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 - 23 August 2024

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 >

Ahmed M. Alghamdi^1,*, Khalid Hamid², Muhammad Waseem Iqbal³, M. Usman Ashraf⁴, Abdullah Alshahrani⁵, Adel Alshamrani⁶

CMC-Computers, Materials & Continua, Vol.74, No.2, pp. 3795-3810, 2023, DOI:10.32604/cmc.2023.033976 - 31 October 2022

Abstract In various fields, different networks are used, most of the time not of a single kind; but rather a mix of at least two networks. These kinds of networks are called bridge networks which are utilized in interconnection networks of PC, portable networks, spine of internet, networks engaged with advanced mechanics, power generation interconnection, bio-informatics and substance intensify structures. Any number that can be entirely calculated by a graph is called graph invariants. Countless mathematical graph invariants have been portrayed and utilized for connection investigation during the latest twenty years. Nevertheless, no trustworthy evaluation has… 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 - 22 September 2022

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 >

Khalid Hamid¹, Muhammad Waseem Iqbal^2,*, Erssa Arif¹, Yasir Mahmood^3,4, Ahmad Salman Khan³, Nazri Kama⁴, Azri Azmi⁴, Atif Ikram^5,6

CMC-Computers, Materials & Continua, Vol.73, No.3, pp. 5423-5440, 2022, DOI:10.32604/cmc.2022.030927 - 28 July 2022

Abstract Any number that can be uniquely determined by a graph is called graph invariants. During the most recent twenty years’ innumerable numerical graph invariants have been described and used for correlation analysis. In the fast and advanced environment of manufacturing of networks and other products which used different networks, no dependable assessment has been embraced to choose, how much these invariants are connected with a network graph or molecular graph. In this paper, it will talk about three distinct variations of bridge networks with great capability of expectation in the field of computer science, chemistry,… More >

Khalid Hamid¹, Muhammad Waseem Iqbal^2,*, Abaid Ur Rehman Virk³, Muhammad Usman Ashraf⁴, Ahmed Mohammed Alghamdi⁵, Adel A. Bahaddad⁶, Khalid Ali Almarhabi⁷

CMC-Computers, Materials & Continua, Vol.73, No.1, pp. 15-31, 2022, DOI:10.32604/cmc.2022.028406 - 18 May 2022

Abstract Any number that can be uniquely determined by a graph is called a graph invariant. During the last twenty years’ countless mathematical graph invariants have been characterized and utilized for correlation analysis. However, no reliable examination has been embraced to decide, how much these invariants are related with a network graph or molecular graph. In this paper, it will discuss three different variants of bridge networks with good potential of prediction in the field of computer science, mathematics, chemistry, pharmacy, informatics and biology in context with physical and chemical structures and networks, because k-banhatti sombor More >

Asadullah Shaikh^1,*, Syed Rizwan², Abdullah Alghamdi¹, Noman Islam², M.A. Elmagzoub¹, Darakhshan Syed²

Intelligent Automation & Soft Computing, Vol.31, No.3, pp. 1529-1546, 2022, DOI:10.32604/iasc.2022.021163 - 09 October 2021

Abstract Fault localization is one of the main tasks of software debugging. Developers spend a lot of time, cost, and effort to locate the faults correctly manually. For reducing this effort, many automatic fault localization techniques have been proposed, which inputs test suites and outputs a sorted list of faulty entities of the program. For further enhancement in this area, we developed a system called SILearning, which is based on invariant analysis. It learns from some existing fixed bugs to locate faulty methods in the program. It combines machine-learned ranking, program invariant differences, and spectrum-based fault… More >

Nazeran Idrees^{1, *}, Raghisa Khalid¹, Fozia Bashir Farooq², Sumiya Nasir³

CMC-Computers, Materials & Continua, Vol.63, No.3, pp. 1119-1132, 2020, DOI:10.32604/cmc.2020.08166 - 30 April 2020

Abstract A numerical parameter mathematically derived from the graph structure is a topological index. The topological index is the first actual choice in QSAR research and these indices are used to build the correlation model between the chemical structures of various chemicals compounds. Here, we investigate some old degree-based topological indices like Randic index, sum connectivity index, ABC index, GA index, 1^st and 2^nd Zagreb indices, modified second Zagreb index, redefined version of 1^st, 2^nd and 3^rd Zagreb indices, hyper and augmented Zagreb indices, forgotten index and symmetric division degree index, and some new degree-based indices like SK index, SK₁ index, More >

H. S. Abdel-Aziz¹, M. Khalifa Saad^1,2,*, A. A. Abdel-Salam¹

CMC-Computers, Materials & Continua, Vol.57, No.3, pp. 389-415, 2018, DOI:10.32604/cmc.2018.02149

Abstract In this paper, we study the pseudo-spherical evolutes of curves in three dimensional hyperbolic space. We use techniques from singularity theory to investigate the singularities of pseudo-spherical evolutes and establish some relationships between singularities of these curves and geometric invariants of curves under the action of the Lorentz group. Besides, we defray with illustration some computational examples in support our main results. More >