{"title":"Multipoint Hermite–Padé approximants for three beta functions","authors":"V. Sorokin","doi":"10.1090/MOSC/276","DOIUrl":"https://doi.org/10.1090/MOSC/276","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/MOSC/276","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46019969","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":"Simple solutions of three equations of mathematical physics","authors":"V. Beloshapka","doi":"10.1090/MOSC/280","DOIUrl":"https://doi.org/10.1090/MOSC/280","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/MOSC/280","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45584784","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 the solvability of a boundary value problem in $p$-adic string theory","authors":"K. Khachatryan","doi":"10.1090/MOSC/281","DOIUrl":"https://doi.org/10.1090/MOSC/281","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/MOSC/281","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42706149","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":"The simplest critical cases in the dynamics of nonlinear systems with small diffusion","authors":"S. Kashchenko","doi":"10.1090/MOSC/285","DOIUrl":"https://doi.org/10.1090/MOSC/285","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/MOSC/285","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45512533","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":"Bifurcations of the ‘heart’ polycycle in generic 2-parameter families","authors":"A. Dukov","doi":"10.1090/MOSC/284","DOIUrl":"https://doi.org/10.1090/MOSC/284","url":null,"abstract":"","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44624040","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}
Our aim is to give an explicit description of the Arens-Michael envelope for the universal enveloping algebra of a finite-dimensional nilpotent complex Lie algebra. It turns out that the Arens-Michael envelope belongs to a class of completions introduced by R.~Goodman in 70s. To find a precise form of this algebra we preliminary characterize the set of holomorphic functions of exponential type on a simply connected nilpotent complex Lie group. This approach leads to unexpected connections to Riemannian geometry and the theory of order and type for entire functions. As a corollary, it is shown that the Arens-Michael envelope considered above is a homological epimorphism. So we get a positive answer to a question investigated earlier by Dosi and Pirkovskii.
{"title":"Arens–Michael envelopes of nilpotent Lie algebras, holomorphic functions of exponential type, and homological epimorphisms","authors":"O. Aristov","doi":"10.1090/mosc/301","DOIUrl":"https://doi.org/10.1090/mosc/301","url":null,"abstract":"Our aim is to give an explicit description of the Arens-Michael envelope for the universal enveloping algebra of a finite-dimensional nilpotent complex Lie algebra. It turns out that the Arens-Michael envelope belongs to a class of completions introduced by R.~Goodman in 70s. To find a precise form of this algebra we preliminary characterize the set of holomorphic functions of exponential type on a simply connected nilpotent complex Lie group. This approach leads to unexpected connections to Riemannian geometry and the theory of order and type for entire functions. \u0000As a corollary, it is shown that the Arens-Michael envelope considered above is a homological epimorphism. So we get a positive answer to a question investigated earlier by Dosi and Pirkovskii.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43784353","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}
Torus manifolds are topological generalization of smooth projective toric manifolds. We compute the rational cohomology ring of a class of smooth locally standard torus manifolds whose orbit space is a connected sum of simple polytopes.
{"title":"Cohomology rings of a class of torus manifolds","authors":"Soumen Sarkar, Donald Stanley","doi":"10.1090/MOSC/303","DOIUrl":"https://doi.org/10.1090/MOSC/303","url":null,"abstract":"Torus manifolds are topological generalization of smooth projective toric manifolds. We compute the rational cohomology ring of a class of smooth locally standard torus manifolds whose orbit space is a connected sum of simple polytopes.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43604761","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}
K. Cherednichenko, Yulia Ershova, A. Kiselev, S. Naboko
A novel approach to critical-contrast homogenisation is proposed. Norm-resolvent asymptotics are explicitly constructed. An essential feature of our approach is that it relates homogenisation limits to a class of time-dispersive media.
{"title":"Unified approach to critical-contrast homogenisation with explicit links to time-dispersive media","authors":"K. Cherednichenko, Yulia Ershova, A. Kiselev, S. Naboko","doi":"10.1090/mosc/291","DOIUrl":"https://doi.org/10.1090/mosc/291","url":null,"abstract":"A novel approach to critical-contrast homogenisation is proposed. Norm-resolvent asymptotics are explicitly constructed. An essential feature of our approach is that it relates homogenisation limits to a class of time-dispersive media.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49600371","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}
In this paper we obtain a series of asymptotic formulae in the sum--product phenomena over the prime field $mathbf{F}_p$. In the proofs we use usual incidence theorems in $mathbf{F}_p$, as well as the growth result in ${rm SL}_2 (mathbf{F}_p)$ due to Helfgott. Here some of our applications: $bullet~$ a new bound for the number of the solutions to the equation $(a_1-a_2) (a_3-a_4) = (a'_1-a'_2) (a'_3-a'_4)$, $,a_i, a'_iin A$, $A$ is an arbitrary subset of $mathbf{F}_p$, $bullet~$ a new effective bound for multilinear exponential sums of Bourgain, $bullet~$ an asymptotic analogue of the Balog--Wooley decomposition theorem, $bullet~$ growth of $p_1(b) + 1/(a+p_2 (b))$, where $a,b$ runs over two subsets of $mathbf{F}_p$, $p_1,p_2 in mathbf{F}_p [x]$ are two non--constant polynomials, $bullet~$ new bounds for some exponential sums with multiplicative and additive characters.
{"title":"On asymptotic formulae in some sum–product questions","authors":"I. Shkredov","doi":"10.1090/MOSC/283","DOIUrl":"https://doi.org/10.1090/MOSC/283","url":null,"abstract":"In this paper we obtain a series of asymptotic formulae in the sum--product phenomena over the prime field $mathbf{F}_p$. In the proofs we use usual incidence theorems in $mathbf{F}_p$, as well as the growth result in ${rm SL}_2 (mathbf{F}_p)$ due to Helfgott. Here some of our applications: \u0000$bullet~$ a new bound for the number of the solutions to the equation $(a_1-a_2) (a_3-a_4) = (a'_1-a'_2) (a'_3-a'_4)$, $,a_i, a'_iin A$, $A$ is an arbitrary subset of $mathbf{F}_p$, \u0000$bullet~$ a new effective bound for multilinear exponential sums of Bourgain, \u0000$bullet~$ an asymptotic analogue of the Balog--Wooley decomposition theorem, \u0000$bullet~$ growth of $p_1(b) + 1/(a+p_2 (b))$, where $a,b$ runs over two subsets of $mathbf{F}_p$, $p_1,p_2 in mathbf{F}_p [x]$ are two non--constant polynomials, \u0000$bullet~$ new bounds for some exponential sums with multiplicative and additive characters.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/MOSC/283","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45986289","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}
We extend Matsuki duality to arbitrary ind-varieties of maximal generalized flags, in other words, to any homogeneous ind-variety $mathbf{G}/mathbf{B}$ for a classical ind-group $mathbf{G}$ and a splitting Borel ind-subgroup $mathbf{B}subsetmathbf{G}$. As a first step, we present an explicit combinatorial version of Matsuki duality in the finite-dimensional case, involving an explicit parametrization of $K$- and $G^0$-orbits on $G/B$. After proving Matsuki duality in the infinite-dimensional case, we give necessary and sufficient conditions on a Borel ind-subgroup $mathbf{B}subsetmathbf{G}$ for the existence of open and closed $mathbf{K}$- and $mathbf{G}^0$-orbits on $mathbf{G}/mathbf{B}$, where $left(mathbf{K},mathbf{G}^0right)$ is an aligned pair of a symmetric ind-subgroup $mathbf{K}$ and a real form $mathbf{G}^0$ of $mathbf{G}$.
我们将Matsuki对偶性扩展到极大广义标志的任意ini -变异，换句话说，对于一个经典ini -群$mathbf{G}$和一个分裂Borel ini -子群$mathbf{B}子集$ mathbf{G}$，我们将Matsuki对偶性扩展到任意齐次ini -变异$mathbf{G}/mathbf{B}$。作为第一步，我们给出了有限维情况下Matsuki对偶的显式组合版本，涉及$K$-和$G^0$-轨道在$G/B$上的显式参数化。在证明了无限维情况下的Matsuki对偶性后，给出了Borel子群$mathbf{B}子集$ mathbf{G}$上$mathbf{K}$-和$mathbf{G}^0$-轨道存在的充分必要条件，其中$左(mathbf{K}，mathbf{G}^0右)$ $是对称子群$mathbf{K}$和$mathbf{G}$的实数形式$mathbf{G}^0$的一对对齐。
{"title":"Orbit duality in ind-varieties of maximal generalized flags","authors":"Lucas Fresse, I. Penkov","doi":"10.1090/MOSC/266","DOIUrl":"https://doi.org/10.1090/MOSC/266","url":null,"abstract":"We extend Matsuki duality to arbitrary ind-varieties of maximal generalized flags, in other words, to any homogeneous ind-variety $mathbf{G}/mathbf{B}$ for a classical ind-group $mathbf{G}$ and a splitting Borel ind-subgroup $mathbf{B}subsetmathbf{G}$. As a first step, we present an explicit combinatorial version of Matsuki duality in the finite-dimensional case, involving an explicit parametrization of $K$- and $G^0$-orbits on $G/B$. After proving Matsuki duality in the infinite-dimensional case, we give necessary and sufficient conditions on a Borel ind-subgroup $mathbf{B}subsetmathbf{G}$ for the existence of open and closed $mathbf{K}$- and $mathbf{G}^0$-orbits on $mathbf{G}/mathbf{B}$, where $left(mathbf{K},mathbf{G}^0right)$ is an aligned pair of a symmetric ind-subgroup $mathbf{K}$ and a real form $mathbf{G}^0$ of $mathbf{G}$.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/MOSC/266","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60560564","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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