A strong limit theorem for generalized Cantor-like random sequences

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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.     

Theory of electron tunneling through a bridge molecule with two electronic levels at low temperatures

A theory of electron tunneling through a single-center bridge redox group that has two electronic levels participating in the electron transfer process is presented. The temperature is presumed to be low enough to ignore activation redox conversions of the bridge group. Salient features of this system are due both to the presence of two electroactive states of the bridge group and to relaxation processes along the reaction coordinate. The processes in question make the tunneling current time-dependent at fixed potentials and can bring about hysteresis in current-voltage curves when cycling the bias potential. Effects of inelastic tunneling with excitation of vibrations of a local quantum degree of freedom are considered.     

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.     

Estimation of the dimensions of nano-capillaries from gas adsorption data

A new approach is presented to determine the dimensions of cylindrical nanopores from adsorption measurements.     

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.     

Nitrogen Adsorption Study of MCM-41 Molecular Sieves Synthesized Using Hydrothermal Restructuring

Nitrogen desorption scanning hysteresis loops (DSHLs) for large-pore MCM-41 silicas (pore diameter from 4.0 to 6.5 nm) are reported for the first time. DSHLs for MCM-41 were compared with those of conventional mesoporous silicas and no appreciable differences were found, although hysteresis loops and DSHLs for the latter were usually broader. Since desorption behavior of conventional porous silicas is appreciably influenced by pore connectivity, the observed similarity in hysteresis behavior suggests single-pore blocking effects for MCM-41 due to variation of pore diameter along its nonintersecting channels. It was also shown that the steepness of nitrogen desorption branches at relative pressures close to 0.4 often results from proximity of the lower pressure limit of adsorption-desorption irreversibility and consequently it is not justified to consider it as an indication of narrow pore size distribution. Thus, application of desorption data in calculations of pore size distributions may be grossly misleading.     

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.     

Bifurcation phenomena near homoclinic systems: A two-parameter analysis

The bifurcations of periodic orbits in a class of autonomous three-variable, nonlinear-differential-equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues ( ±i,), where ¦/¦ < 1 (Sil'nikov's condition), are studied in a two-parameter space. The perturbed homoclinic systems undergo a countable set of tangent bifurcations followed by period-doubling bifurcations leading to periodic orbits which may be attractors if ¦/¦ < 1/2. The accumulation rate of the critical parameter values at the homoclinic system is exp(-2¦/¦). A global mechanism for the onset of homoclinicity in strongly contractive flows is analyzed. Cusp bifurcations with bistability and hysteresis phenomena exist locally near the onset of homoclinicity. A countable set of these cusp bifurcations with scaling properties related to the eigenvalues±i of the stationary state are shown to occur in infinitely contractive flows. In the two-parameter space, the periodic orbit attractor domain exhibits a spiral structure globally, around the set of homoclinic systems, in which all the different periodic orbits are continuously connected.