Quasi-deformations of sl2 (F) with base ℝ[t,t −1]

In this paper we construct quasi-deformations of sl₂(?) with the Laurent polynomials over the reals as base algebra and general vector fields for sl₂(?) in the base of the quasideformation.     

Semiconductor nanowires for novel one-dimensional devices

Low-dimensional semiconductors offer interesting physical phenomena but also the possibility to realize novel types of devices based on, for instance, 1D structures. By using traditional top-down fabrication methods the performance of devices is often limited by the quality of the processed device structures. In many cases damage makes ultra-small devices unusable. In this work we present a recently developed method for bottom-up fabrication of epitaxially nucleated semiconductor nanowires based on metallic nanoparticle-induced formation of self-assembled nanowires. Further development of the vapor–liquid–solid growth method have made it possible to control not only the dimension and position of nanowires but also to control heterostructures formed inside the nanowires. Based on these techniques we have realized a series of transport devices such as resonant tunneling and single-electron transistors but also optically active single quantum dots positioned inside nanowires displaying sharp emission characteristics due to excitons.     

Structure of the starch granule--a curved crystal

A structure model of the molecular arrangement in native starch proposed earlier is further considered, with special regard to the lateral packing of cluster units. The amylopectin molecules are radially distributed, with branches concentrated in clusters. Within each cluster the polyglucan chains form double helices which are hexagonally packed. The clusters form spherically concentric crystalline layers with amylose in an amorphous form acting as a space-filler. A translational mechanism for the change of helical direction at boundaries between clusters is proposed which can account for variations in the curvature of the concentric layers. The model is related to X-ray diffraction data and optical birefringence, considering dissembly at gelatinization. The structure is also discussed in relation to biosynthesis. Some aspects of gelatinization, such as the recent glass-transition approach, are then considered.     

Universal solutions to the simplex equations

We construct a class of solutions to the p-simplex equation in terms of solutions to the Yang-Baxter equation, for every p ≥ slant 3. This may make the construction of solvable p-dimensional lattice models possible.     

Threshold Fields of Parametric Instabilities

The threshold electric fields of parametric decay instabilities in a magnetized plasma have been derived. Consideration is given to a unified presentation of a number of basic processes of particular interest.     

Calculation of the long-range coupling between electrons in lone pairs and double bonds using semiempirical and ab initio methods

The electronic coupling between symmetrically placed lone pairs or π electrons are calculated using semiempirical and ab initio methods and the results compared to experimental numbers. The agreement is satisfactory in cases when there is a small tendency for cancellation between contributions of different signs. We have found nonexponential behavior when the number of intervening cyclohexane units is increased in the case of phenyl endgroups. In this case as well as in the cases with exponential decrease, the CNDO /S method shows a similar behavior as that of the ab initio Hartree–Fock method, which suggests that the former method may be used to calculate the electronic factor in electron transfer systems. © 1992 John Wiley & Sons, Inc.     

List Colouring When The Chromatic Number Is Close To the Order Of The Graph

Ohba has conjectured [7] that if G has 2 (G)+1 or fewer vertices then the list chromatic number and chromatic number of G are equal. In this short note we prove the weaker version of the conjecture obtained by replacing 2 (G)+1 by * This research was partially supported by DIMACS and by CNRS/NSF collaboration grant. Research supported in part by NSF grants DMS-0106589, CCR-9987845 and by the State of New Jersey.     

Packing triangles in a graph and its complement

How few edge‐disjoint triangles can there be in a graph G on n vertices and in its complement ? This question was posed by P. Erd?s, who noticed that if G is a disjoint union of two complete graphs of order n/2 then this number is n²/12 + o(n²). Erd?s conjectured that any other graph with n vertices together with its complement should also contain at least that many edge‐disjoint triangles. In this paper, we show how to use a fractional relaxation of the above problem to prove that for every graph G of order n, the total number of edge‐disjoint triangles contained in G and is at least n²/13 for all sufficiently large n. This bound improves some earlier results. We discuss a few related questions as well. © 2004 Wiley Periodicals, Inc. J Graph Theory 47: 203–216, 2004     

First observation of four-body breakup in electron recombination: C2D+5

We report the first observation of four-body breakup in electron dissociative recombination of a molecular ion: C2D+5. In an ion storage ring experiment, the branching ratio for the process C2D+5 + e(-)-->C2D2 + D + D + D was determined to be 13%. This means that three covalent chemical bonds are broken as a result of the action of a single electron. This is the first time a four-body breakup of chemical bonds has been observed in a low-energy binary reaction.