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Edge DP-Coloring in K4-Minor Free Graphs and Planar Graphs 无 K4 小数图和平面图中的边 DP 着色
IF 2 3区 数学
Axioms Pub Date : 2024-06-03 DOI: 10.3390/axioms13060375
Jingxiang He, Ming Han
{"title":"Edge DP-Coloring in K4-Minor Free Graphs and Planar Graphs","authors":"Jingxiang He, Ming Han","doi":"10.3390/axioms13060375","DOIUrl":"https://doi.org/10.3390/axioms13060375","url":null,"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 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.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141269105","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
Asymptotic Conformality and Polygonal Approximation 渐近共形与多边形逼近
IF 2 3区 数学
Axioms Pub Date : 2024-06-03 DOI: 10.3390/axioms13060376
S. Krushkal
{"title":"Asymptotic Conformality and Polygonal Approximation","authors":"S. Krushkal","doi":"10.3390/axioms13060376","DOIUrl":"https://doi.org/10.3390/axioms13060376","url":null,"abstract":"Univalent functions with asymptotically conformal extension to the boundary form a subclass of functions with quasiconformal extension with rather special features. Such functions arise in various questions of geometric function theory and Teichmüller space theory and have important applications involving conformal and quasiconformal maps. The paper provides an approximative characterization of local conformality and its connection with univalent polynomials. Also, some other quantitative applications of this connection are given.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141269660","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
An Accelerated Dual-Integral Structure Zeroing Neural Network Resistant to Linear Noise for Dynamic Complex Matrix Inversion 用于动态复杂矩阵反演的抗线性噪声加速双积分结构归零神经网络
IF 2 3区 数学
Axioms Pub Date : 2024-06-02 DOI: 10.3390/axioms13060374
FeiXiang Yang, Tinglei Wang, Yun Huang
{"title":"An Accelerated Dual-Integral Structure Zeroing Neural Network Resistant to Linear Noise for Dynamic Complex Matrix Inversion","authors":"FeiXiang Yang, Tinglei Wang, Yun Huang","doi":"10.3390/axioms13060374","DOIUrl":"https://doi.org/10.3390/axioms13060374","url":null,"abstract":"The problem of inverting dynamic complex matrices remains a central and intricate challenge that has garnered significant attention in scientific and mathematical research. The zeroing neural network (ZNN) has been a notable approach, utilizing time derivatives for real-time solutions in noiseless settings. However, real-world disturbances pose a significant challenge to a ZNN’s convergence. We design an accelerated dual-integral structure zeroing neural network (ADISZNN), which can enhance convergence and restrict linear noise, particularly in complex domains. Based on the Lyapunov principle, theoretical analysis proves the convergence and robustness of ADISZNN. We have selectively integrated the SBPAF activation function, and through theoretical dissection and comparative experimental validation we have affirmed the efficacy and accuracy of our activation function selection strategy. After conducting numerous experiments, we discovered oscillations and improved the model accordingly, resulting in the ADISZNN-Stable model. This advanced model surpasses current models in both linear noisy and noise-free environments, delivering a more rapid and stable convergence, marking a significant leap forward in the field.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141273076","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
Dynamical Behaviors of Stochastic SIS Epidemic Model with Ornstein–Uhlenbeck Process 具有 Ornstein-Uhlenbeck 过程的随机 SIS 流行病模型的动力学行为
IF 2 3区 数学
Axioms Pub Date : 2024-05-24 DOI: 10.3390/axioms13060353
Huina Zhang, Jianguo Sun, Peng Yu, Daqing Jiang
{"title":"Dynamical Behaviors of Stochastic SIS Epidemic Model with Ornstein–Uhlenbeck Process","authors":"Huina Zhang, Jianguo Sun, Peng Yu, Daqing Jiang","doi":"10.3390/axioms13060353","DOIUrl":"https://doi.org/10.3390/axioms13060353","url":null,"abstract":"Controlling infectious diseases has become an increasingly complex issue, and vaccination has become a common preventive measure to reduce infection rates. It has been thought that vaccination protects the population. However, there is no fully effective vaccine. This is based on the fact that it has long been assumed that the immune system produces corresponding antibodies after vaccination, but usually does not achieve the level of complete protection for undergoing environmental fluctuations. In this paper, we investigate a stochastic SIS epidemic model with incomplete inoculation, which is perturbed by the Ornstein–Uhlenbeck process and Brownian motion. We determine the existence of a unique global solution for the stochastic SIS epidemic model and derive control conditions for the extinction. By constructing two suitable Lyapunov functions and using the ergodicity of the Ornstein–Uhlenbeck process, we establish sufficient conditions for the existence of stationary distribution, which means the disease will prevail. Furthermore, we obtain the exact expression of the probability density function near the pseudo-equilibrium point of the stochastic model while addressing the four-dimensional Fokker–Planck equation under the same conditions. Finally, we conduct several numerical simulations to validate the theoretical results.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141101604","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
Editorial Conclusion for the Special Issue “New Theory and Applications of Nonlinear Analysis, Fractional Calculus and Optimization” "非线性分析、分数微积分和优化的新理论与应用 "特刊编辑结论
IF 2 3区 数学
Axioms Pub Date : 2024-05-24 DOI: 10.3390/axioms13060350
Wei-Shih Du
{"title":"Editorial Conclusion for the Special Issue “New Theory and Applications of Nonlinear Analysis, Fractional Calculus and Optimization”","authors":"Wei-Shih Du","doi":"10.3390/axioms13060350","DOIUrl":"https://doi.org/10.3390/axioms13060350","url":null,"abstract":"Nonlinear analysis has widespread and significant applications in many areas at the core of many branches of pure and applied mathematics and modern science, including nonlinear ordinary and partial differential equations, critical point theory, functional analysis, fixed point theory, nonlinear optimization, fractional calculus, variational analysis, convex analysis, dynamical system theory, mathematical economics, data mining, signal processing, control theory, and many more [...]","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141100545","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
On Certain Properties of Parametric Kinds of Apostol-Type Frobenius–Euler–Fibonacci Polynomials 论 Apostol 型 Frobenius-Euler-Fibonacci 多项式的参数类的某些性质
IF 2 3区 数学
Axioms Pub Date : 2024-05-24 DOI: 10.3390/axioms13060348
Hao Guan, Waseem Ahmad Khan, Can Kızılateş, Cheon Seoung Ryoo
{"title":"On Certain Properties of Parametric Kinds of Apostol-Type Frobenius–Euler–Fibonacci Polynomials","authors":"Hao Guan, Waseem Ahmad Khan, Can Kızılateş, Cheon Seoung Ryoo","doi":"10.3390/axioms13060348","DOIUrl":"https://doi.org/10.3390/axioms13060348","url":null,"abstract":"This paper presents an overview of cosine and sine Apostol-type Frobenius–Euler–Fibonacci polynomials, as well as several identities that are associated with these polynomials. By applying a partial derivative operator to the generating functions, the authors obtain derivative formulae and finite combinatorial sums involving these polynomials and numbers. Additionally, the paper establishes connections between cosine and sine Apostol-type Frobenius–Euler–Fibonacci polynomials of order α and several other polynomial sequences, such as the Apostol-type Bernoulli–Fibonacci polynomials, the Apostol-type Euler–Fibonacci polynomials, the Apostol-type Genocchi–Fibonacci polynomials, and the Stirling–Fibonacci numbers of the second kind. The authors also provide computational formulae and graphical representations of these polynomials using the Mathematica program.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141101235","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
Isoptic Point of the Complete Quadrangle 完整四边形的等视点
IF 2 3区 数学
Axioms Pub Date : 2024-05-24 DOI: 10.3390/axioms13060349
E. Jurkin, Marija Šimić Horvath, V. Volenec
{"title":"Isoptic Point of the Complete Quadrangle","authors":"E. Jurkin, Marija Šimić Horvath, V. Volenec","doi":"10.3390/axioms13060349","DOIUrl":"https://doi.org/10.3390/axioms13060349","url":null,"abstract":"In this paper, we study the complete quadrangle. We started this investigation in a few of our previous papers. In those papers and here, the rectangular coordinates are used to enable us to prove the properties of the rich geometry of a quadrangle using the same method. Now, we are focused on the isoptic point of the complete quadrangle ABCD, which is the inverse point to A′,B′,C′, and D′ with respect to circumscribed circles of the triangles BCD, ACD, ABD, and ABC, respectively, where A′,B′,C′, and D′ are isogonal points to A,B,C, and D with respect to these triangles. In studying the properties of the quadrangle regarding its isoptic point, some new results are obtained as well.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141102704","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
Local Influence for the Thin-Plate Spline Generalized Linear Model 薄板样条广义线性模型的局部影响
IF 2 3区 数学
Axioms Pub Date : 2024-05-23 DOI: 10.3390/axioms13060346
Germán Ibacache-Pulgar, Pablo Pacheco, Orietta Nicolis, Miguel Angel Uribe-Opazo
{"title":"Local Influence for the Thin-Plate Spline Generalized Linear Model","authors":"Germán Ibacache-Pulgar, Pablo Pacheco, Orietta Nicolis, Miguel Angel Uribe-Opazo","doi":"10.3390/axioms13060346","DOIUrl":"https://doi.org/10.3390/axioms13060346","url":null,"abstract":"Thin-Plate Spline Generalized Linear Models (TPS-GLMs) are an extension of Semiparametric Generalized Linear Models (SGLMs), because they allow a smoothing spline to be extended to two or more dimensions. This class of models allows modeling a set of data in which it is desired to incorporate the non-linear joint effects of some covariates to explain the variability of a certain variable of interest. In the spatial context, these models are quite useful, since they allow the effects of locations to be included, both in trend and dispersion, using a smooth surface. In this work, we extend the local influence technique for the TPS-GLM model in order to evaluate the sensitivity of the maximum penalized likelihood estimators against small perturbations in the model and data. We fit our model through a joint iterative process based on Fisher Scoring and weighted backfitting algorithms. In addition, we obtained the normal curvature for the case-weight perturbation and response variable additive perturbation schemes, in order to detect influential observations on the model fit. Finally, two data sets from different areas (agronomy and environment) were used to illustrate the methodology proposed here.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141105297","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
Strong Comonotonic Additive Systemic Risk Measures 强同调相加系统性风险措施
IF 2 3区 数学
Axioms Pub Date : 2024-05-23 DOI: 10.3390/axioms13060347
Heyan Wang, Shuo Gong, Yijun Hu
{"title":"Strong Comonotonic Additive Systemic Risk Measures","authors":"Heyan Wang, Shuo Gong, Yijun Hu","doi":"10.3390/axioms13060347","DOIUrl":"https://doi.org/10.3390/axioms13060347","url":null,"abstract":"In this paper, we propose a new class of systemic risk measures, which we refer to as strong comonotonic additive systemic risk measures. First, we introduce the notion of strong comonotonic additive systemic risk measures by proposing new axioms. Second, we establish a structural decomposition for strong comonotonic additive systemic risk measures. Third, when both the single-firm risk measure and the aggregation function in the structural decomposition are convex, we also provide a dual representation for it. Last, examples are given to illustrate the proposed systemic risk measures. Comparisons with existing systemic risk measures are also provided.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141102872","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
An Optimization Problem for Computing Predictive Potential of General Sum/Product-Connectivity Topological Indices of Physicochemical Properties of Benzenoid Hydrocarbons 计算苯碳氢化合物理化性质的一般总和/产物连通性拓扑指标预测潜力的优化问题
IF 2 3区 数学
Axioms Pub Date : 2024-05-22 DOI: 10.3390/axioms13060342
Sakander Hayat, Azri Arfan, Asad Khan, Haziq Jamil, Mohammed J. F. Alenazi
{"title":"An Optimization Problem for Computing Predictive Potential of General Sum/Product-Connectivity Topological Indices of Physicochemical Properties of Benzenoid Hydrocarbons","authors":"Sakander Hayat, Azri Arfan, Asad Khan, Haziq Jamil, Mohammed J. F. Alenazi","doi":"10.3390/axioms13060342","DOIUrl":"https://doi.org/10.3390/axioms13060342","url":null,"abstract":"For a graph G=(VG,EG), a degree-based graphical index GId takes the general form GId=∑xy∈EGϕ(dx,dy), where ϕ is a symmetric map and di is the degree of i∈VG. For α∈R, if ϕ=(dxdy)α (resp. ϕ=(dx+dy)α), the index is called the general product-connectivity Rα (resp. general sum-connectivity SCIα) index. In this paper, by formulating an optimization problem, we determine the value(s) of α, for which the linear/multiple correlation coefficient of Rα and SCIα with physicochemical properties of benzenoid hydrocarbons is the strongest. This, in turn, fills some research gaps left by similar studies in this area.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141112107","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
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