CONVERGENCE OF CASCADE ALGORITHMS AND SMOOTHNESS OF REFINABLE DISTRIBUTIONS

In this paper, the author at first develops a method to study convergence of the cascade algorithm in a Banach space without stable assumption on the initial (see Theorem 2.1), and then applies the previous result on the convergence to characterizing compactly supported refinable distributions in fractional Sobolev spaces and Holder continuous spaces (see Theorems 3.1, 3.3, and 3.4). Finally the author applies the above characterization to choosing appropriate initial to guarantee the convergence of the cascade algorithm (see Theorem 4.2).     

关于多正解问题的某些研究

本文以ｆｐ 同伦方法为工具，借助于一些适当的变换，研究有序的（Ｂ）空间中的集值映象方程的多正解问题；在文中的有关工作中，还使用了集值映象的拟导数的某些性质．     

The π-π-theorem for manifold pairs with boundaries

The surgery obstruction of a normal map to a simple Poincaré pair (X, Y) lies in the relative surgery obstruction group L _*(π ₁(Y) → π ₁(X)). A well-known result of Wall, the so-called π-π-theorem, states that in higher dimensions a normal map of a manifold with boundary to a simple Poincaré pair with π ₁(X) ? π ₁(Y) is normally bordant to a simple homotopy equivalence of pairs. In order to study normal maps to a manifold with a submanifold, Wall introduced the surgery obstruction groups LP _* for manifold pairs and splitting obstruction groups LS _*. In the present paper, we formulate and prove for manifold pairs with boundary results similar to the π-π-theorem. We give direct geometric proofs, which are based on the original statements of Wall’s results and apply obtained results to investigate surgery on filtered manifolds.     

Category with a natural cone

Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples are given. We point out that the main results of this paper were already stated in [3], and the purpose of this article is to give full details of the foregoing.     

The Convergence of (r|~)_s(b_0h_n-h_1b_(n-1))

This paper computes the Thorn map onγ2 and proves that it is represented by 2b2,0h1,2 in the ASS. The authors also compute the higher May differential of 62,0, from which it is proved thatγs(b0hn-h1bn-1) for 2≤s < p - 1 are permanent cycles in the ASS.     

Computational experience with general equilibrium problems

We report on computational experience with an implementation of three algorithms for the general economic equilibrium problem. As a result we get that the projection algorithm for variational inequalities increases the size of solvable models by a factor of 5–10 in comparison with the classical homotopy method. As a third approach we implemented a simulated annealing heuristic which might be suitable to estimate equilibria for very large models.Supported by the German Research Association (Deutsche Forschungsgemeinschaft, SFB 303).     

球面稳定同伦中的复合元素α1β1γs的非平凡性

本文证明:当p≥7任意奇素数,3≤s相似文献   

Calculus I: The first derivative of pseudoisotopy theory

Let P be the (stable, smooth) pseudoisotopy space of the space X. For any map Y: YX of spaces, we identify the homotopy type of the fiber of P(f): P(f) P(f) in a stable range, roughly twice the connectivity of the map YX. We establish some language for discussing and manipulating such stable-range relative calculations for any homotopy functor. The theorem about P has a corollary about Waldhausen's A. Dedicated to Alexander GrothendieckResearch supported in part by NSF grant DMS-8806444 and by a Sloan Fellowship. Research at MSRI supported in part by NSF grant DMS-8505550.     

Reactivity of stable neopentyl-Pd intermediates in the absence of nucleophile

In the absence of any trapping agent, stable neopentyl-Pd intermediates can terminate a catalytic cycle by undergoing a regioselective C-H activation, leading to various spiro or fused cyclopropane derivatives in a straightforward manner. If the neopentyl-Pd intermediate contains a heteroatom at a suitable position, C-H activation does not occur and stable palladacycles are isolated.     

Synthesis of triphenylene derivatives by Pd-catalyzed Suzuki coupling/intramolecular CH activation between arylboronic acids and dibromobiphenyls

An efficient and regioselective synthesis of functionalized triphenylenes via palladium-catalyzed Suzuki-Miyaura coupling and subsequent intramolecular CH activation between arylboronic acids and dibromobiphenyls was developed. This methodology showed excellent atomic economy and regiospecificity as well as synthetic feasibility of unsymmetrical triphenylenes.