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A hyperbolicity criterion for a class of diffeomorphisms of an infinite-dimensional torus 一类无限维环面微分同态的双曲性判据
IF 0.8 4区 数学 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.1070/SM9535
S. Glyzin, A. Kolesov
On an infinite-dimensional torus , where is an infinite-dimensional real Banach space and is an abstract integer lattice, a special class of diffeomorphisms is considered. It consists of the maps equal to sums of invertible bounded linear operators preserving and -smooth periodic additives. Necessary and sufficient conditions ensuring that such maps are hyperbolic (that is, are Anosov diffeomorphisms) are obtained. Bibliography: 15 titles.
在无限维环面上,考虑了一类特殊的微分同态,其中无限维实巴拿赫空间为抽象整数格。它由可逆有界线性算子和-光滑周期加法的映射组成。得到了保证这种映射是双曲的(即是ananosov微分同态)的充分必要条件。参考书目:15篇。
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引用次数: 1
Lyapunov instability of stationary flows of a polymeric fluid in a channel with perforated walls 聚合物流体在带孔壁面通道中固定流动的Lyapunov不稳定性
IF 0.8 4区 数学 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.1070/SM9507
A. Blokhin, D. Tkachev
The rheological Pokrovskii-Vinogradov model for flows of solutions or melts of an incompressible viscoelastic polymeric medium is studied in the case of flows in an infinite planar channel with perforated walls. The linear Lyapunov instability is proved for the base solution with constant flow rate in the class of perturbations periodic in the variable varying along the channel wall. Bibliography: 14 titles.
研究了不可压缩粘弹性聚合物介质中溶液或熔体流动的流变Pokrovskii-Vinogradov模型。证明了沿通道壁面变化变量的周期扰动类中具有恒定流量的基解的线性Lyapunov不稳定性。参考书目:14篇。
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引用次数: 1
A Chisini Theorem for almost generic covers of the projective plane 关于投影平面几乎一般覆盖的一个奇西尼定理
IF 0.8 4区 数学 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.1070/SM9568
V. Kulikov
Results related to Chisini’s Conjecture and contained in (Izv. Math. 63:6 (1999), 1139–1170) and (Izv. Math. 65:1 (2001), 71–74) are extended to the case of almost generic covers of the projective plane. Bibliography: 11 titles.
与奇西尼猜想有关的结果包含在(Izv.)。数学。63:6(1999),1139-1170)和(Izv。数学。65:1(2001),71-74)被推广到投影平面的几乎一般覆盖的情况。参考书目:11篇。
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引用次数: 1
Asymptotics of the sphere and front of a flat sub-Riemannian structure on the Martinet distribution 马提尼特分布下平面亚黎曼结构的球面和前沿的渐近性
IF 0.8 4区 数学 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.1070/sm9560
I. Bogaevsky
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引用次数: 0
Extremal functional -interpolation on an arbitrary mesh on the real axis 在实轴上任意网格上的极值函数插值
IF 0.8 4区 数学 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.1070/SM9628
Yu. N. Subbotin, V. T. Shevaldin
The Golomb-de Boor problem of extremal interpolation of infinite real sequences with smallest -norm of the th derivative of the interpolant, , on an arbitrary mesh on the real axis is studied under constraints on the norms of the corresponding divided differences. For this smallest norm, lower estimates are obtained for any in terms of -splines. For the second derivative, this quantity is estimated from below and above by constants depending on the parameter . Bibliography: 13 titles.
研究了在实数轴上任意网格上的无限实数序列的极值插值的最小范数的Golomb-de Boor问题,该问题具有相应的可分差的范数约束。对于这个最小的范数,用-样条表示的任何值都可以得到较低的估计。对于二阶导数,这个量是根据参数的常数从下面和上面估计的。参考书目:13篇。
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引用次数: 0
On the cohomology rings of partially projective quaternionic Stiefel manifolds 部分射影四元数Stiefel流形的上同调环
IF 0.8 4区 数学 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.1070/SM9601
G. E. Zhubanov, F. Y. Popelenskii
The quaternionic Stiefel manifold is the total space of a fibre bundle over the corresponding Grassmannian . The group acts freely on the fibres of this bundle. The quotient space is called the quaternionic projective Stiefel manifold. Its real and complex analogues were actively studied earlier by a number of authors. A finite group acting freely on the three-dimensional sphere also acts freely and discretely on the fibres of the quaternionic Stiefel bundle. The corresponding quotient spaces are called partially projective Stiefel manifolds. The cohomology rings of partially projective quaternionic Stiefel manifolds with coefficients in , where is prime, are calculated. Bibliography: 14 titles.
四元数Stiefel流形是纤维束在相应的格拉斯曼流形上的总空间。这个群在这个束的纤维上自由活动。商空间称为四元数投影Stiefel流形。它的真实和复杂的类似物早前被一些作者积极地研究过。自由作用于三维球面上的有限群也自由而离散地作用于四元数Stiefel束的纤维上。相应的商空间称为部分射影Stiefel流形。计算了系数为的部分投影四元数Stiefel流形的上同调环,其中为素数。参考书目:14篇。
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引用次数: 0
Existence of solutions of nonlinear elliptic equations with measure data in Musielak-Orlicz spaces Musielak-Orlicz空间中测量数据非线性椭圆方程解的存在性
IF 0.8 4区 数学 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.1070/SM9632
A. P. Kashnikova, L. M. Kozhevnikova
A second-order quasilinear elliptic equation with a measure of special form on the right-hand side is considered. Restrictions on the structure of the equation are imposed in terms of a generalized -function such that the conjugate function obeys the -condition and the corresponding Musielak-Orlicz space is not necessarily reflexive. In an arbitrary domain satisfying the segment property, the existence of an entropy solution of the Dirichlet problem is proved. It is established that this solution is renormalized. Bibliography: 29 titles.
研究了一类二阶拟线性椭圆方程,方程的右边有一个特殊形式的测度。对方程结构的限制以广义-函数的形式施加,使得共轭函数满足-条件,相应的Musielak-Orlicz空间不一定是自反的。在满足分段性质的任意定义域上,证明了狄利克雷问题熵解的存在性。证明了该解是重整化的。参考书目:29篇。
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引用次数: 0
A necessary and sufficient condition for the existence of simple closed geodesics on regular tetrahedra in spherical space 球面空间正四面体上简单封闭测地线存在的充分必要条件
IF 0.8 4区 数学 Q2 Mathematics Pub Date : 2022-01-01 DOI: 10.1070/SM9576
A. Borisenko
A necessary and sufficient condition is obtained for the existence of a simple closed geodesic of type on a regular tetrahedron in spherical space. Bibliography: 6 titles.
得到了球面空间中正四面体上存在一类简单封闭测地线的充分必要条件。参考书目:6篇。
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引用次数: 2
Slide polynomials and subword complexes 滑动多项式和子词复合体
IF 0.8 4区 数学 Q2 Mathematics Pub Date : 2021-12-14 DOI: 10.1070/sm9477
E. Yu. Smirnov, A. A. Tutubalina

Subword complexes were defined by Knutson and Miller in 2004 to describe Grbner degenerations of matrix Schubert varieties. Subword complexes of a certain type are called pipe dream complexes. The facets of such a complex are indexed by pipe dreams, or, equivalently, by monomials in the corresponding Schubert polynomial. In 2017 Assaf and Searles defined a basis of slide polynomials, generalizing Stanley symmetric functions, and described a combinatorial rule for expanding Schubert polynomials in this basis. We describe a decomposition of subword complexes into strata called slide complexes. The slide complexes appearing in such a way are shown to be homeomorphic to balls or spheres. For pipe dream complexes, such strata correspond to slide polynomials.

Bibliography: 14 titles.

子词复合体由Knutson和Miller于2004年定义,用于描述矩阵Schubert变的Grbner退化。某种类型的子词复合体被称为白日梦复合体。这样一个复合体的面由白日梦索引,或者,等价地,由相应的舒伯特多项式中的单项式索引。2017年,Assaf和Searles定义了slide多项式的基,推广了Stanley对称函数,并描述了在此基上展开Schubert多项式的组合规则。我们描述了子词复合体分解成称为滑动复合体的地层。以这种方式出现的滑动配合物被证明是与球或球体同胚的。对于白日梦复合体,这样的地层对应于滑动多项式。参考书目:14篇。
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引用次数: 0
Jordan property for groups of bimeromorphic automorphisms of compact Kähler threefolds 紧的双纯自同构群Kähler三叠的Jordan性质
IF 0.8 4区 数学 Q2 Mathematics Pub Date : 2021-12-05 DOI: 10.4213/sm9743e
A. Golota
Let $X$ be a non-uniruled compact K"ahler space of dimension 3. We show that the group of bimeromorphic automorphisms of $X$ is Jordan. More generally, the same result holds for any compact K"ahler space admitting a quasi-minimal model.
设X是一个3维的非正则紧K ahler空间。证明了$X$的双纯自同构群是Jordan。更一般地说,同样的结果适用于任何允许准极小模型的紧K ahler空间。
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引用次数: 4
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Sbornik Mathematics
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