Journal of Mathematics最新文献

{"title":"On Implicit Atangana–Baleanu–Caputo Fractional Integro-Differential Equations with Delay and Impulses","authors":"Panjaiyan Karthikeyann, Sadhasivam Poornima, Kulandhaivel Karthikeyan, Chanon Promsakon, Thanin Sitthiwirattham","doi":"10.1155/2024/5531984","DOIUrl":"https://doi.org/10.1155/2024/5531984","url":null,"abstract":"In this paper, we study the existence and uniqueness of solutions for impulsive Atangana-Baleanu-Caputo <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 43.0822 11.5564\" width=\"43.0822pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,4.498,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,15.613,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,27.963,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,38.324,0)\"></path></g></svg> fractional integro-differential equations with boundary conditions. Schaefer’s fixed point theorem and Banach contraction principle are used to prove the existence and uniqueness results. An example is presented to illustrate the results.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"55 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New Proof of the Property of Stirling Number Based on Fubini Polynomials","authors":"Li Wang, Xiaoge Liu","doi":"10.1155/2024/4461499","DOIUrl":"https://doi.org/10.1155/2024/4461499","url":null,"abstract":"The main purpose of this article is using the elementary methods and the properties of the Fubini polynomials to study the congruence properties of a signless Stirling number of the first kind and solve a conjecture proposed by J. H. Zhao and Z. Y. Chen. Without a doubt, the novel approach employed in this work provides a useful reference for researching the congruence properties of other nonlinear binary recursive sequences.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"49 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction","authors":"Sheng Ma, Qin Jiang, Zaiqiang Ku","doi":"10.1155/2024/3692883","DOIUrl":"https://doi.org/10.1155/2024/3692883","url":null,"abstract":"The minimum average variance estimation (MAVE) method has proven to be an effective approach to sufficient dimension reduction. In this study, we apply the computationally efficient optimization algorithm named alternating direction method of multipliers (ADMM) to a particular approach (MAVE or minimum average variance estimation) to the problem of sufficient dimension reduction (SDR). Under some assumptions, we prove that the iterative sequence generated by ADMM converges to some point of the associated augmented Lagrangian function. Moreover, that point is stationary. It also presents some numerical simulations on synthetic data to demonstrate the computational efficiency of the algorithm.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"28 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140930073","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some Conditions and Perturbation Theorem of Irregular Wavelet/Gabor Frames in Sobolev Space","authors":"Hui-Min Liu, Yu Tian","doi":"10.1155/2024/9932668","DOIUrl":"https://doi.org/10.1155/2024/9932668","url":null,"abstract":"Due to its potential applications in image restoration and deep convolutional neural networks, the study of irregular frames has interested some researchers. This paper addresses irregular wavelet systems (IWSs) and irregular Gabor systems (IGSs) in Sobolev space <span><svg height=\"12.2245pt\" style=\"vertical-align:-2.268109pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.95639 33.8159 12.2245\" width=\"33.8159pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,10.923,-5.741)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,14.901,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,19.399,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,29.11,0)\"></path></g></svg>.</span> We obtain the sufficient and necessary conditions for IWS and IGS to be frames. By applying these conditions, we also derive the characterizations of IWS and IGS to be frames. Finally, we discuss the perturbation theorem of irregular wavelet frames (IWFs) and irregular Gabor frames (IGFs). We also provided some examples to support our results.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"56 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140929978","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Subgradient Extragradient Method for Finite Lipschitzian Demicontractions and Variational Inequality Problems in a Hilbert Space","authors":"Sarawut Suwannaut","doi":"10.1155/2024/7793048","DOIUrl":"https://doi.org/10.1155/2024/7793048","url":null,"abstract":"In this research, the modified subgradient extragradient method and <span><svg height=\"8.68572pt\" style=\"vertical-align:-0.0498209pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 9.95144 8.68572\" width=\"9.95144pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg>-</span>mapping generated by a finite family of finite Lipschitzian demicontractions are introduced. Then, a strong convergence theorem for finding a common element of the common fixed point set of finite Lipschitzian demicontraction mappings and the common solution set of variational inequality problems is established. Furthermore, numerical examples are given to support the main theorem.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"19 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modern Approach in Pattern Recognition Using Circular Fermatean Fuzzy Similarity Measure for Decision Making with Practical Applications","authors":"Revathy Aruchsamy, Inthumathi Velusamy, Prasantha Bharathi Dhandapani, Suleman Nasiru, Christophe Chesneau","doi":"10.1155/2024/6503747","DOIUrl":"https://doi.org/10.1155/2024/6503747","url":null,"abstract":"The circular Fermatean fuzzy (CFF) set is an advancement of the Fermatean fuzzy (FF) set and the interval-valued Fermatean fuzzy (IVFF) set which deals with uncertainty. The CFF set is represented as a circle of radius ranging from 0 to <svg height=\"13.1484pt\" style=\"vertical-align:-1.3645pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.7839 16.3323 13.1484\" width=\"16.3323pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,-1.543)\"></path></g><rect height=\"0.65243\" width=\"6.26339\" x=\"9.96925\" y=\"-11.0816\"></rect><g transform=\"matrix(.013,0,0,-0.013,9.969,0)\"></path></g></svg> with the center at the degree of association (DA) and degree of nonassociation (DNA). If multiple people are involved in making decisions, the CFF set, as an alternative to the FF and IVFF sets, can deal with ambiguity more effectively by encircling the decision values within a circle rather than taking an average. Using algorithms, a pattern can be observed computationally or visually. Machine learning algorithm utilizes pattern recognition as an instrument for identifying patterns and also similarity measure (SM) is a beneficial pattern recognition tool used to classify items, discover variations, and make future predictions for decision making. In this work, we introduce the CFF cosine and Dice similarity measures (CFFDMs and CFFSMs), and their properties are studied. Unlike traditional approaches of decision making, which emphasize a single number, the proposed CFFSMs observe the pattern over the circular region to help in dealing with uncertainty more effectively. We introduce an innovative decision-making method in the FF setting. Available bank loans and applicants’ eligibility levels are represented as CFF set using their FF criteria and are taken as loan patterns and customer eligibility patterns. The loan is allocated to the applicant by measuring the CFFCSM and CFFDSM between the two patterns. Also, laptops are suggested to the customers by measuring the similarity between specification pattern and requirement pattern. The correctness and consistency of the proposed models are ensured by comparison analysis and graphical simulations of the input and similarity CFFNs.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"18 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global Well-Posedness and Convergence Results to a 3D Regularized Boussinesq System in Sobolev Spaces","authors":"Ridha Selmi, Shahah Almutairi","doi":"10.1155/2024/4495266","DOIUrl":"https://doi.org/10.1155/2024/4495266","url":null,"abstract":"We consider a regularized periodic three-dimensional Boussinesq system. For a mean free initial temperature, we use the coupling between the velocity and temperature to close the energy estimates independently of time. This allows proving the existence of a global in time unique weak solution. Also, we establish that this solution depends continuously on the initial data. Moreover, we prove that this solution converges to a Leray-Hopf weak solution of the three-dimensional Boussinesq system as the regularizing parameter vanishes.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"16 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Solution Matrix by IEVP under the Central Principle Submatrix Constraints","authors":"Vineet Bhatt, Manpreet Kaur, I. Ahmed M. AL-Hammadi, Sunil Kumar","doi":"10.1155/2024/7908231","DOIUrl":"https://doi.org/10.1155/2024/7908231","url":null,"abstract":"The <span><svg height=\"7.35473pt\" style=\"vertical-align:-0.3499303pt\" version=\"1.1\" viewbox=\"-0.0498162 -7.0048 17.063 7.35473\" width=\"17.063pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,9.432,0)\"></path></g></svg><span></span><svg height=\"7.35473pt\" style=\"vertical-align:-0.3499303pt\" version=\"1.1\" viewbox=\"19.9181838 -7.0048 6.703 7.35473\" width=\"6.703pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,19.968,0)\"><use xlink:href=\"#g113-111\"></use></g></svg></span> real matrix <svg height=\"8.68572pt\" style=\"vertical-align:-0.0498209pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 8.15071 8.68572\" width=\"8.15071pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg> is called centrosymmetric matrix if <span><svg height=\"10.2124pt\" style=\"vertical-align:-1.576501pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 19.289 10.2124\" width=\"19.289pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-81\"></use></g><g transform=\"matrix(.013,0,0,-0.013,11.658,0)\"></path></g></svg><span></span><svg height=\"10.2124pt\" style=\"vertical-align:-1.576501pt\" version=\"1.1\" viewbox=\"22.8711838 -8.6359 26.759 10.2124\" width=\"26.759pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,22.921,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,31.072,0)\"><use xlink:href=\"#g113-81\"></use></g><g transform=\"matrix(.013,0,0,-0.013,38.315,0)\"><use xlink:href=\"#g113-83\"></use></g><g transform=\"matrix(.013,0,0,-0.013,46.466,0)\"></path></g></svg><span></span></span> where <svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 8.28119 8.8423\" width=\"8.28119pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-83\"></use></g></svg> is permutation matrix with ones on cross diagonal (bottom left to top right) and zeroes elsewhere. In this article, the solvability conditions for left and right inverse eigenvalue problem (which is special case of inverse eigenvalue problem) under the submatrix constraint for generalized centrosymmetric matrices are derived, and the general solution is also given. In addition, we provide a feasible algorithm for computing the general solution, which is proved by a numerical example.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"24 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A New Statistical Approach Based on the Access of Electricity Application with Some Modified Control Charts","authors":"Riffat Jabeen, Mashhood Ahmad, Azam Zaka, Mahmoud M. Mansour, Abdussalam Aljadani, Enayat M. Abd Elrazik","doi":"10.1155/2024/6584791","DOIUrl":"https://doi.org/10.1155/2024/6584791","url":null,"abstract":"This article introduces a new probability model based on reflected parameter called the reflected Pareto (RP) distribution. The key properties of the RP model are investigated. A simulation study of the RP model is conducted to evaluate the performances of its estimators. A real-life application is considered to examine the performance of proposed model. The different criteria are discussed numerically as well as graphically to show the flexibility of the RP model. The exponential weighted moving average control charts based on the maximum likelihood and modified maximum likelihood estimators for the shape parameter of the RP distribution are obtained. Detailed simulation results of proposed charts are performed to examine and analyze the performance of these charts with three in-control average run length values and two sample sizes. Finally, the application of the proposed control charts is shown by considering a real-life data set.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"3 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Flag-Transitive 2- Designs Admitting a Two-Dimensional Projective Group","authors":"Suyun Ding, Yajie Wang, Xiaoqin Zhan","doi":"10.1155/2024/5521696","DOIUrl":"https://doi.org/10.1155/2024/5521696","url":null,"abstract":"The focus of this study is to classify flag-transitive 2-designs. We have come to the conclusion that if &lt;svg height=\"9.25986pt\" style=\"vertical-align:-0.2455397pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.01432 11.6478 9.25986\" width=\"11.6478pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,0,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt; is a nontrivial 2-design having block size 5 and &lt;svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 9.02496 8.8423\" width=\"9.02496pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,0,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt; is a two-dimensional projective special linear group which acts flag-transitively on &lt;svg height=\"9.25986pt\" style=\"vertical-align:-0.2455397pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.01432 11.6478 9.25986\" width=\"11.6478pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,0,0)\"&gt;&lt;use xlink:href=\"#g198-5\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt; with &lt;span&gt;&lt;svg height=\"11.7782pt\" style=\"vertical-align:-3.42938pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.34882 19.867 11.7782\" width=\"19.867pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,0,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,19.867,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,12.194,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span&gt;&lt;/span&gt;&lt;svg height=\"11.7782pt\" style=\"vertical-align:-3.42938pt\" version=\"1.1\" viewbox=\"25.5861838 -8.34882 6.415 11.7782\" width=\"6.415pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,25.636,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt; (mod 4), then &lt;svg height=\"9.25986pt\" style=\"vertical-align:-0.2455397pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.01432 11.6478 9.25986\" width=\"11.6478pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,0,0)\"&gt;&lt;use xlink:href=\"#g198-5\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt; is a 2-(11, 5, 2) design, a 2-(11, 5, 12) design, a 2-&lt;span&gt;&lt;svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 21.418 12.7178\" width=\"21.418pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,0,0)\"&gt;&lt;use xlink:href=\"#g113-41\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,4.498,0)\"&gt;&lt;use xlink:href=\"#g113-114\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,13.787,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span&gt;&lt;/span&gt;&lt;svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"24.2731838 -9.28833 9.204 12.7178\" width=\"9.204pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,24.323,0)\"&gt;&lt;use xlink:href=\"#g113-50\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,30.563,0)\"&gt;&lt;use xlink:href=\"#g113-45\"&gt;&lt;/use&gt;&lt;/g&gt;","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}