Development of Non-linear Mathematical Models for Mouse Cell’s Conductivity in Pulsed Electric Field | Chapter 07 | Current Topics on Chemistry and Biochemistry Vol. 1

 Based on approximation by algebraic and transcendental functions, non-linear mathematical models were built for the empirically observed dependences of the conductivity of mouse reproductive and embryonic cells on the strength of the pulsed electric field applied. To estimate experimental data, the least squares method was employed. Extrema, inflections, crossings, and curvature of approximating functions were all discovered. These distinctive points were determined using typical mathematical analysis methods. This was accomplished using well-known analytical geometry and algebraic methods for solving equations. In order to calculate the coordinates of junction positions and curvature, the 1st and 2nd derivatives of non-linear functions were also computed. A link has been established between the estimated coordinates of distinctive spots and the modes of membrane electroporation during the linear growth of electric field intensity applied to a cell. The intensity of a pulsed electric field may be computed using mathematical models of experimental conductometric curves, which is necessary and sufficient for the implementation of any electroporation-based electro-manipulation technologies.

Author(S) Details

V. A. Shigimaga
Department of Technical Systems and Technologies of Animal Husbandry, P. Vasilenko Kharkov National Technical University of Agriculture, Moscovsky Prospekt, 45, Kharkov, 61000, Ukraine .

R. A. Faizullin
Federal State Budgetary Institution of Science, Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences, 34, T. Baramzina st., Izhevsk, 426067, Russia.

A. S. Osokina
Federal State Budgetary Institution of Science, Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences, 34, T. Baramzina st., Izhevsk, 426067, Russia.

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Determination of a Special Case of Symmetric Matrices and Their Applications| Chapter 3 | Current Topics on Mathematics and Computer Science Vol. 6

The elements of a given n-dimensional vector XRn, n=2m, mN are used to build matrices of transpositions (Tr matrices), which are a particular instance of symmetric matrices. Tr matrices have been shown to be both symmetric and persymmetric. As a Hadamard product of Tr matrix and matrix, a new approach for creating transposition matrices with mutually orthogonal rows (Trs matrices) of dimensions 2, 4, and 8 has been presented. Hadamard, and their use in QR decomposition and n-dimensional rotation matrix production has been examined. Obtaining an orthogonal Trs matrix of sizes 4 and 8 that rotates a given vector to the direction of one of the coordinate axes takes less processing time than obtaining a Housholder matrix of the same size, according to tests and analysis of the technique. The Tr and Trs matrices are so useful in matrix calculations.

Author (S) Details

Dr. Ognyan Ivanov Zhelezov
Nikola Vaptsarov Naval Academy, Varna, 9000, Bulgaria.

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An Algorithm for Generating N-Dimensional Rotation Matrix | Chapter 2 | Current Topics on Mathematics and Computer Science Vol. 6

This paper describes a new approach for producing an N-dimensional rotation matrix M that rotates a given N-dimensional vector X in the same dimension in the direction of a given N-dimensional vector Y. The Ndimensional Rotation Matrix Generation Algorithm (NRMG) rotates supplied vectors X and Y in the direction of coordinate axis x1 using two-dimensional rotations. Matrix M is generated by multiplying matrix MX by the square root of the square root of the square root of the square root of the square root of the square The inverse of matrix MY, which spins the provided vectors in the axis x1 direction. The Mx and My matrices are not calculated using the RMG algorithm. There is a suggested algorithm for calculating them using rotations in the coordinate planes, but they can alternatively be computed using the Householder transformation, which is more efficient for "dense" vectors. The possibility of executing two-dimensional rotation computations in parallel is also studied.

Author (S) Details

Dr. Ognyan Ivanov Zhelezov
Nikola Vaptsarov Naval Academy, Varna, 9000, Bulgaria.

View Book :- https://stm.bookpi.org/CTMCS-V6/article/view/2582