Pub Date : 2023-12-15DOI: 10.51286/albjm/1685536799
Michael D. Fried
{"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}
Pub Date : 2023-12-12DOI: 10.51286/albjm/1701717650
Sajad Salami
{"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}
Pub Date : 2023-12-12DOI: 10.51286/albjm/1702292327
S. A. Broughton, Eduardo Brandani da Silva
{"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}
Pub Date : 2023-06-15DOI: 10.51286/albjm/1677838370
Francesco Calogero, Andrea Giansanti, Farrin Payandeh
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.
{"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}
Pub Date : 2023-06-15DOI: 10.51286/albjm/1675936273
Adrian Clingher, Thomas Hill, Andreas Malmendier
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.
{"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}
Pub Date : 2023-06-15DOI: 10.51286/albjm/1675941338
Elira Curri, Tony Shaska, Caleb Shor
{"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}
Pub Date : 2023-06-15DOI: 10.51286/albjm/1675936045
James Cogdell, Jay Jorgenson, Lejla Smajlović
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.
在Cogdell et al.， LMS Lecture Notes Series 459, 393-427(2020)中，作者证明了在任意光滑Kähler流形X上与任意因子D相关的一类Kronecker极限公式，假设D在余维1上是光滑的。在本文中，说明了上述的Kronecker极限公式的类比如何应用于Weil互易性的否定和推广。更准确地说，我们将Weil互易推广到光滑紧致Riemann曲面上偶权的亚纯模形式(适当规范化)，并给出了一类在对称空间的有限体积商或紧致光滑投影Kähler变体上具有特殊奇点类型的调和函数的Weil互易的一个变体。我们也证明了一个紧致光滑射影Kähler簇的Weil互易性的一个积分版本。
{"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}
Pub Date : 2023-06-15DOI: 10.51286/albjm/1675941730
Caleb M. Shor
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.
{"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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