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Application of Computer Tools in the Study of Mathematical Problems

Submission Deadline: 30 April 2023 (closed) View: 5

Guest Editors

Prof. Wenpeng Zhang, Northwest University, China
Prof. Jie Wu, French National Center for Scientific Research, France
Prof. Taekyun Kim, Kwangwoon University, South Korea

Summary

It is well known that number theory and combinatorics are two very important research branches of pure mathematics, many mathematical problems are closely related to them, such as Riemann hypothesis, Waring problem, Goldbach conjecture, twin prime conjecture, etc. Number theory and combinatorics is mainly concerned with numbers, thus many problems on these two fields can be converted or expressed by computable formulae. Because of this, computer tools are widely applied to these problems. To be concrete, computer tools help to verify the accuracy of conjectures, improve the error term of the estimations of inequalities, calculate the numerical results of computational formulae and so on. Therefore, it is necessary to conduct in-depth research in these fields, in order to make some progress in the study of certain mathematical theoretical problems. This special issue will focus on the contents of the study of number theory and combinatorics, especially those pure mathematical problems that can be realized with the help of computer tools. We will convert such mathematical problems into the forms suitable for computers to solve. Of course, we are not limited to these.

 

The aim of this special issue is to study various recurrence sequences, combinatorial identities and the calculation of the power mean of exponential sums and character sums, and to obtain some precise calculation formulae for them. Due to the computational complexity of such problems, we try to solve them by using mathematical modeling or computer programming, in order to achieve better results.  

 

Potential topics include but are not limited to the following:

 

· Recurrence sequences

· Various exponential sums and their power mean

· Combinatorial identities

· Mathematical modeling

· Computer programming


Keywords

Recurrence sequences; combinatorial identities; exponential sums; character sums; mathematical modeling

Published Papers


  • Open Access

    ARTICLE

    Reliability Analysis of HEE Parameters via Progressive Type-II Censoring with Applications

    Heba S. Mohammed, Mazen Nassar, Refah Alotaibi, Ahmed Elshahhat
    CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.3, pp. 2761-2793, 2023, DOI:10.32604/cmes.2023.028826
    (This article belongs to the Special Issue: Application of Computer Tools in the Study of Mathematical Problems)
    Abstract A new extended exponential lifetime model called Harris extended-exponential (HEE) distribution for data modelling with increasing and decreasing hazard rate shapes has been considered. In the reliability context, researchers prefer to use censoring plans to collect data in order to achieve a compromise between total test time and/or test sample size. So, this study considers both maximum likelihood and Bayesian estimates of the Harris extended-exponential distribution parameters and some of its reliability indices using a progressive Type-II censoring strategy. Under the premise of independent gamma priors, the Bayesian estimation is created using the squared-error and… More >

  • Open Access

    ARTICLE

    Multi-Stage Improvement of Marine Predators Algorithm and Its Application

    Chuandong Qin, Baole Han
    CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 3097-3119, 2023, DOI:10.32604/cmes.2023.026643
    (This article belongs to the Special Issue: Application of Computer Tools in the Study of Mathematical Problems)
    Abstract The metaheuristic algorithms are widely used in solving the parameters of the optimization problem. The marine predators algorithm (MPA) is a novel population-based intelligent algorithm. Although MPA has shown a talented foraging strategy, it still needs a balance of exploration and exploitation. Therefore, a multi-stage improvement of marine predators algorithm (MSMPA) is proposed in this paper. The algorithm retains the advantage of multi-stage search and introduces a linear flight strategy in the middle stage to enhance the interaction between predators. Predators further away from the historical optimum are required to move, increasing the exploration capability… More >

    Graphic Abstract

    Multi-Stage Improvement of Marine Predators Algorithm and Its Application

  • Open Access

    ARTICLE

    Easy to Calibrate: Marker-Less Calibration of Multiview Azure Kinect

    Sunyoung Bu, Suwon Lee
    CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 3083-3096, 2023, DOI:10.32604/cmes.2023.024460
    (This article belongs to the Special Issue: Application of Computer Tools in the Study of Mathematical Problems)
    Abstract Reconstructing a three-dimensional (3D) environment is an indispensable technique to make augmented reality and augmented virtuality feasible. A Kinect device is an efficient tool for reconstructing 3D environments, and using multiple Kinect devices enables the enhancement of reconstruction density and expansion of virtual spaces. To employ multiple devices simultaneously, Kinect devices need to be calibrated with respect to each other. There are several schemes available that calibrate 3D images generated from multiple Kinect devices, including the marker detection method. In this study, we introduce a markerless calibration technique for Azure Kinect devices that avoids the More >

    Graphic Abstract

    Easy to Calibrate: Marker-Less Calibration of Multiview Azure Kinect

  • Open Access

    ARTICLE

    On the Mean Value of High-Powers of a Special Character Sum Modulo a Prime

    Xiaodan Yuan, Wenpeng Zhang
    CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 943-953, 2023, DOI:10.32604/cmes.2023.024363
    (This article belongs to the Special Issue: Application of Computer Tools in the Study of Mathematical Problems)
    Abstract In this paper, we use the elementary methods, the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime, and derive an exact computational formula. It can be conveniently programmed by the “Mathematica” software, by which we can get the exact results easily. More >

  • Open Access

    ARTICLE

    Prediction System for Diagnosis and Detection of Coronavirus Disease-2019 (COVID-19): A Fuzzy-Soft Expert System

    Wencong Liu, Ahmed Mostafa Khalil, Rehab Basheer, Yong Lin
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2715-2730, 2023, DOI:10.32604/cmes.2023.024755
    (This article belongs to the Special Issue: Application of Computer Tools in the Study of Mathematical Problems)
    Abstract In early December 2019, a new virus named “2019 novel coronavirus (2019-nCoV)” appeared in Wuhan, China. The disease quickly spread worldwide, resulting in the COVID-19 pandemic. In the current work, we will propose a novel fuzzy soft modal (i.e., fuzzy-soft expert system) for early detection of COVID-19. The main construction of the fuzzy-soft expert system consists of five portions. The exploratory study includes sixty patients (i.e., forty males and twenty females) with symptoms similar to COVID-19 in (Nanjing Chest Hospital, Department of Respiratory, China). The proposed fuzzy-soft expert system depended on five symptoms of COVID-19 More >

    Graphic Abstract

    Prediction System for Diagnosis and Detection of Coronavirus Disease-2019 (COVID-19): A Fuzzy-Soft Expert System

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