GnA ω +∆+AC-qf ⊢ ∀u, k∀v ≤τ tuk∃w A0(u, k, v, w), (where t is a closed term, A0 is quantifier-free and contains only u, k, v, w free, γ ≤ 2, ρ is an arbitrary type and ≤τ is defined pointwise) one can extract (by monotone functional interpretation) a uniform bound Φ on ∃w which is given by a closed term of GnA ω and does not depend on v, i.e. ∀u, k∀v ≤ tuk∃w ≤ ΦukA0(u, k, v, w) holds in the ful...

Let fB H (u)g u2R be a fractional Brownian motion (fBm) with index H 2 (0; 1) and sp(B H) be the closure in L 2 (() of the span sp(B H) of the increments of fBm B H. It is well-known that, when B H = B 1=2 is the usual Brownian motion (Bm), an element X 2 sp(B 1=2) can be characterized by a unique function f X 2 L 2 (R), in which case one writes X in an integral form as X = R R f X (u)dB 1=2 (u...

The second order Ordinary Differential Equation which describes the unknown part of the solution space of some vacuum Bianchi Cosmologies is completely integrated for Type III, thus obtaining the general solution to Einstein’s Field Equations for this case. Imposing the space-time generalization of a ”hidden” symmetry of the generic Type III spatial slice, enables us to retrieve a two-parameter...

Labyrinthic patterns are observed both in systems where the uniform states are metastable, as a result of a front instability, and in systems displaying a cellular instability, when the band of excited Fourier modes is wide enough to support resonant interactions between modes lying on different shells. We show that the phase formalism is a suitable description for low-density labyrinthic patte...

Sagan, B.E., Inductive proofs of q-log concavity, Discrete Mathematics 99 (1992) 289-306. We give inductive proofs of q-log concavity for the Gaussian polynomials and the q-Stirling numbers of both kinds. Similar techniques are applied to show that certain sequences of elementary and complete symmetric functions are q-log concave.

An enormous variety of nonlinear differential equations and functions have been recast exactly in the canonical form called an S-system. This is a system of nonlinear ordinary differential equations, each with the same structure: the change in a variable is equal to a difference of products of power-law functions. We review the development of S-systems, prove that the minimum for the range of e...

We construct the systems of generalised coherent states for the discrete and continuous spectra of the hydrogen atom. These systems are expressed in terms of elementary functions and are invariant under the SO(3, 2) (discrete spectrum) and SO(4, 1) (continuous spectrum) subgroups of the dynamical symmetry group SO(4, 2) of the hydrogen atom. Both systems of coherent states are particular cases ...

One possible approach to exact real arithmetic is to use linear fractional transformations (LFT's) to represent real numbers and computations on real numbers. Recursive expressions built from LFT's are only convergent (i.e., denote a well-deened real number) if the involved LFT's are suuciently contractive. In this paper, we deene a notion of contrac-tivity for LFT's. It is used for convergence...

In this Letter we derive exact closed-form expressions for the outage probability (OP) in η-μ fading channels. First, a general expression in terms of the confluent Lauricella function is derived for arbitrary values of μ. Next, we restrict the analysis to physical η-μ channel models, i.e. to integer values of 2μ, and obtain exact closed-form expressions for the OP in terms of Marcum Q, Bessel ...

Motivated by recent work of Florian Pop, we study the connections between three notions of equivalence of function fields: isomorphism, elementary equivalence, and the condition that each of a pair of fields can be embedded in the other, which we call isogeny. Some of our results are purely geometric: we give an isogeny classification of Severi-Brauer varieties and quadric surfaces. These resul...