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Algebraic and geometric characterizations related to the quantization problem of the $$C_{2,8}$$ channel 与 $$C_{2,8}$ 信道量化问题有关的代数和几何特征
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-18 DOI: 10.1007/s40314-024-02890-5
Anderson José de Oliveira, Giuliano Gadioli La Guardia, Reginaldo Palazzo, Clarice Dias de Albuquerque, Cátia Regina de Oliveira Quilles Queiroz, Leandro Bezerra de Lima, Vandenberg Lopes Vieira
{"title":"Algebraic and geometric characterizations related to the quantization problem of the $$C_{2,8}$$ channel","authors":"Anderson José de Oliveira, Giuliano Gadioli La Guardia, Reginaldo Palazzo, Clarice Dias de Albuquerque, Cátia Regina de Oliveira Quilles Queiroz, Leandro Bezerra de Lima, Vandenberg Lopes Vieira","doi":"10.1007/s40314-024-02890-5","DOIUrl":"https://doi.org/10.1007/s40314-024-02890-5","url":null,"abstract":"<p>In this paper, we consider the steps to be followed in the analysis and interpretation of the quantization problem related to the <span>(C_{2,8})</span> channel, where the Fuchsian differential equations, the generators of the Fuchsian groups, and the tessellations associated with the cases <span>(g=2)</span> and <span>(g=3)</span>, related to the hyperbolic case, are determined. In order to obtain these results, it is necessary to determine the genus <i>g</i> of each surface on which this channel may be embedded. After that, the procedure is to determine the algebraic structure (Fuchsian group generators) associated with the fundamental region of each surface. To achieve this goal, an associated linear second-order Fuchsian differential equation whose linearly independent solutions provide the generators of this Fuchsian group is devised. In addition, the tessellations associated with each analyzed case are identified. These structures are identified in four situations, divided into two cases <span>((g=2)</span> and <span>(g=3))</span>, obtaining, therefore, both algebraic and geometric characterizations associated with quantizing the <span>(C_{2,8})</span> channel.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"9 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177994","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
Temperature effects on the impurity segregation in diluted metallic alloys 温度对稀释金属合金中杂质偏析的影响
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-17 DOI: 10.1007/s40314-024-02821-4
D. G. Teixeira, A. C. de Castro Barbosa
{"title":"Temperature effects on the impurity segregation in diluted metallic alloys","authors":"D. G. Teixeira, A. C. de Castro Barbosa","doi":"10.1007/s40314-024-02821-4","DOIUrl":"https://doi.org/10.1007/s40314-024-02821-4","url":null,"abstract":"<p>The impurity segregation in diluted transition-metal bimetallic alloys is a subject of study in many fields of interest and still deserves more understanding. Using a tight-binding model for the case of a single substitutional metal impurity the segregation is investigated analysing the segregation energy. Different impurity positions are considered from the (001) top surface to a number of planes below it on a simple cubic lattice. With only one orbital per site, the impurity potentials are determined in order to satisfy charge neutrality through the Friedel sum rule. In particular, our attention will be mainly directed to the substitutional impurity located in the surface and in the bulk. Temperature effects are considered through the Sommerfeld Expansion. Interesting effects on the segregation energy are pointed out such as the appearance of a quantum interference on the electronic states due to the surface itself. The obtained trend of the segregation energy profile is in good agreement with the surface concentration experimental data.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"97 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177995","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
Alternative Arnoldi process for ill-conditioned tensor equations with application to image restoration 针对无条件张量方程的替代阿诺德过程，并将其应用于图像复原
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-16 DOI: 10.1007/s40314-024-02886-1
Mahsa Bagheri, Azita Tajaddini, Faranges Kyanfar, Abbas Salemi
{"title":"Alternative Arnoldi process for ill-conditioned tensor equations with application to image restoration","authors":"Mahsa Bagheri, Azita Tajaddini, Faranges Kyanfar, Abbas Salemi","doi":"10.1007/s40314-024-02886-1","DOIUrl":"https://doi.org/10.1007/s40314-024-02886-1","url":null,"abstract":"<p>This paper is concerned with developing an iterative tensor Krylov subspace method to solve linear discrete ill-posed systems of equations with a particular tensor product structure. We use the well-known Frobenius inner product for two tensors and the n-mode matrix-product of a tensor with a matrix to define tensor QR decomposition and alternative Arnoldi algorithms. Moreover, we illustrate how the tensor alternative Arnoldi process can be exploited to solve ill-posed problems by recovering blurry color images and videos in conjunction with the Tikhonov regularization technique, to derive approximate regularized solutions. We also review a generalized cross-validation technique for selecting the regularization parameter in the Tikhonov regularization. Theoretical properties of this method are demonstrated and applications including image deblurring and video processing are investigated. Numerical examples compare the proposed method with several other methods and illustrate the potential superiority of mentioned methods.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"79 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177997","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
Error analysis of fully decoupled SAV scheme for two phase magnetohydrodynamic diffuse interface model 两相磁流体扩散界面模型全解耦 SAV 方案的误差分析
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-16 DOI: 10.1007/s40314-024-02891-4
Danxia Wang, Zhaowei Wang, Chenhui Zhang, Hongen Jia, Jianwen Zhang
{"title":"Error analysis of fully decoupled SAV scheme for two phase magnetohydrodynamic diffuse interface model","authors":"Danxia Wang, Zhaowei Wang, Chenhui Zhang, Hongen Jia, Jianwen Zhang","doi":"10.1007/s40314-024-02891-4","DOIUrl":"https://doi.org/10.1007/s40314-024-02891-4","url":null,"abstract":"<p>In this paper, we propose an error analysis of fully decoupled time-discrete scheme for the Cahn–Hilliard-MHD (CHMHD) diffuse interface model. Firstly, we use the “zero-energy-contribution\" technique to reconstruct the system by introducing three scalar auxiliary variables (SAV). Secondly, we construct first-order semi-discrete SAV scheme for this new system by using pressure-correction method, and we also demonstrate its unconditional stability in energy. Then, we give a detailed implementation procedure to show that the proposed scheme is linear and fully decoupled, and only a series of elliptic equations with constant coefficients need to be solved at each time step. Moreover, we establish the optimal convergence rate by rigorous error analysis. Finally, we present numerical experiments to validate the accuracy, stability and efficiency of the proposed scheme.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"18 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142178000","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 sign function of tensors with Einstein product and its application in solving Yang–Baxter tensor equation 带爱因斯坦积的张量符号函数及其在求解杨-巴克斯特张量方程中的应用
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-16 DOI: 10.1007/s40314-024-02892-3
Raziyeh Erfanifar, Masoud Hajarian
{"title":"On sign function of tensors with Einstein product and its application in solving Yang–Baxter tensor equation","authors":"Raziyeh Erfanifar, Masoud Hajarian","doi":"10.1007/s40314-024-02892-3","DOIUrl":"https://doi.org/10.1007/s40314-024-02892-3","url":null,"abstract":"<p>In recent years, tensor problems have been studied in multiple fields of science and engineering including applied mathematics, the theory of completely integrable quantum, data mining, statistics, physics, chemistry, machine learning, medical engineering, and others. In machine learning, the word tensor informally refers to two different concepts that organize and represent data. In this work, at first, the concept of the sign function of a tensor is developed using the sign function of a matrix. Then, we propose an iterative method to find the sign function of a tensor. We prove that the order of convergence of the proposed method is three. Finally, we extend the iterative method for solving the Young–Baxter equation, which has many applications in fully integrable quantum theory, classical systems, and exactly solvable models of statistical physics. The accuracy and effectiveness of the proposed method in comparison to well-known methods are demonstrated by various numerical examples.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"46 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177996","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
Inertial methods for split common fixed point problems: application to binary classification in machine learning 分割常见定点问题的惯性方法：应用于机器学习中的二元分类
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-15 DOI: 10.1007/s40314-024-02876-3
M. Eslamian, A. Kamandi, A. Tahmasbi
{"title":"Inertial methods for split common fixed point problems: application to binary classification in machine learning","authors":"M. Eslamian, A. Kamandi, A. Tahmasbi","doi":"10.1007/s40314-024-02876-3","DOIUrl":"https://doi.org/10.1007/s40314-024-02876-3","url":null,"abstract":"<p>The aim of this paper is to introduce a new two-step inertial method for approximating a solution to a generalized split common fixed point problem, which is a unique solution to a variational inequality problem. We establish a strong convergence theorem for the sequence generated by the algorithm. We explore various special cases related to fundamental problems, including the split feasibility problem, the split common null point problem, and the constrained convex minimization problem. To demonstrate the efficacy and performance of our proposed algorithm, we apply it to a practical scenario involving support vector machines for binary classification. The algorithm is employed on diverse datasets sourced from the UC Irvine Machine Learning Repository, serving as the training set.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"16 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177999","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
Eberlein almost periodic solutions for some evolution equations with monotonicity 一些具有单调性的演化方程的埃伯林几乎周期解
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-15 DOI: 10.1007/s40314-024-02875-4
El Hadi Ait Dads, Brahim Es-Sebbar, Samir Fatajou, Zakaria Zizi
{"title":"Eberlein almost periodic solutions for some evolution equations with monotonicity","authors":"El Hadi Ait Dads, Brahim Es-Sebbar, Samir Fatajou, Zakaria Zizi","doi":"10.1007/s40314-024-02875-4","DOIUrl":"https://doi.org/10.1007/s40314-024-02875-4","url":null,"abstract":"<p>This paper investigates the existence of Eberlein weakly almost periodic solutions for differential equations of the form <span>(u'=Au+f(t))</span> and <span>(u'=A(t)u+f(t))</span>. In the first scenario, when <i>A</i> generates a strongly asymptotically semigroup, we establish the existence of Eberlein-weakly almost periodic solutions, thereby extending and improving a previous result in Zaidman(Ann Univ Ferrara 14(1): 29–34, 1969). In the second case, we consider a more general situation where <i>A</i>(<i>t</i>) is a (possibly nonlinear) operator satisfying a monotony condition. Unlike most existing works in the literature, our approach does not rely on tools of exponential dichotomy and Lipschitz nonlinearity. Lastly, we illustrate the practical relevance of our findings by presenting real-world models, including a hematopoiesis model, that exemplify the key findings. A numerical simulation is also provided.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"44 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177998","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
Large time behavior of 3D functional Brinkman–Forchheimer equations with delay term 带延迟项的三维布林克曼-福克海默函数方程的大时间行为
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-14 DOI: 10.1007/s40314-024-02893-2
Rong Yang, Xin-Guang Yang, Lu-Bin Cui, Jinyun Yuan
{"title":"Large time behavior of 3D functional Brinkman–Forchheimer equations with delay term","authors":"Rong Yang, Xin-Guang Yang, Lu-Bin Cui, Jinyun Yuan","doi":"10.1007/s40314-024-02893-2","DOIUrl":"https://doi.org/10.1007/s40314-024-02893-2","url":null,"abstract":"<p>The relationship is studied here between the 3D incompressible Brinkman–Forchheimer problem with delay and its generalized steady state. First, with some restrictive condition on the delay term, the global well-posedness of 3D Brinkman–Forchheimer problem and its steady state problem are obtained by compactness method and Brouwer fixed point method respectively. Then the global <span>(textbf{L}^{p}~ (2le p&lt;infty ))</span> decay estimates are established for weak solution of non-autonomous Brinkman–Forchheimer equations with delay by using a retarded integral inequality. The global decay estimates can be proved for strong solution as well. Finally, the exponential stability property is investigated for weak solution of the 3D non-autonomous Brinkman–Forchheimer problem by a direct approach and also for the autonomous system by using a retarded integral inequality. Furthermore, the Razumikhin approach is utilized to achieve the asymptotic stability for strong solution of autonomous system under a relaxed restriction.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"108 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142178002","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
Dynamic analysis of the fractional-order logistic equation with two different delays 具有两种不同延迟的分数阶逻辑方程的动态分析
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-13 DOI: 10.1007/s40314-024-02877-2
H. A. A. El-Saka, D. El. A. El-Sherbeny, A. M. A. El-Sayed
{"title":"Dynamic analysis of the fractional-order logistic equation with two different delays","authors":"H. A. A. El-Saka, D. El. A. El-Sherbeny, A. M. A. El-Sayed","doi":"10.1007/s40314-024-02877-2","DOIUrl":"https://doi.org/10.1007/s40314-024-02877-2","url":null,"abstract":"<p>In this paper, we analyze the stability and Hopf bifurcation of the fractional-order logistic equation with two different delays <span>(tau _{1}, tau _{2}&gt;0)</span>: <span>(D^{alpha }y(t)=rho y(t-tau _{1})left( 1-y(t-tau _{2})right) )</span>, <span>(t&gt;0)</span>, <span>(rho &gt;0)</span>. We describe stability regions by using critical curves. We explore how the fractional order <span>(alpha )</span>, <span>(rho )</span>, and time delays influence the stability and Hopf bifurcation of the model. Then, by choosing <span>(rho )</span>, fractional order <span>(alpha )</span>, and time delays as bifurcation parameters, the existence of Hopf bifurcation is studied. An Adams-type predictor–corrector method is extended to solve fractional-order differential equations involving two different delays. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of theoretical results.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"152 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142178001","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 analysis of a class of generalized Chua’s systems with infinitely many attractors 一类具有无限多吸引子的广义蔡氏系统的动力学分析
IF 2.6 3区 数学
Computational and Applied Mathematics Pub Date : 2024-08-12 DOI: 10.1007/s40314-024-02833-0
Manyu Zhao, Qigui Yang, Xu Zhang
{"title":"Dynamical analysis of a class of generalized Chua’s systems with infinitely many attractors","authors":"Manyu Zhao, Qigui Yang, Xu Zhang","doi":"10.1007/s40314-024-02833-0","DOIUrl":"https://doi.org/10.1007/s40314-024-02833-0","url":null,"abstract":"<p>The study of the existence of finitely many chaotic attractors in the Chua’s system is a classical topic. In this article, a class of generalized Chua’s systems is introduced, where the nonlinear items are extended by a type of polynomial functions. The existence of infinitely many chaotic attractors is studied, which can not be observed in the classical Chua’s system. A lot of interesting dynamical behavior can be obtained in this kind of systems under certain conditions: (i) the coexistence of infinitely many self-excited attractors; (ii) the existence of multi-scroll attractors as well as strange dynamics with growing-scroll, where growing-scroll refers to the number of the scrolls of the attractors is increasing as time is increasing; (iii) the coexistence of infinitely many hidden attractors. Furthermore, the circuit simulations for two examples from this kind of generalized Chua’s systems illustrate the possible existence of infinitely many hidden and multi-scroll attractors under certain conditions.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"30 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944481","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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