IF 2 3区数学

Axioms Pub Date : 2023-12-11 DOI: 10.3390/axioms12121113

J. Sánchez-Pérez, Joaquín Solano-Ramírez, Enrique Castro, M. Conesa, Fulgencio Marín-García, G. García-Ros

{"title":"Analysis of the Burgers–Huxley Equation Using the Nondimensionalisation Technique: Universal Solution for Dirichlet and Symmetry Boundary Conditions","authors":"J. Sánchez-Pérez, Joaquín Solano-Ramírez, Enrique Castro, M. Conesa, Fulgencio Marín-García, G. García-Ros","doi":"10.3390/axioms12121113","DOIUrl":"https://doi.org/10.3390/axioms12121113","url":null,"abstract":"The Burgers–Huxley equation is important because it involves the phenomena of accumulation, drag, diffusion, and the generation or decay of species, which are common in various problems in science and engineering, such as heat transmission, the diffusion of atmospheric contaminants, etc. On the other hand, the mathematical technique of nondimensionalisation has proven to be very useful in the appropriate grouping of the variables involved in a physical–chemical phenomenon and in obtaining universal solutions to different complex engineering problems. Therefore, a deep analysis using this technique of the Burgers–Huxley equation and its possible boundary conditions can facilitate a common understanding of these problems through the appropriate grouping of variables and propose common universal solutions. Thus, in this case, the technique is applied to obtain a universal solution for Dirichlet and symmetric boundary conditions. The validation of the methodology is carried out by comparing different cases, where the coefficients or the value of the boundary condition are varied, with the results obtained through a numerical simulation. Furthermore, one of the cases presented presents a boundary condition that changes at a certain time. Finally, after applying the technique, it is studied which phenomenon is predominant, concluding that from a certain value diffusion predominates, with the rest being practically negligible.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"8 10","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138980866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Using SNAP to Analyze Policy Measures in e-Learning Roadmaps 使用 SNAP 分析电子学习路线图中的政策措施

IF 2 3区数学

Axioms Pub Date : 2023-12-11 DOI: 10.3390/axioms12121110

Nikola Kadoić, Nina Begičević Ređep, Dragana Kupres

{"title":"Using SNAP to Analyze Policy Measures in e-Learning Roadmaps","authors":"Nikola Kadoić, Nina Begičević Ređep, Dragana Kupres","doi":"10.3390/axioms12121110","DOIUrl":"https://doi.org/10.3390/axioms12121110","url":null,"abstract":"Creating policy measures is the final step in the process of e-learning roadmap development. Policy measures can be seen as long-term activities that need to be implemented and constantly upgraded to achieve strategic goals. For resource allocation, it is useful to prioritize policy measures. Prioritization can be implemented using multi-criteria decision-making methods. This paper analyzes policy measures in the Maldives National University’s e-learning roadmap using the social network analysis process (SNAP), which includes the analytic hierarchy process (AHP), the decision-making trial and evaluation laboratory (DEMATEL), and the PageRank centrality. In policy measure evaluation, there were more than 20 participants: persons with managerial functions at the Maldives National University (MNU) (deans, heads of departments) and persons in lecturer and researcher positions. By using the AHP, participants prioritized policy measures with respect to their importance to them. By using the DEMATEL, participants identified and prioritized policy measures with respect to their effect on other measures. Finally, by using the SNAP, it was possible to determine the prioritization list for resource allocation since it aggregates the aspects of the policy measures, their importance, and their effect on other measures.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"88 3","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138978580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

More Effective Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of a Class of Third-Order Functional Differential Equations 测试一类三阶函数微分方程解的渐近和振荡行为的更有效标准

IF 2 3区数学

Axioms Pub Date : 2023-12-11 DOI: 10.3390/axioms12121112

Fahd Masood, O. Moaaz, Ghada AlNemer, H. El-Metwally

引用次数: 0

Certain Bounds of Formulas in Free Temporal Algebras 自由时态结构中公式的若干界限

IF 2 3区数学

Axioms Pub Date : 2023-12-11 DOI: 10.3390/axioms12121111

Francisco Miguel García-Olmedo, Antonio Jesús Rodríguez-Salas, P. González-Rodelas

引用次数: 0

On the Method of Transformations: Obtaining Solutions of Nonlinear Differential Equations by Means of the Solutions of Simpler Linear or Nonlinear Differential Equations 论变换方法：通过较简单线性或非线性微分方程的解获得非线性微分方程的解

IF 2 3区数学

Axioms Pub Date : 2023-12-08 DOI: 10.3390/axioms12121106

N. Vitanov

{"title":"On the Method of Transformations: Obtaining Solutions of Nonlinear Differential Equations by Means of the Solutions of Simpler Linear or Nonlinear Differential Equations","authors":"N. Vitanov","doi":"10.3390/axioms12121106","DOIUrl":"https://doi.org/10.3390/axioms12121106","url":null,"abstract":"Transformations are much used to connect complicated nonlinear differential equations to simple equations with known exact solutions. Two examples of this are the Hopf–Cole transformation and the simple equations method. In this article, we follow an idea that is opposite to the idea of Hopf and Cole: we use transformations in order to transform simpler linear or nonlinear differential equations (with known solutions) to more complicated nonlinear differential equations. In such a way, we can obtain numerous exact solutions of nonlinear differential equations. We apply this methodology to the classical parabolic differential equation (the wave equation), to the classical hyperbolic differential equation (the heat equation), and to the classical elliptic differential equation (Laplace equation). In addition, we use the methodology to obtain exact solutions of nonlinear ordinary differential equations by means of the solutions of linear differential equations and by means of the solutions of the nonlinear differential equations of Bernoulli and Riccati. Finally, we demonstrate the capacity of the methodology to lead to exact solutions of nonlinear partial differential equations on the basis of known solutions of other nonlinear partial differential equations. As an example of this, we use the Korteweg–de Vries equation and its solutions. Traveling wave solutions of nonlinear differential equations are of special interest in this article. We demonstrate the existence of the following phenomena described by some of the obtained solutions: (i) occurrence of the solitary wave–solitary antiwave from the solution, which is zero at the initial moment (analogy of an occurrence of particle and antiparticle from the vacuum); (ii) splitting of a nonlinear solitary wave into two solitary waves (analogy of splitting of a particle into two particles); (iii) soliton behavior of some of the obtained waves; (iv) existence of solitons which move with the same velocity despite the different shape and amplitude of the solitons.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"84 12","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138586701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Novel Fractional Multi-Order High-Gain Observer Design to Estimate Temperature in a Heat Exchange Process 估算热交换过程中温度的新型分数多阶高增益观测器设计

IF 2 3区数学

Axioms Pub Date : 2023-12-08 DOI: 10.3390/axioms12121107

Vicente Borja-Jaimes, Manuel Adam-Medina, Jarniel García-Morales, Alan Cruz-Rojas, Alfredo Gil-Velasco, Antonio Coronel-Escamilla

{"title":"A Novel Fractional Multi-Order High-Gain Observer Design to Estimate Temperature in a Heat Exchange Process","authors":"Vicente Borja-Jaimes, Manuel Adam-Medina, Jarniel García-Morales, Alan Cruz-Rojas, Alfredo Gil-Velasco, Antonio Coronel-Escamilla","doi":"10.3390/axioms12121107","DOIUrl":"https://doi.org/10.3390/axioms12121107","url":null,"abstract":"In the present manuscript, we design a fractional multi-order high-gain observer to estimate temperature in a double pipe heat exchange process. For comparison purposes and since we want to prove that when using our novel technique, the estimation is more robust than the classical approach, we design a non-fractional high-gain observer, and then we compare the performance of both observers. We consider three scenarios: The first one considers the estimation of the system states by measuring only one output with no noise added on it and under ideal conditions. Second, we add noise to the measured output and then reconstruct the system states, and, third, in addition to the noise, we increase the gain parameter in both observers (non-fractional and fractional) due to the fact that we want to prove that the robustness changes in this parameter. The results showed that, using our approach, the estimated states can be recovered under noise circumstances in the measured output and under parameter change in the observer, contrary to using classical (non-fractional) observers where the states cannot be recovered. In all our tests, we used the normalized root-mean-square, integral square error, and integral absolute error indices, resulting in a better performance for our approach than that obtained using the classical approach. We concluded that our fractional multi-order high-gain observer is more robust to input noise than the classical high-gain observer.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"4 5","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138589636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Describing Conditional Independence Statements Using Undirected Graphs 使用无向图描述条件独立性语句

IF 2 3区数学

Axioms Pub Date : 2023-12-08 DOI: 10.3390/axioms12121109

D. Malouche

{"title":"Describing Conditional Independence Statements Using Undirected Graphs","authors":"D. Malouche","doi":"10.3390/axioms12121109","DOIUrl":"https://doi.org/10.3390/axioms12121109","url":null,"abstract":"This paper investigates the capability of undirected graphs (UGs) to represent a set of Conditional Independence (CI) statements derived from a given probability distribution of a random vector. While it is established that certain axioms can govern this set, providing sufficient conditions for UGs to capture specific CI statements, our focus is on covariance and concentration graphs. These remain the only known families of UGs capable of describing CI statements. We explore the issue of complete representation of CI statements through their corresponding covariance and concentration graphs. Two parameters are defined, one each from the covariance and concentration graphs, to determine the limitations concerning the cardinality of the conditioning subset that the graph can represent. We establish a relationship between these parameters and the cardinality of the separators in each graph, providing a straightforward computational method to evaluate them. In conclusion, we enhance the aforementioned procedure and introduce criteria to ascertain, without additional computations, whether the graphs can fully represent a given set of CI statements. We demonstrate that either the concentration or the covariance graph forms a cycle, and when considered in conjunction, they can represent the entire relation. These criteria also enable us, in specific cases, to deduce the covariance graph from the concentration graph and vice versa.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"93 ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139010914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Note on Finite Dimensional Odd Contact Lie Superalgebra in Prime Characteristic 素特性有限维奇数接触列超代数注释

IF 2 3区数学

Axioms Pub Date : 2023-12-08 DOI: 10.3390/axioms12121108

Xiaoning Xu, Qiyuan Wang

引用次数: 0

A Simplified Approach to the Pricing of Vulnerable Options with Two Underlying Assets in an Intensity-Based Model 在基于强度的模型中为具有两种相关资产的脆弱期权定价的简化方法

IF 2 3区数学

Axioms Pub Date : 2023-12-07 DOI: 10.3390/axioms12121105

Geonwoo Kim

引用次数: 0

Proportional Odds Hazard Model for Discrete Time-to-Event Data 离散时间到事件数据的比例概率危险模型