Mathematics and Computer Science

Volume 8, Issue 2, March 2023

  • Construction of an Approximate-Analytical Solution for Boundary Value Problems of a Parabolic Equation

    Dalabaev Umurdin, Hasanova Dilfuza

    Issue: Volume 8, Issue 2, March 2023
    Pages: 39-45
    Received: 11 February 2023
    Accepted: 27 February 2023
    Published: 9 March 2023
    Abstract: The article considers an approximate analytical solution (AAS) of a linear parabolic equation with initial and boundary conditions with one spatial variable. Many problems in engineering applications are reduced to solving an initial boundary value problem of a parabolic type. There are various analytical, approximate-analytical and numerical metho... Show More
  • Witten Complex of Transitive Digraph and Its Convergence

    Chong Wang, Xin Lai, Rongge Yu, Yaxuan Zheng, Baowei Liu

    Issue: Volume 8, Issue 2, March 2023
    Pages: 46-50
    Received: 21 February 2023
    Accepted: 24 March 2023
    Published: 27 March 2023
    Abstract: Digraphs are generalization of graphs in which each edge is given one or two directions. For each digraph, there exists a transitive digraph containing it. Moreover, all the formal linear combinations of allowed elementary paths form a basis of the path complex for a transitive digraph. Hence, the study of discrete Morse theory on transitive digrap... Show More
  • Some Upper Bounds of Maximum E-Eigenvalues of Uniform Hypergraphs

    Hongyu Zhang, Feng Fu, Caoji Yin

    Issue: Volume 8, Issue 2, March 2023
    Pages: 51-56
    Received: 25 February 2023
    Accepted: 16 March 2023
    Published: 28 March 2023
    Abstract: A hypergraphs, as a generalization of a general graph, is often used as an effective tool to describe complex structures in discrete mathematics, computer science and other fields. Hypergraph theory and related parameters of hypergraph are important research topics in hypergraph theory. In particular, the problem of spectral extremum of graphs has ... Show More
  • Analysis and Optimization of Improved Index Calculus Algorithm

    Hu Jianjun

    Issue: Volume 8, Issue 2, March 2023
    Pages: 57-61
    Received: 5 April 2023
    Accepted: 30 March 2023
    Published: 13 April 2023
    Abstract: IC (Index Calculus) algorithm is the most effective probability algorithm for solving discrete logarithm of finite prime fields, and IICA (improved Index Calculus algorithm) is an improved algorithm based on IC in the third stage. The essence of IICA is to convert the number required to solve the discrete logarithm into the product of the power of ... Show More
  • The Free Boundary Problem of a Predator-Prey Model with Fear Effect and Stage Structure

    Chao Shao, Jingfu Zhao

    Issue: Volume 8, Issue 2, March 2023
    Pages: 62-67
    Received: 25 March 2023
    Accepted: 15 April 2023
    Published: 23 April 2023
    Abstract: In this paper, fear effect and stage structure are introduced in a free boundary problem of a prey-predator model. This system simulates the spread of an invasive or newly introduced predator species, taking into account the presence of both immature and mature stages of prey that are affected by fear of the predator. The predator's predation behav... Show More