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Higher-order traps for some strongly degenerate quantum control systems 一些强退化量子控制系统的高阶陷阱
4区 数学 Q1 MATHEMATICS
Russian Mathematical Surveys
Pub Date : 2023-01-01 DOI: 10.4213/rm10069e
Boris Olegovich Volkov, Alexander Nikolaevich Pechen
Quantum control is necessary for a variety of modern quantum technologies as it allows to optimally manipulate quantum systems. An important problem in quantum control is to establish whether the control objective functional has trapping behaviour or no, namely if it has or no traps -- controls from which it is difficult to escape by local search optimization methods. Higher order traps were previously introduced in [A. N. Pechen, D. J. Tannor,"Are there traps in quantum control landscapes?", Phys. Rev. Lett., 106 (2011), 120402], where 3-rd order traps were found. In this note we show that traps of arbitrarily high order exist for controllable quantum systems with special symmetry in the Hamiltonian.
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引用次数: 0
Maps to virtual braids and braid representations 映射到虚拟辫子和辫子表示
4区 数学 Q1 MATHEMATICS
Russian Mathematical Surveys
Pub Date : 2023-01-01 DOI: 10.4213/rm10087e
Vassily Olegovich Manturov, Igor Mikhailovich Nikonov
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引用次数: 0
The number of components of the Pell-Abel equations with primitive solutions of given degree 具有给定阶元解的Pell-Abel方程的分量数
IF 0.9 4区 数学 Q1 MATHEMATICS
Russian Mathematical Surveys
Pub Date : 2023-01-01 DOI: 10.4213/rm10082e
A. Bogatyrev, Q. Gendron
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引用次数: 0
Index of minimal surfaces in the 3-sphere 球面上最小曲面的指数
4区 数学 Q1 MATHEMATICS
Russian Mathematical Surveys
Pub Date : 2023-01-01 DOI: 10.4213/rm10094e
Egor Aleksandrovich Morozov, Alexei Viktorovich Penskoi
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引用次数: 0
Geometry of Diophantine exponents 丢番图指数几何
4区 数学 Q1 MATHEMATICS
Russian Mathematical Surveys
Pub Date : 2023-01-01 DOI: 10.4213/rm10089e
Oleg Nikolaevich German
Diophantine exponents are some of the simplest quantitative characteristics responsible for the approximation properties of linear subspaces of a Euclidean space. This survey is aimed at describing the current state of the area of Diophantine approximation that studies Diophantine exponents and relations they satisfy. We discuss classical Diophantine exponents arising in the problem of approximating zero with the set of the values of several linear forms at integer points, their analogues in Diophantine approximation with weights, multiplicative Diophantine exponents, and Diophantine exponents of lattices. We pay special attention to the transference principle. Bibliography: 99 titles.
丢芬图指数是欧几里得空间线性子空间近似性质的最简单的定量特征。本文旨在描述丢番图近似领域的现状，即研究丢番图指数及其满足的关系。我们讨论了在整数点上用若干线性形式的值的集合逼近零问题中出现的经典丢番图指数，它们在带权的丢番图近似中的类似物，乘法丢番图指数，以及格的丢番图指数。我们特别注意移情原则。参考书目:99个标题。
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引用次数: 0
Cyclic Frobenius algebras 循环Frobenius代数
IF 0.9 4区 数学 Q1 MATHEMATICS
Russian Mathematical Surveys
Pub Date : 2023-01-01 DOI: 10.4213/rm10096e
V. Buchstaber, A. Mikhailov
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引用次数: 2
Left-invariant optimal control problems on Lie groups that are integrable by elliptic functions 椭圆函数可积李群上的左不变最优控制问题
IF 0.9 4区 数学 Q1 MATHEMATICS
Russian Mathematical Surveys
Pub Date : 2023-01-01 DOI: 10.4213/rm10063e
Y. Sachkov
Left-invariant optimal control problems on Lie groups are an important class of problems with a large symmetry group. They are theoretically interesting because they can often be investigated in full and general laws can be studied by using these model problems. In particular, problems on nilpotent Lie groups provide a fundamental nilpotent approximation to general problems. Also, left-invariant problems often arise in applications such as classical and quantum mechanics, geometry, robotics, visual perception models, and image processing. The aim of this paper is to present a survey of the main concepts, methods, and results pertaining to left-invariant optimal control problems on Lie groups that can be integrated by elliptic functions. The focus is on describing extremal trajectories and their optimality, the cut time and cut locus, and optimal synthesis. Bibliography: 162 titles.
李群上的左不变最优控制问题是一类具有大对称群的重要问题。它们在理论上很有趣，因为它们通常可以被完整地研究，并且可以通过使用这些模型问题来研究一般定律。特别地，幂零李群问题为一般问题提供了一个基本的幂零近似。此外，左不变问题经常出现在经典力学和量子力学、几何、机器人、视觉感知模型和图像处理等应用中。本文的目的是介绍有关可由椭圆函数积分的李群上的左不变最优控制问题的主要概念、方法和结果。重点是描述极值轨迹及其最优性，切割时间和切割轨迹，以及最优合成。参考书目:162篇。
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引用次数: 2
Extremal problems in geometric function theory 几何函数理论中的极值问题
4区 数学 Q1 MATHEMATICS
Russian Mathematical Surveys
Pub Date : 2023-01-01 DOI: 10.4213/rm10076e
Farit Gabidinovich Avkhadiev, Ilgiz Rifatovich Kayumov, Semen Rafailovich Nasyrov
This survey is devoted to a number of achievements in the theory of extremal problems in geometric function theory. The approaches to the solution of problems under consideration and the methods used are based on conformal isomorphisms and on the theory of univalent functions developed since the beginning of the 20th century. Results on integral means of conformal mappings of a disc are presented and, in particular, Dolzenko's inequality for rational functions is extended to arbitrary domains with rectifiable boundaries. Investigations in the field of Bohr-type inequalities are described. An emphasis is made on integral inequalities of Hardy and Rellich type, in which the analytic properties of inequalities are intertwined with geometric characteristics of the boundaries of domains. Results related to the solution of the Vuorinen problem on the behaviour of conformal moduli under unlimited dilations of the plane are presented. Formulae for the variation of Robin capacity are obtained. One-parameter families of rational and elliptic functions whose critical values vary in accordance with a prescribed law are characterized. The last results on Smale's conjecture and Smale's dual conjecture are described. Bibliography: 149 titles.
本文综述了几何函数理论中关于极值问题的一些研究成果。所考虑的问题的解决方法和所使用的方法是基于共形同构和自20世纪初以来发展起来的一元函数理论。给出了圆盘共形映射的积分均值的结果，并将有理函数的Dolzenko不等式推广到具有可整流边界的任意区域。描述了玻尔型不等式领域的研究。重点讨论了Hardy和Rellich类型的积分不等式，其中不等式的解析性质与域边界的几何特征交织在一起。给出了平面无限膨胀下共形模量行为的Vuorinen问题的解的有关结果。得到了Robin容量的变化公式。对临界值按一定规律变化的有理函数和椭圆函数的单参数族进行了刻画。给出了关于斯梅尔猜想和斯梅尔对偶猜想的最后结果。参考书目:149篇。
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引用次数: 0
Neurobehavioral and Biochemical Evidences in Support of Protective Effect of Marrubiin (Furan Labdane Diterpene) from Marrubium vulgare Linn. and Its Extracts after Traumatic Brain Injury in Experimental Mice. 实验小鼠脑外伤后神经行为和生化证据支持 Marrubiin（呋喃拉巴旦二萜）及其提取物的保护作用
4区 数学 Q1 MATHEMATICS
Russian Mathematical Surveys
Pub Date : 2022-05-24 eCollection Date: 2022-01-01 DOI: 10.1155/2022/4457973
Nidhi, Govind Singh, Rekha Valecha, Govind Shukla, Deepak Kaushik, Mohammad Akhlaquer Rahman, Rupesh K Gautam, Kumud Madan, Vineet Mittal, Rajeev K Singla

Traumatic brain injuries due to sudden accidents cause major physical and mental health problems and are one of the main reasons behind the mortality and disability of patients. Research on alternate natural sources could be a boon for the rehabilitation of poor TBI patients. The literature indicates the Marrubium vulgare Linn. and its secondary metabolite marrubiin (furan labdane diterpene) possess various pharmacological properties such as vasorelaxant, calcium channel blocker, antioxidant, and antiedematogenic activities. Hence, in the present research, both marrubiin and hydroalcoholic extracts of the plant were evaluated for their neuroprotective effect after TBI. The neurological severity score and oxidative stress parameters are significantly altered by the test samples. Moreover, the neurotransmitter analysis indicated a significant change in GABA and glutamate. The histopathological study also supported the observed results. The improved neuroprotective potential of the extract could be attributed to the presence of a large number of secondary metabolites including marrubiin.

突发事故造成的创伤性脑损伤会引发严重的身心健康问题，是导致患者死亡和残疾的主要原因之一。对替代性天然来源的研究可为贫困的创伤性脑损伤患者的康复带来福音。文献表明，马鲁草（Marrubium vulgare Linn.）及其次生代谢物马鲁宾（呋喃拉巴旦二萜）具有多种药理特性，如血管舒张剂、钙通道阻滞剂、抗氧化剂和抗致畸活性。因此，在本研究中，我们评估了大黄素和水醇提取物对创伤性脑损伤后神经的保护作用。测试样本明显改变了神经系统严重程度评分和氧化应激参数。此外，神经递质分析表明 GABA 和谷氨酸发生了明显变化。组织病理学研究也支持观察到的结果。萃取物的神经保护潜力得到提高，这可能是由于其中含有大量的次生代谢物，包括 marrubiin。
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引用次数: 0
The normal derivative lemma and surrounding issues 正规导数引理及其相关问题
IF 0.9 4区 数学 Q1 MATHEMATICS
Russian Mathematical Surveys
Pub Date : 2022-04-01 DOI: 10.1070/RM10049
D. Apushkinskaya, A. Nazarov
In this survey we describe the history and current state of one of the key areas in the qualitative theory of elliptic partial differential equations related to the strong maximum principle and the boundary point principle (normal derivative lemma). Bibliography: 234 titles.
本文描述了椭圆型偏微分方程定性理论中与强极大值原理和边界点原理(正规导数引理)有关的一个关键领域的历史和现状。参考书目:234种。
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引用次数: 10
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