基于增广矩阵束方法的平面天线阵列综合

针对平面阵列的稀布优化问题,提出了一种基于增广矩阵束方法的减少阵元数目、求解阵元位置和设计幅度激励的优化方法。首先对期望平面阵的方向图进行采样并由采样点数据构造增广矩阵,对此矩阵进行奇异值(SVD)分解,确定在误差允许范围内所需的最小阵元数目;然后基于广义特征值分解分别计算两组特征值,并根据类ESPRIT算法对特征值进行配对;最后在最小二乘准则条件下根据正确的特征值对求解平面阵列的阵元位置和激励。仿真结果表明该算法具有较高的计算效率和数值精度。     

DCT- and DST-based splitting methods for Toeplitz systems

New splitting iterative methods for Toeplitz systems are proposed by means of recently developed matrix splittings based on discrete sine and cosine transforms due to Kailath and Olshevsky [Displacement structure approach to discrete-trigonometric transform-based preconditioners of G. Strang type and of T. Chan type, SIAM J. Matrix Anal. Appl. 26 (2005), pp. 706–734]. Theoretical analysis shows that new splitting iterative methods converge to the unique solution of a symmetric Toeplitz linear system. Moreover, an upper bound of the contraction factor of our new splitting iterations is derived. Numerical examples are reported to illustrate the effectiveness of new splitting iterative methods.     

Quantum analysis of measurement results

It is shown that a stochastic matrix operator (quantum measurement matrix) may be considered in some cases as a density matrix. Results of measurements in the form of figure numbers, interconnected with a matrix of quantum measurements, are similar to quantum observable quantities determined in quantum statistical theory. __________ Translated from Izmeritel’naya Tekhnika, No. 12, pp. 3–8, December, 2006.     

Micro- and nano-scale deformation behavior of nylon 66-based binary and ternary nanocomposites

The primary aim of this paper is to provide an insight on the effect of the location of organoclay on the micro- and nano-scale deformation processes in melt-compounded nylon 66/organoclay/SEBS-g-MA ternary nanocomposites prepared by different blending sequences. In addition, the deformation processes of the ternary nanocomposites were compared to the binary nanocomposites (nylon 66/organoclay and nylon 66/SEBS-g-MA) and neat nylon 66. The incorporation of SEBS-g-MA particles toughened nylon 66 markedly; but the flexural modulus and strength were both reduced. Conversely, the use of organoclay increased the modulus but decreased the fracture toughness of nylon 66. Nylon 66/SEBS-g-MA/organoclay ternary nanocomposites exhibited balanced elastic stiffness and toughness. Stress-whitening studies of the fracture surfaces in terms of gray level were also performed and an attempt was made to correlate the optical reflectivity characteristics with fracture toughness. It was concluded that the capability of SEBS-g-MA particles to cavitate was decreased by the presence of organoclay in the SEBS-g-MA phase, resulting in reduced toughening efficiency. The best micro-structure for toughness and other mechanical properties is thus to maximize the amount of exfoliated organoclay in the nylon 66 matrix rather than to have it embedded in the finely dispersed SEBS-g-MA particles.     

Machinability of Metal Matrix Composites Reinforced by 3-D Network Structure

Metal matrix composites reinforced by three-dimensional (3-D) continuous network structure reinforcement (3DCNRMMC) are difficult to machine due to serious tool wear and poor surface roughness caused by the brittle and hard reinforcement which interpenetrate into ductile matrix. In order to achieve the approach of low cost of 3DCNRMMC, the machinability of it needs to be understood. The influences of three cutting parameters and volume fraction of reinforcement on cutting force were analyzed in detail. The results indicate that: (1) Due to the brittle phase(s) introduced into ductile matrix of composites, there is a large fluctuation of cutting force causing deterioration of machinability. The fluctuation ranges of cutting forces, initially increase rapidly with the increase of volume fraction of reinforcement and then decrease finally, are largest at the range of the volume fraction of 55–65%; (2) The influence of cutting parameters on cutting force is obvious. With the increases of cutting speed, cutting force decreases gradually unless cutting speed exceeds the value of 209 m/min. Cutting forces increase with increasing feed rate and depth of cut; (3) Owing to the large fluctuation of cutting force, there were some cratered surfaces caused by Si₃N₄ reinforcement pulling-out and flaking-off. Some brittle phase protruding from the machined surface caused the deterioration of machined surface.     

谱映像定理在欧氏空间中的另类证明

以泛函分析中的谱映像定量为基础,利用矩阵可以约化为若当型的特点,用一种非常简便的方法证明了欧氏空间中的谱映像定理,给出了一类矩阵指数特征值与原矩阵特征值之间的关系,并给出具体的实例验证结果的有效性.     

一次同余方程组的一种矩阵解法

同余方程组是数论中一个极为有用的课题。文中考虑的是具有一个未知数而具有不同的模的一次同余方程组。一般可以用中国剩余定理或者递推算法等方法给出一次同余方程组的解法。利用矩阵的初等变换和矩阵的Sm ith标准形给出了求解一次同余方程组的一种矩阵解法。     

Second-Order Stiffness Matrix and Loading Vector of a Beam-Column with Semirigid Connections on an Elastic Foundation

The second-order stiffness matrix and corresponding loading vector of a prismatic beam–column subjected to a constant axial load and supported on a uniformly distributed elastic foundation (Winkler type) along its span with its ends connected to elastic supports are derived in a classical manner. The stiffness coefficients are expressed in terms of the ballast coefficient of the elastic foundation, applied axial load, support conditions, bending, and shear deformations. These individual parameters may be dropped when the appropriate effect is not considered; therefore, the proposed model captures all the different models of beams and beam–columns including those based on the theories of Bernoulli–Euler, Timoshenko, Rayleigh, and bending and shear.The expressions developed for the load vector are also general for any type or combinations of transverse loads including concentrated and partially nonuniform distributed loads. In addition, the transfer equations necessary to determine the transverse deflections, rotations, shear, and bending moments along the member are also developed and presented.