Pub Date : 2022-07-12DOI: 10.3103/s0027132222020036
T. R. Igonina, V. M. Keselman, O. R. Paraskevopulo
Abstract
A fairly general concept of an integral capacity on a Riemannian manifold is considered, which includes the concepts of capacity known for the geometric theory of functions such as the classical and conformal capacities. In terms of this general capacity, as in the case of the classical capacity, the concept of capacitive type of Riemannian manifold is defined. In this paper, we present some integral criteria of the capacitive type of a non-compact Riemannian manifold, which complement and, in certain cases, strengthen the known criteria of the classical capacitive type of a Riemannian manifold.
{"title":"Some Criteria of Capacitive Type of a Noncompact Riemannian Manifold","authors":"T. R. Igonina, V. M. Keselman, O. R. Paraskevopulo","doi":"10.3103/s0027132222020036","DOIUrl":"https://doi.org/10.3103/s0027132222020036","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A fairly general concept of an integral capacity on a Riemannian manifold is considered, which includes the concepts of capacity known for the geometric theory of functions such as the classical and conformal capacities. In terms of this general capacity, as in the case of the classical capacity, the concept of capacitive type of Riemannian manifold is defined. In this paper, we present some integral criteria of the capacitive type of a non-compact Riemannian manifold, which complement and, in certain cases, strengthen the known criteria of the classical capacitive type of a Riemannian manifold.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":"2 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138531978","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 : 2022-07-12DOI: 10.3103/s0027132222020097
M. E. Vishnikin
Abstract
It is proved that unique typed basic categorial grammars are not closed under any natural language operations.
摘要证明了唯一类型的基本范畴语法在任何自然语言操作下都是不封闭的。
{"title":"Unique Typed Basic Categorial Grammars","authors":"M. E. Vishnikin","doi":"10.3103/s0027132222020097","DOIUrl":"https://doi.org/10.3103/s0027132222020097","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>It is proved that unique typed basic categorial grammars are not closed under any natural language operations.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":"2 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138531976","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 : 2022-07-12DOI: 10.3103/s0027132222020024
D. A. Badulin, A. L. Kanunnikov
Abstract
All gradings of quadratic Kummer extensions by a group are described. These extensions have a natural grading by Galois group and its subgroups. Sufficient and necessary conditions for such extensions to have nontrivial gradings by other groups are determined.
{"title":"Gradings of Quadratic Kummer Extensions","authors":"D. A. Badulin, A. L. Kanunnikov","doi":"10.3103/s0027132222020024","DOIUrl":"https://doi.org/10.3103/s0027132222020024","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>All gradings of quadratic Kummer extensions by a group are described. These extensions have a natural grading by Galois group and its subgroups. Sufficient and necessary conditions for such extensions to have nontrivial gradings by other groups are determined.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":"54 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138531977","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 : 2022-06-01DOI: 10.3103/S0027132222030056
A. Chashkin
{"title":"On the Implementation of Monotone Boolean Functions by Memoryless Programs","authors":"A. Chashkin","doi":"10.3103/S0027132222030056","DOIUrl":"https://doi.org/10.3103/S0027132222030056","url":null,"abstract":"","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":"77 1","pages":"136 - 143"},"PeriodicalIF":0.4,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49080555","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 : 2022-06-01DOI: 10.3103/s0027132222030044
I. P. Baksova, Y. Tarannikov
{"title":"The Bounds on the Number of Partitions of the Space $$mathbf{F}_{mathbf{2}}^{boldsymbol{m}}$$ into $$boldsymbol{k}$$-Dimensional Affine Subspaces","authors":"I. P. Baksova, Y. Tarannikov","doi":"10.3103/s0027132222030044","DOIUrl":"https://doi.org/10.3103/s0027132222030044","url":null,"abstract":"","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46311689","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 : 2022-06-01DOI: 10.3103/S0027132222030068
V. Kochergin
{"title":"Comparing the Computational Complexity of Monomials and Elements of Finite Abelian Groups","authors":"V. Kochergin","doi":"10.3103/S0027132222030068","DOIUrl":"https://doi.org/10.3103/S0027132222030068","url":null,"abstract":"","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":"77 1","pages":"113 - 119"},"PeriodicalIF":0.4,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42649231","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 : 2022-06-01DOI: 10.3103/S0027132222030081
N. P. Red’kin
{"title":"On the Complexity of Implementation of Characteristic Functions of the Spheres by Circuits of Functional Elements","authors":"N. P. Red’kin","doi":"10.3103/S0027132222030081","DOIUrl":"https://doi.org/10.3103/S0027132222030081","url":null,"abstract":"","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":"77 1","pages":"127 - 130"},"PeriodicalIF":0.4,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48794815","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 : 2022-06-01DOI: 10.3103/s0027132222030032
V. Alekseev
{"title":"On the Cardinality of Interval Int(Pol$${}_{boldsymbol{k}}$$) in Partial $$boldsymbol{k}$$-Valued Logic","authors":"V. Alekseev","doi":"10.3103/s0027132222030032","DOIUrl":"https://doi.org/10.3103/s0027132222030032","url":null,"abstract":"","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46121384","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 : 2022-06-01DOI: 10.3103/S002713222203007X
S. A. Lozhkin
{"title":"Refined Bounds on Shannon’s Function for Complexity of Circuits of Functional Elements","authors":"S. A. Lozhkin","doi":"10.3103/S002713222203007X","DOIUrl":"https://doi.org/10.3103/S002713222203007X","url":null,"abstract":"","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":"77 1","pages":"144 - 153"},"PeriodicalIF":0.4,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69422488","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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