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81.
Marc Chardin Kamran Divaani-Aazar 《Proceedings of the American Mathematical Society》2008,136(8):2749-2754
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.
82.
Radu Ioan Bo? Sorin-Mihai Grad 《Journal of Mathematical Analysis and Applications》2008,337(2):1315-1325
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. 相似文献
83.
84.
Qinghong Zhang 《Central European Journal of Operations Research》2008,16(2):205-213
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. 相似文献
85.
A. V. Zykina 《Computational Mathematics and Mathematical Physics》2008,48(11):1971-1980
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. 相似文献
86.
Yunfeng Jiang 《理论物理通讯》2021,73(5):57201
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. 相似文献
87.
Starting from a sigma‐model for a doubled target‐space geometry, we show that the number of target‐space dimensions can be reduced by half through a gauging procedure. We apply this formalism to a class of backgrounds relevant for double field theory, and illustrate how choosing different gaugings leads to string‐theory configurations T‐dual to each other. We furthermore discuss that given a conformal doubled theory, the reduced theories are conformal as well. As an example we consider the three‐dimensional WZW model and show that the only possible reduced backgrounds are the cigar and trumpet CFTs in two dimensions, which are indeed T‐dual to each other. 相似文献
88.
89.
考虑目标函数是线性函数约束条件为线性矩阵不等式的LMI优化问题,讨论了LMI优化问题中的四个择一性定理.每种类型的择一性定理包含两个线性不等式和(或)等式系统,一个原始系统和一个对偶系统.弱择一性定理说明两系统中至多只有其一有解;基于凸集分离理论得到的强择一性定理说明两系统有且仅有其一有解.并在此基础上推导了LMI优化... 相似文献
90.
HAO Liang & LONG GuiLu Key Laboratory for Atomic Molecular NanoSciences 《中国科学:物理学 力学 天文学(英文版)》2011,(5)
In this work, we demonstrated a fixed-point quantum search algorithm in the nuclear magnetic resonance (NMR) system. We constructed the pulse sequences for the pivotal operations in the quantum search protocol. The experimental results agree well with the theoretical predictions. The generalization of the scheme to the arbitrary number of qubits has also been given. 相似文献