On the simplicity of some kac-moody groups

Recently, Marcuson extended the classical construction of Tits systems in Steinberg groups to include the Kac-Moody Steinberg groups associated with the infinite dimensional versions of the great Lie algebras. If these Lie algebras and their Kac-Moody groups are viewed as limits of their finite dimensional counterparts, more direct methods may be employed. In fact, the Kac-Moody Chevalley groups of these Lie algebras are seen to be simple.     

Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.     

Camptothecin@HMSNs/thermosensitive hydrogel composite for applications in preventing local breast cancer recurrence

The CPT was loaded into the HMSNs with the high loading capacity. Then the CPT@HMSNs were loaded into the PLEL thermosensitive hydrogels for local therapy to prevent the recurrence of breast cancer after the tumor was resected.     

A perturbed martingale approach to global optimization

A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as ‘coalescence’ and ‘scrambling’. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization.     

Sobolev spaces on Lie groups: Embedding theorems and algebra properties

Let G be a noncompact connected Lie group, denote with ρ a right Haar measure and choose a family of linearly independent left-invariant vector fields X on G satisfying Hörmander's condition. Let χ be a positive character of G and consider the measure ${\mu }_{\chi }$ whose density with respect to ρ is χ. In this paper, we introduce Sobolev spaces $L_{\alpha }^p({\mu }_{\chi })$ adapted to X and ${\mu }_{\chi }$ ($1<p<\infty$, $\alpha \ge 0$) and study embedding theorems and algebra properties of these spaces. As an application, we prove local well-posedness and regularity results of solutions of some nonlinear heat and Schrödinger equations on the group.     

地方高校高分子材料与工程专业生产实习协同创新模式探讨

地方高校已成为我国高等教育的重要组成部分,由于办学目标、生源构成、服务地区不同于部属高校,其生产实习教学环节面临各种困境。寻求有效的途径突破生产实习的困境成为当前各地方高校亟待解决的问题。本文以广东工业大学为例,在分析该校的办学特点以及高分子材料与工程专业近年来生产实习状况的基础上,介绍该校以大学联盟为平台的生产实习新模式,并详细说明其实施方案。该模式基于该校的协同创新战略,已取得良好的教学效果。