The vertex distance complement (VDC) matrix \(\textit{C}\), of a connected graph \(G\) with set consisting \(n\) vertices, is real symmetric \([c_{ij}]\) that takes the value \(n - d_{ij}\) where \(d_{ij}\) between vertices \(v_i\) and \(v_j\) for \(i \neq j\) 0 otherwise. spectrum subdivision join, \(G_1 \dot{\bigvee} G_2\) edge join \underline{\bigvee} regular graphs \(G_1\) \(G_2\) in terms ...

we shall also denote by P [∂ x ] the differential operator P (∂ x) = P The transposition that interchanges x i and x j will be denoted s ij. It is easily shown that for any P ∈ R and 1 ≤ i < j ≤ n we have the factorization (1 − s ij)P (x) = (x i − x j) 1+2r P ij (x) I .1 with r ≥ 0, P ij (x) prime with (x i − x j) and symmetric in x i , x j. This given, a polynomial P (x) ∈ Q[X n ] is said to b...

This paper studies the scattering matrix S(E;~) of the problem −~ψ(x) + V (x)ψ(x) = Eψ(x) for positive potentials V ∈ C(R) with inverse square behavior as x→ ±∞. It is shown that each entry takes the form Sij(E;~) = S (0) ij (E;~)(1 + ~σij(E;~)) where S (0) ij (E;~) is the WKB approximation relative to the modified potential V (x) + ~ 2 4 〈x〉−2 and the correction terms σij satisfy |∂ k Eσij (E;...

The entomopathogenic nematode species Steinernema feltiae and Heterorhabditis bacteriophora were compared for survival and infectivity of infective juveniles (IJ) collected with a standard White trap (i.e., emerging from hosts and accumulating in water) and later applied to sand (treatment A) to IJ allowed to emerge from hosts into sand (treatment C). Percentage IJ survival and infectivity was ...

By using a fixed point theorem of strict-set-contraction, some sufficient conditions are obtained for the existence of positive periodic solutions for a periodic neutral Lotka-Volterra competition system on time scales of the form x ∆ i (t) = x i (t) r i (t) − n j=1 a ij (t)x j (t) − n j=1 b ij (t)x j (t − τ ij (t, x 1 (t),. .. , x n (t))) − n j=1 c ij (t)x

We study Wigner ensembles of symmetric random matrices A = (a ij) i; j = 1; : : : ; n with matrix elements a ij ; i j being independent symmetrically distributed random variables a ji = ij n 1 2 : We assume that Var ij = 1 4 , for i < j, Var ii 6const and that all higher moments of ij also exist and grow not faster than the Gaussian ones. Under formulated conditions we prove the central limit t...

This study was carried out to investigate the isolation and characterization of lactic acid bacteria (LAB) from naturally fermented sauce-type kimchi. Sauce-type kimchi was prepared with fresh, chopped ingredients (Korean cabbage, radish, garlic, ginger, green onion, and red pepper). The two isolated bacteria from sauce-type kimchi were identified as Pediococcus pentosaceus and Lactobacillus br...

A formulation to include the e ects of wall proximity in a second moment closure model that utilizes a tensor representation for the redistribution terms in the Reynolds stress equations is presented The wall proximity e ects are modeled through an elliptic relaxation process of the tensor expansion coef cients that properly accounts for both correlation length and time scales as the wall is ap...