Let p be an odd prime, and let m divide p−1. Let ζ = e and let ω = e. The field extension Q(ω) ⊂ Q(ω, ζ) is Galois with cyclic Galois group isomorphic to (Z/pZ)×. The unique field between Q(ω) and Q(ω, ζ) having degree m over Q(ω) takes the form Q(ω, τ) where τ is a Gauss sum, to be described below. Furthermore, under some conditions we can compute τ as an element α of Q(ω), thus expressing the...

In this paper an extension of a behavioural subset of UML Statecharts for modeling mobility issues is proposed. In this extension we relax the unique association between each Statechart in a collection of Statecharts modeling a system and its input-queue and we allow the use of (queue) name variables in communication actions. The resulting communication paradigm is much more flexible than the s...

In this paper we present a convex optimization problem for solving the rational covariance extension problem. Given a partial covariance sequence and the desired zeros of the modeling filter, the poles are uniquely determined from the unique minimum of the corresponding optimization problem. In this way we obtain an algorithm for solving the covariance extension problem, as well as a constructi...

In this paper, we consider local moves on classical and welded diagrams of string links, the notion extension a move. Such extensions being non-unique in general, idea is to find topological criterion which could isolate one from others. To that end, turn relation between links knotted surfaces [Formula: see text], ribbon subclass these surfaces. This provides interpretation as surgeries surfac...

Let H be the symmetric second-order differential operator on L2(R) with domain C c (R) and action Hφ = −(c φ ) where c ∈ W 1,2 loc (R) is a real function which is strictly positive on R\{0} but with c(0) = 0. We give a complete characterization of the self-adjoint extensions and the submarkovian extensions of H . In particular if ν = ν+ ∨ ν− where ν±(x) = ± ∫ ±1 ±x c then H has a unique self-ad...

The proposed Drosophila melanogaster L23a ribosomal protein features a conserved C-terminal amino acid signature characteristic of other L23a family members and a unique N-terminal extension [Koyama et al. (Poly(ADP-ribose) polymerase interacts with novel Drosophila ribosomal proteins, L22 and l23a, with unique histone-like amino-terminal extensions. Gene 1999; 226: 339-345)], absent from Sacch...

We classify the general linear boundary conditions involving u′′, u′ and u on the boundary {a, b} so that a Sturm-Liouville operator on [a, b] has a unique self-adjoint extension on a suitable Hilbert space.