基于四元数体上的几个矩阵不等式

四元数矩阵的特征值与奇异值在四元数矩阵理论的应用中起着重要作用.借助于分块矩阵及相关恒等式,给出了关于四元数矩阵特征值与奇异值的几个新的不等式,推广了实或复数域上矩阵特征值与奇异值不等式的相应结果,它们可望有助于推动四元数代数在量子力学、机器人技术等学科中的进一步应用.     

一元二次四元数单边多项式的求根公式

随着四元数代数广泛应用于量子力学、惯性导航及控制论等学科,四元数多项式的求根问题被许多学者关注。最近Janovska和Opfer从理论上给出了一种n次四元数单边多项式零点的求解方法,Feng和Zhao进一步给出了一般n次四元数单边多项式的零点显性表达式。 本文根据Feng和Zhao的结果对一元二次四元数单边方程的根进行了讨论,并利用复数域上四次多项式的Ferrari求根公式建立了一元二次四元数单边方程的求解公式。与文献中现有的结果相比,本文建立的求根公式在许多方面展现了优越性。     

四元数长方矩阵的同时复对角化

利用四元数矩阵的奇异值分解(SVD),对两个四元数长矩阵给出了其同时复对角化的充要条件,进一步对一个四元数长矩阵集合,针对其同时复对角化问题,给出了一系列充分必要条件.     

一类广义延拓四元数矩阵的奇异值分解

从普通四元数矩阵的奇异值分解出发,给出了具有行或列对称结构的一类四元数矩阵(即广义四元数延拓矩阵)的奇异值、奇异向量与其母矩阵的奇异值、奇异向量之间的定量关系,推广了现有文献的结果。理论分析和数值实验的结果表明,就一大类广义四元数延拓矩阵而言,仅用母矩阵进行奇异值分解不但可以节省计算量和存储量,而且不影响任何数值精度。     

四元数在火控中的应用

介绍了四元数的定义、代数运算、三角形式和指数形式以及球面表示形式;综述了四元数在刚体姿态控制,计算机三维图像旋转,彩色图像处理和信号处理分析等实际应用中表示的物理含义,着重探讨了四元数理论在火控领域中应用方法,并对比传统欧拉角火控模型,分析了应用四元数火控模型的优点。最后从理论上得出,四元数理论方法在常规兵器火控系统有广阔的应用前景。     

电子组态中包含两个或两个以上非闭合壳层时原子静电能矩阵元的一种计算方法

应用Racah代数和反对称化子技巧,求得了LS耦合下组态为l~nl′~(n′)l″(n″)…的原子静电能矩阵元。在矩阵元的表达式中只合有6j、9j符号和单电子主亲态比系数。因此,可以比较容易地算出原子静电能。有时烧蚀蒸汽中包含原子序数较高的原子或离子。利用这种方法可以计算出它们的能级。     

基座高频运动时捷联姿态算法的扩展

1.引言 用于惯性导航的捷联系统其特点是它的敏感元件感受高的动态范围。因此,在选择系统姿态算法时需要考虑基座高频运动的影响。 通常捷联系统用的姿态算法有欧拉法、方向余弦法和四元数法、在这些算法中,四元数方法是最常用的,其优点是没有奇异性、简单和节省计算时间。最近,伯斯、泽旦和米勒提出了旋转矢量的概念,进一步改进了四元数方法的性能。事实证明,附加了旋转矢量概念的四元数方法能有效的抑制非交换误差这一姿态计算中的重要误差源。     

应用于四旋翼无人机角速度估计的几何滑模观测器设计

对四旋翼无人机的角速度进行估计时,传统的基于单位四元数的滑模观测器需要引入强制比例重调,因而影响了跟踪精度。本文提出一种基于数值积分的李群方法的滑模观测器设计框架。该算法基于等变映射思想,在齐性流形空间的等价李代数空间中设计滑模反馈,从而避免了直接在流形空间中设计反馈的复杂性,并消除了传统方法在每个积分步骤中强制加入的比例重调,提高了观测器的跟踪性能。仿真结果表明,几何滑模观测器算法可以有效的对四旋翼无人机的角速度进行估计。     

一类典型结构矩阵的WZ分解

WZ类矩阵分解是设计线性方程组求解中一类并行算法的数学理论基础。针对对称p-三对角矩阵,提出并证明该类典型结构矩阵的WZ分解式及其性质。进一步,当实对称p-三对角矩阵正定时,证明其WZ分解式中W因子具有元素均为实数的特点;当W因子对角线元素均为正实数时,分解式惟一。     

用矩阵求解反射光线的运动轨迹

在轰炸瞄准具、激光测距仪、红外探索跟踪装置中,往往借助反射棱镜或平面反射镜绕两个互相垂直的轴的转动,来实现瞄准线(或是激光束等)在方位或俯仰方向上的扫描(此时反射棱镜或平面反射镜基本上都是安置在乎行光路中)。瞄准线在通过绕轴转动的反射棱镜或平面反射镜以后,其反射光线在空间的运动轨迹可利用作图法、向量代数法、向量四元数和矩阵求解。但是用作图的方法求出反射光线的运动轨迹比较困难,     

Putin – the masked nemesis of the strategy of ambiguity

Recent events demonstrate the complex and adaptive approach employed by Russia to reassert influence in Europe. The changing face of Russia’s strategy commenced in 2007 when it launched a crippling cyber-attack against Estonia. This was followed by a large Russian conventional attack against Georgia in 2008, occupying two large areas of the nation. 2014 witnessed the Russian annexation of Crimea where in just a week, Russia seized control of Crimea “without firing a shot.” The annexation of Crimea was rapidly followed by a Russian inspired and led subversive war in eastern Ukraine. The common thread among these diverse Russian operations is its use of ambiguity to confound and confuse decision makers in the West.     

India's counter-insurgency experience: the ‘trust and nurture’ strategy

The Indian Army, a force trained primarily for conventional warfare, has been engaged in internal counter-insurgency operations since the 1950s. Despite such a long innings on a counter-insurgency mode, little attention has been accorded within military circles to doctrinal innovation for waging sub-conventional warfare in India's democratic political context. At best, the Army continues to view counter-insurgency duty as secondary to its primary duty of defending India from external conventional threats. By conceptualizing a counter-insurgency strategy of ‘trust and nurture’, this article aims to fill this critical doctrinal gap in India's military policy. The author argues that a counter-insurgency strategy of ‘trust and nurture’ based on democratic political culture, measured military methods, special counter-insurgency forces, local social and cultural awareness and an integrative nation-building approach will result in positive handling of India's internal security problems. The author utilizes India's counter-insurgency experiences in Assam, Mizoram, Nagaland, Punjab, and Operation ‘Sadhbhavana’ in Jammu and Kashmir as illustrative empirical indicants in order to validate the ‘trust and nurture’ strategy.     

An Unlikely Alliance: Portuguese and South African Airpower in Angola, 1968–1974

The war that Portugal was obliged to fight in Africa began in 1961 and immediately stretched the resources of its armed forces. Nowhere was this thinness more apparent than in policing the vast territory of Angola. The east and southeast of Angola were particularly vulnerable, as the area was a vast, sparsely populated region characterised by enormous featureless plains or chanas covered in tall grass and broken by an extensive river system and mountainous forests. The only military solution to policing these immense spaces was aviation and specifically the helicopter that could carry troops into battle, protect them with a gunship and bring them home when the operation was concluded. The immediate problem for the Portuguese Air Force (Força Aérea Portuguesa or FAP) in Angola and elsewhere was a scarcity of helicopters. The solution was an alliance with South Africa, which had a strong inventory of Alouette IIIs, to help in policing the east. This move was likewise in the interest of South Africa, as its threat came from Zambia through south-eastern Angola. This article examines the strategic and tactical development of this unusual, cross-cultural alliance and the symbiotic relationship that resulted in destruction of the enemies of both in Angola.     

国内外结构钢焊条研究的现状与发展

本文主要介绍了国外焊条的现状和发展趋势,包括焊条的高韧性、高效率、低尘低毒和耐吸潮性能,为国内的焊条研究提供了参考依据。     

A Sign of Victory?: ‘Scottish Swords’ and Other Weapons in the Possession of the ‘Auld Innemie’

Many late medieval documents, notably inventories of arms and armour, of Englishmen contain references to ‘Scottish swords’ and other weapons. What did the compilers of these documents mean when they described a weapon as ‘Scottish’? How did such weapons come to be in the possession of these men? This article will attempt to explain this phenomenon drawing on primary documentary sources and surviving material culture from Glasgow Museums’ collections and others, as well as artworks from the period.     

Helping hands: civil–military cooperation and Italy's military operation abroad

In the Post-Bipolar Era the growing complexity of the military operations requires a new approach for the resolution of international crises. Since the end of the Cold War, peace support operations (PSO) have become the mainstay and principal occupation of most Western armies. At the same time, Italy has been one of the most important actors in such an area. The article focuses on the cooperation between military and civil components (a process called CIMIC) as a key variable in the Italian PSOs. We will analyse in detail the main lessons learned from past military interventions as well as the general context in which new tendencies are taking place. The maintaining of a minimum security frame becomes essential to fulfil activities ‘collateral’ to the mission: reconstructing services and infrastructure, food distribution, water and medication, law and order, de-mining, training of local forces, and supporting local institutions. These are the main tasks to obtain thrust and support from the population.     

Terrorism,insurgency, kidnapping,and security in Africa's energy sector

Energy continues to serve as the bedrock of modern economies and the main driver of modern society. For Africa, the production and supply of energy resources such as crude oil, natural gas, uranium, coal, biomass, biofuels and other renewables are an important source of employment, rents, taxes, royalties and profits. This sector brings in several tens of billions of dollars of revenue annually. The production and delivery of such resources, however, depend on critical infrastructures such as pipelines, refineries, processing plants, terminals, rigs, electrical energy pylons, substations, pump stations, vessels, and tankers. These infrastructures have been attacked by terrorists, insurgents, vandals and saboteurs, all of whom see them as targets against which to register their grievances and extract concessions from the state. This paper is a chronological account of some of the documented incidents of terrorism, insurgency, kidnapping, destruction, sabotage, and human casualties suffered in the oil and gas sectors in Africa between 1999 and 2012. It is based on data extracted from the databases of the RAND Database of World Terrorism Incidents and the University of Maryland's Global Terrorism Database (GTD).     

Cyberpower in Strategic Affairs: Neither Unthinkable nor Blessed

Abstract

This article explores the effect of connectivity on strategic affairs. It argues that the effect on war's character is potentially, although not yet shown in practice, considerably large. Its effect upon the distribution of power among states in the international system is small, contrary to the claims of ‘cyberwar’ alarmists. All told, however, its effect upon strategic affairs is complex. On the one hand, it represents a significant advance in the ‘complexification’ of state strategies, understood in the sense of the production of intended effects. On the other hand, strategists today – still predominantly concerned with the conflicts and confrontations of states and organised military power – are generally missing the power which non-traditional strategic actors, better adapted to the network flows of the information age, are beginning to deploy. These new forms of organization and coercion will challenge the status quo.