地震子波估计─高阶累积量矩阵方程法

应用高阶累积量辨识ＦＩＲ系统的方法已在众多领域得到广泛的应用研究．本文提出了一种估计地震于波方法－高阶累积量矩阵方程法．该方法在反射系数序列为非高斯、统计独立的随机过程假设条件下．适用于任意相让子波和任意加性高斯色噪声的情况，且运算时间较短，精度较为理想．模型和实际数据实验表明，该方法对于地震资料处理中的子波估计具有较好的应用前景．

力矩分配的矩阵方程法

为提高力矩分配的计算效率和计算精度,在传统力矩分配法的基础上,使用方程方法,引入矩阵形式,建立矩阵方程法,从而提高了结构计算效率,解题思路步骤清晰,且计算结果是精确解。

度量观测方程系数矩阵复共线性的最小相对范数法

当法方程系数矩阵N(N=ATA)具有较强的复共线性时,其结构是"病态"的。"病态"的N将破坏参数LS估值的优良性质和质量。因而,度量N的复共线性对判断其是否病态很重要。度量矩阵复共线性的方法有多种,其中,矩阵的条件数法最为常用。针对条件数法的不足,提出一种直接度量观测方程系数矩阵A的复共线性的新方法。这种方法是对矩阵A中n个列向量α1实施Gram Schmidt正交化,求每一个向量正交化前后的范数及其相应的比值,以一组比值中的最小值作为该矩阵复共线性的度量。这种方法的显著特点是:度量有明确的上、下界,度量值仅反映参数列向量间的复共线性,根据参考指标可以有效地判断矩阵的病态性。依据这种方法,便于研究矩阵复共线性的产生原因与解决方案;作者将此方法概括为最小相对范数法。

根据算子方程得到矩阵方程的新方法-基函数展开法(英文)

矩量法在计算电磁学中占有重要地位。矩量法是选择适当的基函数和权函数,进而得到矩阵方程。但该方法得到的阻抗矩阵是一个满阵,在复杂电磁学问题中,不论是阻抗矩阵填充还是求逆都会花费大量时间。提出了一种根据算子方程得到矩阵方程的新方法-基函数展开法,并给出应用该方法的一个例子。可看到该方法中不需要选择权函数,且阻抗矩阵是一个对角阵,从而大大节省阻抗矩阵填充时间和求逆时间。

Numerical Methods for a Class of Quadratic Matrix Equations

Quadratic matrix equations arise in many elds of scienti c computing and engineering applications.In this paper,we consider a class of quadratic matrix equations.Under a certain condition,we rst prove the existence of minimal nonnegative solution for this quadratic matrix equation,and then propose some numerical methods for solving it.Convergence analysis and numerical examples are given to verify the theories and the numerical methods of this paper.

儿童碰撞假人几何与材料参数反求

汽车碰撞测试用Q6儿童假人结构较复杂、没有公开几何及材料参数,难以对其进行深入研究和改进。因此,利用CT技术,对Q6假人无金属反光几何边界进行反求;设计并制作了质心测量仪,采用试错法,基于质心一致进行金属件反求,并用转动惯量校正。设计了新型排水法,应用于髋部和锁骨的材料密度反求;设计并利用矩阵方程法进行多材料组合部件的密度反求。通过以上方法获得了Q6假人主要部件的几何模型及材料参数。

Forced Axial and Torsional Vibrations of a Shaft Line Using the Transfer Matrix Method Related to Solution Coefficients

This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the propeller and intermediate shafts, under the influence of propeller-induced static and variable hydrodynamic excitations are also studied. The transfer matrix method related to the constant coefficients of differential equation solutions is used. The advantage of the latter as compared with a well-known method of transfer matrix associated with state vector is the possibility of reducing the number of multiplied matrices when adjacent shaft segments have the same material properties and diameters. The results show that there is no risk of buckling and confirm that the strength of the shaft line depends on the value of the static tangential stresses which is the most important component of the stress tensor.

CONSTRUCTION OF THE ENCRYPTION MATRIX BASED ON CHEBYSHEV CHAOTIC NEURAL NETWORKS

The paper proposes a novel algorithm to get the encryption matrix. Firstly, a chaotic sequence generated by Chebyshev chaotic neural networks is converted into a series of low-order integer matrices from which available encryption matrices are selected. Then, a higher order encryption matrix relating real world application is constructed by means of tensor production method based on selected encryption matrices. The results show that the proposed algorithm can produce a "one-time pad cipher" encryption matrix with high security; and the encryption results have good chaos and auto-correlation with the natural frequency of the plaintext being hidden and homogenized.

Integrable Properties Associated with a Discrete Three-by-Three Matrix Spectral Problem

Based on a new discrete three-by-three matrix spectral problem, a hierarchy of integrable lattice equations with three potentials is proposed through discrete zero-curvature representation, and the resulting integrable lattice equation reduces to the classical Toda lattice equation. It is shown that the hierarchy possesses a HamiItonian structure and a hereditary recursion operator. Finally, infinitely many conservation laws of corresponding lattice systems are obtained by a direct way.

Generalized Cauchy Matrix Approach for Lattice Boussinesq-Type Equations

The authors generalize the Cauchy matrix approach to get exact solutions to the lattice Boussinesq-type equations:lattice Boussinesq equation,lattice modified Boussinesq equation and lattice Schwarzian Boussinesq equation.Some kinds of solutions including soliton solutions,Jordan block solutions and mixed solutions are obtained.

Electrical Properties of an m × n Hammock Network

Electrical property is an important problem in the field of natural science and physics, which usually involves potential, current and resistance in the electric circuit. We investigate the electrical properties of an arbitrary hammock network, which has not been resolved before, and propose the exact potential formula of an arbitrary m × n hammock network by means of the Recursion-Transform method with current parameters(RT-I) pioneered by one of us [Z. Z. Tan, Phys. Rev. E 91(2015) 052122], and the branch currents and equivalent resistance of the network are derived naturally. Our key technique is to setting up matrix equations and making matrix transformation, the potential formula derived is a meaningful discovery, which deduces many novel applications. The discovery of potential formula of the hammock network provides new theoretical tools and techniques for related scientific research.

Darboux Transformations and N-soliton Solutions of Two (2+1)-Dimensional Nonlinear Equations

Two Darboux transformations of the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawaka(CDGKS)equation and(2+1)-dimensional modified Korteweg-de Vries(mKdV) equation are constructed through the Darboux matrix method, respectively. N-soliton solutions of these two equations are presented by applying the Darboux transformations N times. The right-going bright single-soliton solution and interactions of two and three-soliton overtaking collisions of the(2+1)-dimensional CDGKS equation are studied. By choosing different seed solutions, the right-going bright and left-going dark single-soliton solutions, the interactions of two and three-soliton overtaking collisions, and kink soliton solutions of the(2+1)-dimensional mKdV equation are investigated. The results can be used to illustrate the interactions of water waves in shallow water.

Variational algorithms for linear algebra

Quantum algorithms have been developed for efficiently solving linear algebra tasks.However,they generally require deep circuits and hence universal fault-tolerant quantum computers.In this work,we propose variational algorithms for linear algebra tasks that are compatible with noisy intermediate-scale quantum devices.We show that the solutions of linear systems of equations and matrix–vector multiplications can be translated as the ground states of the constructed Hamiltonians.Based on the variational quantum algorithms,we introduce Hamiltonian morphing together with an adaptive ans?tz for efficiently finding the ground state,and show the solution verification.Our algorithms are especially suitable for linear algebra problems with sparse matrices,and have wide applications in machine learning and optimisation problems.The algorithm for matrix multiplications can be also used for Hamiltonian simulation and open system simulation.We evaluate the cost and effectiveness of our algorithm through numerical simulations for solving linear systems of equations.We implement the algorithm on the IBM quantum cloud device with a high solution fidelity of 99.95%.

An orthogonally accumulated projection method for symmetric linear system of equations

A direct as well as iterative method(called the orthogonally accumulated projection method, or the OAP for short) for solving linear system of equations with symmetric coefficient matrix is introduced in this paper. With the Lanczos process the OAP creates a sequence of mutually orthogonal vectors, on the basis of which the projections of the unknown vectors are easily obtained, and thus the approximations to the unknown vectors can be simply constructed by a combination of these projections. This method is an application of the accumulated projection technique proposed recently by the authors of this paper, and can be regarded as a match of conjugate gradient method(CG) in its nature since both the CG and the OAP can be regarded as iterative methods, too. Unlike the CG method which can be only used to solve linear systems with symmetric positive definite coefficient matrices, the OAP can be used to handle systems with indefinite symmetric matrices. Unlike classical Krylov subspace methods which usually ignore the issue of loss of orthogonality, OAP uses an effective approach to detect the loss of orthogonality and a restart strategy is used to handle the loss of orthogonality.Numerical experiments are presented to demonstrate the efficiency of the OAP.

Density matrix method and ultrafast processes

When femtosecond （fs） timeresolved experiments are used to study ultrafast processes, quantum beat phenomena are often observed. In this paper, to analyze the fs timeresolved spectra, we will present the density matrix method, a powerful theoretical technique, which describes the dynamics of population and coherence of the system. How to employ it to study the pumpprobe experiments and fs ultrafast processes is described. The transition of pyrazine is used as an example to demonstrate the application of the density matrix method. Recently, Suzuki＇s group have employed the 22 fs time resolution laser to study the dynamics of the state of pyrazine. In this case, conical intersection is commonly believed to play an important role in this nonadiabatic process. How to treat the effect of conical intersection on nonadiabatic processes and fs timeresolved spectra is presented. Another important ultrafast process, vibrational relaxation, which takes place in subps and ps range and has never been carefully studied, is treated in this paper. The vibrational relaxation in water dimer is chosen to demonstrate the calculation. It should be noted that the vibrational relaxation of （H20）2 has not been experimentally studied but it can be accomplished by the pump-probe experiments.