The HOMA (Harmonic Oscillator Model of Aromaticity) index, reformulated in 1993, has been very often applied to describe π-electron delocalization for monoand polycyclic π-electron systems. However, different measures of π-electron delocalization were employed for the CC, CX, and XY bonds, and this index seems to be inappropriate for compounds containing heteroatoms. In order to describe proper...

Our work addresses automatic detection of enunciations and segments with reformulations in French spoken corpora. The proposed approach is syntagmatic. It is based on reformulation markers and specificities of spoken language. The reference data are built manually and have gone through consensus. Automatic methods, based on rules and CRF machine learning, are proposed in order to detect the enu...

Barrett [1] makes three observations relevant to IIT 3.0 as discussed by Tononi & Koch [2]. Firstly, for many systems, F—as outlined in IIT 3.0—may not be computable as it may never be practical to carry out all possible discrete grainings in space, time and relevant functional elements and maximize over these. Of course, as Barrett himself points out, the fact that something may not be computa...

Let G be an affine algebraic group over an algebraically closed field k of characteristic zero. In this paper, we consider finite G-equivariant morphisms F : X → Y of irreducible affine varieties. First we determine under which conditions on Y the induced map FG : X//G → Y//G of quotient varieties is also finite. This result is reformulated in terms of kernels of derivations on k-algebras A ⊂ B...

We show that Carathéodory’s conjecture, on umbilical points of closed convex surfaces, may be reformulated in terms of the existence of at least one umbilic in the graphs of functions f : R → R whose gradient decays uniformly faster than 1/r. The divergence theorem then yields a pair of integral equations for the normal curvatures of these graphs, which establish some weaker forms of the conjec...

Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$.  For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G...

We propose and analyze a numerical method for solving the nonlinear Poisson equation −Δu = f(·, u) on the unit disk with zero Dirichlet boundary conditions. The problem is reformulated as a nonlinear integral equation. We use a Galerkin method with polynomials as approximations. The speed of convergence is shown to be very rapid; and experimentally the maximum error is exponentially decreasing ...

‎let $g=(v(g),e(g))$ be a simple connected graph with vertex set $v(g)$ and edge‎ ‎set $e(g)$‎. ‎the (first) edge-hyper wiener index of the graph $g$ is defined as‎: ‎$$ww_{e}(g)=sum_{{f,g}subseteq e(g)}(d_{e}(f,g|g)+d_{e}^{2}(f,g|g))=frac{1}{2}sum_{fin e(g)}(d_{e}(f|g)+d^{2}_{e}(f|g)),$$‎ ‎where $d_{e}(f,g|g)$ denotes the distance between the edges $f=xy$ and $g=uv$ in $e(g)$ and $d_{e}(f|g)=s...