一类特殊矩阵行列式计算方法浅析

本文针对一类特殊矩阵的行列式进行了研究,通过剖析矩阵的杨辉三角性质,我们定义了范德蒙初等行列式变换,并以此为依据构建了化简矩阵的步骤,进而得到了一套计算该类矩阵行列式的操作办法。

行列式的计算方法与技巧

本文作者在文中给出了矩阵的性质之后,在此基础上,本文进一步探讨了矩阵的计算方法,并给出了解题技巧。

一种基于不可区分混淆的侧信道防护方案设计

针对侧信道攻击,研究者们通常采用隐藏技术和掩码技术来进行防护,本文提出了一类基于不可区分混淆的新型侧信道防护方案,通过对一种用于仿射行列式程序的不可区分混淆方案进行改进,将不可区分混淆与侧信道防护结合在一起,并将其应用于区块链分层确定性钱包BIP-0032的嵌入式设备场景中,对该协议中用到的SHA-2哈希算法进行了抗侧信道攻击的不可区分混淆.通过对应用场景的测试和采集的功耗曲线进行Welch’s t-test,验证了该方案的高效性和安全性.已有的不可区分混淆虽然在理论上存在,但运行代价过高,无法实际应用于真实场景中.本文有效地将不可区分混淆应用在现实的侧信道防护中,在保证安全性的同时还兼顾了效率.相对于传统的侧信道防护方法,减少了随机数的使用且有着良好的效率和可维护性,给目前的侧信道防护研究提供了一种新的思路.

多线圈并接耦合时的等效自感系数计算

从法拉第电磁感应定律出发,通过计算N个并接耦合线圈的感应电动势,得到了一个齐次微分方程组.然后,通过行列式的变换关系,导出了N个并接耦合线圈的等效自感系数,并对三个并接线圈的情形进行了分析讨论.

Inverse problem in linear algebra

With the increasingly widespread application of linear algebra theory, and in its opposite direction is not enough emphasis, linear algebra, several important points： matrix, determinant, linear equations, linear transformations, matrix keratosis and other anti-deepening understanding of the basics and improve the comprehensive ability to solve problems.

THE DETERMINANT REPRESENTATION OF THE GAUGE TRANSFORMATION OPERATORS

The determinant representation of the gauge transformation operators is establised. In this process, the generalized Wronskian determinant is introduced. As a simple application, the authors present a construction of the special T-function obtained firstly by Chau et al. (Commun. Math. Phys., 149(1992), 263), which involves the generalized Wronskian determinant. Also, some properties of this determinant are given.

DETERMINANT SOLUTIONS OF THE NONAUTONOMOUS DISCRETE TODA EQUATION ASSOCIATED WITH THE DEAUTONOMIZED DISCRETE KP HIERARCHY

It is shown that the nonautonomous discrete Toda equation and its Backlund transformation can be derived from the reduction of the hierarchy of the discrete KP equation and the discrete two-dimensional Toda equation. Some explicit examples of the determinant solutions of the nonautonomous discrete Toda equation including the Askey-Wilson polynomial are presented. Finally we discuss the relationship between the nonautonomous discrete Toda system and the nonautonomous discrete Lotka- Volterra equation.

N-Soliton Solution and Soliton Resonances for the (2+1)-Dimensional Inhomogeneous Gardner Equation

We derive the Lax pair and Darboux transformation for the(2+1)-dimensional inhomogeneous Gardner equation via the two-singular manifold method from Painlev′e analysis. N-soliton solution in a compact determinant representation of Grammian type is presented. As an application, dynamic properties of the bright and dark soliton solutions under periodic and parabolic oscillations up to second order are shown. Resonant behaviors of two bright and two dark solitons are studied, and asymptotic analysis of the corresponding resonant bright and dark two-soliton solutions are performed, respectively.

Darboux transformation and positons of the inhomogeneous Hirota and the Maxwell-Bloch equation

In this paper,we derive Darboux transformation of the inhomogeneous Hirota and the Maxwell-Bloch(IH-MB)equations which are governed by femtosecond pulse propagation through inhomogeneous doped fibre.The determinant representation of Darboux transformation is used to derive soliton solutions,positon solutions to the IH-MB equations.