Stories about groups and sequences

The main theme of this article is that counting orbits of an infinite permutation group on finite subsets or tuples is very closely related to combinatorial enumeration; this point of view ties together various disparate stories. Among these are reconstruction problems, the relation between connected and arbitrary graphs, the enumeration of N-free posets, and some of the combinatorics of Stirling numbers.Dedicated to Hanfried Lenz on the occasion of his 80th birthday.     

NMR analysis of the microstructure of poly(methyl acrylate-co-N-vinylcarbazole)

The microstructure of a series of high conversion copolymers of methyl acrylate (MA) and N-vinylcarbazole (NVC) was characterized by NMR. ¹H- and ¹³C-NMR spectra were assigned by comparison to the homopolymers and by using heteronuclear shift correlation spectroscopy. MA-centered triad distributions were obtained from the carbonyl carbon. Distributions of NVC sequences were determined from aromatic carbons 1 and 8a, and aromatic proton 1 These experimentally determined sequence distributions were compared to those calculated from reactivity ratios approximated from the copolymer compositions. Agreement was very good for low NVC content copolymers. Three signals were particularly useful in providing rapid assessment of the distribution of NVC units within low NVC content copolymers: proton 1 and carbon 1 of NVC and the carbonyl carbon of MA. © 1992 John Wiley & Sons, Inc.     

On the correlation of the glass transition temperature of a copolymer with its comonomer sequences

The glass transition temperature of a copolymer depends not only on chemical composition but also on its comonomer sequences. This experimental fact is explained by Barton's and Johnston's equations. Their equations, though complicated, become simple, if a suitable parameter is used to describe the comonomer sequences. It is shown that with these new expressions, their equations can be used to understand glass transition temperatures of two additional types of copolymers, compatible multiblock copolymers and homopolymers with various tacticities treated as steric copolymers.Dedicated to Professor Bernhard Wunderlich on the occasion of his 65th birthdayWe wish to thank the reviewer for his/her kind linguistic improvement of this article.     

Analyzing functional similarity of protein sequences with discrete wavelet transform

This paper applies discrete wavelet transform (DWT) with various protein substitution models to find functional similarity of proteins with low identity. A new metric, 'S' function, based on the DWT is proposed to measure the pair-wise similarity. We also develop a segmentation technique, combined with DWT, to handle long protein sequences. The results are compared with those using the pair-wise alignment and PSI-BLAST.     

Copolymerization of ethylene and 1-butene with highly active Ticl4/THF/Mgcl2, Ticl4/THF/Mgcl2/SiO2, and TiCl3.1/3AlCl3 catalysts

Highly active catalysts for copolymerization have been prepared by the precipitation of MgCl₂/ToCl₄ complex with or without high surface area silica. Copolymerization of ethylene and 1-butene has been tested by using the prepared catalysts at various concentrations of 1-butene. The catalytic activities are 20–80 kg/g Ti h. The rate of copolymerization is strongly affected by the addition of 1-butene. The decay rate of copolymerization is first order with respect to time. Analyses of copolymers with solvent extraction, DSC, IR, XRD, and NMR were performed. Ethylene reactivity ratio (k₁₁) for TiCl₄/MgCl₂/THF catalyst is calculated to be about 26 by NMR spectrum. © 1994 John Wiley & Sons, Inc.     

ELASTIC BEHAVIOR OF PROTEIN-LIKE SINGLE CHAIN

The conformational properties and elastic behaviors of protein-like single chains in the process of tensile elongation were investigated by means of Monte Carlo method. The sequences of protein-like single chains contain two types of residues: hydrophobic (H) and hydrophilic (P). The average conformations and thermodynamics statistical properties of protein-like single chains with various elongation ratio λ were calculated. It was found that the mean-square end-to-end distance r increases with elongation ratio,λ. The tensor eigenvalues ratio of : decreases with elongation ratio λ for short (HP)x protein-like polymers, however, the ratio of : increases with elongation ratioλ,especially for long (H)x sequence. Average energy per bond increases with elongation ratioλ, especially for(H)x protein-like single chains. Helmholtz free energy per bond also increases with elongation ratioλ. Elastic force (f), energy contribution to force (fU) and entropy contribution to force (fs) for different protein-like single chains were also calculated.These investigations may provide some insights into elastic behaviors of proteins.     

Ionization potential of excited states of Be‐like sequence in the concept of iso‐spectrum‐level series

With the introduction of the concept of the iso‐spectrum‐level series, a linear relationship is found between the first differences of the ionization potential of excited states and nuclear charge Z along an iso‐spectrum‐level series, and the ionization potential of excited states of Be‐like sequence are studied systematically on the basis of the weakest bound electron potential model theory. The expression of nonrelativistic ionization potential is derived from the weakest bound electron potential model theory, and relativistic effects are included by using a fourth‐order polynomial in Z. As a demonstration, the ionization potentials of [He]2s2p ³P, [He]2s3s ¹S₀, [He]2s3p ¹P, [He]2s3d ¹D₂, and [He]2s4d ¹D₂ series for a range of Be‐like sequence from Z = 4–23 are calculated. The results are compared with the experimental data and the recent sophisticated ab initio results. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 344–350, 2003     

Allowed transitions in silicon isoelectronic ions

Dipole‐allowed transitions have been studied for the first few members of the Si isoelectronic sequence. Transition energies, oscillator strengths, transition probabilities and quantum defect values have been estimated for the low‐ and high‐lying excited states of s and d symmetries up to the principal quantum number n=7 for these 3p open shell ions from P⁺ to Cr¹⁰⁺. Time‐dependent coupled Hartree–Fock (TDCHF) theory has been utilized to calculate such transition properties. Most of the results for transition energies, oscillator strengths, and transition probabilities for higher excited states are new. The transition energies for low‐lying excited states agree well with experimental data wherever available. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001