Unifying hidden-variable problems from quantum mechanics by logics of dependence and independence

We study hidden-variable models from quantum mechanics and their abstractions in purely probabilistic and relational frameworks by means of logics of dependence and independence, which are based on team semantics. We show that common desirable properties of hidden-variable models can be defined in an elegant and concise way in dependence and independence logic. The relationship between different properties and their simultaneous realisability can thus be formulated and proven on a purely logical level, as problems of entailment and satisfiability of logical formulae. Connections between probabilistic and relational entailment in dependence and independence logic allow us to simplify proofs. In many cases, we can establish results on both probabilistic and relational hidden-variable models by a single proof, because one case implies the other, depending on purely syntactic criteria. We also discuss the ‘no-go’ theorems by Bell and Kochen-Specker and provide a purely logical variant of the latter, introducing non-contextual choice as a team-semantical property.     

双折射光纤中克尔效应及光纤－光学逻辑门

本文详细地研究了单模双折射光纤中的克尔效应．讨论了其应用于光纤－光学逻辑门的优点,给出了有关的理论分析和计算结果以实验装置,确定了强度型逻辑门的“１／０”状态,测出了输出光脉冲宽度．理论分析和实验结果符合良好．     

Unprovability of a “precognition” effect in quantum mechanics

It is shown that nonlocality gives rise to an undecidable proposition, meaning it cannot be proved true nor proved false from the usual assumptions, but is independent of them. A variation on the usual thought experiment is considered in which the observers are timelike separated, but the nonlocality fails to become a precognition effect because of this independence result.     

On representations of affine Kac-Moody groups and related loop groups

We demonstrate a one to one correspondence between the irreducible projective representations of an affine Kac-Moody group and those of the related loop group, which leads to the results that every non-trivial representation of an affine Kac-Moody group must have its degree greater than or equal to the rank of the group and that the equivalence appears if and only if the group is of type for some . Moreover the characteristics of the base fields for the non-trivial representations are found being always zero.

     

Wiener's test for space-time random walks and its applications

This paper establishes a criterion for whether a -dimensional random walk on the integer lattice visits a space-time subset infinitely often or not. It is a precise analogue of Wiener's test for regularity of a boundary point with respect to the classical Dirichlet problem. The test obtained is applied to strengthen the harder half of Kolmogorov's test for the random walk.

     

On the minimal time function for distributed control systems in Banach spaces

In this paper, it is shown that the minimal time function is locally Lipschitz continuous for the control systemx=Ax+u in a Banach spadeE, under either of two conditions:A is linear and generates aC ₀-semigroup of bounded linear operators; orA is nonlinear, possibly multivalued, and dissipative. The main tool used for the nonlinear case is a result of Barbu concerning the null controllability of the system.     

Rumer's transformation,in biology,as the negation,in classical logic

In this article, we make a connection between the Rumer transformation, used in the study of the genetic code‐doublets, and the negation of classic logic. A unified classification is given, relying on two Klein's 4‐groups describing the symmetries of the 16 doublets of nitrogenous bases and those of the 16 binary connectives of classic logic, both groups being subgroups of a larger noncommutative group with eight elements we identify as the dihedral group D₄. Also, some connections with other works are briefly considered. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Relevance and truthfulness in information correction and fusion

A general approach to information correction and fusion for belief functions is proposed, where not only may the information items be irrelevant, but sources may lie as well. We introduce a new correction scheme, which takes into account uncertain metaknowledge on the source’s relevance and truthfulness and that generalizes Shafer’s discounting operation. We then show how to reinterpret all connectives of Boolean logic in terms of source behavior assumptions with respect to relevance and truthfulness. We are led to generalize the unnormalized Dempster’s rule to all Boolean connectives, while taking into account the uncertainties pertaining to assumptions concerning the behavior of sources. Eventually, we further extend this approach to an even more general setting, where source behavior assumptions do not have to be restricted to relevance and truthfulness. We also establish the commutativity property between correction and fusion processes, when the behaviors of the sources are independent.     

A constructive proof by elementary transformations of Roth's removal theorems in the theory of matrix equations

W. E. Roth gave necessary and sufficient conditions for the existence of solution(s) of certain types of linear matrix equations. Proofs were based on invariant factors and were long and complicated. Other shorter but non-constructive proofs have since been provided by later authors. We present here very brief constructive proofs based on the simplest of mathematical techniques, namely row- and column-reduction of a matrix.