A conformal partition function Pm n (s), which arised in the theory of Diophantine equations supplemented with additional restrictions, is concerned also with the reciprocal and skew-reciprocal algebraic equations based on the polynomial invariants of the symmetric group Sn. Making use of the relationship between Gaussian generating function for conformal partitions and Molien generating functi...

Abstract This article addresses the problem of computing an upper bound degree d a polynomial solution P ( x ) algebraic difference equation form G − τ 1 , … s + 0 = when such with coefficients in field K characteristic zero exists and where is non-linear s-variable [ ] . It will be shown that if quadratic constant then one can construct countable family polynomials f l u there (minimal) index ...

If $G$ is a connected graph with vertex set $V$, then the eccentric connectivity index of $G$, $xi^c(G)$, is defined as $sum_{vin V(G)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. In this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.

Stem cells are thought to balance self-renewal and differentiation through asymmetric and symmetric divisions, but whether such divisions occur during hematopoietic development remains unknown. Using a Notch reporter mouse, in which GFP acts as a sensor for differentiation, we image hematopoietic precursors and show that they undergo both symmetric and asymmetric divisions. In addition we show ...

In future high-speed self-routing photonic networks based on all-optical time division multiplexing (OTDM) it is highly desirable to carry out packet switching, clock recovery and demultplexing in the optical domain in order to avoid the bottleneck due to the optoelectronics conversion. In this paper we propose a self-routing OTDM node structure composed of an all-optical router and demultiplex...

The eccentric connectivity index ξ is a novel distance–based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. It is defined as ξ(G) = ∑ v∈V (G) deg(v) · ε(v) , where deg(v) and ε(v) denote the vertex degree and eccentricity of v , respectively. We survey some mathematical properties of this index and furthermore support ...

This study investigated the spatial frequency selectivity of the human visual motion system using the technique of adaptation in which motion aftereffect (MAE) duration was taken as an index of aftereffect magnitude. Eight observers adapted to two vertically oriented, oppositely drifting, luminance-defined gratings that were spatially separated in the vertical dimension. The spatial frequency o...

If G is a connected graph with vertex set V (G), then the degree distance of G is defined as DD(G) = ∑ {u,v}∈V (G)(deg u + deg v)d(u, v), where deg u is the degree of vertex u, and d(u, v) denotes the distance between u and v. In the chemical literature, DD(G) is better known under ‡Corresponding author. If possible, send your correspondence via e-mail. the name Schultz index. In the class of p...

The adjacent eccentric distance sum index of a graph G is defined as ξsv(G) = ∑ v∈V (G) ε(v)D(v) deg(v) , where ε(v), deg(v) denote the eccentricity, the degree of the vertex v, respectively, and D(v) = ∑ u∈V (G) d(u, v) is the sum of all distances from the vertex v. In this paper we derive some upper or lower bounds for the adjacent eccentric distance sum in terms of some graph invariants or t...

The Randić index R(G) of a graph G is the sum of weights (deg(u) deg(v))−0.5 over all edges uv of G, where deg(v) denotes the degree of a vertex v. We prove that for any tree T with n1 leaves R(T ) ≥ ad(T ) + max(0,n1 − 2), where ad(T ) is the average distance between vertices of T . As a consequence we resolve the conjecture R(G) ≥ ad(G) given by Fajtlowicz in 1988 for the case when G is a tree.