The Klein-Gordon equation in a domain with time-dependent boundary

We solve a Dirichlet boundary value problem for the Klein–Gordon equation posed in a time-dependent domain. Our approach is based on a general transform method for solving boundary value problems for linear and integrable nonlinear PDE in two variables. Our results consist of the inversion formula for a generalized Fourier transform, and of the application of this generalized transform to the solution of the boundary value problem.

Some general comparative points on Chao’s and Zelterman’s estimators of population size

Two simple and frequently used capture–recapture estimates of the population size are compared: Chao's lower-bound estimate and Zelterman's estimate allowing for contaminated distributions. In the Poisson case it is shown that if there are only counts of ones and twos, the estimator of Zelterman is always bounded above by Chao's estimator. If counts larger than two exist, the estimator of Zelterman is becoming larger than that of Chao's, if only the ratio of the frequencies of counts of twos and ones is small enough. A similar analysis is provided for the binomial case. For a two-component mixture of Poisson distributions the asymptotic bias of both estimators is derived and it is shown that the Zelterman estimator can experience large overestimation bias. A modified Zelterman estimator is suggested and also the bias-corrected version of Chao's estimator is considered. All four estimators are compared in a simulation study.

Haploids in flowering plants: origins and exploitation

The first haploid angiosperm, a dwarf form of cotton with half the normal chromosome complement, was discovered in 1920, and in the ninety years since then such plants have been identified in many other species. They can occur either spontaneously or can be induced by modified pollination methods in vivo, or by in vitro culture of immature male or female gametophytes. Haploids represent an immediate, one-stage route to homozygous diploids and thence to F(1) hybrid production. The commercial exploitation of heterosis in such F(1) hybrids leads to the development of hybrid seed companies and subsequently to the GM revolution in agriculture. This review describes the range of techniques available for the isolation or induction of haploids and discusses their value in a range of areas, from fundamental research on mutant isolation and transformation, through to applied aspects of quantitative genetics and plant breeding. It will also focus on how molecular methods have been used recently to explore some of the underlying aspects of this fascinating developmental phenomenon.

Global transcript analysis of rice leaf and seed using SAGE technology.

We have compiled two comprehensive gene expression profiles from mature leaf and immature seed tissue of rice (Oryza sativa ssp. japonica cultivar Nipponbare) using Serial Analysis of Gene Expression (SAGE) technology. Analysis revealed a total of 50 519 SAGE tags, corresponding to 15 131 unique transcripts. Of these, the large majority (approximately 70%) occur only once in both libraries. Unexpectedly, the most abundant transcript (approximately 3% of the total) in the leaf library was derived from a type 3 metallothionein gene. The overall frequency profiles of the abundant tag species from both tissues differ greatly and reveal seed tissue as exhibiting a non-typical pattern of gene expression characterized by an over abundance of a small number of transcripts coding for storage proteins. A high proportion ( approximately 80%) of the abundant tags (> or = 9) matched entries in our reference rice EST database, with many fewer matches for low abundant tags. Singleton transcripts that are common to both tissues were collated to generate a summary of low abundant transcripts that are expressed constitutively in rice tissues. Finally and most surprisingly, a significant number of tags were found to code for antisense transcripts, a finding that suggests a novel mechanism of gene regulation, and may have implications for the use of antisense constructs in transgenic technology.