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Rigid body dynamics from the Euler equations to the spacecraft attitude control in the works of scientists from Saint Petersburg State University. Part 1 从欧拉方程到航天器姿态控制的刚体动力学在圣彼得堡国立大学科学家的著作中。第1部分
Pub Date : 2023-01-01 DOI: 10.21638/spbu01.2023.303
Аleksey А. Tikhonov
This survey, which consists of several articles, is dedicated to the 300th anniversary ofSaint Petersburg State University (SPbSU) and is an attempt to analyze the scientific achievements of the Saint Petersburg School of Mathematics and Mechanics in the field achievements of the period from the founding of SPbSU to the mid-1970s. Due to the anniversary nature of this work, the scientific results obtained at SPbSU are considered in the context of events inextricably linked with the founding of the Academy of Sciences, the University and the gymnasium in 1724 and their further development over the next 250 years. Due to the impossibility to cover even briefly all the publications that appeared during this period, attention is focused on the most important general areas of scientific thought and on those outstanding scientists of SPbSU, whose works enriched these areas.
该调查由几篇文章组成,旨在纪念圣彼得堡国立大学(SPbSU)成立300周年,并试图分析圣彼得堡数学和力学学院从建校到20世纪70年代中期的科学成就。由于这项工作的周年性质,在SPbSU获得的科学成果被认为与1724年科学院,大学和体育馆的成立以及它们在未来250年的进一步发展有着千丝万缕的联系。由于不可能简单地涵盖这一时期出现的所有出版物,因此注意力集中在科学思想的最重要的一般领域和北京外国语大学的杰出科学家身上,他们的作品丰富了这些领域。
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引用次数: 0
Examining the possibility of insurance contract conclusion based on utility function 基于效用函数的保险合同订立可能性研究
Pub Date : 2023-01-01 DOI: 10.21638/11701/spbu10.2023.305
Alexander V. Sachkov
The problem of a potential insurance contract conclusion is considered taking into account client’s money utility function. A basic model is employed for practical calculations and a formula is proposed and tried for two utility functions corresponding to polar income decile groups. Conclusions are made with suggested future research directions.
考虑到客户的货币效用函数,考虑了潜在的保险合同订立问题。采用基本模型进行实际计算,提出并尝试了对应两极收入十分位数组的两个效用函数的公式。最后,对今后的研究方向提出了建议。
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引用次数: 0
The role of business culture in modelling the firm’s internal environment 企业文化在塑造公司内部环境中的作用
Pub Date : 2023-01-01 DOI: 10.21638/spbu05.2023.306
Igor Arenkov, Vladimir Zyabrikov, Igor Shevazutskii
A variety of firm’s internal environment models has been formed for about half a century, starting with S. Gibson triad (strategy — structure — systems), which first formulated the sequence of strategic planning stages, and ending with the PEST-atom model, which reflects not only the composition of the elements of internal environment, but also the relationships between them. The article shows that a modern system, which would reflect the structure of the elements of firm’s internal environment, should be built on the basis of its key element, inextricably linked to the essence of the firm and, at the same time, synchronously changing with it in the course of movement along the trajectory of the life cycle. Such element, which directly determines the degree of maturity of a firm, is its culture. Business culture is the central connecting element of the internal environment of a firm, providing a harmonious combination of all its other elements: strategy, organizational structure, motivation system, etc. and making the firm attractive for investment. At the same time the type of business culture is the main indicator of the stage of the life cycle of a firm, and since the diversity of culture types is limited to four types: the cultures of a professional, leader, bureaucrat andentrepreneur, the process of movement of a firm through the stages of its life cycle can be turned into a manageable one. In order to do this in the second half of the firm’s maturity stage the role of professional should be made dominant, and the decline stage should be transformed into the revival stage. This transition will require the transformation of the internal environment of a firm in accordance with the model of intelligent organization, which is a logical development of the concept of a self-learning organization.The paper shows that in the course of movement along the trajectory of its life cycle a firm, by ensuring innovative attractiveness and reducing operating costs per unit, consistently implements the following “chain of criteria”: innovativeness (introduction stage) — efficiency (start-up stage) — productivity (growth stage) — effectiveness (maturity stage). The possibility of applying the theoretical aspects proposed by the authors is confirmed in practice in the study of the life cycle of Rodnik LLC.
大约半个世纪以来,各种各样的企业内部环境模型已经形成,从S. Gibson triad(战略-结构-系统)开始,它首先制定了战略规划阶段的顺序,以pest -原子模型结束,它不仅反映了内部环境要素的组成,而且反映了它们之间的关系。现代企业内部环境制度应以企业内部环境要素结构为基础,与企业本质紧密相连,并在企业生命周期的运动过程中与企业本质同步变化,以反映企业内部环境要素的结构。这种直接决定企业成熟程度的因素就是企业文化。企业文化是企业内部环境的中心连接要素,是企业战略、组织结构、激励制度等要素的和谐结合,使企业对投资具有吸引力。同时,企业文化的类型是企业生命周期阶段的主要指标,由于文化类型的多样性仅限于四种类型:专业人员,领导者,官僚和企业家的文化,因此企业通过其生命周期阶段的运动过程可以变成一个可管理的过程。要在企业成熟期的后半段做到这一点,就应该使专业人员的作用发挥主导作用,把衰退期转变为复兴期。这种转变将要求企业内部环境按照智能组织的模式进行改造,这是自学习型组织概念的逻辑发展。本文表明,企业在其生命周期的运动轨迹中,通过确保创新吸引力和降低单位运营成本,始终贯彻以下“准则链”:创新性(引入阶段)-效率(启动阶段)-生产率(成长阶段)-有效性(成熟阶段)。作者提出的理论方面在罗德尼克有限责任公司生命周期研究的实践中得到了证实。
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引用次数: 0
Scientific school of non-equilibrium aeromechanics in Saint Petersburg State University 圣彼得堡国立大学非平衡空气力学科学学院
Pub Date : 2023-01-01 DOI: 10.21638/spbu01.2023.302
Yulia N. Voroshilova, Vladimir A. Istomin, Ol’ga V. Kunova, Elena V. Kustova, Ekaterina A. Nagnibeda, Maria A. Rydalevskaya
The review is devoted to the foundation and development of the scientific school of S. V. Vallander at the Leningrad (now St Petersburg) State University. The achievements of the scientific school in the development of the kinetic theory methods for modeling nonequilibrium flows, construction of rigorous self-consistent mathematical models of varying complexity for strong and weak deviations from equilibrium, and the use of the developed models in challenging problems of modern aerodynamics are discussed. Particular attention is paid to the study of non-equilibrium kinetics and transport processes in carbon dioxide, identification of key relaxation mechanisms of polyatomic molecules, derivation of physically based reduced hybrid models, and optimization of non-equilibrium flow numerical simulations using modern machine learning methods. Correct description of electronic excitation in the kinetics and transport processes, models of local equilibrium gas flows with multiple ionization, and features of modeling bulk viscosity in polyatomic gases are discussed.
该评论致力于列宁格勒(现圣彼得堡)国立大学S. V. Vallander科学学院的建立和发展。本文讨论了科学学派在发展非平衡流动建模的动力学理论方法、为平衡的强弱偏差建立严格的自洽数学模型以及在现代空气动力学难题中的应用等方面所取得的成就。特别关注二氧化碳的非平衡动力学和输运过程的研究,多原子分子的关键松弛机制的确定,基于物理的简化混合模型的推导,以及使用现代机器学习方法优化非平衡流动数值模拟。讨论了动力学和输运过程中电子激发的正确描述,多次电离的局部平衡气体流动模型,以及多原子气体体粘度的建模特点。
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引用次数: 0
Transgression effect in the problem of motion of a rod on a cylinder 杆在圆柱上运动问题中的海侵效应
Pub Date : 2023-01-01 DOI: 10.21638/spbu01.2023.310
Alexander S. Kuleshov, Nikita M. Vidov
The problem of motion of a heavy rigid thin rod on a perfectly rough right circular cylinder is considered. It is assumed that the generatrix of the cylinder has a nonzero angle with the direction of gravity. The equilibrium positions of the rod on a cylinder form the equilibria manifold (for all these equilibria the rod touches the cylinder by its center of mass). The effect of transgression (nontrivial evolution along the equilibria manifold) of the rod on the cylinder is studied by the normal form method.
研究了一根重刚性细杆在完全粗糙的右圆柱上的运动问题。假设柱体母线与重力方向夹角不为零。杆在圆柱体上的平衡位置形成平衡流形(对于所有这些平衡,杆通过其质心接触圆柱体)。采用范式方法研究了杆的超进(沿平衡流形的非平凡演化)对圆柱体的影响。
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引用次数: 0
Inequalities for the derivative of rational functions with prescribed poles and restricted zeros 具有规定极点和限制零点的有理函数导数的不等式
Pub Date : 2023-01-01 DOI: 10.21638/spbu01.2023.309
Uzma M. Ahanger, Wal M. Shah
In this paper, instead of assuming that a rational function r(z) with prescribed poles has a zero of order s at origin, we suppose that it has a zero of multiplicity s at any point inside the unit circle, whereas the remaining zeros are within or outside a circle of radius k and prove some results which besides generalizing some inequalities for rational functions include refinements of some polynomial inequalities as special cases.
本文不再假设具有规定极点的有理函数r(z)在原点处有一个s阶的零点,而是假设它在单位圆内任意点处有一个s阶的零点,其余零点在半径为k的圆内或圆外,并证明了一些结果,这些结果除了推广有理函数的一些不等式外,还包括一些多项式不等式的特殊改进。
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引用次数: 0
Microgrid control for renewable energy sources based on deep reinforcement learning and numerical optimization approaches 基于深度强化学习和数值优化方法的可再生能源微电网控制
Pub Date : 2023-01-01 DOI: 10.21638/11701/spbu10.2023.307
Anastasia Yu. Zhadan, Haitao Wu, Pavel S. Kudin, Yuyi Zhang, Ovanes L. Petrosian
Optimal scheduling of battery energy storage system plays crucial part in dis- tributed energy system. As a data driven method, deep reinforcement learning does not require system knowledge of dynamic system, present optimal solution for nonlinear optimization problem. In this research, financial cost of energy con- sumption reduced by scheduling battery energy using deep reinforcement learning method (RL). Reinforcement learning can adapt to equipment parameter changes and noise in the data, while mixed-integer linear programming (MILP) requires high accuracy in forecasting power generation and demand, accurate equipment parameters to achieve good performance, and high computational cost for large- scale industrial applications. Based on this, it can be assumed that deep RL based solution is capable of outperform classic deterministic optimization model MILP. This study compares four state-of-the-art RL algorithms for the battery power plant control problem: PPO, A2C, SAC, TD3. According to the simulation results, TD3 shows the best results, outperforming MILP by 5% in cost savings, and the time to solve the problem is reduced by about a factor of three.
电池储能系统的优化调度在分布式能源系统中起着至关重要的作用。作为一种数据驱动的方法,深度强化学习不需要动态系统的系统知识,为非线性优化问题提供最优解。在本研究中,采用深度强化学习方法(RL)对电池能量进行调度,降低了能源消耗的财务成本。强化学习可以适应设备参数变化和数据中的噪声,而混合整数线性规划(MILP)对发电量和需求的预测精度要求高,对设备参数的准确性要求高,以达到良好的性能,对大规模工业应用的计算成本要求高。基于此,可以假设基于深度强化学习的解决方案能够优于经典的确定性优化模型MILP。本研究比较了电池电厂控制问题的四种最先进的RL算法:PPO, A2C, SAC, TD3。根据仿真结果,TD3显示出最好的结果,在节省成本方面比MILP高出5%,并且解决问题的时间减少了大约三分之一。
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引用次数: 0
Matrix representations of endomorphism rings for torsion-free abelian groups 无扭阿贝尔群的自同态环的矩阵表示
Pub Date : 2023-01-01 DOI: 10.21638/spbu01.2023.304
Ekaterina А. Blagoveshchenskaya, Alexander V. Mikhalev
Non-isomorphic direct decompositions of torsion-free abelian groups are reflected in their endomorphism ring decompositions which admit matrix representations. The set of possible direct decompositions of a special kind matrix rings into direct sums of one-sided indecomposable ideals is described. This leads to the combinatorial constructions of isomorphisms between non-commutative differently decomposable ring structures.
无扭阿贝尔群的非同构直接分解反映在其允许矩阵表示的自同构环分解上。描述了一类特殊矩阵环可能直接分解为单侧不可分解理想的直接和的集合。这导致了非交换的不同可分解环结构之间同构的组合构造。
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引用次数: 0
On probabilities of large deviations of combinatorial sums of independent random variables satisfying Linnik’s condition 满足林尼克条件的独立随机变量组合和的大偏差概率
Pub Date : 2023-01-01 DOI: 10.21638/spbu01.2023.308
Аndrei N. Frolov
We derive new results on asymptotic behaviour for probabilities of large deviations of combinatorial sums of independent random variables satisfying Linnik’s condition. We find zones in which these probabilities are equivalent to the tail of the standard normal law. The author earlier obtained such results under Bernstein’s condition. The truncations method is applied in proofs of results.
我们得到了满足Linnik条件的独立随机变量组合和的大偏差概率的渐近性的新结果。我们找到了这些概率等于标准正态定律尾部的区域。笔者之前在Bernstein的条件下得到了这样的结果。截断法应用于结果的证明。
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引用次数: 0
Expected effects of projected institutional changes in digital out-of-home advertising 数字户外广告预计制度变化的预期影响
Pub Date : 2023-01-01 DOI: 10.21638/spbu05.2023.303
Andrey Shastitko, Anton Morozov, Anastasia Morosanova
During the political, economic instability and uncertainty, both the goals of economic regulation and the methods of decision-making are changing. Against the backdrop of changes in state policy, the need to ensure national security is becoming more acute, while there are still decision-making risks associated with the rent-seeking behavior of the regulatory authority or some market players. This article considers Draft law no. 160605–8 “On Amendments to the Federal Law “On Advertising” in context of regulating relations in the outdoor advertising, both in terms of the legislative innovation effectsand the compliance of these norms with the criteria for “promising trajectories” of institutional changes. After a resonant discussion in the media, the Draft law was rejected by the State Duma in its second reading, which confirms the importance of public discussions on lawmaking and economic analysis of the proposed measures. With the regulatory impact assessment methodology, we get a qualitative and quantitative estimation of organizational and technical measures of the proposed regulation (namely, the emergence of a private single operator of digital advertising structures). We also offer alternative institutional solutions that allow achieving the proclaimed goal of the draft law with greater efficiency: the introduction of business requirements (licensing, accreditation, maintaining a registry) or implementation of market self-organization. We conclude that granting control functions to one of the market players creates risks associated with an unresolved conflict of interest, which can lead to monopolization of digital out-of-home services and budget losses.
在政治、经济不稳定和不确定时期,经济调控的目标和决策方式都在发生变化。在国家政策变化的背景下,保障国家安全的需求日益迫切,但监管部门或部分市场主体的寻租行为仍存在决策风险。本条考虑第2号法律草案。160605-8《论联邦广告法修正案在规范户外广告关系的背景下,从立法创新效果和这些规范与制度变化“有希望的轨迹”标准的遵从性两方面来看》。经过媒体的热烈讨论,国家杜马在二读中否决了该法律草案,这证实了公众讨论立法和对拟议措施进行经济分析的重要性。通过监管影响评估方法,我们对拟议监管的组织和技术措施(即数字广告结构的私人单一运营商的出现)进行了定性和定量估计。我们还提供了其他制度解决方案,可以更有效地实现法律草案所宣布的目标:引入业务要求(许可、认证、维护注册)或实施市场自组织。我们得出的结论是,将控制职能授予一个市场参与者会产生与未解决的利益冲突相关的风险,这可能导致数字户外服务的垄断和预算损失。
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引用次数: 1
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Вестник Санкт-Петербургского университета
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