Quantum discord is Bohr’s notion of non-mechanical disturbance introduced to counter the Einstein–Podolsky–Rosen argument

By rigorously formalizing the Einstein–Podolsky–Rosen (EPR) argument, and Bohr’s reply, one can appreciate that both arguments were technically correct. Their opposed conclusions about the completeness of quantum mechanics hinged upon an explicit difference in their criteria for when a measurement on Alice’s system can be regarded as not disturbing Bob’s system. The EPR criteria allow their conclusion–incompleteness–to be reached by establishing the physical reality of just a single observable q$q$ (not of both q$q$ and its conjugate observable p$p$), but I show that Bohr’s definition of disturbance prevents the EPR chain of reasoning from establishing even this. Moreover, I show that Bohr’s definition is intimately related to the asymmetric concept of quantum discord from quantum information theory: if and only if the joint state has no Alice-discord, she can measure any observable without disturbing (in Bohr’s sense) Bob’s system. Discord can be present even when systems are unentangled, and this has implications for our understanding of the historical development of notions of quantum nonlocality.     

Polynomial approximation: a structural and operational study

This is a summary of the most important results of the author’s PhD thesis. This thesis, supervised by Vangelis Th. Paschos, was defended in October 2005 at the Université Paris Dauphine. It is written in French and is available on-line. The thesis is focused on combinatorial optimization problems, studied from the standpoint of polynomial approximation theory. We were interested both in structural concerns (mainly completeness in approximation classes and logical expressivity) and operational ones (with the study of satisfiability, coloring and covering problems). http://www.lamsade.dauphine.fr/~escoffier/fichiers/TheseEscoffier.pdf     

Completeness of security markets and solvability of linear backward stochastic differential equations

For a standard Black-Scholes type security market, completeness is equivalent to the solvability of a linear backward stochastic differential equation (BSDE, for short). An ideal case is that the interest rate is bounded, there exists a bounded risk premium process, and the volatility matrix has certain surjectivity. In this case the corresponding BSDE has bounded coefficients and it is solvable leading to the completeness of the market. However, in general, the risk premium process and/or the interest rate could be unbounded. Then the corresponding BSDE will have unbounded coefficients. For this case, do we still have completeness of the market? The purpose of this paper is to discuss the solvability of BSDEs with possibly unbounded coefficients, which will result in the completeness of the corresponding market.     

Spectrum of a non-self-adjoint operator associated with the periodic heat equation

We study the spectrum of the linear operator L=−θ_∂−?θ_∂(sinθθ_∂) subject to the periodic boundary conditions on θ∈[−π,π]. We prove that the operator is closed in with the domain in for |?|<2, its spectrum consists of an infinite sequence of isolated eigenvalues and the set of corresponding eigenfunctions is complete. By using numerical approximations of eigenvalues and eigenfunctions, we show that all eigenvalues are simple, located on the imaginary axis and the angle between two subsequent eigenfunctions tends to zero for larger eigenvalues. As a result, the complete set of linearly independent eigenfunctions does not form a basis in .     

子句集的神经网络归结

给出基于神经网络的归结方法。首先将子句集S表示为δ形式，并且用算子对(⊙， )引入两种类型的神经元；然后用这两种神经元构造子句集S的神经网络结构；而后给出基于子句集的神经网络的归结算法；最后证明了该算法的完备性，并用实例进行了验证。     

Modal sequents for normal modal logics

We present sequent calculi for normal modal logics where modal and propositional behaviours are separated, and we prove a cut elimination theorem for the basic system K, so as completeness theorems (in the new style) both for K itself and for its most popular enrichments. MSC: 03B45, 03F05.     

（LF）-空间的完备性

设（E，ξ）=indlim（E．，ξn）为Frechel空间序列的诱导权限，我们证明了：若每个（Enξ|En）正速完备，则（E，ξ）=indlim（En，ξn）为完备，进而证明了；若对于每个自然数n，存在自然数m（n）使对于任意p≥m（n）有En；则（E，ξ）为完备．     

Analog of <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> with a subadditive measure

For a subadditive fuzzy measure (not assumed finite), a Minkowski type triangle inequality, with Choquet integrals in place of Lebesgue integrals, is shown to hold. It is immediate that the set of functions for which a certain positive power of the absolute values have finite Choquet integrals is closed under addition, leading to a linear space analogous to the Lebesgue space L ^p , with a metric related to the integral of that power. Under the additional condition that the subadditive fuzzy measure is inner continuous (Sugeno), the space is shown to be complete. Consequences of the Minkowski type inequality are illustrated in two specific instances.      

Elastodynamics and Elastostatics by a Unified Method of Potentials for x 3-Convex Domains

A new general solution in terms of two scalar potential functions for classical elastodynamics of x ₃-convex domains is presented. Through the establishment and usage of a set of basic mathematical lemmas, a demonstration of its connection to Kovalevshi–Iacovache–Somigliana elastodynamic solution, and thus its completeness, is realized with the aid of the theory of repeated wave equations and Boggio’s theorem. With the time dependence of the potentials suppressed, the new decomposition can, unlike Lamé’s, degenerate to a complete solution for elastostatic problems.      

n维模糊度量空间及其完备性

定义了n维模糊向量的模糊距离、n维模糊度量空间及其完备性的概念,实现了用R上的模糊数度量模糊向量间距离的目的,不仅使得模糊距离的度量更加合理、更加贴切,也创立一套独立于实数的模糊数学分析理论打下了基础。