Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

In this paper we consider minimizers of the functional$\min \{{\lambda }_1(\mathrm{\Omega })+\cdots +{\lambda }_k(\mathrm{\Omega })+\mathrm{\Lambda }|\mathrm{\Omega }|,:\mathrm{\Omega }\subset D\text{ open}\}$ where $D\subset {\mathbb{R}}^d$ is a bounded open set and where $0<{\lambda }_1(\mathrm{\Omega })\le \cdots \le {\lambda }_k(\mathrm{\Omega })$ are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets ${\mathrm{\Omega }}^{⁎}$ have finite perimeter and that their free boundary $\partial {\mathrm{\Omega }}^{⁎}\cap D$ is composed of a regular part, which is locally the graph of a $C^{1,\alpha }$-regular function, and a singular part, which is empty if $d<d^{⁎}$, discrete if $d=d^{⁎}$ and of Hausdorff dimension at most $d-d^{⁎}$ if $d>d^{⁎}$, for some $d^{⁎}\in \{5,6,7\}$.     

HTK参数对普米语孤立词识别率的影响

普米语是一种无文字的少数民族语言,目前已处于濒危状态,建立语音语料库及开展语音识别研究是保护和传承普米语的重要手段.基于HTK的语音识别中,参数的选取对不同语言的识别率有很大的影响.针对MFCC维数、HMM状态数及GMM个数这3个参数对普米语的识别率进行研究,结果表明:普米语语音识别的最佳MFCC维数为13维,最佳HMM状态数为8个,最佳GMM个数为3个.     

大学英语教学中中国传统文化渗透路径探究

文化与语言有着密切的联系，一定的文化背景知识有助于促进语言应用能力的提高。大学英语教学的同时也应该是对文化的传授，英语教学不仅是语言知识的教授，更应该是文化知识的传播。从多模态视角出发，探究中国传统文化导入大学英语教学的必要性及途径，有助于提高当代大学生的英语识读能力及文化传播的能力。     

现代信息检索理论架构研究

信息作为一种新的资源,对当代经济和社会的发展起着非常重要的作用,如何高效快捷地利用现代信息是当前我国信息检索领域研究的重要问题。阐述了现代信息检索理论架构研究的前提,分析了当前主要的信息检索理论,探讨了网络信息检索的主要方法。     

Thermally induced solid-state transformation of cimetidine. A multi-spectroscopic/chemometrics determination of the kinetics of the process and structural elucidation of one of the products as a stable N3-enamino tautomer

Exposure of cimetidine (CIM) to dry heat (160–180 °C) afforded, upon cooling, a glassy solid containing new and hitherto unknown products. The kinetics of this process was studied by a second order chemometrics-assisted multi-spectroscopic approach. Proton and carbon-13 nuclear magnetic resonance (NMR), as well as ultraviolet and infrared spectroscopic data were jointly used, whereas multivariate curve resolution with alternating least squares (MCR-ALS) was employed as the chemometrics method to extract process information. It was established that drug degradation follows a first order kinetics.     

基于语料库的韩语因果复句语义及句法特征探析

韩国语中存在着各种各样的因果复句,以口语和书面语中使用频率极高的""四种因果复句作为研究对象,通过21世纪世宗计划语料库中的具体实例来考查分析它们的语义及句法特征,对于韩国语复句教学及韩国语学习者学习并运用韩国语因果复句,能够提供一个良好的理论基础和参考依据。     

音序、形序、义序:并存还是取代?——也谈词典词目编排法

按词目的编排方法分,词典可分为三大类:音序词典、形序词典和义序词典。这三类词典各有优点和缺点;它们之间的关系应该是“长期共存,互相补足”,而不是谁取代谁。以此取代彼,没有必要性,也没有可能性。     

实时系统开发与PEARL语言

本文讨论了实时系统的特征、开发方法、设计工具、实现手段工具等开发过程中的主要问题,论述了实时系统开发语言PEARL及该语言的对实时系统的主要支持.     

数学难以理解的逻辑透视

对数学教学内容的逻辑结构、逻辑规则和方法以及数学语言进行逻辑透视，探讨数学难以理解的客观因素及对策．