Iterative method for solving a nonlinear fourth order boundary value problem

AbstractIn the study of transverse vibrations of a hinged beam there arises a boundary value problem for fourth order ordinary differential equation, where a significant difficulty lies in a nonlinear term under integral sign. In recent years several authors considered finite approximation of the problem and proposed an iterative method for solving the system of nonlinear equations obtained. The essence of the iteration is the simple iteration method for a nonlinear equation, although this is not shown in the papers of the authors.In this paper we propose a new approach to the solution of the problem, which is based on the reduction of it to finding a root of a nonlinear equation. In both cases, when the explicit form of this equation is found or not, the use of the Newton or Newton-type methods generate fast convergent iterative process for the original problem. The results of many numerical experiments confirm the efficiency of the proposed approach

Spectrum of mutations in the RB1 gene in Vietnamese patients with retinoblastoma

Purpose: Retinoblastoma (RB) is a rare childhood malignant disorder caused by the biallelic inactivation of the RB1 gene. Early diagnosis and identification of carriers of heritable mutations in RB1 can improve disease outcome and management. In this study, we present the spectrum of mutations in the RB1 gene in Vietnamese patients with RB. Methods: Tumor RNA from 50 probands with RB, including 12 bilateral and 38 unilateral cases, was extracted. cDNA, after reverse transcription, was sequenced to identify the RNA mutation of the RB1 gene. At the genomic DNA level, mutational analysis of all RB1 exons, exon–intron boundaries, and the promoter region was conducted using PCR and direct sequencing. Multiplex ligation-dependent probe amplification (MLPA) analysis was performed for patients for whom the first two results were negative. For patients for whom either the sequencing or MLPA results were positive for a tumor mutation, patients’ and their parents’ blood DNA was analyzed to determine the germline mutation. Results: Forty-one different kinds of RB1 tumor mutations were identified in 41 probands (82.0%), including 11 of 12 bilateral cases (91.7%) and 30 of 38 unilateral cases (78.9%). The majority of the detected mutations were nonsense (15 different kinds), followed by frameshift (11 kinds), and splice site mutations (nine kinds). Each splice site mutation was confirmed to create a deletion of the corresponding exon with RNA sequencing. The single promoter mutation c.-197G>A was reported previously; however, both missense mutations identified in exon 6 (c.601G>C: p.A201P) and exon 22 (c.2264T>C: p.F755S) were novel. Gross deletions were detected with MLPA in three probands. The detection rate of germline mutations in bilateral and unilateral cases with mutations were 81.8% and 30.0%, respectively. Only one father out of the 20 parents tested was positive for a germline mutation. Conclusions: Mutations in the RB1 gene in Vietnamese patients were heterogeneous and highly prevalent with pathogenic truncated mutations. With advancement in therapeutics, early detection of RB is important for eye salvation