On mesh restrictions to satisfy comparison principles,maximum principles,and the non-negative constraint: Recent developments and new results

This article concerns mesh restrictions that are needed to satisfy several important mathematical properties—maximum principles, comparison principles, and the nonnegative constraint—for a general linear second-order elliptic partial differential equation. We critically review some recent developments in the field of discrete maximum principles, derive new results, and discuss some possible future research directions in this area. In particular, we derive restrictions for a three-node triangular (T3) element and a four-node quadrilateral (Q4) element to satisfy comparison principles, maximum principles, and the nonnegative constraint under the standard single-field Galerkin formulation. Analysis is restricted to uniformly elliptic linear differential operators in divergence form with Dirichlet boundary conditions specified on the entire boundary of the domain. Various versions of maximum principles and comparison principles are discussed in both continuous and discrete settings. In the literature, it is well-known that an acute-angled triangle is sufficient to satisfy the discrete weak maximum principle for pure isotropic diffusion. Herein, we show that this condition can be either too restrictive or not sufficient to satisfy various discrete principles when one considers anisotropic diffusivity, advection velocity field, or linear reaction coefficient. Subsequently, we derive appropriate restrictions on the mesh for simplicial (e.g., T3 element) and nonsimplicial (e.g., Q4 element) elements. Based on these conditions, an iterative algorithm is developed to construct simplicial meshes that preserve discrete maximum principles using existing open source mesh generators. Various numerical examples based on different types of triangulations are presented to show the pros and cons of placing restrictions on a computational mesh. We also quantify local and global mass conservation errors using representative numerical examples and illustrate the performance of metric.     

Fluorinated Phosphorene: Electrochemical Synthesis,Atomistic Fluorination,and Enhanced Stability

Phosphorene has attracted great interest due to its unique electronic and optoelectronic properties owing to its tunable direct and moderate band‐gap in association with high carrier mobility. However, its intrinsic instability in air seriously hinders its practical applications, and problems of technical complexity and in‐process degradation exist in currently proposed stabilization strategies. A facile pathway in obtaining and stabilizing phosphorene through a one‐step, ionic liquid‐assisted electrochemical exfoliation and synchronous fluorination process is reported in this study. This strategy enables fluorinated phosphorene (FP) to be discovered and large‐scale, highly selective few‐layer FP (3?6 atomic layers) to be obtained. The synthesized FP is found to exhibit unique morphological and optical characteristics. Possible atomistic fluorination configurations of FP are revealed by core‐level binding energy shift calculations in combination with spectroscopic measurements, and the results indicate that electrolyte concentration significantly modulates the fluorination configurations. Furthermore, FP is found to exhibit enhanced air stability thanks to the antioxidation and antihydration effects of the introduced fluorine adatoms, and demonstrate excellent photothermal stability during a week of air exposure. These findings pave the way toward real applications of phosphorene‐based nanophotonics.     

产品细节形态设计探究

目的探究产品细节形态设计中的设计原则和方法。方法结合现有产品的调研汇总、基本模型的建立分析以及问卷调查的结果,对影响产品外观细节形态的两个基本要素——圆角和分割线的属性对产品视觉美感的影响进行研究,并给出相关实例验证。结论分析了产品细节形态中圆角和分割线两个视觉元素对产品视觉感受的影响,提出了在产品细节形态设计中合理设计圆角和分割线的原则和方法,给出了从圆角和分割线两个方面提升整体产品视觉美感的优化方案。     

不同浓度Cu掺杂SnO2材料电学和力学性质的研究

为研究Cu掺入对SnO_2性能的影响,本文采用密度泛函理论和平面波赝势法,建立了未掺杂SnO_2和不同比例Cu掺杂的SnO_2晶胞模型,对Sn_(1-x)Cu_xO_2(x=0、0.083、0.125、0.167、0.25、0.5)超晶胞体系进行优化计算、能量计算和弹性模量计算,得到晶格常数、弹性模量、电荷分布、能带结构和态密度图.研究表明:掺杂能够使得材料的弹性模量大幅减小,对应的硬化函数值降低,易于材料加工;在电性质方面,掺杂后,材料均属于直接带隙半导体材料.当x0.25时,由于掺杂浓度过高使得晶格发生畸变,电性质与未掺杂情况类似;当x0.25时,随着掺杂浓度的降低,导带收缩加剧,局域性增强,禁带宽度变窄,使得电子从价带受激跃迁所需能量降低,故掺杂后材料表现出半金属性,导电性增强.     

Jumps and logic in the law

The main stream of legal theory tends to incorporate unwritten principles into the law. Weighing of principles plays a great role in legal argumentation, inter alia in statutory interpretation. A weighing and balancing of principles and other prima facie reasons is a jump. The inference is not conclusive.To deal with defeasibility and weighing, a jurist needs both the belief-revision logic and the nonmonotonic logic. The systems of nonmonotonic logic included in the present volume provide logical tools enabling one to speak precisely about various kinds of rules about rules, dealing with such things as applicability of rules, what is assumed by rules, priority between rules and the burden of proof. Nonmonotonic logic is an example of an extension of the domain of logic. But the more far-reaching the extension is, the greater problems it meets. It seems impossible to make logical reconstruction of the totality of legal argumentation.The lawyers' search for reasons has no obvious end point. Ideally, the search for reasons may end when one arrives at a coherent totality of knowledge. In other words, coherence is the termination condition of reasoning. Both scientific knowledge and knowledge of legal and moral norms progresses by trial and error, and that one must resort to a certain convention to define what error means. The main difference is, however, that conventions of science are much more precise than those of legal scholarship.Consequently, determination of error in legal science is often holistic and circular. The reasons determining that a legal theory is erroneous are not more certain than the contested theory itself. A strict and formal logical analysis cannot give us the full grasp of legal rationality. A weaker logical theory, allowing for nonmonotonic steps, comes closer, at the expense of an inevitable loss of computational efficiency. Coherentist epistemology grasps even more of this rationality, at the expense of a loss of preciseness.     

一种改进的生物模糊记忆入侵检测模型

入侵检测技术是保证计算机网络安全的核心技术之一,在网络安全领域内发挥着重要的作用。但是目前的入侵检测系统不够完善,文章通过对记忆原理和模糊理论的分析将其应用在已有的入侵检测系统中,提出了一种新的基于生物模糊记忆的入侵检测系统模型,并用实验证明该模型具有更好的检测效果。     

电视台网络安全系统的研究

由于全台网是业务整合、信息整合,其规模越来越大,所以安全的问题也更加突出。致使安全生产播出成为电视台的生命线,是一切工作的重点。网络安全一般是指防范黑客攻击和病毒传播等造成的安全威胁,需要通过采用适合的安全技术手段,建立完善的网络安全体系。该文通过对电视台的网络系统进行描述,了解网络安全的重要性和必要性,从而得到一套适合电视台的网络安全系统策略和解决办法。     

医学信息类专业《计算机组成原理》课程教学探讨

结合高等医科院校的实际情况,针对医学信息类专业的特点,探讨了《计算机组成原理》课程教学过程q-的几点心得。分别从教学内容的选择、教学方法的改进和教学实践的改革等方面作了详细的阐述。     

编译原理中的LR类分析方法的教学研究

编译原理课程的教学不仅要介绍编译的基本原理和技术,还要培养学生的学习兴趣、专业思维和科学研究的方法及能力,文章以LR类分析方法为例,以还原知识的发现过程为主线,重现解决问题的思路与方法,以期培养学生的专业学习兴趣和科研能力。     

谈色彩在包装设计中的运用原则

色彩是包装设计的重要视觉语言。成功的包装色彩运用,不仅能够清晰传达商品信息,而且能够提高商品形象感染力和经济附加值,满足人们的审美心理,树立品牌形象。文章通过市场调查深入探讨了包装色彩设计中的五大运用原则,使包装色彩应用有了明确定位,它将进一步提高商品的市场竞争力。