Well-posedness of two pseudo-parabolic problems for electrical conduction in heterogeneous media

We prove a well-posedness result for two pseudo-parabolic problems, which can be seen as two models for the same electrical conduction phenomenon in heterogeneous media, neglecting the magnetic field. One of the problems is the concentration limit of the other one, when the thickness of the dielectric inclusions goes to zero. The concentrated problem involves a transmission condition through interfaces, which is mediated by a suitable Laplace-Beltrami type equation.     

Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

多运营商高铁隧道移动网络覆盖方案

高铁移动网络覆盖是国内三大通信运营商的一个重点,而高铁隧道内移动网络覆盖更是运营商的一大难点痛点。文章根据我国中部省份某高铁线路覆盖规划实例,采用“设备+POI+泄漏电缆”模式,即三家运营商信号源设备通过同一POI(point of interface,多系统接入平台)接入,信号输出到泄漏电缆进行隧道覆盖,隧道口场坪站安装宽频切换天线对隧道外进行延伸覆盖,通过链路预算合理布置各运营商主设备信号源,从而实现隧道到室外的无缝覆盖。最后,根据已有成熟网络覆盖解决方案,对未来5G高铁隧道移动网络覆盖方案进行了探讨。     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

法国电信集团运营模式研究

中国电信企业经过多年的高速发展，逐渐步入成熟期，增长率下降、利润降低将是必然趋势，因此目前亟需探索新的运营模式，向综合型全业务电信运营商的方向发展。法国电信集团历史悠久，市场转型起步早．其发展经验有许多地方值得借鉴，包括法国电信集团具有特色的品牌战咯、灵活的经营模式、为企业提供全方位服务的经营手段。中国电信企业应积极开展全业务经营，加快发展企业网市场，完善合作运营模式，争取早日走向世界。     

基于形态学top-hat算子的多传感器图像融合

本文根据形态学top-hat算子能够提取图像中极大值与极小值区域的特点,将其应用于多传感器图像融合的两个重要领域——多聚焦图像融合和高分辨、多光谱图像融合.实验中将本文方法与Laplacian塔型变换、子波变换、主分量分析等方法进行了比较,结果表明本文所提的基于top-hat算子的融合方法具有优越的性能,拓广了top-hat算子的应用范围.     

Inner derivations and norm equality

We characterize when the norm of the sum of two bounded operators on a Hilbert space is equal to the sum of their norms.