Siberian Mathematical Journal最新文献_第7页

Light 3-Paths in 3-Polytopes without Adjacent Triangles 无相邻三角形的 3 多面体中的光 3 路径

IF 0.5 4区数学

Siberian Mathematical Journal Pub Date : 2024-03-25 DOI: 10.1134/s0037446624020022

O. V. Borodin, A. O. Ivanova

{"title":"Light 3-Paths in 3-Polytopes without Adjacent Triangles","authors":"O. V. Borodin, A. O. Ivanova","doi":"10.1134/s0037446624020022","DOIUrl":"https://doi.org/10.1134/s0037446624020022","url":null,"abstract":"Let ( w_{k} ) be the maximum of the minimum degree-sum (weight) of vertices in ( k )-vertex paths (( k )-paths) in 3-polytopes.\u0000Trivially, each 3-polytope has a vertex of degree at most 5, and so ( w_{1}leq 5 ).\u0000Back in 1955, Kotzig proved that ( w_{2}leq 13 ) (so there is an edge of weight at most 13), which is sharp.\u0000In 1993, Ando, Iwasaki, and Kaneko proved that ( w_{3}leq 21 ), which is also sharp\u0000due to a construction by Jendrol’ of 1997.\u0000In 1997, Borodin refined this by proving that ( w_{3}leq 18 ) for 3-polytopes with ( w_{2}geq 7 ),\u0000while ( w_{3}leq 17 ) holds for 3-polytopes\u0000with ( w_{2}geq 8 ), where the sharpness of 18 was confirmed by Borodin et al. in 2013,\u0000and that of 17 was known long ago.\u0000Over the last three decades, much research has been devoted to structural and coloring problems\u0000on the plane graphs that are sparse in this or that sense.\u0000In this paper we deal with 3-polytopes without adjacent 3-cycles that is without chordal 4-cycle\u0000(in other words, without ( K_{4}-e )).\u0000It is known that such 3-polytopes satisfy ( w_{1}leq 4 ); and, moreover, ( w_{2}leq 9 ) holds, where\u0000both bounds are sharp (Borodin, 1992).\u0000We prove now that each 3-polytope without chordal 4-cycles\u0000has a 3-path of weight at most 15; and so ( w_{3}leq 15 ), which is sharp.","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300061","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}

引用次数: 0

Quasidenseness in $ ��^{��} $ and Projective Parallelotopes $�^{��}中的类等性与投影平行拓扑

IF 0.5 4区数学

Siberian Mathematical Journal Pub Date : 2024-03-25 DOI: 10.1134/s0037446624020034

A. E. Gutman, I. A. Emelianenkov

引用次数: 0

The Stability by Linear Approximation of Discrete-Time Nonlinear Singular Systems 离散时间非线性奇异系统的线性近似稳定性

IF 0.5 4区数学

Siberian Mathematical Journal Pub Date : 2024-03-01 DOI: 10.1134/s0037446624020137

A. A. Shcheglova

引用次数: 0

On the Relation between Denjoy–Khintchine and $ operatorname{HK}_{r} $ -Integrals 论丹乔伊-欣钦因与 $ operatorname{HK}_{r} $ - 积分的关系

IF 0.5 4区数学

Siberian Mathematical Journal Pub Date : 2024-03-01 DOI: 10.1134/s0037446624020162

引用次数: 0

Character Contractibility and Amenability of Banach Algebras with Applications to Quantum Groups 巴拿赫代数的特性可约性和可悔改性及其在量子群中的应用

IF 0.5 4区数学

Siberian Mathematical Journal Pub Date : 2024-03-01 DOI: 10.1134/s0037446624020174

S. Soltani Renani, Z. Yari

引用次数: 0

On the Spectral Properties of Selfadjoint Partial Integral Operators with a Nondegenerate Kernel 论具有非enerate 内核的自兼偏积分算子的谱特性

IF 0.5 4区数学

Siberian Mathematical Journal Pub Date : 2024-03-01 DOI: 10.1134/s0037446624020204

{"title":"On the Spectral Properties of Selfadjoint Partial Integral Operators with a Nondegenerate Kernel","authors":"","doi":"10.1134/s0037446624020204","DOIUrl":"https://doi.org/10.1134/s0037446624020204","url":null,"abstract":"<h3>Abstract</h3> We consider bounded selfadjoint linear integral operators ( T_{1} ) and ( T_{2} ) in the Hilbert space ( L_{2}([a,b]times[c,d]) ) which are usually called partial integral operators. We assume that ( T_{1} ) acts on a function ( f(x,y) ) in the first argument and performs integration in ( x ) , while ( T_{2} ) acts on ( f(x,y) ) in the second argument and performs integration in ( y ) . We assume further that ( T_{1} ) and ( T_{2} ) are bounded but not compact, whereas ( T_{1}T_{2} ) is compact and ( T_{1}T_{2}=T_{2}T_{1} ) . Partial integral operators arise in various areas of mechanics, the theory of integro-differential equations, and the theory of Schrödinger operators. We study the spectral properties of ( T_{1} ) , ( T_{2} ) , and ( T_{1}+T_{2} ) with nondegenerate kernels and established some formula for the essential spectra of ( T_{1} ) and ( T_{2} ) . Furthermore, we demonstrate that the discrete spectra of ( T_{1} ) and ( T_{2} ) are empty, and prove a theorem on the structure of the essential spectrum of ( T_{1}+T_{2} ) . Also, under study is the problem of existence of countably many eigenvalues in the discrete spectrum of ( T_{1}+T_{2} ) .","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299646","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}

引用次数: 0

The Injectivity Radius and Shortest Arcs of the Oblate Ellipsoid of Revolution 旋转椭圆体的注入半径和最短弧线

IF 0.5 4区数学

Siberian Mathematical Journal Pub Date : 2024-02-07 DOI: 10.1134/s0037446624010026

V. N. Berestovskii, A. Mustafa

引用次数: 0

Estimates of Alexandrov’s $ n $ -Width of the Compact Set of $ C^{infty} $ -Smooth Functions on a Finite Segment 亚历山德罗夫有限段上$ C^{infty} $光滑函数紧凑集的$ n $宽的估计值

IF 0.5 4区数学

Siberian Mathematical Journal Pub Date : 2024-02-07 DOI: 10.1134/s0037446624010014

V. N. Belykh

引用次数: 0

Topological Properties of Mappings with Finite Distortion on Carnot Groups 卡诺群上有限畸变映射的拓扑特性

IF 0.5 4区数学

Siberian Mathematical Journal Pub Date : 2024-02-07 DOI: 10.1134/s0037446624010063

D. V. Isangulova

引用次数: 0

On the Separability of Abelian Subgroups of the Fundamental Groups of Graphs of Groups. II 论图形群基本群的无性子群的可分性。(英)

IF 0.5 4区数学

Siberian Mathematical Journal Pub Date : 2024-02-07 DOI: 10.1134/s0037446624010166

E. V. Sokolov

引用次数: 0