Examples and Counterexamples最新文献

{"title":"On the non-existence of a discrete power series distribution with a constant coefficient of variation","authors":"Rahul Bhattacharya ,&nbsp;Taranga Mukherjee","doi":"10.1016/j.exco.2023.100104","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100104","url":null,"abstract":"<div><p>Non-existence of distributions with constant coefficient of variation(CV) is investigated within the discrete Power Series and Modified Power Series families of distributions. The development is used to revisit and comment on the problem of existence of a better but biased estimator.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"3 ","pages":"Article 100104"},"PeriodicalIF":0.0,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50203798","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}

{"title":"Partial groups, examples and applications","authors":"Solomon Jekel","doi":"10.1016/j.exco.2023.100103","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100103","url":null,"abstract":"<div><p>Partial Group structures occur naturally in several topological and geometrical contexts. We formulate the basic definitions, and present some results and examples. The objective is to provide a step toward the development of a theory of partial groups, and to motivate the search for further applications.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"3 ","pages":"Article 100103"},"PeriodicalIF":0.0,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50203799","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}

{"title":"Generalized commutative Jacobsthal quaternions and some matrices","authors":"Dorota Bród,&nbsp;Anetta Szynal-Liana","doi":"10.1016/j.exco.2023.100102","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100102","url":null,"abstract":"<div><p>In this paper, some examples of matrix generators for generalized commutative Jacobsthal quaternions were given. The generating matrices are useful tools for the number sequences satisfying a recurrence relation. They can be used for an algebraic representation and for obtaining some identities.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"3 ","pages":"Article 100102"},"PeriodicalIF":0.0,"publicationDate":"2023-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50180783","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}

{"title":"Rainbow Cascades and permutation-labeled hypercube tilings","authors":"Lon Mitchell","doi":"10.1016/j.exco.2023.100099","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100099","url":null,"abstract":"<div><p>We explore a new view of the Rainbow Cascades Conjecture using permutations. Infinitely many new 6-satisfactory colorings are found, and evidence is provided that suggests only finitely many 7-satisfactory colorings exist.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"3 ","pages":"Article 100099"},"PeriodicalIF":0.0,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50203718","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}

{"title":"An upper bound for difference of energies of a graph and its complement","authors":"Harishchandra S. Ramane ,&nbsp;B. Parvathalu ,&nbsp;K. Ashoka","doi":"10.1016/j.exco.2023.100100","DOIUrl":"https://doi.org/10.1016/j.exco.2023.100100","url":null,"abstract":"<div><p>The <span><math><mi>A</mi></math></span>-energy of a graph <span><math><mi>G</mi></math></span>, denoted by <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>A</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span>, is defined as sum of the absolute values of eigenvalues of adjacency matrix of <span><math><mi>G</mi></math></span>. Nikiforov in Nikiforov (2016) proved that <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>A</mi></mrow></msub><mrow><mo>(</mo><mover><mrow><mi>G</mi></mrow><mo>¯</mo></mover><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>A</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≤</mo><mn>2</mn><msub><mrow><mover><mrow><mi>μ</mi></mrow><mo>¯</mo></mover></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>A</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>A</mi></mrow></msub><mrow><mo>(</mo><mover><mrow><mi>G</mi></mrow><mo>¯</mo></mover><mo>)</mo></mrow><mo>≤</mo><mn>2</mn><msub><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></span> for any graph <span><math><mi>G</mi></math></span> and posed a problem to find best possible upper bound for <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>A</mi></mrow></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>−</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>A</mi></mrow></msub><mrow><mo>(</mo><mover><mrow><mi>G</mi></mrow><mo>¯</mo></mover><mo>)</mo></mrow></mrow></math></span>, where <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><mover><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mo>¯</mo></mover></math></span> are the largest adjacency eigenvalues of <span><math><mi>G</mi></math></span> and its complement <span><math><mover><mrow><mi>G</mi></mrow><mo>¯</mo></mover></math></span> respectively. We attempt to provide an answer by giving an improved upper bound on a class of graphs where regular graphs become particular case. As a consequence, it is proved that there is no strongly regular graph with negative eigenvalues greater than <span><math><mrow><mo>−</mo><mn>1</mn></mrow></math></span>. The obtained results also improves some of the other existing results.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"3 ","pages":"Article 100100"},"PeriodicalIF":0.0,"publicationDate":"2023-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50203715","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}

{"title":"Editorial - Recent Fails and Findings of Numerical Methods in Mechanics","authors":"Fleurianne Bertrand,&nbsp;Katrin Mang","doi":"10.1016/j.exco.2022.100098","DOIUrl":"https://doi.org/10.1016/j.exco.2022.100098","url":null,"abstract":"","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"3 ","pages":"Article 100098"},"PeriodicalIF":0.0,"publicationDate":"2022-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50203804","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}

{"title":"All minimal [9,4]2-codes are hyperbolic quadrics","authors":"Valentino Smaldore","doi":"10.1016/j.exco.2022.100097","DOIUrl":"https://doi.org/10.1016/j.exco.2022.100097","url":null,"abstract":"<div><p>Minimal codes are being intensively studied in last years. <span><math><msub><mrow><mrow><mo>[</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>]</mo></mrow></mrow><mrow><mi>q</mi></mrow></msub></math></span>-minimal linear codes are in bijection with strong blocking sets of size <span><math><mi>n</mi></math></span> in <span><math><mrow><mi>P</mi><mi>G</mi><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>,</mo><mi>q</mi><mo>)</mo></mrow></mrow></math></span> and a lower bound for the size of strong blocking sets is given by <span><math><mrow><mrow><mo>(</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>q</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>≤</mo><mi>n</mi></mrow></math></span>. In this note we show that all strong blocking sets of length 9 in <span><math><mrow><mi>P</mi><mi>G</mi><mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> are the hyperbolic quadrics <span><math><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mo>+</mo></mrow></msup><mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"3 ","pages":"Article 100097"},"PeriodicalIF":0.0,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50203717","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}

{"title":"Families of finite sets in which no set is covered by the union of the others","authors":"Guillermo Alesandroni","doi":"10.1016/j.exco.2022.100095","DOIUrl":"https://doi.org/10.1016/j.exco.2022.100095","url":null,"abstract":"<div><p>Let <span><math><mi>ℱ</mi></math></span> be a finite nonempty family of finite nonempty sets. We prove the following: (1) <span><math><mi>ℱ</mi></math></span> satisfies the condition of the title if and only if for every pair of distinct subfamilies <span><math><mrow><mo>{</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>}</mo></mrow></math></span>, <span><math><mrow><mo>{</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>}</mo></mrow></math></span> of <span><math><mi>ℱ</mi></math></span>, <span><math><mrow><munderover><mrow><mo>⋃</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>r</mi></mrow></munderover><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>≠</mo><munderover><mrow><mo>⋃</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>s</mi></mrow></munderover><msub><mrow><mi>B</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></math></span>. (2) If <span><math><mi>ℱ</mi></math></span> satisfies the condition of the title, then the number of subsets of <span><math><mrow><munder><mrow><mo>⋃</mo></mrow><mrow><mi>A</mi><mo>∈</mo><mi>ℱ</mi></mrow></munder><mi>A</mi></mrow></math></span> containing at least one set of <span><math><mi>ℱ</mi></math></span> is odd. We give two applications of these results, one to number theory and one to commutative algebra.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"3 ","pages":"Article 100095"},"PeriodicalIF":0.0,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50203716","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}

{"title":"Augmentation of magnetohydrodynamic nanofluid flow through a permeable stretching sheet employing Machine learning algorithm","authors":"P. Priyadharshini,&nbsp;M. Vanitha Archana","doi":"10.1016/j.exco.2022.100093","DOIUrl":"https://doi.org/10.1016/j.exco.2022.100093","url":null,"abstract":"<div><p>An incompressible MHD nanofluid boundary layer flow over a vertical stretching permeable surface employing Buongiorno’s design investigated by considering the convective states. The Brownian motion and thermophoresis effects are used to implement the nanofluid model. Operating the similarity transmutations, to transform the governing partial differential equations into ordinary differential equations consisting of the momentum, energy, and concentration fields and later worked by using a program written together with the stiffness shifting in Wolfram Language. The consequences of various physical parameters on the velocity, temperature, and concentration fields are analyzed, such as magnetic parameter <span><math><mi>M</mi></math></span>, Brownian motion parameter <span><math><mrow><mi>N</mi><mi>b</mi></mrow></math></span>, thermophoresis parameter <span><math><mrow><mi>N</mi><mi>t</mi></mrow></math></span>, Lewis number <span><math><mrow><mi>L</mi><mi>e</mi></mrow></math></span>, temperature Biot number <span><math><mrow><mi>B</mi><msub><mrow><mi>i</mi></mrow><mrow><mi>θ</mi></mrow></msub></mrow></math></span>, concentration Biot number <span><math><mrow><mi>B</mi><msub><mrow><mi>i</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></mrow></math></span>, and suction parameter <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>w</mi></mrow></msub></math></span>. Furthermore, the Skin friction coefficient, local Nusselt, and local Sherwood numbers concerning magnetic parameter for various values of physical parameters (i.e. <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>w</mi></mrow></msub></math></span>, <span><math><mrow><mi>N</mi><mi>b</mi></mrow></math></span>) are obtained graphically, then the outcome is validated with other recent works. Finally, introduced a new environment to employ machine learning by performing the sensitivity analysis based on the iterative method for predicting the Skin friction coefficient, reduced Nusselt number, and Sherwood number with respect to magnetic parameter for suction parameter and Brownian motion parameter. Machine learning algorithms provide a strong and quick data processing structure to enhance the actual research procedures and industrial application of fluid mechanics. These techniques have been upgraded and organized for fluid flow characteristics. The present optimization process has the potential for a new perspective on the metallurgical process, heat exchangers in electronics, and some medicinal applications.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"3 ","pages":"Article 100093"},"PeriodicalIF":0.0,"publicationDate":"2022-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50203719","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}

{"title":"Algebraic constructions of group divisible designs","authors":"Shyam Saurabh ,&nbsp;Kishore Sinha","doi":"10.1016/j.exco.2022.100094","DOIUrl":"https://doi.org/10.1016/j.exco.2022.100094","url":null,"abstract":"<div><p>Some series of Group divisible designs using generalized Bhaskar Rao designs over Dihedral, Symmetric and Alternating groups are obtained.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"3 ","pages":"Article 100094"},"PeriodicalIF":0.0,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50203720","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}