GH-CONGRUENCE CANONICAL FORM OF QUATERNION MATRIX AND SIMULTANEOUS DIAGONALIZATION OF MATRICES

In this paper,the GH-congruence canonical forms of positive semidefinite and definte inite and definite(need not be self-conjugate)quaternion matrices are given,and a neccessary and sufficientcondition of GH-congruence for two positive semidifinite(definite)quaternion matrices isgiven also.Then simultaneous GH-congruence reduced forms for two self-conjugate matri-ces and some result about the simultaneous GH-congruence diagonalization of quaternionmatrices are obtained.

TO SOLVE MATRIX EQUATION sum (A^iXBi=c) BY THE SMITH NORMAL FORM

By using the Smith normal form of polynomial matrix and algebraic methods, this paper discusses the solvability for the linear matrix equation A iXB i=C over a field, and obtains the explicit formulas of general solution or unique solution.

Quasi-Rational Canonical Forms of a Matrix over a Number Field

A matrix is similar to Jordan canonical form over the complex field and the rational canonical form over a number field, respectively. In this paper, we further study the rational canonical form of a matrix over any number field. We firstly discuss the elementary divisors of a matrix over a number field. Then, we give the quasi-rational canonical forms of a matrix by combining Jordan and the rational canonical forms. Finally, we show that a matrix is similar to its quasi-rational canonical forms over a number field.

THE EQUATIONS OF MOTION OF A MECHANICAL SYSTEM IN MATRIX FORM

This work recommends methods of construction of equations of motion of mechanical systems in matrix form. The use of a matrix form allows one to write an equation of dynamics in compact form, convenient for the in vestigation of multidimensional mechanical systems with the help of computers. Use is made of different methods of constructing equations of motion, based on the basic laws of dynamics as well as on the principles of D Alambert-Le range, Hamilton-Ostrogradski and Gauss.

Closed-form Solutions to the Matrix Equation AX-EXF=BY with F in Companion Form

A closed-form solution to the linear matrix equation AX-EXF = BY with X and Y unknown and matrix F being in a companion form is proposed, and two equivalent forms of this solution are also presented. The results provide great convenience to the computation and analysis of the solutions to this class of equations, and can perform important functions in many analysis and design problems in descriptor system theory. The results proposed here are parallel to and more general than our early work about the linear matrix equation AX-XF = BY .

Schur Forms and Normal-Nilpotent Decompositions

Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.

FORMING PROCESS OF HOT-EXTRUDED SiCw/6061Al COMPOSITES(Ⅰ)

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Microstructural and mechanical behavior of blended powder semisolid formed Al7075/B_4C composites under different experimental conditions

This work aimed to fabricate B4C reinforced aluminum matrix composites via blended powder semisolid forming that is an implementation of the benefits of semisolid forming to the powder metallurgy. Al7075 elements were incrementally added to ethanol solution under mechanical mixing. Al7075 constituents and B4C particles were blended in a high energy ball mill. Cold compacted Al7075/B4C blends were pressed at semisolid state. The effects of the size of the matrix（20, 45 and 63 μm）, reinforcing volume fraction（5%, 10% and 20%） and semisolid compaction pressure（50 and 100 MPa） on the morphology, microstructure, density, hardness, compression and bending strength were thoroughly analyzed. Experimental results revealed that the highest microstructural uniformity was achieved when large B4C particles（45 μm） were distributed within the small particles（20 μm） of the matrix phase. Composites with matrix particles larger than reinforcing phase indicated agglomerations in loadings more than 10%（volume fraction）. Agglomerated regions resisted against penetration of the liquid phase to the pores and lowered the density and strength of these composites. Composites with 20 μm Al7075 and 20%（volume fraction） 45 μm B4C powder pressed under 100 MPa exhibited the highest values of hardness（HV 190） and compressive strength（336 MPa）.

Laser in-situ synthesis of titanium matrix composite coating with TiB-Ti network-like structure reinforcement

To avoid high crack sensitivity of TiB-Ti composite coating during laser cladding process,network-like structure composite coating was fabricated with laser in-situ technique on titanium alloy using 5 μm TiB2 powder as the cladding material.The microstructure,phase structure and properties of the coatings were analyzed by SEM,XRD,EPMA,TEM,hardness tester and fretting wear meter.It was observed that the outer ring of the network-like structure was mainly TiB strengthening phase,while the inner ring was α-Ti grain,and the interface between TiB and Ti matrix was very clean and had a consistent orientation relationship.The hardness of the cladding layer with network-like structure gradually decreased from the surface toward the interface,but the average hardness was nearly two times that of the substrate.In the fretting wear test,it was found that the wear resistance of the cladding layer with network-like structure was larger than that of the substrate under low load(40 N).The results revealed that the hardness and fretting wear resistance of the titanium-based composite coating could be improved by the introduction of network-like structure.

Effects of Processing Technologies on Mechanical Properties of SiC Particulate Reinforced Magnesium Matrix Composites

Mg matrix composites with SiC particles ranging from 5vol%-25vol% were prepared using stirring casting method. Die casting, squeezing casting, and extrusion were applied for inhibiting or eliminating the defects such as gas porosity and shrinkage void. Through die casting and squeezing casting, most of the defects in Mg matrix composites could be eliminated, but the mechanical properties were improved limitedly. On the other hand, after hot extrusion, not only most of the defects of as-cast composites ingots were eliminated, but also the mechanical properties were improved markedly. With the addition of SiC, the tensile strength, yield strength and elastic modulus of as extrusion SiCp/AZ61 composites increased remarkably, and the elongation decreased obviously.

A New Approach for Inverting the Pascal Matrix Plus a Scalar

In this paper,using the Jordan canonical form of the Pascal matrix Pn,we present a new approach for inverting the Pascal matrix plus a scalar Pn+aIn for arbitrary real number a≠1.

On Horn Matrix Function <i>H₂(A,A′,B,B′;C;z,w)</i>of Two Complex Variables under Differential Operator

The aim of this paper deals with the study of the Horn matrix function of two complex variables. The convergent properties, an integral representation of H2(A,A′,B,B′;C;z,w) is obtained and recurrence matrix relations are given. Some result when operating on Horn matrix function with the differential operator D and a solution of certain partial differential equations are established. The Hadamard product of two Horn’s matrix functions is studied, certain results as, the domain of regularity, contiguous functional relations and operating with the differential operator D and D2 are established.

Analysis and Design of Different Methods to Reach Optimum Power in Butler Matrix

With the increasing demand for high speed reliable communications, smart antennas, such as the Butler Matrix array, can be used to develop a system that increases the performance of a wireless system. The Butler matrix is a switched beam array system which can produce orthogonal uniform beams. The main objective is to improve the efficiency of the power in a 90-degree bend. Also, the double-mitered bend is particularly interesting since it provides a substantially lower reflection coefficient and a lower value of S12 at a frequency of 2.4 GHz compared to an unmitered one. Therefore, this paper describes an optimum design using a double-mitered method with a 2 × 2 and a 4 × 4 Butler Matrix array, operating at 2.4 GHz which is used in wireless systems with an FR4 substrate.

满约束轴向拼接张拉整体结构的自稳定性分析

为获得更多张拉整体构型和拓扑结构,本文基于平衡方程,研究张拉整体拼接结构自稳定条件下的结构参数关系的求取方法。基于三杆张拉整体单元轴向拼接形成的臂状张拉整体结构,以减少结构节点约束数为目的去除索构件,获得一种新型满约束轴向拼接张拉整体结构;分析此结构的节点坐标、构件向量的求取方法,推导结构的平衡方程;依据节点和构件之间的连接关系,以获得方阵形式的平衡矩阵为目标,提出了平衡方程缩减原则;根据平衡方程有非零解,平衡矩阵行列式为零的原则,获得保证张拉整体结构自稳定的结构参数关系。通过具体实例分析,证明此方法正确,获得的结构参数关系能够保证确定的满约束轴向拼接张拉整体结构的自稳定性。

基于奇异值分解张拉整体结构找形方法

张拉整体结构是由一组不连续的受压单元包含于连续受拉单元组成的稳定自平衡结构,为了寻找自平衡状态下的构型,引入奇异值分解的方法,将寻找张拉整体结构的自平衡构型问题转化为最小奇异值的判定。通过广义节点坐标和构件之间的连接关系建立结构的数学模型;引入力密度的概念,对张拉整体结构进行受力分析,列写包含平衡矩阵的平衡方程;对平衡矩阵进行奇异值分解,利用分解获得的最小奇异值判断平衡方程是否有解,对张拉整体结构是否存在自平衡构型进行初步判定,再依据获得的力密度的均匀性(同组构件力密度大小相等)和正负属性(杆的力密度小于0,索的力密度大于0)对结构自平衡状态进一步判断;通过实例分析对该找形方法的可行性进行了验证,结果表明:该方法可以找到张拉整体结构自平衡构型。本文为寻找自平衡张拉整体结构提供了一种思路。

夹杂物对42CrMo4钢塑性及韧性的影响分析

风电主轴材质42CrMo4钢内部夹杂物的存在导致大锻件热成形中易出现微裂纹等缺陷。针对不同种类的夹杂物进行研究,探究其在热成形中的损伤失效行为。对原铸态42CrMo4钢进行取样、抛磨、腐蚀后进行夹杂物形貌的SEM观察与EDS成分检测,并对基体损伤较大的夹杂物做纳米压痕实验以获得其真实的力学性能参数。结果表明:铸态42CrMo4钢室温下组织为铁素体和珠光体的共存组织,主要存在Al_(2)O_(3)、TiN、硅酸盐类夹杂物及少量的CaS类夹杂物。纳米压痕实验表征得到在相同载荷下TiN的残余压痕深度最小,说明其塑性变形最小,弹性回复能力最好,Al_(2)O_(3)次之;室温下基体弹性性能最差,其塑性变形最大。在夹杂物附近观察到了部分孔洞,表明夹杂物较基体硬度大,在成形过程中会破坏基体的连续性,形成裂纹等缺陷从而影响产品质量。

成型温度对CF/PPEK复合材料的缺陷和力学性能影响

分别采用溶液浸渍法及真空热压成型法制备了连续碳纤维增强含杂萘联苯结构聚芳醚酮(CF/PPEK)预浸料和复合材料,对不同成型温度制备的复合材料进行了超声相控阵和三维X射线显微镜(XRM)无损检测,利用旋转流变仪、电子万能试验机、动态力学分析仪(DMA)、红外光谱仪(FT-IR)、扫描电镜(SEM)、金相显微镜对CF/PPEK复合材料进行了表征,系统研究了成型温度对纤维的浸润质量以及复合材料孔隙率、弯曲行为和层间剪切性能的影响,通过力学性能分析和断口形貌表征研究了断裂机理及缺陷对其性能产生的影响。试验结果表明:成型温度为350℃时,CF/PPEK复合材料的弯曲模量和层间剪切强度分别为125 GPa和64 MPa;成型温度为360℃时,CF/PPEK复合材料的缺陷最少,弯曲强度可达1376 MPa;而370℃高温下,复合材料出现明显缺陷,各方面性能急剧下降。

矩阵式函数迭代惯导解算的FPGA实现

惯性导航解算的目的是处理陀螺仪和加速度计的输出信号,以获取运动物体的姿态、速度和位置信息。函数迭代惯导解算方法(iNavFIter)将运动不可交换性误差降低到了计算机截断误差水平,但计算负担是经典双子样算法的10倍左右。为了提高计算效率,提出了iNavFIter-M算法,将函数迭代惯导解算重新编排为矩阵向量形式,并在硬件FPGA上实现了iNavFIter-M算法的IP核。数值结果表明:所设计的iNavFIter-M算法IP核实现了1000Hz采样率下的高精度实时计算。

基于光Blass矩阵的光控二维多波束产生

多波束是电子信息装备实现多功能、多任务、大容量信息传输与处理的关键。围绕新一代相控阵系统对宽带多波束形成网络的应用需求,提出一种基于光Blass矩阵的两级级联结构产生二维多波束的实现方法。通过光域相干波束形成技术完成第一级水平方向的波束合成,再利用光域非相干波束形成技术实现第二级垂直方向的波束合成,进而获得空域二维波束。采用该架构,一方面可突破光波长数量不足对光控波束形成网络阵列规模的限制,可将光控相控阵系统的单元规模从数十个提升至数百个甚至更多;另一方面可大幅减少光控多波束芯片的数量,对于阵元数N×N、波束数量M×M的多波束系统,波束芯片数量可从M^(2)个减少到(N+M)个。同时该方案可采用光子集成技术手段实现,在简化多波束系统结构与提升系统可靠性方面具有无可比拟的优势。