Two approaches for defining fractional derivatives of periodic distributions are presented. The first is a distributional version of the Weyl fractional derivative in which a derivative of arbitrary order of a periodic distribution is defined via Fourier series. The second is based on the Grünwald-Letnikov formula for defining a fractional derivative as a limit of a fractional difference quotient. The equivalence of the two approaches is established and an application to a fractional diffusion equation, posed in a space of periodic distributions, is also discussed.
Introduction of a bean phenylalanine ammonia-lyase (PAL) transgene into tobacco plants results in epigenetic post-transcriptional gene silencing which is unstable, such that after self-pollination first generation progeny may become PAL over-expressors. The change from gene silencing to PAL over-expression is accompanied by a loss of cytosine methylation of the PAL transgene and reduced methylation of the endogenous tobacco PAL2 gene, but not the PAL1 gene. These changes are associated with the appearance of high levels of bean PAL and tobacco PAL2 transcripts in the total RNA fraction from PAL over-expressing plants. However, tobacco PAL2 transcripts are inefficiently recruited into polysomes, and tobacco PAL2 protein is not detected in leaves of PAL over-expressing or wild-type lines. Thus, in spite of the post-transcriptionally controlled increase in tobacco PAL2 transcripts in PAL over-expressors, the increased PAL activity is primarily the result of the increase in bean PAL transcripts and corresponding enzymatic activity. These results reveal a complex cross-talk between expression of the PAL transgene and the corresponding endogenous PAL genes at the levels of transcription, transcript stability and polysomal recruitment during sense transgene-mediated silencing and subsequent over-expresson of PAL in tobacco.
This workshop was convened to address common issues and concerns associated with risk management of endocrine-disrupting chemicals (EDCs). The talks described the tools and policies for key Japanese, Australian, German, and U.S. regulatory agencies. The agencies participating in the workshop were responsible for the regulation of various substances including: chemicals, pesticides, environmental contamination, pharmaceuticals, and food additives. The panel also described the role of the Organization for Economic Cooperation and Development (OECD) in standardizing the tools and validation of testing and screening methods. The panel also included nongovernmental organizations presenting the views of the World Wildlife Fund, and the chemical industry from industrialized nations; each organization described its concerns and proposed approaches to risk management of EDCs. This summary highlights the most important areas of common points of view of government, industry, and environmentalists. We also try to identify issues upon which viewpoints diverge.
Canada has long been a colonial country and an extractive economy. In the 20th century, with the adoption of multiculturalism and a global peace keeping mission, the country seemed to embrace a new ethos. However, Canada remains deeply colonial and, in spite of a judiciary that since the repatriation of the Constitution in 1982, increasingly recognizes Indigenous land, resource and identity rights, its economy continues to be extractive, with abiding impacts on the Indigenous peoples of Turtle Island (North America). Our study of the knowledge, ignorance and social attitudes of exiting undergraduate students at Queen’s University suggests that students in this part of Canada (Ontario) are educated to misunderstand the fundamental geographies of Indigenous peoples, their land, and their identity. But the contradiction between image and reality is beginning to attract the students’ attention and disrupt their sense of being part of a just society.