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Axioms
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Advances in Mathematics: Theory and Applications
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Advances in Mathematics: Theory and Applications

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (30 April 2024) | Viewed by 6913

Special Issue Editors

Dr. Ricardo Abreu-Blaya

E-Mail Website
Guest Editor
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Chilpancingo de los Bravo, Chilpancingo 39070, México
Interests: complex and hypercomplex analysis; boundary value problems and singular integral equations
Dr. Juan Carlos Hernández Gómez

E-Mail Website
Guest Editor
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No. 54, Col. Garita, Acapulco 39650, Mexico
Interests: discrete mathematics; graph theory; differential equations; fractional differential equations; mathematical modelling in biology processes; ecoepidemiology

Special Issue Information

Dear Colleagues,

Mathematics has undoubtedly undergone diversification through the incorporation of new theories and techniques. Theories for which the application was not initially clear are now used to solve multiple theoretical–practical problems. Therefore, it makes sense to provide a space for the publication of research articles associated with discrete mathematics, graph theory, topological indices, domination theory, polynomials in graphs, Gromov's hyperbolicity, complex systems, discrete geometry, differential equations, fractional differential equations, fractional integral operators, and discrete and fractional inequalities, as well as complex analysis, boundary value problems, and singular integral equations.

The aim of this Special Issue is to present a platform for the publication of articles on theoretical developments and their applications in different areas of human knowledge, such as chemistry, physics, biology, and economics.

Dr. Ricardo Abreu-Blaya
Dr. Juan Carlos Hernández Gómez
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • graph theory
  • mathematical chemistry
  • domination theory
  • complex systems
  • fractional differential equations
  • conformable and non-conformable calculus
  • mathematical modelling
  • complex analysis
  • boundary value problems
  • singular integral equations

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (5 papers)

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Research

15 pages, 3403 KiB  
Article
Edge DP-Coloring in K4-Minor Free Graphs and Planar Graphs
by Jingxiang He and Ming Han
Axioms 2024, 13(6), 375; https://doi.org/10.3390/axioms13060375 - 3 Jun 2024
Viewed by 482
Abstract
The edge DP-chromatic number of G, denoted by χDP′(G), is the minimum k such that G is edge DP-k-colorable. In 1999, Juvan, Mohar, and Thomas proved that the edge list chromatic number of [...] Read more.
The edge DP-chromatic number of G, denoted by χDP′(G), is the minimum k such that G is edge DP-k-colorable. In 1999, Juvan, Mohar, and Thomas proved that the edge list chromatic number of K4-minor free graph G with Δ≥3 is Δ. In this paper, we prove that if G is a K4-minor free graph, then χDP′(G)∈{Δ,Δ+1}, and equality χDP′(G)=Δ+1 holds for some K4-minor free graph G with Δ=3. Moreover, if G is a planar graph with Δ≥9 and with no intersecting triangles, then χDP′(G)=Δ. Full article
(This article belongs to the Special Issue Advances in Mathematics: Theory and Applications)
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16 pages, 1080 KiB  
Article
A Binary-State Continuous-Time Markov Chain Model for Offshoring and Reshoring
by Chiara Brambilla, Luca Grosset and Elena Sartori
Axioms 2024, 13(5), 300; https://doi.org/10.3390/axioms13050300 - 1 May 2024
Viewed by 867
Abstract
We present a two-country model (North and South) that describes the phenomenon of offshoring and reshoring. The model is a continuous time-controlled Markov chain with binary states. The main trade-off involves production costs and transaction costs between one country and another. In the [...] Read more.
We present a two-country model (North and South) that describes the phenomenon of offshoring and reshoring. The model is a continuous time-controlled Markov chain with binary states. The main trade-off involves production costs and transaction costs between one country and another. In the first part of this paper, we identify the key parameters of the model: the difference in unit production costs between the two countries considered, the marginal cost of transitioning between countries, and the incentive paid by the North country to all companies that have not relocated at the end of the planning interval. The final goal of our paper is to understand how national tax incentives can influence this process. Full article
(This article belongs to the Special Issue Advances in Mathematics: Theory and Applications)
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20 pages, 6955 KiB  
Article
Generalized Partially Functional Linear Model with Unknown Link Function
by Weiwei Xiao, Songxuan Li and Haiyan Liu
Axioms 2023, 12(12), 1089; https://doi.org/10.3390/axioms12121089 - 28 Nov 2023
Viewed by 1097
Abstract
In existing models with an unknown link function, the issue of predictors containing both multiple functional data and multiple scalar data has not been studied. To fill this gap, we propose a generalized partially functional linear model, which not only models the relationship [...] Read more.
In existing models with an unknown link function, the issue of predictors containing both multiple functional data and multiple scalar data has not been studied. To fill this gap, we propose a generalized partially functional linear model, which not only models the relationship between multiple scalar and functional predictors and responses, but also automatically estimates the link function. Specifically, we use the functional principal component analysis method to reduce the dimensionality of functional predictors, estimate the regression coefficients using the maximum likelihood estimation method, estimate the link function using the method of local linear regression, iteratively obtain the final estimator, and establish the asymptotic normality of the estimator. The asymptotic normality is illustrated through simulation experiments. Finally, the proposed model is applied to study the influence of environmental, economic, and medical levels on life expectancy in China. In the study, functional predictors are the daily air quality index, temperature, and humidity of 58 cities in 2020, and scalar predictors are GDP and the number of beds in hospitals. The experimental results indicate that the unknown link function model has a smaller prediction error and better performance than both the model with the known link function and the model without a link function. Full article
(This article belongs to the Special Issue Advances in Mathematics: Theory and Applications)
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14 pages, 426 KiB  
Article
The Boundary Integral Equation for Kinetically Limited Dendrite Growth
by Ekaterina A. Titova, Peter K. Galenko, Margarita A. Nikishina, Liubov V. Toropova and Dmitri V. Alexandrov
Axioms 2023, 12(11), 1016; https://doi.org/10.3390/axioms12111016 - 28 Oct 2023
Cited by 2 | Viewed by 953
Abstract
The boundary integral equation defining the interface function for a curved solid/liquid phase transition boundary is analytically solved in steady-state growth conditions. This solution describes dendrite tips evolving in undercooled melts with a constant crystallization velocity, which is the sum of the steady-state [...] Read more.
The boundary integral equation defining the interface function for a curved solid/liquid phase transition boundary is analytically solved in steady-state growth conditions. This solution describes dendrite tips evolving in undercooled melts with a constant crystallization velocity, which is the sum of the steady-state and translational velocities. The dendrite tips in the form of a parabola, paraboloid, and elliptic paraboloid are considered. Taking this solution into account, we obtain the modified boundary integral equation describing the evolution of the patterns and dendrites in undercooled binary melts. Our analysis shows that dendritic tips always evolve in a steady-state manner when considering a kinetically controlled crystallization scenario. The steady-state growth velocity as a factor that is dependent on the melt undercooling, solute concentration, atomic kinetics, and other system parameters is derived. This expression can be used for determining the selection constant of the stable dendrite growth mode in the case of kinetically controlled crystallization. Full article
(This article belongs to the Special Issue Advances in Mathematics: Theory and Applications)
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15 pages, 306 KiB  
Article
The Clustering Coefficient for Graph Products
by Jhon J. Aguilar-Alarcón, Juan C. Hernández-Gómez and Jesús Romero-Valencia
Axioms 2023, 12(10), 968; https://doi.org/10.3390/axioms12100968 - 14 Oct 2023
Cited by 2 | Viewed by 2158
Abstract
The clustering coefficient of a vertex v, of degree at least 2, in a graph Γ is obtained using the formula [...] Read more.
The clustering coefficient of a vertex v, of degree at least 2, in a graph Γ is obtained using the formula C(v)=2t(v)deg(v)(deg(v)−1), where t(v) denotes the number of triangles of the graph containing v as a vertex, and the clustering coefficient of Γ is defined as the average of the clustering coefficient of all vertices of Γ, that is, C(Γ)=1|V|∑v∈VC(v), where V is the vertex set of the graph. In this paper, we give explicit expressions for the clustering coefficient of corona and lexicographic products, as well as for the Cartesian sum; such expressions are given in terms of the order and size of factors, and the degree and number of triangles of vertices in each factor. Full article
(This article belongs to the Special Issue Advances in Mathematics: Theory and Applications)
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