in this paper some upper and lower bounds for the greatest eigenvalues of the pi and vertex pimatrices of a graph g are obtained. those graphs for which these bounds are best possible arecharacterized.

structural codes vis-a-vis structural counts, like polynomials of a molecular graph, areimportant in computing graph-theoretical descriptors which are commonly known astopological indices. these indices are most important for characterizing carbon nanotubes(cnts). in this paper we have computed sadhana index (sd) for phenylenes and theirhexagonal squeezes using structural codes (counts). sadhan...

Resistance to Meloidogyne arenaria race 1 is not currently available in commercial peanut cultivars. Moderate levels of resistance have been identified in Arachis hypogaea plant introductions (PI) in previous greenhouse studies. The purpose of this work was to evaluate the effects of resistance in peanut PI on populations dynamics of M. arenaria in field plots. The PI designated as resistant in...

1 Formulas Suppose that Y has a multinomial distribution with parameters (p1, . . . , pm). (That is to say, suppose that Pr(Y = i) = pi for an integer i such that 1 ≤ i ≤ m.) Given a sample Y1, . . . , Yn of multinomial random variables with vector parameter (p1, . . . , pm), the maximum–likelihood (and method of moments) estimator of pi is p̂i = #{j : Yj = i}/n = ni/n (1) where ni = #{j : Yj = ...

BACKGROUND Gingivitis is an inflammatory disease involving the gums. Saffron contains various forms of flavonoids, glycosides, and anthocyanin compounds that are proven to have anti-inflammatory and antioxidant effects. This study evaluates the anti-inflammatory effects of Saffron stigma on gingival indices in patients with marginal generalized plaque-induced gingivitis. METHODS For this stud...

In the present work, we analyze the pi-electronic delocalization in a series of annulenes and their dications and dianions by using electron delocalization indices calculated in the framework of the quantum theory of atoms in molecules. The aim of our study is to discuss the Hückel's 4n + 2 rule from the viewpoint of pi-electronic delocalization. Our results show that there is an important incr...

The Padmakar-Ivan (PI) index is a first-generation topological index (TI) based on sums over all edges between numbers of edges closer to one endpoint and numbers of edges closer to the other endpoint. Edges at equal distances from the two endpoints are ignored. An analogous definition is valid for the Wiener index W, with the difference that sums are replaced by products. A few other TIs are d...

BACKGROUND Oral squamous cell lesions are most commonly diagnosed lesions in India. Both premalignant and malignant lesions are frequently encountered. In this study, we evaluated the role and significance of apoptotic indices (AI) and proliferative indices (PI) in premalignant and malignant squamous cell lesions of the oral cavity. MATERIALS AND METHODS A total of 62 histologically proven ca...

BACKGROUND The brain is perfused at high-volume flow throughout systole and diastole. We explored the association of blood flow in the middle cerebral artery (MCA) with the pulsatile components of blood pressure in the systemic circulation and indices of arterial stiffness. METHODS We enrolled 334 untreated subjects (mean age, 50.9 years; 45.4% women) who had been referred for ambulatory bloo...

In this paper the Wiener and hyper Wiener index of two kinds of dendrimer graphs are determined. Using the Wiener index formula, the Szeged, Schultz, PI and Gutman indices of these graphs are also determined.