瘤和复发性卵巢癌的治疗. 由于其结构的独特性和复杂性, 曲贝替定的合成受到了来自学术界和工业界的深度关注. 本文从曲贝替定的结构和逆合成路线方面, 系统评述了曲贝替定的合成研究进展及其环和手性中心的构建策略.     

Generic compactness reformulated

We point out a connection between reflection principles and generic large cardinals. One principle of pure reflection is introduced that is as strong as generic supercompactness of ₂ by -closed forcing. This new concept implies CH and extends the reflection principles for stationary sets in a canonical way.Mathematics Subject Classification (2000): 03E50, 03E55     

Supersimplicity and quadratic extensions

An elliptic curve over a supersimple field with exactly one extension of degree 2 has an s-generic point. A. Martin-Pizarro would like to express his gratitude to the organisation of the Florida Logic year, in which he took part. Martin-Pizarro research was supported by a DFG-Forschungsstipendium MA3310/1-1. F. O. Wagner is a Membre junior de l’Institut Universitaire de France. Work done during the semester on Model Theory and Applications in Algebra and Analysis at the Isaac Newton Institute for the Mathematical Sciences, whose hospitality is gratefully acknowledged.     

Companionability characterization for the expansion of an o-minimal theory by a dense subgroup

This paper provides a full characterization for when the expansion of a complete o-minimal theory, one that extends the theory of ordered divisible abelian groups, by a unary predicate that picks out a divisible, dense and codense group has a model companion. This result is motivated by criteria and questions introduced in the recent works [14] and [10] concerning the existence of model companions, as well as preservation results for some neostability properties when passing to the model companion. Examples are included both in which the predicate is an additive subgroup of a real ordered vector space, and where it is a multiplicative subgroup of the nonzero elements of an o-minimal expansion of a real closed field. The paper concludes with a brief discussion of neostability properties and examples that illustrate the lack of preservation (from the base o-minimal theory to the model companion of the expansion we define) for properties such as strong, NIP, and NTP₂, though there are also examples for which some or all three of those properties are preserved.     

非饱和土的广义朗肯土压力

本文从 4条基本假设出发 ,建立了非饱和土的广义朗肯土压力公式 ,采用理想试验对该公式进行了验证 ,在北京地铁13号线的东直门车站基坑工程中理论分析结果和实测值非常接近 ,证明了该理论的有效性。土的广义朗肯土压力公式建立了土的试验指标与原位指标的关系 ,从理论上给出了用土的试验指标得到原位主动 (被动 )土压力的方法。对于非饱和土 ,采用简单易得的直剪试验指标应用广义朗肯土压力公式就可以得到相当精确的结果 ,弥补了扩展朗肯土压力理论的不足。而且广义朗肯土压力公式能够合理利用已有的工程经验和工程数据 ,为非饱和土力学的工程实用化提供了一条新的思路。     

Chaos among self-maps of the Cantor space

Glasner and Weiss have shown that a generic homeomorphism of the Cantor space has zero topological entropy. Hochman has shown that a generic transitive homeomorphism of the Cantor space has the property that it is topologically conjugate to the universal odometer and hence far from being chaotic in any sense. We show that a generic self-map of the Cantor space has zero topological entropy. Moreover, we show that a generic self-map of the Cantor space has no periodic points and hence is not Devaney chaotic nor Devaney chaotic on any subsystem. However, we exhibit a dense subset of the space of all self-maps of the Cantor space each element of which has infinite topological entropy and is Devaney chaotic on some subsystem.     

Regenerative cascade homotopies for solving polynomial systems

A key step in the numerical computation of the irreducible decomposition of a polynomial system is the computation of a witness superset of the solution set. In many problems involving a solution set of a polynomial system, the witness superset contains all the needed information. Sommese and Wampler gave the first numerical method to compute witness supersets, based on dimension-by-dimension slicing of the solution set by generic linear spaces, followed later by the cascade homotopy of Sommese and Verschelde. Recently, the authors of this article introduced a new method, regeneration, to compute solution sets of polynomial systems. Tests showed that combining regeneration with the dimension-by-dimension algorithm was significantly faster than naively combining it with the cascade homotopy. However, in this article, we combine an appropriate randomization of the polynomial system with the regeneration technique to construct a new cascade of homotopies for computing witness supersets. Computational tests give strong evidence that regenerative cascade is superior in practice to previous methods.