Towards a world‐sheet description of doubled geometry in string theory

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.     

具广义V-不变凸多目标变分的混合对偶性

在函数广义V-不变凸性的条件下,建立了多目标变分关于有效解的混合对偶理论.     

LMI优化问题的择一性定理与对偶

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...     

Experimental implementation of a fixed-point duality quantum search algorithm in the nuclear magnetic resonance quantum system

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.     

Deformed statistics Kullback-Leibler divergence minimization within a scaled Bregman framework

The generalized Kullback-Leibler divergence (K-Ld) in Tsallis statistics [constrained by the additive duality of generalized statistics (dual generalized K-Ld)] is here reconciled with the theory of Bregman divergences for expectations defined by normal averages, within a measure-theoretic framework. Specifically, it is demonstrated that the dual generalized K-Ld is a scaled Bregman divergence. The Pythagorean theorem is derived from the minimum discrimination information principle using the dual generalized K-Ld as the measure of uncertainty, with constraints defined by normal averages. The minimization of the dual generalized K-Ld, with normal averages constraints, is shown to exhibit distinctly unique features.     

Lagrange-type duality in DC programming

We show a Lagrange-type duality theorem for a DC programming problem, which is a generalization of previous results by J.-E. Martínez-Legaz, M. Volle [5] and Y. Fujiwara, D. Kuroiwa [1] when all constraint functions are real-valued. To the purpose, we decompose the DC programming problem into certain infinite convex programming problems.     

Lightcone dualities for hypersurfaces in the sphere

In this paper, we consider hypersurfaces in the unit lightlike sphere. The unit sphere can be canonically embedded in the lightcone and de Sitter space in Minkowski space. We investigate these hypersurfaces in the framework of the theory of Legendrian dualities between pseudo‐spheres in Minkowski space.