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Algebra, Number Theory, Combinatorics and Their Applications: Mathematical Theory and Computational Modelling

Submission Deadline: 31 August 2022 (closed)

Guest Editors

Prof. Taekyun Kim, Kwangwoon University, Korea
Prof. Dae San Kim, Sogang University, Korea
Prof. Lee-Chae Jang, Konkuk University, Korea

Summary

Historically, computation has been a driving force in the development of mathematics. To help measure the sizes of their fields, the Egyptians invented geometry. To help predict the positions of the planets, the Greeks invented trigonometry. Algebra was invented to deal with equations that arose when mathematics was used to model the world.

In order to solve these equations of algebra, computational modelling in number theory arose. In particular, Mathematical and computational modelling in number theory have been applied in engineering, science and medicine to study phenomena at a wide range of size scales. In pure mathematics we also compute, and many of our great theorems and conjectures are, at root, motivated by computational experience.

Thanks to advances in computers, many problems in science and engineering can be modeled by polynomial optimization. We aim to design this special issue for researchers with interesting mathematical and computational modelling in Number theory, algebra, and combinatorics. This special issue aims to present theories, methods, and applications of recent/current mathematical and computational modelling related to number theory in various areas.

Each paper published in this special issue aims to enrich the understanding of current research problems, theories, and applications on the chosen topics. The emphasis will be to present the basic developments concerning an idea in full detail, and also contain the most recent advances made in the area of mathematical theory and computational modelling related to number theory.

 

Potential topics include but are not limited to the following:

 

• Mathematical and computational modelling in Number theory

• Computational modeling related to degenerate functions and polynomials

• Properties and theories to degenerate umbral and umbral calculus

• Analytical properties and applications of polylogarithm and polyexponential functions

• Applications of degenerate polylogarithmic and polyexponential functions.

• Random variables and degenerate Poisson random variable

related to computational modeling

• p-adic q-integral on Zp related to Special numbers and polynomials

• Properties of ordinary and general families of Special Polynomials

• Multiple zeta functions

• Operational techniques involving Special Polynomials...etc


Keywords

Laguerre polynomials, degenerate Poisson random variable, degenerate Bernstein polynomials, computational modelling in number theory, Dowling lattice, r-truncated Poisson random variables, degenerate binomial random variable, umbral calculus, degenerate umbral calculus, polyexponential function, degenerate poly-Bernoulli polynomials.

Published Papers


  • Open Access

    ARTICLE

    A Note on Bell-Based Bernoulli and Euler Polynomials of Complex Variable

    N. Alam, W. A. Khan, S. Obeidat, G. Muhiuddin, N. S. Diab, H. N. Zaidi, A. Altaleb, L. Bachioua
    CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 187-209, 2023, DOI:10.32604/cmes.2022.021418
    (This article belongs to the Special Issue: Algebra, Number Theory, Combinatorics and Their Applications: Mathematical Theory and Computational Modelling)
    Abstract In this article, we construct the generating functions for new families of special polynomials including two parametric kinds of Bell-based Bernoulli and Euler polynomials. Some fundamental properties of these functions are given. By using these generating functions and some identities, relations among trigonometric functions and two parametric kinds of Bell-based Bernoulli and Euler polynomials, Stirling numbers are presented. Computational formulae for these polynomials are obtained. Applying a partial derivative operator to these generating functions, some derivative formulae and finite combinatorial sums involving the aforementioned polynomials and numbers are also obtained. In addition, some remarks and More >

  • Open Access

    ARTICLE

    Some Properties of Degenerate r-Dowling Polynomials and Numbers of the Second Kind

    Hye Kyung Kim, Dae Sik Lee
    CMES-Computer Modeling in Engineering & Sciences, Vol.133, No.3, pp. 825-842, 2022, DOI:10.32604/cmes.2022.022103
    (This article belongs to the Special Issue: Algebra, Number Theory, Combinatorics and Their Applications: Mathematical Theory and Computational Modelling)
    Abstract The generating functions of special numbers and polynomials have various applications in many fields as well as mathematics and physics. In recent years, some mathematicians have studied degenerate version of them and obtained many interesting results. With this in mind, in this paper, we introduce the degenerate r-Dowling polynomials and numbers associated with the degenerate r-Whitney numbers of the second kind. We derive many interesting properties and identities for them including generating functions, Dobinski-like formula, integral representations, recurrence relations, differential equation and various explicit expressions. In addition, we explore some expressions for them that can be More >

  • Open Access

    ARTICLE

    gscaLCA in R: Fitting Fuzzy Clustering Analysis Incorporated with Generalized Structured Component Analysis

    Ji Hoon Ryoo, Seohee Park, Seongeun Kim, Heungsun Hwang
    CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.3, pp. 801-822, 2022, DOI:10.32604/cmes.2022.019708
    (This article belongs to the Special Issue: Algebra, Number Theory, Combinatorics and Their Applications: Mathematical Theory and Computational Modelling)
    Abstract Clustering analysis identifying unknown heterogenous subgroups of a population (or a sample) has become increasingly popular along with the popularity of machine learning techniques. Although there are many software packages running clustering analysis, there is a lack of packages conducting clustering analysis within a structural equation modeling framework. The package, gscaLCA which is implemented in the R statistical computing environment, was developed for conducting clustering analysis and has been extended to a latent variable modeling. More specifically, by applying both fuzzy clustering (FC) algorithm and generalized structured component analysis (GSCA), the package gscaLCA computes membership prevalence and… More >

  • Open Access

    ARTICLE

    Strategy for Creating AR Applications in Static and Dynamic Environments Using SLAM- and Marker Detector-Based Tracking

    Chanho Park, Hyunwoo Cho, Sangheon Park, Sung-Uk Jung, Suwon Lee
    CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.1, pp. 529-549, 2022, DOI:10.32604/cmes.2022.019214
    (This article belongs to the Special Issue: Algebra, Number Theory, Combinatorics and Their Applications: Mathematical Theory and Computational Modelling)
    Abstract Recently, simultaneous localization and mapping (SLAM) has received considerable attention in augmented reality (AR) libraries and applications. Although the assumption of scene rigidity is common in most visual SLAMs, this assumption limits the possibilities of AR applications in various real-world environments. In this paper, we propose a new tracking system that integrates SLAM with a marker detection module for real-time AR applications in static and dynamic environments. Because the proposed system assumes that the marker is movable, SLAM performs tracking and mapping of the static scene except for the marker, and the marker detector estimates… More >

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