A duality theorem for generalized local cohomology

We prove a duality theorem for graded algebras over a field that implies several known duality results: graded local duality, versions of Serre duality for local cohomology and of Suzuki duality for generalized local cohomology, and Herzog-Rahimi bigraded duality.

     

On strong and total Lagrange duality for convex optimization problems

We give some necessary and sufficient conditions which completely characterize the strong and total Lagrange duality, respectively, for convex optimization problems in separated locally convex spaces. We also prove similar statements for the problems obtained by perturbing the objective functions of the primal problems by arbitrary linear functionals. In the particular case when we deal with convex optimization problems having infinitely many convex inequalities as constraints the conditions we work with turn into the so-called Farkas-Minkowski and locally Farkas-Minkowski conditions for systems of convex inequalities, recently used in the literature. Moreover, we show that our new results extend some existing ones in the literature.     

复函数Cauchy微分中值定理的推广

以分割区域D为基础将解析函数与共轭解析函数的微分中值定理推广到高阶形式.     

Uniform LP duality for semidefinite and semi-infinite programming

Recently, a semidefinite and semi-infinite linear programming problem (SDSIP), its dual (DSDSIP), and uniform LP duality between (SDSIP) and (DSDSIP) were proposed and studied by Li et al. (Optimization 52:507–528, 2003). In this paper, we show that (SDSIP) is an ordinary linear semi-infinite program and, therefore, all the existing results regarding duality and uniform LP duality for linear semi-infinite programs can be applied to (SDSIP). By this approach, the main results of Li et al. (Optimization 52:507–528, 2003) can be obtained easily.     

Inverse complementarity in a resource deficit model

The concept of inverse complementarity for a parametric family of optimization problems is introduced. This concept is an effective tool for solving complicated applied problems arising in socioeconomic systems. As an example, a nonlinear resource deficit model is constructed in which the equilibrium is characterized by an external market value of resources coinciding with internal objectively determined resource estimates. An extraproximal method is proposed for computing an equilibrium solution. The convergence of the method is proved. Original Russian Text. A.V. Zykina, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 11, pp. 1968–1978.     

A Coupling Framework for Multi-Domain Modelling and Multi-Physics Simulations

This paper describes a coupling framework for parallel execution of different solvers for multi-physics and multi-domain simulations with an arbitrary number of adjacent zones connected by different physical or overlapping interfaces. The coupling architecture is based on the execution of several instances of the same coupling code and relies on the use of smart edges (i.e., separate processes) dedicated to managing the exchange of information between two adjacent regions. The collection of solvers and coupling sessions forms a flexible and modular system, where the data exchange is handled by independent servers that are dedicated to a single interface connecting two solvers’ sessions. Accuracy and performance of the strategy is considered for turbomachinery applications involving Conjugate Heat Transfer (CHT) analysis and Sliding Plane (SP) interfaces.     

气膜孔角度对动叶前缘冲击/气膜复合冷却的影响

本文针对GE-E3第一级动叶前缘的冲击/气膜复合冷却结构进行了热流耦合数值研究。采用标准k-ω湍流模型,分析了前缘气膜孔对称布置时,其角度对透平动叶前缘冲击/气膜复合冷却特性的影响;在五种冷气质量流量比(MFR=0.005,0.010,0.016,0.020,0.025)下,研究了气膜孔在不同角度(β=20°,25°,30°,40°,50°,60°)时的透平动叶前缘冷却换热效果。研究结果表明:在本文研究范围内,气膜孔角度越小,透平动叶前缘的平均综合冷却效率越高;随着冷气质量流量比增大,透平动叶前缘的平均综合冷却效率逐渐提高。     

A pedagogical review on solvable irrelevant deformations of 2D quantum field theory

This is a pedagogical review on ■ deformation of two dimensional quantum field theories. It is based on three lectures which the author gave at ITP-CAS in December 2018. This review consists of four parts. The first part is a general introduction to ■ deformation. Special emphasises are put on the deformed classical Lagrangian and the exact solvability of the spectrum. The second part focuses on the torus partition sum of the ■ deformed conformal field theories and modular invariance/covariance. In the third part, different perspectives of ■ deformation are presented, including its relation to random geometry, 2D topological gravity and holography. We summarize more recent developments until January 2021 in the last part.