关于Euler公式的一个应用

欧拉公式是研究平面图性质的一个重要工具、利用欧拉公式可以得到许多平面图，特别是一些特殊的平面图的点、边、面的关系。本利用欧拉公式讨论平面图、外平面图的一些性质。     

Electromechanical coupling model and analysis of transient behavior for inertial vibrating machines

A mathematical model of electromechanical coupling system for a planar inertial vibrating machine is built by setting up dynamical equations of discrete systems with a matrix methodology proposed. The substance of the transient behavior of the machine is unveiled by analyzing the results of the computer simulation to the model, and new methods are presented for diminishing the transient amplitude of the vibrating machine and improving the transient behavior. The reliable mathematical model is provided for intelligent control of the transient behavior of the equipment.     

自适应雷达目标参数估计的Cramer-Rao下界

在窄带信号和窄带阵列假设下,分析了均匀面阵(UPA)自适应雷达中目标参数的最大似然估计.首先分析了UPA信号模型,随后给出了目标参数的最大似然估计和相应的CR下界.通过Jacobian矩阵给出了目标俯仰角、方位角、径向速度、模和相位的CRB.分析结果是1-D均匀线性阵列(ULA)到2-D(UPA)的推广,可用于空中运动目标参数估计的性能分析.     

围长较大的平面图的全染色的一个结果

图G的一个k全染色是用k种颜色对图G的顶点集和边集进行染色使得相邻接的或相关联的元素染不同的颜色,图G的全色数χ＂（G）为图G的k-全染色中的最小k值.Behzad和Vizing猜想任意简单图G的全色数都不超过Δ（G）＋2,已经证明了此猜想对最大度不是6的平面图成立,而且最大度不小于9的平面图G的全色数为Δ（G）＋1.本文利用差值转移方法研究了最大度小于9的一些情况,证明了最大度为4,5,6,7,8的平面图G,如果其围长不小于8,则其全色数也为Δ（G）＋1.     

一般平面封闭折线的余弦定律

将三角形中的余弦定律进行推广,得到一般平面封闭折线的余弦定律.     

浅谈数码时代《平面构成》课程教学改革

文章先是论述了数码时代给课程教学带来的机遇,进而分析了平面构成课程的教学现状,然后从积极利用好数码时代的教学工具、采用多样化的教学手段、提升学生的专业理论修养等这三个方面探析了数码时代平面构成的教学改革,以期能通过教学改革,有效培养学生的二维设计能力及抽象思维能力等,使学生的基础设计能力能符合数码时代社会的需求,能满足于目前整个社会对艺术设计的要求。     

Scalable fabrication of printed Zn//MnO2 planar micro-batteries with high volumetric energy density and exceptional safety

The rapid development of printed and microscale electronics imminently requires compatible micro-batteries (MBs) with high performance, applicable scalability, and exceptional safety, but faces great challenges from the ever-reported stacked geometry. Herein the first printed planar prototype of aqueous-based, high-safety Zn//MnO₂ MBs, with outstanding performance, aesthetic diversity, flexibility and modularization, is demonstrated, based on interdigital patterns of Zn ink as anode and MnO₂ ink as cathode, with high-conducting graphene ink as a metal-free current collector, fabricated by an industrially scalable screen-printing technique. The planar separator-free Zn//MnO₂ MBs, tested in neutral aqueous electrolyte, deliver a high volumetric capacity of 19.3 mAh/cm³ (corresponding to 393 mAh/g) at 7.5 mA/cm³, and notable volumetric energy density of 17.3 mWh/cm³, outperforming lithium thin-film batteries (≤10 mWh/cm³). Furthermore, our Zn//MnO₂ MBs present long-term cyclability having a high capacity retention of 83.9% after 1300 cycles at 5 C, which is superior to stacked Zn//MnO₂ batteries previously reported. Also, Zn//MnO₂ planar MBs exhibit exceptional flexibility without observable capacity decay under serious deformation, and remarkably serial and parallel integration of constructing bipolar cells with high voltage and capacity output. Therefore, low-cost, environmentally benign Zn//MnO₂ MBs with in-plane geometry possess huge potential as high-energy, safe, scalable and flexible microscale power sources for direction integration with printed electronics.     

关于平面设计语言的解析

平面设计作为设计范畴的重要组成部分,其知识点范围覆盖广、类别复杂,随着科学技术的进步在不断更新。通过对平面设计的深入研究,认为平面设计是一门语言,并将其归纳为形式、色彩、材质,通过三个层面对平面设计语言进行深入解析,为平面设计的学习与应用提供更深入的认知与更清晰的思路。     

n维立方体的性质

n维立方体是一个n-正则的二部图,既有实际应用价值又有理论价值。文中重点研究了n维立方体的Hamilton性质及可平面性质,证明了n维立方体是Hamilton图及非平面图,并且给出了一个具体构造Hamilton圈的方法。     

具有小直径平面图的电力控制数

The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known vertex covering and dominating set problems in graph theory. In this paper, it was shown that the power domination number of an outerplanar graph with the diameter two or a 2-connected outerplanar graph with the diameter three is precisely one. Upper bounds on the power domination number for a general planar graph with the diameter two or three were determined as an immediate consequences of results proven by Dorfling, et al. Also, an infinite family of outerplanar graphs with the diameter four having arbitrarily large power domination numbers were given.