The Graphical Spin Algebra Method Applied to U(2N) Generators

An efficient method for the evaluation of the matrix elements of U(2n) spin-dependent generators in a fully spin adapted Gelfand-Tsetlin basis is given. This is done by evaluating the matric elements of the U(2n) generators in a Yamanouchi-Kotani basis whose orbital part is equivalent, up to phase factors, to the Gelfand-Tsetlin basis. This allows the expression for the matrix elements to be separated into products of creation and annihilation operators, which are evaluated using Wick's theorem, and products of SU(2) Clebsch-Gordan coefficients, whose spin graphs are factorized into easily evaluated segment diagrams. The matrix elements of a single U(2n) generator reduce to a sum of products of segment values. These values are given in formula form involving 3-j and 6-j symbols and in table form, where the formulas have been evaluated for all the nonvanishing segments. (C) 1995 American Institute of Physics

Solid-Liquid Crystal Interfaces Probed by Optical Second-Harmonic Generation

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Plant Epigenetic Mechanisms in Response to Biotic Stress

The environment changes faster than the ability of genetic recombination to generate natural genetic diversity. In this context, epigenetic regulation of gene expression has the potential to provide organisms with an alternative mechanism for phenotypic variation by controlling the extent of plasticity that can be achieved in response to environmental changes. There is now substantial evidence suggesting roles for epigenetic regulation of several different aspects of the plant response to biotic stress. At the basic level of gene expression, posttranscriptional gene silencing mediated by small RNAs and chromatin remodelling controlling transcriptional gene silencing are essential for the induced resistance responses activated during pest and pathogen attack. Beyond this, there is also evidence that histone modifications and DNA methylation are associated with immune memory, or defence priming, such as systemic acquired resistance (SAR). In addition, recent evidence indicates that epigenetic modifications can also generate longer-term defence priming responses that can be inherited across generations. In this chapter, we will discuss the roles of epigenetics in these different modes of biotic stress resistance, and suggest ways in which we may in the future be able to exploit epigenetic systems for crop protection