All solutions of the Yang–Baxter-like matrix equation for diagonalizable coefficient matrix with two different eigenvalues

2020 ◽  
Vol 101 ◽  
pp. 106048
Author(s):  
Dongmei Shen ◽  
Musheng Wei
Keyword(s):  
Matrix Equation ◽  
Coefficient Matrix ◽  
All Solutions

scholarly journals Membangkitkan Suatu Matriks Unimodular Dengan Python

2018 ◽  
Vol 5 (2) ◽  
pp. 1-9
Author(s):  
Samsul Arifin ◽  
Indra Bayu Muktyas
Keyword(s):  
Matrix Method ◽  
Coefficient Matrix ◽  
Inverse Matrix ◽  
Solution Vector ◽  
Unimodular Matrix ◽  
All Solutions ◽  
Cramer’S Rule

An SPL can be represented as a multiplication of the coefficient matrix and solution vector of the SPL. Determining the solution of an SPL can use the inverse matrix method and Cramer's rule, where both can use the concept of the determinant of a matrix. If the coefficient matrix is a unimodular matrix, then all solutions of an SPL are integers. In this paper we will present a method of generating a unimodular matrix using Python so that it can be utilized on an SPL. Keywords: SPL, Unimodular Matrix, Python

scholarly journals A Real Representation Method for Solving Yakubovich-j-Conjugate Quaternion Matrix Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Caiqin Song ◽  
Jun-e Feng ◽  
Xiaodong Wang ◽  
Jianli Zhao
Keyword(s):  
Matrix Equation ◽  
Equivalent Form ◽  
Closed Form Solution ◽  
Coefficient Matrix ◽  
Form Solution ◽  
Complex Conjugate ◽  
Quaternion Matrix ◽  
Real Representation ◽  
Quaternion Matrix Equation ◽  
Representation Method

A new approach is presented for obtaining the solutions to Yakubovich-j-conjugate quaternion matrix equationX−AX^B=CYbased on the real representation of a quaternion matrix. Compared to the existing results, there are no requirements on the coefficient matrixA. The closed form solution is established and the equivalent form of solution is given for this Yakubovich-j-conjugate quaternion matrix equation. Moreover, the existence of solution to complex conjugate matrix equationX−AX¯B=CYis also characterized and the solution is derived in an explicit form by means of real representation of a complex matrix. Actually, Yakubovich-conjugate matrix equation over complex field is a special case of Yakubovich-j-conjugate quaternion matrix equationX−AX^B=CY. Numerical example shows the effectiveness of the proposed results.

scholarly journals Pipe Hydraulic Resistances Identification of District Heating Networks Based on Matrix Analysis

Energies ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 3007
Author(s):  
Yongxin Liu ◽  
Peng Wang ◽  
Peng Luo
Keyword(s):  
Matrix Equation ◽  
District Heating ◽  
Coefficient Matrix ◽  
Operating Conditions ◽  
Adverse Impact ◽  
Matrix Analysis ◽  
Critical Step ◽  
The North ◽  
Relative Errors ◽  
Heating Networks

District heating networks (DHNs) are essential municipal infrastructure in the north of China. Obtaining accurate resistance characteristics is a critical step to improve the operating regulation level of DHNs. In this paper, pipe hydraulic resistances (PHRs) are introduced to express the resistance characteristics. A hydraulic model of a DHN can be established by using observed data of pressures and discharges. The boundary nodes are taken as observed sites. After establishing a matrix equation and analyzing the rank of its coefficient matrix, the authors propose a method to determine all the PHRs uniquely, by using a small number of observed sites and operating conditions. Furthermore, when observed errors are introduced, the adverse impact can be weakened by increasing the number of operating conditions and the accuracy of observed devices. When the observed error ranges are 1% and 0.5%, the results show that the average relative errors of identified PHRs are 2.4% and 1.1% respectively, which can be acceptable in engineering. Then, a loop DHN can be transformed into several branch DHNs, which are identified individually.

scholarly journals Trapezoidal Fully Fuzzy Sylvester Matrix Equation with Arbitrary Coefficients

2021 ◽  
Author(s):  
Ahmed Elsayed ◽  
Nazihah Ahmad ◽  
Ghassan Malkawi
Keyword(s):  
Linear Equation ◽  
Matrix Equation ◽  
Analytical Methods ◽  
Fuzzy Numbers ◽  
Coefficient Matrix ◽  
Sylvester Matrix Equation ◽  
Numerical Examples ◽  
Trapezoidal Fuzzy Numbers ◽  
Sylvester Matrix ◽  
Methods Numerical

Abstract Almost every existing method for solving trapezoidal fully fuzzy Sylvester matrix equation restricts the coefficient matrix and the solution to be positive fuzzy numbers only. In this paper, we develop new analytical methods to solve a trapezoidal fully fuzzy Sylvester matrix equation with restricted and unrestricted coefficients. The trapezoidal fully fuzzy Sylvester matrix equation is transferred to a system of crisp equations based on the sign of the coefficients by using Ahmd arithmetic multiplication operations between trapezoidal fuzzy numbers. The constructed method not only obtain a simple crisp system of linear equation that can be solved by any classical methods but also provide a widen the scope of the trapezoidal fully fuzzy Sylvester matrix equation in scientific applications. Furthermore, these methods have less steps and conceptually easy to understand when compared with existing methods. To illustrate the proposed methods numerical examples are solved.

scholarly journals All Solutions of the Yang–Baxter-Like Matrix Equation for Nilpotent Matrices of Index Two

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Duanmei Zhou ◽  
Jiawen Ding
Keyword(s):  
Matrix Equation ◽  
Matrix Equations ◽  
Original Matrix ◽  
Nilpotent Matrix ◽  
System Of Matrix Equations ◽  
All Solutions ◽  
Nilpotent Matrices ◽  
Rank 2

Let A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation AXA=XAX. We first obtain a system of matrix equations of smaller sizes to find all the solutions of the original matrix equation. When A is a nilpotent matrix with rank 1 and rank 2, we get all solutions of the Yang–Baxter-like matrix equation.

ALL SOLUTIONS OF THE YANG-BAXTER-LIKE MATRIX EQUATION WHEN A3 = A

2019 ◽  
Vol 9 (3) ◽  
pp. 1022-1031
Author(s):  
Mansour Saeed Ibrahim Adam ◽  
◽  
Jiu Ding ◽  
Qianglian Huang ◽  
Lanping Zhu ◽  
...  
Keyword(s):  
Matrix Equation ◽  
All Solutions

Exogeneous factors are not necessary in attachment, spreading and polarization of hela cells

1978 ◽  
Vol 36 (2) ◽  
pp. 310-311
Author(s):  
W. Liebrich
Keyword(s):  
Hela Cells ◽  
Calf Serum ◽  
Glass Tube ◽  
Serum Free Medium ◽  
Nacl Solution ◽  
Free Medium ◽  
Minimum Essential Medium ◽  
Serum Free ◽  
All Solutions ◽  
Glass Support

HeLa cells were grown for 2-3 days in EAGLE'S minimum essential medium with 10% calf serum (S-MEM; Seromed, München) and then incubated for 24 hours in serum free medium (MEM). After detaching the cells with a solution of 0. 14 % EDTA and 0. 07 % trypsin (Difco, 1 : 250) they were suspended in various solutions (S-MEM = control, MEM, buffered salt solutions with or without Me++ions, 0. 9 % NaCl solution) and allowed to settle on glass tube slips (Leighton-tubes). After 5, 10, 15, 20, 25, 30, 1 45, 60 minutes 2, 3, 4, 5 hours cells were prepared for scanning electron microscopy as described by Paweletz and Schroeter. The preparations were examined in a Jeol SEM (JSM-U3) at 25 KV without tilting.The suspended spherical HeLa cells are able to adhere to the glass support in all solutions. The rate of attachment, however, is faster in solutions without serum than in the control. The latter is in agreement with the findings of other authors.

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