{"title":"TAMING GENUS 0 (OR 1) COMPONENTS ON VARIABLES-SEPARATED EQUATIONS","authors":"Michael D. Fried","doi":"10.51286/albjm/1685536799","DOIUrl":"https://doi.org/10.51286/albjm/1685536799","url":null,"abstract":"","PeriodicalId":484514,"journal":{"name":"Albanian journal of mathematics","volume":"14 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139001049","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":"ON POWERFUL VALUES OF POLYNOMIALS OVER NUMBER FIELDS","authors":"Sajad Salami","doi":"10.51286/albjm/1701717650","DOIUrl":"https://doi.org/10.51286/albjm/1701717650","url":null,"abstract":"","PeriodicalId":484514,"journal":{"name":"Albanian journal of mathematics","volume":"1 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139009173","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":"TRIANGULATIONS OF UNORIENTABLE SURFACES","authors":"S. A. Broughton, Eduardo Brandani da Silva","doi":"10.51286/albjm/1702292327","DOIUrl":"https://doi.org/10.51286/albjm/1702292327","url":null,"abstract":"","PeriodicalId":484514,"journal":{"name":"Albanian journal of mathematics","volume":"34 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139009894","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}
Francesco Calogero, Andrea Giansanti, Farrin Payandeh
{"title":"EXPLICIT SOLUTIONS OF AN EPIDEMIOLOGICAL MODEL OF THE SIR TYPE","authors":"Francesco Calogero, Andrea Giansanti, Farrin Payandeh","doi":"10.51286/albjm/1677838370","DOIUrl":"https://doi.org/10.51286/albjm/1677838370","url":null,"abstract":"A system of 4 nonlinearly-coupled Ordinary Differential Equations has been recently introduced to investigate the evolution of human respiratory virus epidemics. In this paper we prove that some explicit solutions of that system can be obtained by algebraic operations, provided the parameters of the model satisfy certain constraints.","PeriodicalId":484514,"journal":{"name":"Albanian journal of mathematics","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135860134","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":"JACOBIAN ELLIPTIC FIBRATIONS ON THE GENERALIZED INOSE QUARTIC OF PICARD RANK SIXTEEN","authors":"Adrian Clingher, Thomas Hill, Andreas Malmendier","doi":"10.51286/albjm/1675936273","DOIUrl":"https://doi.org/10.51286/albjm/1675936273","url":null,"abstract":"We consider the family of complex algebraic K3 surfaces 𝒳 with Picard lattice containing the unimodular lattice H⊕E7(−1)⊕E7(−1). The surface 𝒳 admits a birational model isomorphic to a quartic hypersurface that generalizes the Inose quartic. We prove that a general member of this family admits exactly four inequivalent Jacobian elliptic fibrations and construct explicit pencils for them.","PeriodicalId":484514,"journal":{"name":"Albanian journal of mathematics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135860395","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":"EMMA PREVIATO AND HER MATHEMATICAL LIFE (1952-2022)","authors":"Elira Curri, Tony Shaska, Caleb Shor","doi":"10.51286/albjm/1675941338","DOIUrl":"https://doi.org/10.51286/albjm/1675941338","url":null,"abstract":"","PeriodicalId":484514,"journal":{"name":"Albanian journal of mathematics","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135860394","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 ANALYTIC PERSPECTIVE OF WEIL RECIPROCITY","authors":"James Cogdell, Jay Jorgenson, Lejla Smajlović","doi":"10.51286/albjm/1675936045","DOIUrl":"https://doi.org/10.51286/albjm/1675936045","url":null,"abstract":"In Cogdell et al., LMS Lecture Notes Series 459, 393–427 (2020), the authors proved a type of Kronecker’s limit formula associated to any divisor D on any smooth Kähler manifold X, assuming that D is smooth in codimension one. In the present article, it is shown how the aforementioned analogue of Kronecker’s limit formula applies to reprove and generalize Weil reciprocity. More precisely, we extend Weil reciprocity to (suitably normalized) meromorphic modular forms of even weight on a smooth, compact Riemann surface, and present a variant of Weil reciprocity for a class of harmonic functions with special types of singularities on a finite volume quotient of a symmetric space or a compact, smooth projective Kähler variety. We also prove an integral version of Weil reciprocity for a compact, smooth projective Kähler variety.","PeriodicalId":484514,"journal":{"name":"Albanian journal of mathematics","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135860133","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":"REFLECTIVE NUMERICAL SEMIGROUPS","authors":"Caleb M. Shor","doi":"10.51286/albjm/1675941730","DOIUrl":"https://doi.org/10.51286/albjm/1675941730","url":null,"abstract":"We define a reflective numerical semigroup of genus g as a numerical semigroup that has a certain reflective symmetry when viewed within ℤ as an array with g columns. Equivalently, a reflective numerical semigroup has one gap in each residue class modulo g. In this paper, we give an explicit description for all reflective numerical semigroups. With this, we can describe the reflective members of well-known families of numerical semigroups as well as obtain formulas for the number of reflective numerical semigroups of a given genus or given Frobenius number.","PeriodicalId":484514,"journal":{"name":"Albanian journal of mathematics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135860135","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}
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