4 research outputs found
Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation
This paper is concerned with periodic traveling wave solutions of
the forced generalized nearly concentric Korteweg-de Vries equation
in the form of (uη+u/(2η)+[f(u)]ξ+uξξξ)ξ+uθθ/η2=h0. The authors first convert this equation into a forced generalized Kadomtsev-Petviashvili equation, (ut+[f(u)]x+uxxx)x+uyy=h0, and then to a nonlinear
ordinary differential equation with periodic boundary conditions.
An equivalent relationship between the ordinary differential
equation and nonlinear integral equations with symmetric kernels is
established by using the Green's function method. The integral
representations generate compact operators in a Banach space of
real-valued continuous functions. The Schauder's fixed point
theorem is then used to prove the existence of nonconstant
solutions to the integral equations. Therefore, the existence of
periodic traveling wave solutions to the forced generalized KP
equation, and hence the nearly concentric KdV equation, is proved
Systematic genome editing of the genes on zebrafish Chromosome 1 by CRISPR/Cas9
Genome editing by the well-established CRISPR/Cas9 technology has greatly facilitated our understanding of many biological processes. However, a complete whole-genome knockout for any species or model organism has rarely been achieved. Here, we performed a systematic knockout of all the genes (1333) on Chromosome 1 in zebrafish, successfully mutated 1029 genes, and generated 1039 germline-transmissible alleles corresponding to 636 genes. Meanwhile, by high-throughput bioinformatics analysis, we found that sequence features play pivotal roles in effective gRNA targeting at specific genes of interest, while the success rate of gene targeting positively correlates with GC content of the target sites. Moreover, we found that nearly one-fourth of all mutants are related to human diseases, and several representative CRISPR/Cas9-generated mutants are described here. Furthermore, we tried to identify the underlying mechanisms leading to distinct phenotypes between genetic mutants and antisense morpholino-mediated knockdown embryos. Altogether, this work has generated the first chromosome-wide collection of zebrafish genetic mutants by the CRISPR/Cas9 technology, which will serve as a valuable resource for the community, and our bioinformatics analysis also provides some useful guidance to design gene-specific gRNAs for successful gene editing