φ(t) = F (t, φ(t)), t ∈ [a, b], φ(a) = φa. (1.1) where φa, φ(t) ∈ C n and F : R × C → C. Let {t}n=0 be equally spaced nodes in the interval [a, b] with t0 = a, tN = b. Let {t j n} M j=0 be the Legendre-Gauss-Lobatto nodes in the subinterval [tn, tn+1] with t 0 n = tn, t M n = tn+1. Denote ∆n = t j+1 n − t j n. 1.1 Forward Euler Scheme The Picard integral equation in each [tn, tn+1] associated w...

Let Tn denote a tree of order n and Wm a wheel of order m + 1. Baskoro et al. conjectured in [2] that if Tn is not a star, then R(Tn,Wm) = 2n − 1 for m ≥ 6 even and n ≥ m− 1. We disprove the Conjecture in [6]. In this paper, we determine R(Tn,W6) for n ≤ 8 which is the first step for us to determine R(Tn,W6) for any tree Tn.

Enhanced expression of tenascin-C (TN-C) at the invasive edges of glioblastoma multiforme in close association with vascular sprouts, suggests a role for TN-C in microvascular cell migration. To test this hypothesis, we studied the migration of endothelial cells in vitro. In an aggregate migration assay, bovine retinal endothelial cells (BRECs) and human umbilical vein endothelial cells spread ...

Consider the complete rooted binary tree T. We construct a sequence Tn, n = 1, 2, . . . of subtrees of T recursively as follows. T1 consists only of the root. Given Tn, we choose a leaf u uniformly at random from the set of all leaves of Tn and add its two children to the tree to create Tn+1. Thus Tn+1 consists of Tn and the children u1, u2 of u, and contains in total 2n+ 1 nodes, including n+ ...

Polynomials are defined recursively in various ways associated with reciprocation; e.g., Sn+1(x)/Tn+1(x) = Sn(x)/Tn(x) ± Tn(x)/Sn(x). Under certain conditions, the zeros of Sn interlace those of Tn. Identities for Sn, Tn, and related polynomials are derived, as well as recurrence relations and infinite sums involving roots of polynomials.

PURPOSE The receptor-binding cancer antigen expressed on SiSo cells (RCAS1) is a novel tumor-associated antigen. Although evidence suggests that RCAS1 suppresses immunity by inducing tumor-infiltrating lymphocyte (TIL) apoptosis, RCAS1 function in humans is controversial. RCAS1 overexpression leads to the generation of the Tn glycan antigen (N-acetyl-D-galactosamine, GalNAc) recognized by the 2...

OBJECTIVES Malignant mesothelioma (MM) is a fatal tumor of increasing incidence related to asbestos exposure. Microscopic tumor necrosis (TN) is a poor prognostic factor in solid tumors, but it has not been characterized in MM. We wished to evaluate the incidence of TN in MM and its correlations with clinicopathologic factors, angiogenesis, and survival. METHODS TN was graded in 171 routine f...

A progressive increase in the incidence of thyroid cancer (TC) has been reported over the last few decades. This either reflects the increased number of newly discovered and accurately selected thyroid nodules with more sensitive technologies and a relative more potent carcinogenic effect of pathogenetic factors in malignant, but not benign nodules. This observational time-trend study addresses...

Let (Tn)n≥0 be the Tribonacci sequence defined by the recurrence Tn+2 = Tn+1 + Tn + Tn−1, with T0 = 0 and T1 = T2 = 1. In this short note, we prove that there are no integer solutions (u,m) to the Brocard-Ramanujan equation m! + 1 = u2 where u is a Tribonacci number.