Experimental Mathematics最新文献

{"title":"A Computational View on the Non-degeneracy Invariant for Enriques Surfaces","authors":"Riccardo Moschetti, Franco Rota, L. Schaffler","doi":"10.1080/10586458.2022.2113576","DOIUrl":"https://doi.org/10.1080/10586458.2022.2113576","url":null,"abstract":". For an Enriques surface S , the non-degeneracy invariant nd( S ) retains information on the elliptic fibrations of S and its polarizations. In the current paper, we introduce a combinatorial version of the non-degeneracy invariant which depends on S together with a configuration of smooth rational curves, and gives a lower bound for nd( S ) . We provide a SageMath code that computes this combinatorial invariant and we apply it in several examples. First we identify a new family of nodal Enriques surfaces satisfying nd( S ) = 10 which are not general and with infinite automorphism group. We obtain lower bounds on nd( S ) for the Enriques surfaces with eight disjoint smooth rational curves studied by Mendes Lopes–Pardini. Finally, we recover Dolgachev and Kond¯o’s computation of the non-degeneracy invariant of the Enriques surfaces with finite automorphism group and provide additional information on the geometry of their elliptic fibrations.","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44113465","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":"Numerical Verification of the Birch and Swinnerton-Dyer Conjecture for Hyperelliptic Curves of Higher Genus over ℚ up to Squares","authors":"R. V. Bommel","doi":"10.1080/10586458.2019.1592035","DOIUrl":"https://doi.org/10.1080/10586458.2019.1592035","url":null,"abstract":"","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"31 1","pages":"138-145"},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/10586458.2019.1592035","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59683150","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":"Periodic Representations and Approximations of p-adic Numbers Via Continued Fractions","authors":"Stefano Barbero, Umberto Cerruti, N. Murru","doi":"10.1080/10586458.2021.2011491","DOIUrl":"https://doi.org/10.1080/10586458.2021.2011491","url":null,"abstract":"","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"56 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41285030","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":"Evidence of Random Matrix Corrections for the Large Deviations of Selberg’s Central Limit Theorem","authors":"E. Amzallag, L.-P. Arguin, E. Bailey, K. Huib, R. Rao","doi":"10.1080/10586458.2021.2011806","DOIUrl":"https://doi.org/10.1080/10586458.2021.2011806","url":null,"abstract":"<p><b>Abstract</b></p><p>Selberg’s central limit theorem states that the values of <span><noscript><img alt=\"\" src=\"/na101/home/literatum/publisher/tandf/journals/content/uexm20/0/uexm20.ahead-of-print/10586458.2021.2011806/20211220/images/uexm_a_2011806_ilm0001.gif\"/></noscript><img alt=\"\" data-formula-source='{\"type\" : \"image\", \"src\" : \"/na101/home/literatum/publisher/tandf/journals/content/uexm20/0/uexm20.ahead-of-print/10586458.2021.2011806/20211220/images/uexm_a_2011806_ilm0001.gif\"}' src=\"//:0\"/><span></span></span><span><img alt=\"\" data-formula-source='{\"type\" : \"mathjax\"}' src=\"//:0\"/><math display=\"inline\"><mrow><mtext>log</mtext><mo> </mo><mo>|</mo><mi>ζ</mi><mo stretchy=\"false\">(</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>+</mo><mi mathvariant=\"normal\">i</mi><mi>τ</mi><mo stretchy=\"false\">)</mo><mo>|</mo></mrow></math></span>, where <i>τ</i> is a uniform random variable on <span><noscript><img alt=\"\" src=\"/na101/home/literatum/publisher/tandf/journals/content/uexm20/0/uexm20.ahead-of-print/10586458.2021.2011806/20211220/images/uexm_a_2011806_ilm0002.gif\"/></noscript><img alt=\"\" data-formula-source='{\"type\" : \"image\", \"src\" : \"/na101/home/literatum/publisher/tandf/journals/content/uexm20/0/uexm20.ahead-of-print/10586458.2021.2011806/20211220/images/uexm_a_2011806_ilm0002.gif\"}' src=\"//:0\"/><span></span></span><span><img alt=\"\" data-formula-source='{\"type\" : \"mathjax\"}' src=\"//:0\"/><math display=\"inline\"><mrow><mo stretchy=\"false\">[</mo><mi>T</mi><mo>,</mo><mn>2</mn><mi>T</mi><mo stretchy=\"false\">]</mo></mrow></math></span>, are asymptotically distributed like a Gaussian random variable of mean 0 and standard deviation <span><noscript><img alt=\"\" src=\"/na101/home/literatum/publisher/tandf/journals/content/uexm20/0/uexm20.ahead-of-print/10586458.2021.2011806/20211220/images/uexm_a_2011806_ilm0003.gif\"/></noscript><img alt=\"\" data-formula-source='{\"type\" : \"image\", \"src\" : \"/na101/home/literatum/publisher/tandf/journals/content/uexm20/0/uexm20.ahead-of-print/10586458.2021.2011806/20211220/images/uexm_a_2011806_ilm0003.gif\"}' src=\"//:0\"/><span></span></span><span><img alt=\"\" data-formula-source='{\"type\" : \"mathjax\"}' src=\"//:0\"/><math display=\"inline\"><mrow><msqrt><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mtext>log</mtext><mo> </mo><mo> </mo><mtext>log</mtext><mo> </mo><mi>T</mi></mrow></msqrt></mrow></math></span>. It was conjectured by Radziwiłł that this distribution breaks down for values of order <span><noscript><img alt=\"\" src=\"/na101/home/literatum/publisher/tandf/journals/content/uexm20/0/uexm20.ahead-of-print/10586458.2021.2011806/20211220/images/uexm_a_2011806_ilm0004.gif\"/></noscript><img alt=\"\" data-formula-source='{\"type\" : \"image\", \"src\" : \"/na101/home/literatum/publisher/tandf/journals/content/uexm20/0/uexm20.ahead-of-print/10586458.2021.2011806/20211220/images/uexm_a_2011806_ilm0004.gif\"}' src=\"//:0\"/><span></span></span><span><img alt=\"\" data-formula-source='{\"type\" : \"mathjax\"}' src=\"//:0\"/><math displ","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"269 ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505181","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":"Teachers of socially maladjusted children and youth. Occupational burnout - sense of self-efficacy - teachers' life optimism. A comparative study.","authors":"Ewa Sygit-Kowalkowska","doi":"10.5114/cipp.2021.110855","DOIUrl":"10.5114/cipp.2021.110855","url":null,"abstract":"<p><strong>Background: </strong>The psychological specificity of the occupation of teachers in youth fostering centres (<i>Młodzieżowe Ośrodki Wychowawcze</i>, MOW) and youth psychotherapy centres (<i>Młodzieżowe Ośrodki Psychoterapii</i>, MOS) is rarely explored in empirical studies. As indicated in the literature, working in resocialization facilities (such as MOWs or MOSs) requires more effort expended in contacts with students. Study results indicate that teachers at greater risk of experiencing aggression are also at a greater risk of occupational burnout.</p><p><strong>Participants and procedure: </strong>The aim of the current study was to gather data on the intensity of occupational burnout among MOW/MOS teachers and public school teachers as well as to analyse the correlates and predictors of burnout. One hundred and sixty-nine people from two voivodeships in Poland took part in the study. The following measures were used in the study: the Life Orientation Test (LOT-R), the Generalized Self-Efficacy Scale (GSES) and the Link Burnout Questionnaire (LBQ).</p><p><strong>Results: </strong>Psychophysical exhaustion and a sense of a lack of self-efficacy among teachers are related to their workplace conditions. Longer job experience had a significant influence on the intensity of the individual aspects of occupational burnout and sense of self-efficacy. The current study did not reveal a significant influence of life optimism.</p><p><strong>Conclusions: </strong>The current study requires continuation, as detailed scientific analyses of this occupational group are still lacking. There is a need for further studies on the impact of occupational burnout on the effectiveness of teachers' pedagogical interventions.</p>","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"19 1","pages":"48-57"},"PeriodicalIF":1.0,"publicationDate":"2021-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10535544/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81703036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Schwarzian Versus a Family of Moving Parabolic Points","authors":"H. H. Rugh, L. Tan, Fei Yang","doi":"10.1080/10586458.2021.2011807","DOIUrl":"https://doi.org/10.1080/10586458.2021.2011807","url":null,"abstract":"","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43457509","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":"Short, Highly Imprimitive Words Yield Hyperbolic One-Relator Groups","authors":"Christopher H. Cashen, Charlotte Hoffmann","doi":"10.1080/10586458.2021.1982079","DOIUrl":"https://doi.org/10.1080/10586458.2021.1982079","url":null,"abstract":"We give experimental support for a conjecture of Louder and Wilton saying that words of imprimitivity rank greater than two yield hyperbolic one-relator groups.","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"95 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138541170","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":"Free Convolution Powers Via Roots of Polynomials","authors":"S. Steinerberger","doi":"10.1080/10586458.2021.1980751","DOIUrl":"https://doi.org/10.1080/10586458.2021.1980751","url":null,"abstract":"Let $mu$ be a compactly supported probability measure on the real line. Bercovici-Voiculescu and Nica-Speicher proved the existence of a free convolution power $mu^{boxplus k}$ for any real $k geq 1$. The purpose of this short note is to give an elementary description of $mu^{boxplus k}$ in terms of of polynomials and roots of their derivatives. This bridge allows us to switch back and forth between free probability and the asymptotic behavior of polynomials.","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44902678","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":"Small Mahler Measures From Digraphs","authors":"Joshua Coyston, J. McKee","doi":"10.1080/10586458.2021.1980462","DOIUrl":"https://doi.org/10.1080/10586458.2021.1980462","url":null,"abstract":"Abstract We attach Mahler measures to digraphs and find combinatorial realizations of nearly all of the known low-degree ( ) small (< 1.3) one-variable Mahler measures. We find one new such measure not on either of the lists maintained by Mossinghoff and Sac-Épée. Considering limits of sequences of measures attached to families of digraphs, we get combinatorial explanations for 57 of the 61 known irreducible two-variable measures below 1.37.","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"32 1","pages":"527 - 539"},"PeriodicalIF":0.5,"publicationDate":"2021-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44860920","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 4 × 4 Orthostochastic Variety","authors":"Justin Chen, P. Dey, P. Dey","doi":"10.1080/10586458.2021.1982427","DOIUrl":"https://doi.org/10.1080/10586458.2021.1982427","url":null,"abstract":"ABSTRACT Orthostochastic matrices are the entrywise squares of orthogonal matrices, and naturally arise in various contexts, including notably definite symmetric determinantal representations of real polynomials. However, defining equations for the real variety were previously known only for 3 × 3 matrices. We study the real variety of 4 × 4 orthostochastic matrices, and find a minimal defining set of equations consisting of 6 quintics and 3 octics. The techniques used here involve a wide range of both symbolic and computational methods, in computer algebra and numerical algebraic geometry.","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45816063","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}