Ashraf Ahmed¹, Yousef AbuHour^2,*, Ammar El-Hassan¹

Intelligent Automation & Soft Computing, Vol.32, No.2, pp. 979-990, 2022, DOI:10.32604/iasc.2022.020726

Abstract The Corona (COVID-19) epidemic has triggered interest in many fields of technology, medicine, science, and politics. Most of the mathematical research in this area focused on analyzing the dynamics of the spread of the virus. In this article, after a review of some current methodologies, a non-linear system of differential equations is developed to model the spread of COVID-19. In order to consider a wide spectrum of scenarios, we propose a susceptible-exposed-infected-quarantined-recovered (SEIQRS)-model which was analyzed to determine threshold conditions for its stability, and the number of infected cases that is an infected person will transmit on a virus to,… More >

M. G. RÍOS-DURÁN*, A. R. HERNÁNDEZ-TÉLLEZ**, C. A. MARTÍNEZ-PALACIOS**, L. G. ROSS***

BIOCELL, Vol.30, Suppl.S, pp. 149-155, 2006

Abstract This article has no abstract. More >

JOSÉ LUIS ARREDONDO-FIGUEROA¹, LAURA GEORGINA NÚÑEZ-GARCÍA², PALOMA ADRIANA HEREDIA-GUZMÁN³ AND JESÚS T. PONCE-PALAFOX⁴.

BIOCELL, Vol.36, No.3, pp. 105-111, 2012, DOI:10.32604/biocell.2012.36.105

Abstract Chirostoma jordani is a native annual species inhabiting lacustrine waters of the Central Mexico Plateau. It is widely distributed and is currently facing high environmental pressures. Five experiments were performed to study the reproductive performance of this species. Four of the experiments were conducted in 270-L indoor recirculation tanks. Two males and one female at the first stage of reproduction were included in each test. A photoperiod of 14 light hours and 10 dark hours was used. In a fifth experiment, 10 females and 15 males were kept in an outdoor 3,000-L recirculation tank under natural photoperiod. The number of… More >

Chein-Shan Liu¹, Su-Ying Zhang², Satya N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.1, pp. 29-48, 2012, DOI:10.3970/cmes.2012.088.029

Abstract With a detailed investigation of n linear algebraic equations Bx=b, we find that the scaled residual dynamics for y∈Sⁿ⁻¹ is equipped with four structures: the Jordan dynamics, the rotation group SO(n), a generalized Hamiltonian formulation, as well as a metric bracket system. Therefore, it is the first time that we can compute the steplength used in the iterative method by a novel algorithm based on the Jordan structure. The algorithms preserving the length of y are developed as the structure preserving algorithms (SPAs), which can significantly accelerate the convergence speed and are robust enough against the noise in the numerical… More >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.4, pp. 395-432, 2011, DOI:10.3970/cmes.2011.073.395

Abstract In this paper we solve a system of nonlinear algebraic equations (NAEs) of a vector-form: F(x) = 0. Based-on an invariant manifold defined in the space of (x,t) in terms of the residual-norm of the vector F(x), we derive a system of nonlinear ordinary differential equations (ODEs) with a fictitious time-like variable t as an independent variable: x^· = λ[αF + (1−α)B^TF], where λ and α are scalars and B_ij = ∂F_i/∂x_j. From this set of nonlinear ODEs, we derive a purely iterative algorithm for finding the solution vector x, without having to invert the Jacobian (tangent stiffness matrix)… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.1, pp. 25-38, 2008, DOI:10.3970/cmes.2008.038.025

Abstract In this paper a complex matrix operator and a complex field are used to express the Maxwell equations, of which the complex field embraces all field variables and the matrix operator embraces the time and space differential operators. By left applying the operator on the complex field one can get all the four Maxwell equations, which are usually expressed by the vector form. The new formulation matches the Lorenz gauge condition, and its mathematical advantage is that it can incorporate the Maxwell equations into a single equation. The introduction of four-potential is possible only under the Lorenz gauge. In terms… More >