Let us mention that every non empty relational structure which is trivial and reflexive is also complete. Let T be a relational structure. A type of T is an element of T . Let T be a relational structure. We say that T is Noetherian if and only if: (Def. 1) The internal relation of T is reversely well founded. Let us observe that every non empty relational structure which is trivial is also Noe...

The r-Hofstadter triangle and the (1 − r)-Hofstadter triangle are proved perspective, and homogeneous trilinear coordinates are found for the perspector. More generally, given a triangle DEF inscribed in a reference triangle ABC, triangles A′B′C′ and A′′B′′C′′ derived in a certain manner from DEF are perspective to each other and to ABC. Trilinears for the three perspectors, denoted by P ∗, P1,...

This note illustrates theoretical worst-case scenarios for groundness analyses obtained through abstract interpretation over the abstract domains of definite (Def) and positive (Pos) Boolean functions. For Def, an example is given for which any Def-based abstract interpretation for groundness analysis follows a chain which is exponential in the number of argument positions as well as in the num...

Let ω0(G) denote the number of odd components of a graph G. The deficiency of G is defined as def(G) = maxX⊆V (G) (ω0(G−X)− |X|), and this equals the number of vertices unmatched by any maximum matching of G. A subset X ⊆ V (G) is called a Tutte set (or barrier set) of G if def(G) = ω0(G − X) − |X|, and an extreme set if def(G − X) = def(G) + |X|. Recently a graph operator, called the Dgraph D(...

In this theoretical work, density functional theory calculations show the effect of small cobalt clusters (Con, n = 1–5) adsorbed on pristine γ-graphyne (γ-GY), and modify N-doped γ-GY monolayers (GYNs-def). Different geometrical configurations are assessed with adsorption energy, charge transfer, states. The system vacancy defects shows a large energy (19.96 eV) for Co5 cluster. This behavior ...

with tn−→∞ as n−→∞. With N(0) def = 0, N(t) max{n : tn ≤ t} denotes the number of points that fall in the interval (0, t], and {N(t) : t ≥ 0} is called the counting process for ψ. (If t1 > t, then N(t) def = 0.) If the tn are random variables then ψ is called a random point process. We sometimes allow a point at the origin and define t0 def = 0. Xn = tn − tn−1, n ≥ 1 is called the nth interarri...

In this paper Y denotes a non empty set. Let k, l be elements of Boolean. The functor k ⇒ l is defined by: (Def. 1) k ⇒ l = ¬k ∨ l. The functor k ⇔ l is defined as follows: (Def. 2) k ⇔ l = ¬(k ⊕ l). Let k, l be elements of Boolean. The predicate k ⋐ l is defined by: (Def. 3) k ⇒ l = true. Let us note that the predicate k ⋐ l is reflexive. One can prove the following three propositions: (1) For...

class SensevalData (s: String ) extends Agent [String , Context ] { val file = new File(s) val trainDataReader = new STAXSensevalDataReader (file); val samples : List[ Ambiguity ] = trainDataReader . getAmbiguities . toList val words : java.util.List[ String ] = trainDataReader . getWords def process ( input : java.util.List[ Annotation [ String ]]) = samples .map( asAnnotation (_)) def asAnnot...

In this paper we study the linearized version of the stationary Navier-Stokes equations on a fixed subdomain Ω of a smooth, compact Riemannian manifold M . Let Tr denote the trace on ∂Ω. With Def standing for the deformation tensor and with d denoting the exterior derivative operator on M , set L = 2 Def∗Def, δ = d∗. We consider the Dirichlet problem for the (modified) Stokes system    L...