Transactions of A Razmadze Mathematical Institute最新文献

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Boundary value problems of statics of thermoelasticity of bodies with microstructure and microtemperatures 具有微观结构和微温度的物体热弹性静力学边值问题

IF 0.2 Q4 MATHEMATICS

Transactions of A Razmadze Mathematical Institute

Pub Date : 2018-04-01 DOI: 10.1016/j.trmi.2017.09.002

L. Giorgashvili, S. Zazashvili

The paper deals with boundary value problems of statics of the thermoelasticity theory of isotropic microstretch materials with microtemperatures and microdilatations. For the system of differential equations of equilibrium the fundamental matrix is constructed explicitly in terms of elementary functions. With the help of the corresponding Green identities the general integral representation formula of solutions by means of generalized layer and Newtonian potentials are derived. The basic Dirichlet and Neumann type boundary value problems are formulated in appropriate function spaces and the uniqueness theorems are proved. The existence theorems for classical solutions are established by using the potential method.

研究了具有微温度和微膨胀的各向同性微拉伸材料的热弹性静力学边值问题。对于平衡微分方程系统，基本矩阵是用初等函数显式构造的。利用相应的格林恒等式，导出了用广义层和牛顿势表示解的一般积分表示公式。在适当的函数空间中构造了基本的Dirichlet型和Neumann型边值问题，并证明了唯一性定理。利用势法建立了经典解的存在性定理。

引用次数: 1

The stability of orthotropic shells of revolution, close to cylindrical ones, with an elastic filler, under the action of torsion, normal pressure and temperature 在扭转、常压和温度作用下，采用弹性填料的接近圆柱形的正交各向异性旋转壳的稳定性

IF 0.2 Q4 MATHEMATICS

Transactions of A Razmadze Mathematical Institute

Pub Date : 2018-04-01 DOI: 10.1016/j.trmi.2017.10.005

Sergo Kukudzhanov

The paper investigates the stability of orthotropic shells of revolution which are by their form close to cylindrical ones, with an elastic filler, under the action of torques, external pressure and temperature. The shell is assumed to be thin and elastic. Temperature is uniformly distributed in the shell body. The filler is simulated by an elastic base. The shells of positive and negative Gaussian curvature are considered. Formulas for finding critical loadings and corresponding forms of stability loss are derived.

本文研究了在力矩、外压力和温度作用下，具有弹性填料的接近圆柱形式的正交各向异性旋转壳的稳定性。壳被假定为薄而有弹性。温度在壳体内均匀分布。填充物用弹性底座模拟。考虑了正高斯曲率壳层和负高斯曲率壳层。导出了求临界荷载的公式和相应的稳定损失形式。

引用次数: 0

On the internal tensor structures of the fibration T(Lm(Vn)) 关于振动的内部张量结构T(Lm(Vn))

IF 0.2 Q4 MATHEMATICS

Transactions of A Razmadze Mathematical Institute

Pub Date : 2018-04-01 DOI: 10.1016/j.trmi.2017.07.003

Gocha Todua

In the present paper we consider some internal tensor structures. It is proved that if on the space $Lm (V n)$ there are tensor fields $a_{j}^{i}$ and $a_{β}^{α}$ defining almost a dual structure, then there exist such lifts of these tensor fields which represent either almost a binary structure, or almost a complex structure on $T (Lm (V n))$ .

本文考虑了一些内张量结构。证明了如果在空间Lm(Vn)上存在定义了几乎对偶结构的张量场aji和aβα，那么在空间T(Lm(Vn))上存在这些张量场的提升，它们要么表示几乎二元结构，要么表示几乎复结构。

引用次数: 0

Generalized semi-open and pre-semiopen sets via ideals 经理想的广义半开和半开集

IF 0.2 Q4 MATHEMATICS

Transactions of A Razmadze Mathematical Institute

Pub Date : 2018-04-01 DOI: 10.1016/j.trmi.2017.08.003

Bishwambhar Roy , Ritu Sen

In this paper we have introduced a new type of sets termed as $μ^{*}$ -open sets which unifies semiopen sets, $β$ -open sets and discussed some of its properties. We have also introduced another type of weak open sets termed as $I_{_{μ}}$ -open sets depending on a GT as well as an ideal on a topological space. Finally the concept of weakly $I_{_{μ}}$ -open sets are investigated.

本文引入了一类新的集，称为μ * -开集，它统一了半开集、β-开集，并讨论了它的一些性质。我们还引入了另一种类型的弱开集，称为i μ开集，它依赖于一个GT和拓扑空间上的一个理想。最后研究了弱i μ开集的概念。

引用次数: 4

Pointwise multipliers for inhomogeneous multi-parameter Besov and Triebel–Lizorkin spaces associated with mixed homogeneities 与混合均匀性相关的非齐次多参数Besov和triiebel - lizorkin空间的点态乘子

IF 0.2 Q4 MATHEMATICS

Transactions of A Razmadze Mathematical Institute

Pub Date : 2018-04-01 DOI: 10.1016/j.trmi.2017.11.002

Jian Tan

In this article, we obtain pointwise multipliers on inhomogeneous multi-parameter Besov and Triebel–Lizorkin spaces associated with mixed homogeneities.

在本文中，我们得到了与混合均匀性相关的非齐次多参数Besov和triiebel - lizorkin空间上的点乘子。

引用次数: 1

Jagged non-zero submatrix data structure 锯齿状非零子矩阵数据结构

IF 0.2 Q4 MATHEMATICS

Transactions of A Razmadze Mathematical Institute

Pub Date : 2018-04-01 DOI: 10.1016/j.trmi.2017.10.002

Giga Chalauri , Vakhtang Laluashvili , Koba Gelashvili

On the basis of C language matrix having rows of different length, we havedeveloped a new storage format for rectangular matrix. It stores non-zero entries, their column indices and is called jagged non-zero sub-matrix data structure or simply jnz-format.

In case of simple applications, when the only requirement from the format is to ensure the serial algorithm of multiplying matrix by vector (e.g. conjugate gradient (CG) method), two following issues are experimentally studied:

•
For what amount of zero-entries do we accept the rectangular matrix as sparse, with respect to used memory and speed;
•
What should the jnz-format’s interface look like.

Determining the interface is comparatively laborious; jnz-format is compared to two approved formats—CRS and Mapped Matrix. In comparisons, CRS format is considered by using two different implementations, whilst jnz and Mapped Matrix —by using one. In comparisons, we use jnz and CRS formats with our own simple interface implementations and CRS and Mapped Matrix with boost’s library interfaces and implementations. Experiments’ results show jnz format’s prospect and visible advantage of the relatively easy interface.

All the material regarding experiments can be seen at https://github.com/vakho10/Sparse-Storage-Formats.

在C语言矩阵具有不同行长度的基础上，我们开发了一种新的矩形矩阵存储格式。它存储非零条目及其列索引，称为锯齿非零子矩阵数据结构或简称为jnz格式。在简单的应用中，当格式的唯一要求是确保矩阵乘以向量的串行算法(例如共轭梯度(CG)方法)时，实验研究了以下两个问题:•对于多少个零项，我们接受矩形矩阵为稀疏，相对于使用的内存和速度;•jnz格式的接口应该是什么样子的。确定接口比较费力;将jnz格式与两种已批准的格式crs和Mapped Matrix进行比较。在比较中，CRS格式是通过使用两个不同的实现来考虑的，而jnz和Mapped Matrix是通过使用一个实现来考虑的。在比较中，我们使用jnz和CRS格式与我们自己的简单接口实现，使用CRS和Mapped Matrix与boost的库接口和实现。实验结果显示了jnz格式的应用前景和相对简单的界面优势。所有关于实验的材料都可以在https://github.com/vakho10/Sparse-Storage-Formats上看到。

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引用次数: 2

On the structure of constituents of finite independent families of convex bodies in R2 and R3 spaces R2和R3空间中凸体有限独立族的成分结构

IF 0.2 Q4 MATHEMATICS

Transactions of A Razmadze Mathematical Institute

Pub Date : 2018-04-01 DOI: 10.1016/j.trmi.2017.10.004

Tengiz Tetunashvili

Properties of certain families of subsets of Euclidean spaces are established. Using the established properties theorems concerning the structure of constituents of finite independent families of convex bodies in $R^{2}$ and $R^{3}$ spaces are proved.

建立了欧几里德空间若干子集族的性质。利用已建立的性质，证明了R2和R3空间中凸体有限独立族组成元结构的定理。

引用次数: 1

Potential operators in modified Morrey spaces defined on Carleson curves Carleson曲线上定义的修正Morrey空间中的势算子

IF 0.2 Q4 MATHEMATICS

Transactions of A Razmadze Mathematical Institute

Pub Date : 2018-04-01 DOI: 10.1016/j.trmi.2017.09.004

I.B. Dadashova , C. Aykol , Z. Cakir , A. Serbetci

<div>In this paper we study the potential operator <math><msubsup><mrow><mi>I</mi></mrow><mrow><mi>Γ</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math>, <math><mn>0</mn><mo><</mo><mn>1</mn></math> in the modified Morrey space <math><msub><mrow><mover><mrow><mi>L</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>p</mi><mo>,</mo><mi>λ</mi></mrow></msub><mrow><mo>(</mo><mi>Γ</mi><mo>)</mo></mrow></math> and the spaces <math><mi>B</mi><mi>M</mi><mi>O</mi><mrow><mo>(</mo><mi>Γ</mi><mo>)</mo></mrow></math> defined on Carleson curves <math><mi>Γ</mi></math>. We prove that for <math><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>λ</mi><mo>)</mo></mrow><mo>∕</mo><mi>α</mi></math> the potential operator <math><msubsup><mrow><mi>I</mi></mrow><mrow><mi>Γ</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math> is bounded from the modified Morrey space <math><msub><mrow><mover><mrow><mi>L</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>p</mi><mo>,</mo><mi>λ</mi></mrow></msub><mrow><mo>(</mo><mi>Γ</mi><mo>)</mo></mrow></math> to <math><msub><mrow><mover><mrow><mi>L</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>q</mi><mo>,</mo><mi>λ</mi></mrow></msub><mrow><mo>(</mo><mi>Γ</mi><mo>)</mo></mrow></math> if and in the case of infinite curve only if <math><mi>α</mi><mo>≤</mo><mn>1</mn><mo>∕</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>∕</mo><mi>q</mi><mo>≤</mo><mi>α</mi><mo>∕</mo><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>λ</mi><mo>)</mo></mrow></math>, and from the spaces <math><msub><mrow><mover><mrow><mi>L</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mn>1</mn><mo>,</mo><mi>λ</mi></mrow></msub><mrow><mo>(</mo><mi>Γ</mi><mo>)</mo></mrow></math> to <math><mi>W</mi><msub><mrow><mover><mrow><mi>L</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>q</mi><mo>,</mo><mi>λ</mi></mrow></msub><mrow><mo>(</mo><mi>Γ</mi><mo>)</mo></mrow></math> if and in the case of infinite curve only if <math><mi>α</mi><mo>≤</mo><mn>1</mn><mo>−</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>q</mi></mrow></mfrac><mo>≤</mo><mfrac><mrow><mi>α</mi></mrow><mrow><mn>1</mn><mo>−</mo><mi>λ</mi></mrow></mfrac></math>. Furthermore, for the limiting case <math><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>λ</mi><mo>)</mo></mrow><mo>∕</mo><mi>α</mi><mo>≤</mo><mi>p</mi><mo>≤</mo><mn>1</mn><mo>∕</mo><mi>α</mi></math> we show that if <math><mi>Γ</mi></math> is an infinite Carleson curve, then the modified potential operator <math><msubsup><mrow><mover><mrow><mi>I</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>Γ</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math> is bounded from <math><msub><mrow><mover><mrow><mi>L</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>p</mi><mo>,</mo><mi>λ</mi></mrow></msub>

本文研究了Carleson曲线Γ上定义的修正Morrey空间L ~ p，λ(Γ)和空间BMO(Γ)中的势算子IΓα， 0<1。证明了对于1<p<(1−λ)∕α，势算子IΓα从修正Morrey空间L ~ p，λ(Γ)到L ~ q，λ(Γ)有界，当且仅当α≤1∕p−1∕q≤α∕(1−λ)，当且仅当无穷曲线时，从空间L ~ 1，λ(Γ)到空间WL ~ q，λ(Γ)有界，当且仅当无穷曲线时，α≤1−1q≤α1−λ。进一步，对于(1−λ)∕α≤p≤1∕α的极限情况，我们证明了如果Γ是无限Carleson曲线，则修正势算子I ~ Γα从L ~ p，λ(Γ)到BMO(Γ)有界，如果Γ是有限Carleson曲线，则算子IΓα从L ~ p，λ(Γ)到BMO(Γ)有界。

引用次数: 4

On some methods of extending invariant and quasi-invariant measures 关于扩展不变测度和拟不变测度的一些方法

IF 0.2 Q4 MATHEMATICS

Transactions of A Razmadze Mathematical Institute

Pub Date : 2018-04-01 DOI: 10.1016/j.trmi.2017.08.002

A. Kirtadze , N. Rusiashvili

In the present paper an approach to some questions in the theory of invariant (quasi-invariant) measures is discussed. It is useful in certain situations, where given topological groups or topological vector spaces are equipped with various nonzero $σ$ -finite left invariant (left quasi-invariant) measures.

本文讨论了不变测度(拟不变测度)理论中若干问题的研究方法。它在某些情况下是有用的，当给定的拓扑群或拓扑向量空间配备了各种非零σ-有限左不变(左拟不变)测度。

引用次数: 0

The loop cohomology of a space with the polynomial cohomology algebra 空间与多项式上同调代数的环上同调

IF 0.2 Q4 MATHEMATICS

Transactions of A Razmadze Mathematical Institute

Pub Date : 2017-12-01 DOI: 10.1016/j.trmi.2017.07.002

Samson Saneblidze

Given a simply connected space $X$ with polynomial cohomology $H^{*} (X; Z_{2}),$ we calculate the loop cohomology algebra $H^{*} (Ω X; Z_{2})$ by means of the action of the Steenrod cohomology operation $S q_{1}$ on $H^{*} (X; Z_{2}) .$ This calculation uses an explicit construction of the minimal Hirsch filtered model of the cochain algebra $C^{*} (X; Z_{2}) .$ As a consequence we obtain that $H^{*} (Ω X; Z_{2})$ is the exterior algebra if and only if $S q_{1}$ is multiplicatively decomposable on $H^{*} (X; Z_{2}) .$ The last statement in fact contains a converse of a theorem of A. Borel (Switzer, 1975, Theorem 15.60).

给定一个具有多项式上同调H∗(X;Z2)的单连通空间X，利用Steenrod上同调运算Sq1对H∗(X;Z2)的作用，计算出循环上同调代数H∗(ΩX;Z2)。此计算使用协链代数C * (X;Z2)的最小Hirsch过滤模型的显式构造。因此，我们得到H∗(ΩX;Z2)是外代数当且仅当Sq1在H∗(X;Z2)上是乘法可分解的。最后一个命题实际上包含了a . Borel (Switzer, 1975, theorem 15.60)的一个定理的逆。

引用次数: 2

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