Artur V. Dmitrenko^1,2,*, Vladislav M. Ovsyannikov²

FDMP-Fluid Dynamics & Materials Processing, Vol.20, No.9, pp. 1925-1939, 2024, DOI:10.32604/fdmp.2024.048389

Abstract The differential equations of continuum mechanics are the basis of an uncountable variety of phenomena and technological processes in fluid-dynamics and related fields. These equations contain derivatives of the first order with respect to time. The derivation of the equations of continuum mechanics uses the limit transitions of the tendency of the volume increment and the time increment to zero. Derivatives are used to derive the wave equation. The differential wave equation is second order in time. Therefore, increments of volume and increments of time in continuum mechanics should be considered as small but finite More >

Khalid Hamid¹, Muhammad Waseem Iqbal^2,*, Muhammad Usman Ashraf³, Ahmed Mohammed Alghamdi⁴, Adel A. Bahaddad⁵, Khalid Ali Almarhabi⁶

CMC-Computers, Materials & Continua, Vol.74, No.1, pp. 363-378, 2023, DOI:10.32604/cmc.2023.032271

Abstract Due to a tremendous increase in mobile traffic, mobile operators have started to restructure their networks to offload their traffic. New research directions will lead to fundamental changes in the design of future Fifth-generation (5G) cellular networks. For the formal reason, the study solves the physical network of the mobile base station for the prediction of the best characteristics to develop an enhanced network with the help of graph theory. Any number that can be uniquely calculated by a graph is known as a graph invariant. During the last two decades, innumerable numerical graph invariants… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.3, pp. 157-176, 2007, DOI:10.3970/cmes.2007.020.157

Abstract In many engineering applications the Lie group calculation is very important. With this in mind, the subject of this paper is for an in-depth investigation of time-varying linear systems, and its accompanied Lie group calculations. In terms of system matrix A in Eq. (11) and a one-order lower fundamental solution matrix associated with the sub-state matrix function A_s^s, we propose two methods to nilpotentlize the time-varying linear systems. As a consequence, we obtain two different calculations of the general linear group. Then, the nilpotent systems are further transformed to a unique new system Ż(t) = B(t)Z(t), which More >