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‘Incomplete’ Pál type interpolation problems on zeros of polynomials with complex coefficients 关于复系数多项式零点的 "不完全 "帕尔型插值问题
Examples and Counterexamples Pub Date : 2024-01-05 DOI: 10.1016/j.exco.2023.100132
Poornima Tiwari , A.K. Pathak
{"title":"‘Incomplete’ Pál type interpolation problems on zeros of polynomials with complex coefficients","authors":"Poornima Tiwari ,&nbsp;A.K. Pathak","doi":"10.1016/j.exco.2023.100132","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100132","url":null,"abstract":"<div><p>We termed the Pál type interpolation problem as PTIP. Here we studied the regularity of <span><math><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span>-PTIP and <span><math><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></math></span>-PTIP, where we omitted a real or complex node from a set of zeros of polynomials with complex coefficients.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100132"},"PeriodicalIF":0.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X23000344/pdfft?md5=31254183438f8f7872d17f7a05aaaad5&pid=1-s2.0-S2666657X23000344-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139107245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Effect of local fractional derivatives on Riemann curvature tensor 局部分数导数对黎曼曲率张量的影响
Examples and Counterexamples Pub Date : 2024-01-02 DOI: 10.1016/j.exco.2023.100134
Muhittin Evren Aydin
{"title":"Effect of local fractional derivatives on Riemann curvature tensor","authors":"Muhittin Evren Aydin","doi":"10.1016/j.exco.2023.100134","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100134","url":null,"abstract":"<div><p>In this paper, we give a main example indicating the ineffectiveness of the local fractional derivatives on the Riemann curvature tensor that is a common tool in calculating curvature of a Riemannian manifold. For this, first we introduce a general local fractional derivative operator that involves the mostly used ones in the literature as conformable, alternative, truncated <span><math><mrow><mi>M</mi><mo>−</mo></mrow></math></span> and <span><math><mrow><mi>V</mi><mo>−</mo></mrow></math></span>fractional derivatives. Then, according to this general operator, a particular Riemannian metric on the real affine space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> that is different from the Euclidean one is defined. In conclusion, our main example states that the Riemann curvature tensor of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> endowed with this particular metric is identically 0, that is, one is locally isometric to Euclidean space.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100134"},"PeriodicalIF":0.0,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X23000368/pdfft?md5=cdf1658da9063967d38270f28537f406&pid=1-s2.0-S2666657X23000368-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139100860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a convex combination of Lotka–Volterra operators 关于洛特卡-伏特拉算子的凸组合
Examples and Counterexamples Pub Date : 2023-12-29 DOI: 10.1016/j.exco.2023.100133
Farrukh Mukhamedov , Chin Hee Pah , Azizi Rosli
{"title":"On a convex combination of Lotka–Volterra operators","authors":"Farrukh Mukhamedov ,&nbsp;Chin Hee Pah ,&nbsp;Azizi Rosli","doi":"10.1016/j.exco.2023.100133","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100133","url":null,"abstract":"<div><p>We consider a convex combination of two classes of Lotka–Volterra operators defined on 2-dimensional simplex. Earlier, the dynamics of a particular case of the considered operators has been investigated. However, its bijective property was not studied. In this paper, we are able to establish that such maps are homeomorphism of the simplex.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100133"},"PeriodicalIF":0.0,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X23000356/pdfft?md5=07391a1148694cb6898e73ab372d547e&pid=1-s2.0-S2666657X23000356-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139100859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New examples of self-dual near-extremal ternary codes of length 48 derived from 2-(47,23,11) designs 从 2-(47,23,11) 设计衍生出长度为 48 的自双近极三元码的新实例
Examples and Counterexamples Pub Date : 2023-12-15 DOI: 10.1016/j.exco.2023.100130
Sanja Rukavina , Vladimir D. Tonchev
{"title":"New examples of self-dual near-extremal ternary codes of length 48 derived from 2-(47,23,11) designs","authors":"Sanja Rukavina ,&nbsp;Vladimir D. Tonchev","doi":"10.1016/j.exco.2023.100130","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100130","url":null,"abstract":"<div><p>In a recent paper (Araya and Harada, 2023), Araya and Harada gave examples of self-dual near-extremal ternary codes of length 48 for 145 distinct values of the number <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>12</mn></mrow></msub></math></span> of codewords of minimum weight 12, and raised the question about the existence of codes for other values of <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>12</mn></mrow></msub></math></span>. In this note, we use symmetric 2-<span><math><mrow><mo>(</mo><mn>47</mn><mo>,</mo><mn>23</mn><mo>,</mo><mn>11</mn><mo>)</mo></mrow></math></span> designs with an automorphism group of order 6 to construct self-dual near-extremal ternary codes of length 48 for 150 new values of <span><math><msub><mrow><mi>A</mi></mrow><mrow><mn>12</mn></mrow></msub></math></span>.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100130"},"PeriodicalIF":0.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X23000320/pdfft?md5=d212aa3ada7931c19aa8f5ca886b223c&pid=1-s2.0-S2666657X23000320-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138656393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On some topological indices of zero divisor graphs of direct product of three finite fields 论三个有限域直积零除子图的一些拓扑指数
Examples and Counterexamples Pub Date : 2023-12-08 DOI: 10.1016/j.exco.2023.100129
Subhash Mallinath Gaded, Nithya Sai Narayana
{"title":"On some topological indices of zero divisor graphs of direct product of three finite fields","authors":"Subhash Mallinath Gaded,&nbsp;Nithya Sai Narayana","doi":"10.1016/j.exco.2023.100129","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100129","url":null,"abstract":"<div><p>In this paper, we determine some degree-based topological indices, such as the Sombor index, the first and second Zagreb indices, the forgotten topological index, the Narumi–Katayama index, the first and second multiplicative Zagreb indices, the atom-bond connectivity index, and eccentricity-based topological indices such as total eccentricity, the first and second Zagreb eccentricity indices, and the eccentricity connectivity index of the zero divisor graph with vertex set non-zero zero divisors of the reduced ring of the direct product of three finite fields.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"5 ","pages":"Article 100129"},"PeriodicalIF":0.0,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X23000319/pdfft?md5=8d93cb32e7a18cf629d5d68fa7ae9cda&pid=1-s2.0-S2666657X23000319-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138557836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamical behavior of fractional order SEIR epidemic model with multiple time delays and its stability analysis 多时滞分数阶SEIR流行病模型的动力学行为及其稳定性分析
Examples and Counterexamples Pub Date : 2023-12-01 DOI: 10.1016/j.exco.2023.100128
Subrata Paul , Animesh Mahata , Supriya Mukherjee , Prakash Chandra Mali , Banamali Roy
{"title":"Dynamical behavior of fractional order SEIR epidemic model with multiple time delays and its stability analysis","authors":"Subrata Paul ,&nbsp;Animesh Mahata ,&nbsp;Supriya Mukherjee ,&nbsp;Prakash Chandra Mali ,&nbsp;Banamali Roy","doi":"10.1016/j.exco.2023.100128","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100128","url":null,"abstract":"<div><p>With multiple time delays, we investigated a Caputo fractional order dynamical system involving susceptible, exposed, infected, and recovered individuals. Positivity and boundedness are also theoretically demonstrated using Laplace transform and Mittag-Leffler function. The stability of the disease-free and epidemic equilibrium points has been studied for both delayed and non-delayed model. For generating numerical solutions to the model system, we used the Adam-Bashforth-Moulton predictor-corrector technique. With the help of MATLAB (2018a), we were able to conduct graphical demonstrations and numerical simulations. The system displays Hopf bifurcation and the solutions are no longer periodic beyond a certain threshold value of the time delay parameters.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"4 ","pages":"Article 100128"},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X23000307/pdfft?md5=edab84a58f8ff0eb993a5fb57ba503c9&pid=1-s2.0-S2666657X23000307-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138480350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exact solutions of a variable coefficient KdV equation: Power law in time-coefficients 变系数KdV方程的精确解:时间系数的幂律
Examples and Counterexamples Pub Date : 2023-11-21 DOI: 10.1016/j.exco.2023.100126
Motlatsi Molati
{"title":"Exact solutions of a variable coefficient KdV equation: Power law in time-coefficients","authors":"Motlatsi Molati","doi":"10.1016/j.exco.2023.100126","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100126","url":null,"abstract":"<div><p>The Lie symmetry analysis of a power law in-time coefficients Korteweg–de Vries (KdV) equation is performed with the aim of specifying the model parameters (powers of <span><math><mi>t</mi></math></span>). That is, the symmetries of the resulting subclasses of the underlying equation are obtained. Further, symmetry reductions and some exact solutions are obtained.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"4 ","pages":"Article 100126"},"PeriodicalIF":0.0,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X23000289/pdfft?md5=e7b499b9a817b8e0282ff728e9b6db5f&pid=1-s2.0-S2666657X23000289-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138395175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Identification of brain tumors based on digitized parameters from magnetic resonance imaging results 基于磁共振成像结果数字化参数的脑肿瘤识别
Examples and Counterexamples Pub Date : 2023-11-19 DOI: 10.1016/j.exco.2023.100125
A.M. Al-Ansi , M. Almadi , V. Ryabtsev , T. Utkina
{"title":"Identification of brain tumors based on digitized parameters from magnetic resonance imaging results","authors":"A.M. Al-Ansi ,&nbsp;M. Almadi ,&nbsp;V. Ryabtsev ,&nbsp;T. Utkina","doi":"10.1016/j.exco.2023.100125","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100125","url":null,"abstract":"<div><p>A methodology is proposed for identifying brain tumors by dividing the database into four parts. The results obtained from the study of sample specimens for each type of brain tumor showed a high degree of similarity in recognition. This methodology can be applied in healthcare facilities to improve the accuracy of disease diagnosis.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"4 ","pages":"Article 100125"},"PeriodicalIF":0.0,"publicationDate":"2023-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X23000277/pdfft?md5=f3100a0e2172cdec05b25d019b3236c5&pid=1-s2.0-S2666657X23000277-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138395174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On two Kuznetsov’s conjectures 关于库兹涅佐夫的两个猜想
Examples and Counterexamples Pub Date : 2023-11-15 DOI: 10.1016/j.exco.2023.100127
Florian Oschmann
{"title":"On two Kuznetsov’s conjectures","authors":"Florian Oschmann","doi":"10.1016/j.exco.2023.100127","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100127","url":null,"abstract":"<div><p>We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"4 ","pages":"Article 100127"},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X23000290/pdfft?md5=3d37c77be6fcc33ff02da1f947a414bc&pid=1-s2.0-S2666657X23000290-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136572155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A family of c-cyclic graphs with a Θ(|V|2log|V|) Kirchhoff index 具有Θ(|V|2log|V|) Kirchhoff指数的c-循环图族
Examples and Counterexamples Pub Date : 2023-10-07 DOI: 10.1016/j.exco.2023.100124
José Luis Palacios
{"title":"A family of c-cyclic graphs with a Θ(|V|2log|V|) Kirchhoff index","authors":"José Luis Palacios","doi":"10.1016/j.exco.2023.100124","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100124","url":null,"abstract":"<div><p>By means of a recurrence, we provide a family of <span><math><mi>c</mi></math></span>-cyclic graphs, <span><math><mrow><mi>c</mi><mo>≥</mo><mn>0</mn></mrow></math></span>, whose Kirchhoff index is <span><math><mrow><mi>Θ</mi><mrow><mo>(</mo><msup><mrow><mrow><mo>|</mo><mi>V</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>log</mo><mrow><mo>|</mo><mi>V</mi><mo>|</mo></mrow><mo>)</mo></mrow></mrow></math></span>.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"4 ","pages":"Article 100124"},"PeriodicalIF":0.0,"publicationDate":"2023-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49883265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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