‎The Narumi-Katayama index was the first topological index defined‎ ‎by the product of some graph theoretical quantities‎. ‎Let $G$ be a ‎simple graph with vertex set $V = {v_1,ldots‎, ‎v_n }$ and $d(v)$ be‎ ‎the degree of vertex $v$ in the graph $G$‎. ‎The Narumi-Katayama ‎index is defined as $NK(G) = prod_{vin V}d(v)$‎. ‎In this paper,‎ ‎the Narumi-Katayama index is generalized using a $n$-ve...

In this paper, I argue that only one of the proposed mechanisms is adequate on both of these counts: lexically specific constraints. Furthermore, I argue that these criteria necessitate the lexical indexation of both markedness and faithfulness constraints. The first of these claims contradicts the position of Anttila (2002), who argues that cophonologies can better meet criterion (1b) than lex...

A classification method, which comprises Fuzzy C-Means method, a modified form of the Huangindex function and Variable Precision Rough Set (VPRS) theory, is proposed for classifying labeled/ unlabeled data sets in this study. This proposed method, designated as the MVPRS-index method, is used to partition the values of per conditional attribute within the data set and to achieve both the optima...

This paper describes a technique for efficiently searching metabolic pathways similar to a given query pathway, from a pathway database. Metabolic pathways can be converted into labeled directed graphs where the nodes represent chemical compounds. Similarity between two graphs can be computed using a metric based on Maximal Common Subgraph (MCS). By maintaining an inverted file that indexes all...

We establish a cartesian presentation of a product of an indexed family of process structures, giving an analogue of a similar presentation of set-theoretic product. Such a presentation is non-trivial due to a speci c nature of the process relation in process structures and forms a basis of the algebraic theory of processes to be developed elsewhere.

The stack of iterated integrals of a path is embedded in a larger algebraic structure where iterated integrals are indexed by decorated rooted trees and where an extended Chen’s multiplicative property involves the Dürr-Connes-Kreimer coproduct on rooted trees. This turns out to be the natural setting for a non-geometric theory of rough paths. MSC: 60H99; 65L99

The electric quadrupole, hexadecapole moments, energy (kJmol -1) for some armchair polyhex carbon nanotubes TUVC6[2p,q] are performed by Beck-Lee-Yang-Parr [B3LYP] on 3-21G basis set using the standard procedure indices GAUSSIAN 98, then the Padmakar-Ivan (PI) index of TUVC6[2p,q] nanotubes in the terms of their circumference (2p) and lengh (q) is calculated and the relationships between the Pa...

Unions, Training, and Firm Performance: Evidence from the British Workplace Employee Relations Survey This paper uses a combination of workplace and matched-employee workplace data from the British 1998 Workplace Employee Relations Survey to examine the impact of unions and firm-provided training (incidence, intensity/coverage, and duration) on establishment performance. The performance effects...

We describe a class of measurable subsets Ω in R such that L2(Ω) has an orthogonal basis of frequencies eλ(x) = e i2πλ·x(x ∈ Ω) indexed by λ ∈ Λ ⊂ R. We show that such spectral pairs (Ω,Λ) have a self-similarity which may be used to generate associated fractal measures μ with Cantor set support. The Hilbert space L2(μ) does not have a total set of orthogonal frequencies, but a harmonic analysis...

In the study of approximation order, particularly in a multivariable setting, quasi-interpolants have played a major role. This report points out some limitations of quasi-interpolants and describes some recent results on approximation order obtained without the benefit of the quasi-interpolant idea. §1. Approximation Order In most general terms, “approximation order” is defined as follows. Def...