Euler's invention of integral transforms

Euler invented integral transforms in the context of second order differential equations. He used them in a fragment published in 1763 and in a chapter of Institutiones Calculi Integralis (1769). In introducing them he made use of earlier work in which a concept akin to the integral transform is implicit. It would, however, be reading too much into that earlier work to see it as contributing to the theory of the integral transform. Other work sometimes cited in this context in fact has different concerns.     

The ascendancy of the Laplace transform and how it came about

The modern Laplace transform is relatively recent. It was first used by Bateman in 1910, explored and codified by Doetsch in the 1920s and was first the subject of a textbook as late as 1937. In the 1920s and 1930s it was seen as a topic of front-line research; the applications that call upon it today were then treated by an older technique — the Heaviside operational calculus. This, however, was rapidly displaced by the Laplace transform and by 1950 the exchange was virtually complete. No other recent development in mathematics has achieved such ready popularisation and acceptance among the users of mathematics and the designers of undergraduate curricula.     

Genome of the marsupial Monodelphis domestica reveals innovation in non-coding sequences

We report a high-quality draft of the genome sequence of the grey, short-tailed opossum (Monodelphis domestica). As the first metatherian ('marsupial') species to be sequenced, the opossum provides a unique perspective on the organization and evolution of mammalian genomes. Distinctive features of the opossum chromosomes provide support for recent theories about genome evolution and function, including a strong influence of biased gene conversion on nucleotide sequence composition, and a relationship between chromosomal characteristics and X chromosome inactivation. Comparison of opossum and eutherian genomes also reveals a sharp difference in evolutionary innovation between protein-coding and non-coding functional elements. True innovation in protein-coding genes seems to be relatively rare, with lineage-specific differences being largely due to diversification and rapid turnover in gene families involved in environmental interactions. In contrast, about 20% of eutherian conserved non-coding elements (CNEs) are recent inventions that postdate the divergence of Eutheria and Metatheria. A substantial proportion of these eutherian-specific CNEs arose from sequence inserted by transposable elements, pointing to transposons as a major creative force in the evolution of mammalian gene regulation.     

The ascendancy of the Laplace transform and how it came about

The modern Laplace transform is relatively recent. It was first used by Bateman in 1910, explored and codified by Doetsch in the 1920s and was first the subject of a textbook as late as 1937. In the 1920s and 1930s it was seen as a topic of front-line research; the applications that call upon it today were then treated by an older technique — the Heaviside operational calculus. This, however, was rapidly displaced by the Laplace transform and by 1950 the exchange was virtually complete. No other recent development in mathematics has achieved such ready popularisation and acceptance among the users of mathematics and the designers of undergraduate curricula. Communicated by C. Truesdell     

Zr基大块非晶挤压特性研究

研究了Zr41.2Ti13.8Cu12.5Ni10Be22.5大块非晶在不同挤压速率和挤压温度等工艺条件下的挤压成形性能.结果表明:合金的流变行为对挤压温度和挤压速率有明显的依赖性.在挤压过程中出现了一个平稳流变的过程,其平稳流变所需的载荷(P1)与合金在高温下屈服强度有关.当应变速率为0.005 mm/s时,从355~415℃温度范围内,保持平稳流变所需的力从1.5 kN到0.5 kN,当温度为395℃,应变速率为0.05 mm/s时,保持平稳流变所需的力高达4 kN.在挤压过程中大块非晶呈现超塑性.     

The development of the Laplace Transform, 1737–1937 II. Poincaré to Doetsch, 1880–1937

An earlier paper, to which this is a sequel, traced the history of the Laplace Transform up to 1880. In that year Poincaré reinvented the transform, but did so in a more powerful context, that of properly conceived complex analysis. Rapid developments followed, culminating in Doetsch' work in which the transform took its modern shape.     

The development of the Laplace transform, 1737–1937

This paper, the first of two, follows the development of theLaplace Transform from its earliest beginnings withEuler, usually dated at 1737, to the year 1880, whenSpitzer was its major, if himself relatively minor, protagonist. The coverage aims at completeness, and shows the state which the technique reached in the hands of its greatest exponent to that time,Petzval. A sequel will trace the development of the modern theory from its beginnings withPoincaré to its present form, due toDoetsch.     

Genome analysis of the platypus reveals unique signatures of evolution

We present a draft genome sequence of the platypus, Ornithorhynchus anatinus. This monotreme exhibits a fascinating combination of reptilian and mammalian characters. For example, platypuses have a coat of fur adapted to an aquatic lifestyle; platypus females lactate, yet lay eggs; and males are equipped with venom similar to that of reptiles. Analysis of the first monotreme genome aligned these features with genetic innovations. We find that reptile and platypus venom proteins have been co-opted independently from the same gene families; milk protein genes are conserved despite platypuses laying eggs; and immune gene family expansions are directly related to platypus biology. Expansions of protein, non-protein-coding RNA and microRNA families, as well as repeat elements, are identified. Sequencing of this genome now provides a valuable resource for deep mammalian comparative analyses, as well as for monotreme biology and conservation.