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Simple closed geodesics on regular tetrahedra in spherical space 球面空间正四面体上的简单封闭测地线
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2021-01-18 DOI: 10.1070/SM9433
A. Borisenko, D. Sukhorebska
We prove that there are finitely many simple closed geodesics on regular tetrahedra in spherical space. Also, for any pair of coprime positive integers , we find constants and depending on and and satisfying the inequality , such that a regular spherical tetrahedron with planar angle has a unique simple closed geodesic of type , up to tetrahedron isometry, whilst a regular spherical tetrahedron with planar angle has no such geodesic. Bibliography: 19 titles.
证明了球面空间中正四面体上存在有限多条简单封闭测地线。此外,对于任意一对协素数正整数,我们找到了依赖于且满足不等式的常数,使得具有平面角的正球面四面体具有唯一的简单封闭测地线类型,直至四面体等距,而具有平面角的正球面四面体没有这样的简单封闭测地线。参考书目:19篇。
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引用次数: 3
Two game-theoretic problems of approach 方法的两个博弈论问题
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2021-01-01 DOI: 10.1070/SM9496
A. Ershov, A. V. Ushakov, V. Ushakov
A nonlinear conflict control system in a finite-dimensional Euclidean space on a finite time interval is considered. Two interrelated game-theoretic problems of making a system approach a compact set at a fixed moment of time are studied. A method for constructing approximate solutions to game problems of approach is presented. Most attention is paid to problems related to constructing approximations of the solvability sets of game problems in the phase space. Bibliography: 35 titles.
研究有限时间区间有限维欧氏空间中的非线性冲突控制系统。研究了使系统在固定时刻趋近于紧集的两个相互关联的博弈论问题。提出了一种构造逼近对策问题近似解的方法。在相空间中构造博弈问题的可解集的近似是最受关注的问题。参考书目:35种。
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引用次数: 0
Polynomial Hermite-Pad� [IMG align=ABSMIDDLE alt=$ m$]tex_sm_4975_img1[/IMG]-system for meromorphic functions on a compact Riemann surface 紧黎曼曲面上亚纯函数的多项式Hermite-Pad [IMG align=ABSMIDDLE alt=$ m$]tex_sm_4975_img1[/IMG]系统
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2021-01-01 DOI: 10.1070/sm9577
A. Komlov
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引用次数: 0
Hua Loo-Keng’s problem for primes of a special form 一种特殊形式质数的华娄铿问题
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2021-01-01 DOI: 10.1070/SM9394
K. M. Éminyan
Hua Loo-Keng’s problem is solved for primes, four of which have binary expansions of a special form, whilst the fifth satisfies the inequality , where . Bibliography: 13 titles.
Hua Loo-Keng的问题解决了质数的问题,其中四个质数具有特殊形式的二进制展开,而第五个满足不等式,其中。参考书目:13篇。
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引用次数: 0
A strengthening of the Bourgain-Kontorovich method: three new theorems bourgin - kontorovich方法的强化:三个新定理
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2021-01-01 DOI: 10.1070/SM9437
I. D. Kan
Consider the set of irreducible denominators of the rational numbers representable by finite continued fractions all of whose partial quotients belong to some finite alphabet . Let the set of infinite continued fractions with partial quotients in this alphabet have Hausdorff dimension satisfying . Then contains a positive share of positive integers. A previous similar result of the author of 2017 was related to the inequality 0.7807dots$?> ; in the original 2011 Bourgain-Kontorovich paper, 0.9839dots$?> . Bibliography: 28 titles.
考虑可由有限连分式表示的有理数的不可约分母的集合,所有这些有理数的部分商都属于某个有限字母。设该字母表中具有部分商的无限连分式集合具有满足的豪斯多夫维数。则包含正整数的正份额。作者在2017年的一个类似结果与不等式0.7807dots$?>;在2011年的Bourgain-Kontorovich论文中,0.9839dots$?>。参考书目:28种。
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引用次数: 4
The preservation of threshold resonances and the splitting off of eigenvalues from the threshold of the continuous spectrum of quantum waveguides 阈值共振的保留和特征值与量子波导连续谱阈值的分离
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2021-01-01 DOI: 10.1070/SM9426
S. A. Nazarov
Threshold resonance arises on the lower bound of the continuous spectrum of a quantum waveguide (the Dirichlet problem for the Laplace operator), provided that for this value of the spectral parameter a nontrivial bounded solution exists which is either a trapped wave decaying at infinity or an almost standing wave stabilizing at infinity. In many problems in asymptotic analysis, it is important to be able to distinguish which of the waves initiates the threshold resonance; in this work we discuss several ways to clarify its properties. In addition, we demonstrate how the threshold resonance can be preserved by fine tuning the profile of the waveguide wall, and we obtain asymptotic expressions for the near-threshold eigenvalues appearing in the discrete or continuous spectrum when the threshold resonance is destroyed. Bibliography: 60 titles.
阈值共振发生在量子波导连续谱的下界(拉普拉斯算子的狄利克雷问题),前提是谱参数的这个值存在一个非平凡的有界解,该解要么是在无穷远处衰减的捕获波,要么是在无穷远处稳定的几乎驻波。在渐近分析的许多问题中,重要的是能够区分哪些波引起阈值共振;在这项工作中,我们讨论了几种澄清其性质的方法。此外,我们还演示了如何通过微调波导壁的轮廓来保留阈值共振,并获得了当阈值共振被破坏时,在离散或连续频谱中出现的近阈值特征值的渐近表达式。参考书目:60篇。
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引用次数: 1
Uniform approximation of functions by solutions of strongly elliptic equations of second order on compact subsets of 的紧子集上二阶强椭圆方程解的函数一致逼近
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2021-01-01 DOI: 10.1070/SM9503
P. V. Paramonov
Criteria for the uniform approximation of functions by solutions of second-order strongly elliptic equations on compact subsets of are obtained using the method of reduction to similar problems in , which were previously investigated by Mazalov. A number of metric properties of the capacities used are established. Bibliography: 16 titles.
利用Mazalov先前研究的一类问题的约化方法,得到了二阶强椭圆型方程在紧子集上解一致逼近函数的准则。建立了所使用的容量的一些度量属性。参考书目:16篇。
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引用次数: 1
Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition 匀化狄利克雷条件下沿规定流形细穿孔区域问题的一致收敛性和渐近性
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2021-01-01 DOI: 10.1070/SM9435
Denis Borisov, A. I. Mukhametrakhimova
A boundary value problem for a second-order elliptic equation with variable coefficients is considered in a multidimensional domain which is perforated by small holes along a prescribed manifold. Minimal natural conditions are imposed on the holes. In particular, all of these are assumed to be of approximately the same size and have a prescribed minimal distance to neighbouring holes, which is also a small parameter. The shape of the holes and their distribution along the manifold are arbitrary. The holes are divided between two sets in an arbitrary way. The Dirichlet condition is imposed on the boundaries of holes in the first set and a nonlinear Robin boundary condition is imposed on the boundaries of holes in the second. The sizes and distribution of holes with the Dirichlet condition satisfy a simple and easily verifiable condition which ensures that these holes disappear after homogenization and a Dirichlet condition on the manifold in question arises instead. We prove that the solution of the perturbed problem converges to the solution of the homogenized one in the -norm uniformly with respect to the right-hand side of the equation, and an estimate for the rate of convergence that is sharp in order is deduced. The full asymptotic solution of the perturbed problem is also constructed in the case when the holes form a periodic set arranged along a prescribed hyperplane. Bibliography: 32 titles.
研究了一类二阶变系数椭圆方程的边值问题,该方程是在一个由小孔沿规定流形穿孔的多维域上。最小的自然条件强加于孔。特别地,所有这些都被假设为尺寸大致相同,并且与邻近孔具有规定的最小距离,这也是一个小参数。孔的形状及其沿流形的分布是任意的。这些洞以任意的方式被分成两组。在第一组空穴边界上施加Dirichlet条件,在第二组空穴边界上施加非线性Robin边界条件。具有狄利克雷条件的孔的大小和分布满足一个简单且易于验证的条件,即这些孔在均匀化后消失,取而代之的是流形上的狄利克雷条件。我们证明了摄动问题的解相对于方程的右侧在-范数下一致收敛于齐化问题的解,并推导了收敛速度的一个极序估计。当孔形成沿规定超平面排列的周期集时,构造了扰动问题的完全渐近解。参考书目:32种。
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引用次数: 9
A trace formula for higher order ordinary differential operators 高阶常微分算子的迹公式
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2021-01-01 DOI: 10.1070/SM9449
E. D. Gal’kovskii, A. Nazarov
We obtain a first-order trace formula for a higher order differential operator on a closed interval in the case where the perturbation operator is the operator of multiplication by a finite complex-valued charge. For operators of even orders , the result contains a term of new type, previously unknown. Bibliography: 15 titles.
我们得到了闭区间上高阶微分算子的一阶迹公式,其中微扰算子是与有限复值电荷相乘的算子。对于偶阶算子,结果包含一个新类型的项,以前未知。参考书目:15篇。
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引用次数: 2
The regularized asymptotics of a solution of the Cauchy problem in the presence of a weak turning point of the limit operator 在极限算子的弱拐点存在下Cauchy问题解的正则渐近性
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2021-01-01 DOI: 10.1070/SM9444
A. Eliseev
An asymptotic solution of the linear Cauchy problem in the presence of a ‘weak’ turning point of the limit operator is built using Lomov’s regularization method. The major singularities of the problem are written out in an explicit form. Estimates are given with respect to , which characterise the behaviour of the singularities as . The asymptotic convergence of the regularized series is proved. The results of the work are illustrated by an example. Bibliography: 8 titles.
利用Lomov正则化方法建立了存在极限算子“弱”拐点的线性Cauchy问题的渐近解。这个问题的主要奇异点是用显式形式写出来的。给出了关于的估计,它将奇点的行为表征为。证明了正则化级数的渐近收敛性。通过一个算例说明了工作的结果。参考书目:8篇。
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引用次数: 1
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