地点：新主楼E1114
报告1
题目：含生成树结构的两阶段随机博弈及其合作解的稳定性研究（working paper）
摘要：本研究探讨了一种含生成树结构的两阶段随机网络博弈模型，旨在考虑参与人在不同博弈阶段的策略选择及其对网络博弈结果的影响。首先，在单阶段博弈中，定义了参与人的合作行为，并引入了特征函数以量化合作所带来的支付。此外，提出一种新的工具“α-矩阵”，以便在博弈中调整网络结构，从而模拟现实世界中不断变化的互动环境。在博弈模型的构建过程中，第一阶段的所有参与人的共同行为，会通过“α-矩阵”对第二阶段的博弈结构产生影响。在此基础上，进一步明确定义了参与人在两阶段随机网络博弈中的合作行为，并计算了联盟的特征函数、确立了合作路径与合作解。为了确保合作行为的稳定性和持续性，本研究通过动态补偿程序（Imputation Distribution Procedure），提出了一种满足强动态稳定性的合作解——动态沙普利向量。该向量不仅能够反映参与人在合作过程中的贡献，还能够适应网络结构的随机变化，保证合作解的动态适应性。同时，研究也探讨了非合作方法在该博弈模型中构建合作解的应用，特别是动态纳什谈判解的构建及其动态稳定性。
报告人简介：李寅，哈尔滨工业大学数学学院副教授，俄罗斯圣彼得堡国立大学切比雪夫实验室计算机系科学委员会委员，圣彼得堡国立大学《人工智能和数据科学》研究中心研究员。博士毕业于圣彼得堡国立大学，曾受中国留学基金委公派博士留学，前华为科技有限公司圣彼得堡研究所自动驾驶网络实验室高级工程师，曾任ICM2022 国际数学家大会卫星会议《Game Theory and Applications》组织委员会委员。师从国际知名博弈论学者Leon Petrosjan院士（圣彼得堡国立大学应用数学系系主任，前国际动态博弈学会主席，亚美尼亚科学院外籍院士）。主要从事动态合作博弈、动态网络博弈等方面的研究。
报告2
题目：CREEP AND LONG-TERM STRENGTH OF HIGH-ENTROPY ALLOYS
摘要:High-entropy alloys (HEAs) are actively being investigated for next-generation structural materials. Gaining a comprehensive understanding of their creep behavior is necessary. These aspects of mechanical properties are especially important because creep resistance determines the use of the alloys in high-temperature applications. Because the materials with superior properties are continuously searched, high-entropy alloys (HEAs), formed by the metallurgy of five or more metallic elements with equal or nearly equal quantities, emerge as a class of revolutionary materials. One decade of dedicated research has revealed that many HEAs possess unparalleled properties in comparison with traditional alloys, for instance, great thermal and microstructural stability, high hardness, high strength at a wide range of temperatures, and excellent resistance to wear, corrosion, fatigue, fracture, and high-temperature softening. Given these merits, applications of HEAs in various fields, particularly in the structural engineering (e.g., used for gas-turbine engines), is being actively explored. Among many performance indices, a thorough understanding of creep behavior of HEAs is crucial and indispensable to their complex engineering applications.
In the work to describe the creep and long-term strength of HEAs a damage conception is used. A system of interconnected kinetic equations for the creep rate and damage parameter is formulated. A compressible medium is considered and the mass conservation law is taking into account. The damage parameter is specifying in the form of the ratio of the current density of the material to the initial one. Exact and approximate analytical solutions of these equations are obtained. The theoretical creep and long-term strength curves are plotted and compared with the experimental results for CrMnFeCoNi alloy. It is shown, that the experimental results are in good agreement with the theoretical ones. Thus, the proposed system of interrelated kinetic equations allows us to describe the creep and long-term strength behavior of HEAs.
报告人简介：Regina Saitova，俄罗斯籍，1993年出生，物理学与数学博士（PhD），圣彼得堡国立大学基础数学与信息学教研室副教授，弹性理论教研室高级研究员。于2011-2016年在圣彼得堡国立大学数学与力学系攻读本科，2016-2020年攻读博士学位，并于2020年在英国基尔大学计算数学学院实习。她的研究领域包括数学力学、高温蠕变、材料损伤、金属蠕变和金属长期强度。Saitova教授已在多个知名期刊上发表21篇同行评审论文，并参与了多个研究项目。
报告3
题目：Tropical Optimization Problems: Solution and Application Examples
摘要：We consider multidimensional optimization problems formulated in the framework of tropical mathematics which deals with the theory and applications of algebraic systems with idempotent operations. We start with a motivational example of a project-scheduling problem. Next, we outline basic definitions and notation of tropical algebra to provide a formal framework for the discussion, and overview some known tropical optimization problems. Finally, we consider practical problems that come from project scheduling and decision making, and present their solutions given in a compact vector form ready for further analysis and straightforward computation.
报告人介绍：NIKOLAI K. KRIVULIN教授，生于1958年，俄罗斯乌里扬诺夫斯克人。现任圣彼得堡国立大学数学与力学系统计建模教研室教授。他在该校获得了计算数学博士学位和应用数学硕士学位。克里武林教授的研究领域包括幂等代数、优化方法、排队系统分析等，并在这些领域发表了多篇研究论文。他的工作得到了多个研究基金会的支持，包括俄罗斯基础研究基金会和人文科学基金会。此外，他还担任了多个学术职务，如博士论文答辩委员会主席等。
科技处 理学院
2024年7月13日