Gray code for derangements

We give a Gray code and constant average time generating algorithm for derangements, i.e., permutations with no fixed points. In our Gray code, each derangement is transformed into its successor either via one or two transpositions or a rotation of three elements. We generalize these results to permutations with number of fixed points bounded between two constants.     

Acute Triangulations of the Regular Icosahedral Surface

We prove here that the surface of the regular icosahedron can be triangulated with 8 non-obtuse and with 12 acute triangles. We also show these numbers to be smallest possible.     

Metric Embeddings—Beyond One-Dimensional Distortion

The extensive study of metric spaces and their embeddings has so far focused on embeddings that preserve pairwise distances. A very intriguing concept introduced by Feige allows us to quantify the extent to which larger structures are preserved by a given embedding. We investigate this concept, focusing on several major graph families such as paths, trees, cubes, and expanders. We find some similarities to the regular (pairwise) distortion, as well as some striking differences.     

Non-protein amino acids in peptide design

An overview of the use of non-protein amino acids in the design of conformationally well-defined peptides, based on work from the author’s laboratory, is discussed. The crystal structures of several designed oligopeptides illustrate the useα-aminoisobutyric acid (Aib) in the construction of helices, D-amino acids in the design of helix termination segments and^DPro-Xxx segments for nucleating ofβ-hairpin structures.β- andγ-amino acid residues have been used to expand the range of designed polypeptide structures. Dedicated to Professor C N R Rao on his 70th birthday     

在几何和参数上表示同一条曲线的两条有理NURBS曲线的权与控制顶点之间的关系

The paper discusses the relationship between weights and control vertices of two rational NURBS curves of degree two or three with all weights larger than zero when they represent the same curve parametrically and geometrically, and gives sufficient and necessary conditions for coincidence of two rational NURBS curves in non-degeneracy case.     

Hyperspaces of Normed Linear Spaces with the Attouch–Wets Topology

Let Cld _AW (X) be the hyperspace of nonempty closed subsets of a normed linear space X with the Attouch–Wets topology. It is shown that the space Cld _AW (X) and its various subspaces are AR's. Moreover, if X is an infinite-dimensional Banach space with weight w(X) then Cld _AW (X) is homeomorphic to a Hilbert space with weight 2 ^w(X).     

On the connectedness of numerical range of matrix polynomials

An investigation on nonconnectedness of numerical range for monic matrix polynomials L(λ) is undertaking here. The distribution of eigenvalues of L(λ) to the components of numerical range and some other algebraic properties are also presented.     

Shell effects in the symmetric-modal fission of pre-actinide nuclei

Mass distributions of fragments in the low-energy fission of nuclei from ¹⁸⁷Ir to ²¹³At have been analysed. This analysis has shown that shell effects in symmetric-mode fragment mass yields from the fission of pre-actinide nuclei could be described if one assumes the existence of two strongly deformed neutron shells in the arising fragments with neutron numbers N₁ ≈ 52 and N₂ ≈ 68. A new method has been proposed for quantitatively describing the mass distributions of the symmetric fission mode for pre-actinides with A ≈ 180–220.     

Electronic molecule-like spectrum of quantum wells in crossed fields

We show that an electron confined to a single finite parabolic quantum well in crossed electric and magnetic fields can behave as a double quantum well system. The magnetic field is parallel to the heterostructure layers and the electric field is perpendicular to those. For a suitable choice of both fields and quantum well width, the electron can be confined to a double quantum well effective potential that is very similar to the electronic potential model for diatomic molecules. The double quantum well spectrum is calculated using a numerical algorithm based on semiclassical methods. A physical interpretation of this quantum system is given based on the analogy to the electrons bound to diatomic molecules.     

Partial structure elucidation of the most abundant octa and nonachlorotoxaphene congeners in marine mammals by using conventional electron ionization mass spectrometry and mass spectrometry/mass spectrometry

Summary Conventional electron ionization (EI) mass spectrometry (MS) and MS/MS techniques were applied to the analysis of two abundant octa and nonachlorobornanes isolated from seals of the Baltic sea and originating from technical toxaphene. The exact sterical structures of the two compounds were previously determined using nuclear magnetic resonance (NMR) spectroscopy by two independent research groups. The MS and MS/MS data generated in this study allowed partial structure elucidation of these polychlorobornanes, in particular revealing the distribution of the Cl substituents between the six-membered carbon ring, the bridge and the bridgehead in the parent bornane structure. Fragmentation of the six-membered carbon ring and the bridge by retro-Diels-Alder (RDA) and related mechanisms was discovered by studying specific parent/daughter ion transitions. The detailed fragmentation pathways formulated may be applicable to the structure elucidation of other toxaphene congeners and the monitoring of strategic transitions is highly selective for the detection of these compounds in technical toxaphene and in environmental samples.