In this paper a new mixing condition for sequences of random variables is considered. This mixing condition is termed γ-mixing. Whereas mixing conditions such as α-mixing are typically defined in terms of entire σ-fields of sets generated by random variables in the distant past and future, γ-mixing is defined in terms of a smaller class of sets: the finite dimensional cylinder sets. This leads ...

We propose a scheme for classifying the entanglement of a tripartite pure qubit state. This classification scheme consists of an ordered list of seven elements. These elements are the Cayley hyper-determinant, and its six associated 2 × 2 subdeterminants. In particular we show that this classification provides a necessary and sufficient condition for separability.

45 eregulation of the energy market is bringing about a fundamental change in the way power equipment assets have to be operated, maintained and replaced. High power-equipment performance is key to cost-efficient energy trading and to the success of the efforts being made by utilities to satisfy end-user demand for high power quality . Three main trends are shaping power equipment life manageme...

Agents often interact strategically to meet conditions involving their own or other agents’ knowledge. This interaction can be modeled using a new method of game construction, knowledge condition games, introduced in this paper. Knowledge condition games are games in which a coalition of agents chooses its strategy in an extensive game form such that an epistemic logic condition is fulfilled. I...

We derive a new generalized imaging condition based on time shifts between source and receiver wavefields. This imaging condition contrasts with other imaging techniques requiring space shifts between the two wavefields. This imaging condition is applicable to both Kirchhoff and wave-equation migrations. The transformation allows us to generate common-image gathers presented as function of eith...

In this paper we first compare Parikh’s condition to various pumping conditions Bar-Hillel’s pumping lemma, Ogden’s condition and Bader-Moura’s condition; secondly, to interchange condition; and finally, to Sokolowski’s and Grant’s conditions. In order to carry out these comparisons we present some properties of Parikh’s languages. The main result is the orthogonality of the previously mentione...

denote its Euclidean operator norm (often called the 2-norm). If  is nonsingular, then its condition number () is defined by () = kk°°−1°° = 1() () where 1 ≥ 1 ≥    ≥  ≥ 0 are the singular values of . The s constitute lengths of the semi-axes of the hyperellipsoid  = { : kk = 1} in -dimensional space; thus  measures elongation of  at its extreme [1]. The role that  ...

This paper investigates the effect of structure-preserving perturbations on the eigenvalues of linearly and nonlinearly structured eigenvalue problems. Particular attention is paid to structures that form Jordan algebras, Lie algebras, and automorphism groups of a scalar product. Bounds and computable expressions for structured eigenvalue condition numbers are derived for these classes of matri...

History.?In October 1910, the patient, Sepoy T. K., 27th Punjabis, showed me some pigmented spots on iiis face, hands and left leg. They first appeared in March, 1U0S, when the patient was living in Jhandola. He believed that quinine, which he was taking prophylactically at that time, caused their appearance. No fresh spots have appeared since then, but some of the original areas have increased...