On the Triality Theory for a Quartic Polynomial Optimization Problem

This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality left in 2003. Results show that the triality theory holds strongly in a tri-duality form if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Four numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the largest local minimum and local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011. arXiv admin note: substantial text overlap with arXiv:1104.297

Comment on "A special attack on the multiparty quantum secret sharing of secure direct communication using single photons"

In this comment, we show that the special attack [S.-J. Qin, F. Gao, Q.-Y. Wen, F.-C. Zhu, Opt. Commun. 281 (2008) 5472.], which claims to be able to obtain all the transmitted secret message bit values of the protocol of the multiparty quantum secret sharing of secure direct communication using single photons with random phase shift operations, fails. Furthermore, a class of similar attacks are also shown to fail to extract the secrete message.Comment: 2 pages (two-column

Orientalismo a su pesar : Gao Xingjian y las paradojas del sistema literario global

This paper shortly reviews a few of the reactions to the Nobel Literature Prize awarded to Gao Xingjian in 2000. It argues that, when circulating within a globalized, cross-cultural literary sistem, both Gao’s figure and work have been defined by an Orientalist hermeneutical perspective that, at certain points, contradicts the postulates of the writer and the value of his work. This is a mechanism to which writer and work are inescapably subjected.Este artículo realiza un breve repaso a algunas reacciones a la concesión del premio Nobel de literatura del año 2000 a Gao Xingjian. El articulo sostiene que, al entrar en circulación dentro de un sistema literario intercultural y globalizado, la figura y la obra de Gao han quedado definidas a través de un prisma interpretativo orientalista que, en algunos puntos, entra en contradicción con los postulados del autor y el valor de su obra. Este es un mecanismo ante el cual escritor y obra están irrevocablemente sujetos

Orientalismo a su pesar : Gao Xingjian y las paradojas del sistema literario global

Este artículo realiza un breve repaso a algunas reacciones a la concesión del premio Nobel de literatura del año 2000 a Gao Xingjian. El articulo sostiene que, al entrar en circulación dentro de un sistema literario intercultural y globalizado, la figura y la obra de Gao han quedado definidas a través de un prisma interpretativo orientalista que, en algunos puntos, entra en contradicción con los postulados del autor y el valor de su obra. Este es un mecanismo ante el cual escritor y obra están irrevocablemente sujetos.This paper shortly reviews a few of the reactions to the Nobel Literature Prize awarded to Gao Xingjian in 2000. It argues that, when circulating within a globalized, cross-cultural literary sistem, both Gao's figure and work have been defined by an Orientalist hermeneutical perspective that, at certain points, contradicts the postulates of the writer and the value of his work. This is a mechanism to which writer and work are inescapably subjected

Analytical Solutions to General Anti-Plane Shear Problems In Finite Elasticity

This paper presents a pure complementary energy variational method for solving anti-plane shear problem in finite elasticity. Based on the canonical duality-triality theory developed by the author, the nonlinear/nonconex partial differential equation for the large deformation problem is converted into an algebraic equation in dual space, which can, in principle, be solved to obtain a complete set of stress solutions. Therefore, a general analytical solution form of the deformation is obtained subjected to a compatibility condition. Applications are illustrated by examples with both convex and nonconvex stored strain energies governed by quadratic-exponential and power-law material models, respectively. Results show that the nonconvex variational problem could have multiple solutions at each material point, the complementary gap function and the triality theory can be used to identify both global and local extremal solutions, while the popular (poly-, quasi-, and rank-one) convexities provide only local minimal criteria, the Legendre-Hadamard condition does not guarantee uniqueness of solutions. This paper demonstrates again that the pure complementary energy principle and the triality theory play important roles in finite deformation theory and nonconvex analysis.Comment: 23 pages, 4 figures. Mathematics and Mechanics of Solids, 201