PρLog is an experimental extension of logic programming with strategic conditional transformation rules, combining Prolog with ρLog calculus. The rules perform nondeterministic transformations on hedges. Strategies provide a control on rule applications in a declarative way. In this short paper we give an overview on programming with strategies in PρLog and demonstrate how rewriting strategies ...

Representations. For the purposes of this paper a representation of G over C is a matrix-valued function ρ : G → Cdρ×dρ such that ρ(x)ρ(y) = ρ(xy) for any x, y ∈ G. We call dρ the order or the dimensionality of ρ. Note that ρ(e) = I for any representation. Two representations ρ1 and ρ2 of the same dimensionality d are said to be equivalent if for some invertible T ∈ Cd×d, ρ1(x) = Tρ2(x)T for an...

Pooling: q1 = 1. Then ρ2 = ρ1, while ρ − 2 can be any ρ 0 ≤ ρ. Optimality in (3) then requires ρ1 ≥ ρ∗2 > ρ0, otherwise the right-hand side would be zero. Let therefore ρ1 > ρ∗2 (leaving aside the measure-zero case where ρ1 = ρ ∗ 2). Given that c/βL < C(λ), this is indeed an equilibrium. Semi-separation: q1 ∈ (0, 1). This implies ρ2 ∈ (ρ1, 1) and ρ2 = 0. Furthermore, (3) must now hold with equa...

We present arguments in favor of the inequalities var(X2 n |X ∈ Bv(ρ)) ≤ 2λnE[X n |X ∈ Bv(ρ)], where X ∼ Nv(0,Λ) is a normal vector in v ≥ 1 dimensions, with zero mean and covariance matrix Λ = diag(λ), and Bv(ρ) is a centered v–dimensional Euclidean ball of square radius ρ. Such relations lie at the heart of an iterative algorithm, proposed by Palombi et al. (2012) [6] to perform a reconstruct...

The paper is consisted of two parts. In the first part, we are presenting the smooth and impulsive solution space B of the system of algebraic and differential equations A (ρ)β (t) = 0, ρ := dt where A (ρ) ∈ R [ρ] (with detA (ρ) 6= 0) is given. The solution space is given in terms of the finite and infinite Jordan pairs of the polynomial matrix A (ρ), and therefore a necessary introduction is g...

Let F be a family of compact convex sets in R. We say that F has a topological ρ-transversal of index (m, k) (ρ < m, 0 < k ≤ d − m) if there are, homologically, as many transversal m-planes to F as m-planes containing a fixed ρ-plane in R. Clearly, if F has a ρ-transversal plane, then F has a topological ρ-transversal of index (m, k), for ρ < m and k ≤ d − m. The converse is not true in general...

The theory of the thermal hydrodynamic fluctuations in bounded systems has been developed only for non-superfluid liquids on the base of the linearized Navier-Stokes equations [1]. However, the study of effect of confined geometry on correlation functions of superfluid liquid is important for explanation of experiments in which capillaries, pores, dense suspensions and other objects are probed ...

Let B be a strictly real commutative real Banach algebra with the carrier space Φ B. If A is a commutative real Banach algebra, then we give a representation of a ring homomorphism ρ : A → B, which needs not be linear nor continuous. If A is a commutative complex Banach algebra, then ρ(A) is contained in the radical of B. 1. Introduction and results. Ring homomorphisms are mappings between two ...

We inspect the relationship between the Ap,q condition for families of norms on vector valued functions and the Ap condition for scalar weights. In particular we will show if we are considering a norm-valued function ρ(·) such that, uniformly in all nonzero vectors x, ρ(·)(x) p ∈ Ap and ρ(·)(x) ∈ Aq then the following hold: If p = q = 2, and functions take values in R then ρ ∈ A2,2. If p = q = ...

The interplane spin cross relaxation time Tx measured by high frequency ESR in X-ray irradiated κ-(BEDT-TTF)2Cu[N(CN)2]Cl is compared to the interplane resisitivity ρ⊥ and the in-plane resistivity ρ‖ between 50 K and 250 K. The irradiation transforms the semiconductor behavior of the non-irradiated crystal into metallic. Irradiation decreases Tx, ρ⊥ and ρ‖ but the ratio Tx/ρ⊥ and ρ⊥/ρ‖ remain u...