Generating-function method for tensor products

This is the first of two articles devoted to a exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We start by reviewing Sharp's character method. An alternative approach to the construction of tensor-product generating functions is then presented which overcomes most of the technical difficulties associated with the character method. It is based on the reformulation of the problem of calculating tensor products in terms of the solution of a set of linear and homogeneous Diophantine equations whose elementary solutions represent ``elementary couplings''. Grobner bases provide a tool for generating the complete set of relations between elementary couplings and, most importantly, as an algorithm for specifying a complete, compatible set of ``forbidden couplings''.Comment: Harvmac (b mode : 39 p) and Pictex; this is a substantially reduced version of hep-th/9811113 (with new title); to appear in J. Math. Phy

Generating-function method for fusion rules

This is the second of two articles devoted to an exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper focuses on fusion rules, using the machinery developed for tensor products in the companion article. Although the Kac-Walton algorithm provides a method for constructing a fusion generating function from the corresponding tensor-product generating function, we describe a more powerful approach which starts by first defining the set of fusion elementary couplings from a natural extension of the set of tensor-product elementary couplings. A set of inequalities involving the level are derived from this set using Farkas' lemma. These inequalities, taken in conjunction with the inequalities defining the tensor products, define what we call the fusion basis. Given this basis, the machinery of our previous paper may be applied to construct the fusion generating function. New generating functions for sp(4) and su(4), together with a closed form expression for their threshold levels are presented.Comment: Harvmac (b mode : 47 p) and Pictex; to appear in J. Math. Phy

Understanding factors associated with grazing efficiency of perennial ryegrass

Understanding factors associated with grazing efficiency of perennial ryegrass. 10. International Symposium on the Nutrition of Herbivores (ISNH

Berenstein-Zelevinsky triangles, elementary couplings and fusion rules

We present a general scheme for describing su(N)_k fusion rules in terms of elementary couplings, using Berenstein-Zelevinsky triangles. A fusion coupling is characterized by its corresponding tensor product coupling (i.e. its Berenstein-Zelevinsky triangle) and the threshold level at which it first appears. We show that a closed expression for this threshold level is encoded in the Berenstein-Zelevinsky triangle and an explicit method to calculate it is presented. In this way a complete solution of su(4)_k fusion rules is obtained.Comment: 14 page

Evaluation of the Performance Characteristics of the CGLSS and NLDN Systems Based on Two Years of Ground-Truth Data from Launch Complex 39B, Kennedy Space Center, Florida

From May 2011 through July 2013, the lightning instrumentation at Launch Complex 39B (LC39B) at the Kennedy Space Center, Florida, has obtained high-speed video records and field change waveforms (dE/dt and three-axis dH/dt) for 54 negative polarity return strokes whose strike termination locations and times are known with accuracy of the order of 10 m or less and 1 s, respectively. A total of 18 strokes terminated directly to the LC39B lighting protection system (LPS), which contains three 181 m towers in a triangular configuration, an overhead catenary wire system on insulating masts, and nine down conductors. An additional 9 strokes terminated on the 106 m lightning protection mast of Launch Complex 39A (LC39A), which is located about 2.7 km southeast of LC39B. The remaining 27 return strokes struck either on the ground or attached to low-elevation grounded objects within about 500 m of the LC39B LPS. Leader/return stroke sequences were imaged at 3200 frames/sec by a network of six Phantom V310 high-speed video cameras. Each of the three towers on LC39B had two high-speed cameras installed at the 147 m level with overlapping fields of view of the center of the pad. The locations of the strike points of 54 return strokes have been compared to time-correlated reports of the Cloud-to-Ground Lightning Surveillance System (CGLSS) and the National Lightning Detection Network (NLDN), and the results of this comparison will be presented and discussed

Blanks, a nuclear siRNA/dsRNA-binding complex component, is required for Drosophila spermiogenesis

Small RNAs and a diverse array of protein partners control gene expression in eukaryotes through a variety of mechanisms. By combining siRNA affinity chromatography and mass spectrometry, we have identified the double-stranded RNA-binding domain protein Blanks to be an siRNA- and dsRNA-binding protein from Drosophila S2 cells. We find that Blanks is a nuclear factor that contributes to the efficiency of RNAi. Biochemical fractionation of a Blanks-containing complex shows that the Blanks complex is unlike previously described RNA-induced silencing complexes and associates with the DEAD-box helicase RM62, a protein previously implicated in RNA silencing. In flies, Blanks is highly expressed in testes tissues and is necessary for postmeiotic spermiogenesis, but loss of Blanks is not accompanied by detectable transposon derepression. Instead, genes related to innate immunity pathways are up-regulated in blanks mutant testes. These results reveal Blanks to be a unique component of a nuclear siRNA/dsRNA-binding complex that contributes to essential RNA silencing-related pathways in the male germ line

Morphological evolution of lamellar forming polystyrene-block-poly(4-vinylpyridine) copolymer under solvent annealing

In this work, we are reporting a very simple and efficient method to form lamellar structures of symmetric polystyrene-block-poly(4-vinylpyridine) (PS-b-P4VP) copolymer thin films with vertically (to the surface plane) orientated lamellae using a solvent annealing approach. The methodology does not require any brush chemistry to engineer a neutral surface and it is the block neutral nature of the film-solvent vapour interface that defines the orientation of the lamellae. The microphase separated structure of two different molecular weight lamellar forming PS-block-P4VP copolymers formed under solvent vapour annealing was monitored using atomic force microscopy (AFM) so as to understand the morphological changes of the films upon different solvent exposure. In particular, the morphology changes from micellar structures to well-defined microphase separated arrangements. The choice of solvent/s (single and dual solvent exposure) and the solvent annealing conditions (temperature, time etc.) has important effects on structural transitions of the films and it was found that a block neutral solvent was required to realize vertically aligned P4VP lamellae. The results of the structural variation of the phase separated nanostructured films through the exposure to ethanol are also described

Formation of sub-7 nm feature size PS-b-P4VP block copolymer structures by solvent vapour process

The nanometer range structure produced by thin films of diblock copolymers makes them a great of interest as templates for the microelectronics industry. We investigated the effect of annealing solvents and/or mixture of the solvents in case of symmetric Poly (styrene-block-4vinylpyridine) (PS-b-P4VP) diblock copolymer to get the desired line patterns. In this paper, we used different molecular weights PS-b-P4VP to demonstrate the scalability of such high χ BCP system which requires precise fine-tuning of interfacial energies achieved by surface treatment and that improves the wetting property, ordering, and minimizes defect densities. Bare Silicon Substrates were also modified with polystyrene brush and ethylene glycol self-assembled monolayer in a simple quick reproducible way. Also, a novel and simple in situ hard mask technique was used to generate sub-7nm Iron oxide nanowires with a high aspect ratio on Silicon substrate, which can be used to develop silicon nanowires post pattern transfer

Automorphism Modular Invariants of Current Algebras

We consider those two-dimensional rational conformal field theories (RCFTs) whose chiral algebras, when maximally extended, are isomorphic to the current algebra formed from some affine non-twisted Kac--Moody algebra at fixed level. In this case the partition function is specified by an automorphism of the fusion ring and corresponding symmetry of the Kac--Peterson modular matrices. We classify all such partition functions when the underlying finite-dimensional Lie algebra is simple. This gives all possible spectra for this class of RCFTs. While accomplishing this, we also find the primary fields with second smallest quantum dimension.Comment: 32 pages, plain Te