Pub Date : 2023-01-01DOI: 10.17323/1609-4514-2023-23-2-243-270
Yuepeng Li, Z. Fang
{"title":"Fujita Type Results for a Parabolic Differential Inequality with Weighted Nonlocal Source","authors":"Yuepeng Li, Z. Fang","doi":"10.17323/1609-4514-2023-23-2-243-270","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-2-243-270","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67827721","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}
Pub Date : 2022-08-23DOI: 10.17323/1609-4514-2023-23-3-401-432
V. Vassiliev
A (conjecturally complete) list of components of complements of discriminant varieties of parabolic singularities of smooth real functions is given. We also promote a combinatorial program that enumerates possible topological types of non-discriminant morsifications of isolated real function singularities and provides a strong invariant of components of complements of discriminant varieties.
{"title":"Complements of Discriminants of Real Parabolic Function Singularities","authors":"V. Vassiliev","doi":"10.17323/1609-4514-2023-23-3-401-432","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-3-401-432","url":null,"abstract":"A (conjecturally complete) list of components of complements of discriminant varieties of parabolic singularities of smooth real functions is given. We also promote a combinatorial program that enumerates possible topological types of non-discriminant morsifications of isolated real function singularities and provides a strong invariant of components of complements of discriminant varieties.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49605059","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}
Pub Date : 2022-05-25DOI: 10.17323/1609-4514-2023-23-3-309-317
A. Buryak
An algorithm to determine all the Gromov-Witten invariants of any smooth projective curve was obtained by Okounkov and Pandharipande in 2006. They identified stationary invariants with certain Hurwitz numbers and then presented Virasoro type constraints that allow to determine all the other Gromov-Witten invariants in terms of the stationary ones. In the case of an elliptic curve, we show that these Virasoro type constraints can be explicitly solved leading to a very explicit formula for the full Gromov-Witten potential in terms of the stationary invariants.
{"title":"A Formula For the Gromov-Witten Potential of an Elliptic Curve","authors":"A. Buryak","doi":"10.17323/1609-4514-2023-23-3-309-317","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-3-309-317","url":null,"abstract":"An algorithm to determine all the Gromov-Witten invariants of any smooth projective curve was obtained by Okounkov and Pandharipande in 2006. They identified stationary invariants with certain Hurwitz numbers and then presented Virasoro type constraints that allow to determine all the other Gromov-Witten invariants in terms of the stationary ones. In the case of an elliptic curve, we show that these Virasoro type constraints can be explicitly solved leading to a very explicit formula for the full Gromov-Witten potential in terms of the stationary invariants.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47840053","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}
Pub Date : 2022-01-02DOI: 10.17323/1609-4514-2023-23-3-369-400
T. Sadykov
Let $x=(x_1,ldots,x_n)in {rm bf C}^n$ be a vector of complex variables, denote by $A=(a_{jk})$ a square matrix of size $ngeq 2,$ and let $varphiinmathcal{O}(Omega)$ be an analytic function defined in a nonempty domain $Omegasubset {rm bf C}.$ We investigate the family of mappings $$ f=(f_1,ldots,f_n):{rm bf C}^nrightarrow {rm bf C}^n, quad f[A,varphi](x):=x+varphi(Ax) $$ with the coordinates $$ f_j : x mapsto x_j + varphileft(sumlimits_{k=1}^n a_{jk}x_kright), quad j=1,ldots,n $$ whose Jacobian is identically equal to a nonzero constant for any $x$ such that all of $f_j$ are well-defined. Let $U$ be a square matrix such that the Jacobian of the mapping $f[U,varphi](x)$ is a nonzero constant for any $x$ and moreover for any analytic function $varphiinmathcal{O}(Omega).$ We show that any such matrix $U$ is uniquely defined, up to a suitable permutation similarity of matrices, by a partition of the dimension $n$ into a sum of $m$ positive integers together with a permutation on $m$ elements. For any $d=2,3,ldots$ we construct $n$-parametric family of square matrices $H(s), sin {rm bf C}^n$ such that for any matrix $U$ as above the mapping $x+left((Uodot H(s))xright)^d$ defined by the Hadamard product $Uodot H(s)$ has unit Jacobian. We prove any such mapping to be polynomially invertible and provide an explicit recursive formula for its inverse.
{"title":"Parameterizing and Inverting Analytic Mappings with Unit Jacobian","authors":"T. Sadykov","doi":"10.17323/1609-4514-2023-23-3-369-400","DOIUrl":"https://doi.org/10.17323/1609-4514-2023-23-3-369-400","url":null,"abstract":"Let $x=(x_1,ldots,x_n)in {rm bf C}^n$ be a vector of complex variables, denote by $A=(a_{jk})$ a square matrix of size $ngeq 2,$ and let $varphiinmathcal{O}(Omega)$ be an analytic function defined in a nonempty domain $Omegasubset {rm bf C}.$ We investigate the family of mappings $$ f=(f_1,ldots,f_n):{rm bf C}^nrightarrow {rm bf C}^n, quad f[A,varphi](x):=x+varphi(Ax) $$ with the coordinates $$ f_j : x mapsto x_j + varphileft(sumlimits_{k=1}^n a_{jk}x_kright), quad j=1,ldots,n $$ whose Jacobian is identically equal to a nonzero constant for any $x$ such that all of $f_j$ are well-defined. Let $U$ be a square matrix such that the Jacobian of the mapping $f[U,varphi](x)$ is a nonzero constant for any $x$ and moreover for any analytic function $varphiinmathcal{O}(Omega).$ We show that any such matrix $U$ is uniquely defined, up to a suitable permutation similarity of matrices, by a partition of the dimension $n$ into a sum of $m$ positive integers together with a permutation on $m$ elements. For any $d=2,3,ldots$ we construct $n$-parametric family of square matrices $H(s), sin {rm bf C}^n$ such that for any matrix $U$ as above the mapping $x+left((Uodot H(s))xright)^d$ defined by the Hadamard product $Uodot H(s)$ has unit Jacobian. We prove any such mapping to be polynomially invertible and provide an explicit recursive formula for its inverse.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48666919","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}
Pub Date : 2022-01-01DOI: 10.17323/1609-4514-2022-22-3-401-426
C. O. Alves, M. Carvalho
{"title":"A Lions Type Result for a Large Class of Orlicz–Sobolev Space and Applications","authors":"C. O. Alves, M. Carvalho","doi":"10.17323/1609-4514-2022-22-3-401-426","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-3-401-426","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67826894","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}
Pub Date : 2022-01-01DOI: 10.17323/1609-4514-2022-22-1-121-132
S. Seo
{"title":"On Universal Norm Elements and a Problem of Coleman","authors":"S. Seo","doi":"10.17323/1609-4514-2022-22-1-121-132","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-1-121-132","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67827311","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}
Pub Date : 2022-01-01DOI: 10.17323/1609-4514-2022-22-3-521-560
Jesús Palma-Márquez
{"title":"Combinatorial Monomialization for Generalized Real Analytic Functions in Three Variables","authors":"Jesús Palma-Márquez","doi":"10.17323/1609-4514-2022-22-3-521-560","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-3-521-560","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67827172","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}
Pub Date : 2022-01-01DOI: 10.17323/1609-4514-2022-22-1-169-169
M. Hindry, A. Pacheco
{"title":"Erratum: An Analogue of the Brauer–Siegel Theorem for Abelian Varieties in Positive Characteristic","authors":"M. Hindry, A. Pacheco","doi":"10.17323/1609-4514-2022-22-1-169-169","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-1-169-169","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67827378","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}
Pub Date : 2022-01-01DOI: 10.17323/1609-4514-2022-22-4-657-703
S. Grushevsky, K. Hulek
{"title":"On the Cone of Effective Surfaces on A 3","authors":"S. Grushevsky, K. Hulek","doi":"10.17323/1609-4514-2022-22-4-657-703","DOIUrl":"https://doi.org/10.17323/1609-4514-2022-22-4-657-703","url":null,"abstract":"","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67827348","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}
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