The nearest neighbor random walk on subspaces of a vector space and rate of convergence

LetX be the collection ofk-dimensional subspaces of ann-dimensional vector spaceV _n overGF(q). A metric may be defined onX by letting

On two--block--factor sequences and one--dependence

The distributions of two--block--factors arising from i.i.d. sequences are observed to coincide with the distributions of the superdiagonals of jointly exchangeable and dissociated arrays . An inequality for superdiagonal probabilities of the arrays is presented. It provides, together with the observation, a simple proof of the fact that a special one--dependent Markov sequence of Aaronson, Gilat and Keane (1992) is not a two--block factor.

     

Renormalization group for Markov chains and application to metastability

In this paper we introduce a new renormalization group method for the study of the long-time behavior of Markov chains with finite state space and with transition probabilities exponentially small in an external parameter. A general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two-dimensional Ising system at low temperature,     

Sensitivity in Supramolecular Architectures of Polyaromatic Salts Containing Two Singly‐Pimerized Bipyridines

Three novel supramolecular arrays of zigzag polyaromatic salts are reported. Both the conformation and disposition of the dications are subjected to various noncovalent interactions. Thus, the presence or absence of the π‐π interacting enclathrated molecules, the efficient packing and the involved hydrogen bonding interactions of anions, as well as the increased hydrophobic property of the dications themselves exert influence.     

Nonstationary Markov chains and convergence of the annealing algorithm

We study the asymptotic behavior as timet + of certain nonstationary Markov chains, and prove the convergence of the annealing algorithm in Monte Carlo simulations. We find that in the limitt + , a nonstationary Markov chain may exhibit phase transitions. Nonstationary Markov chains in general, and the annealing algorithm in particular, lead to biased estimators for the expectation values of the process. We compute the leading terms in the bias and the variance of the sample-means estimator. We find that the annealing algorithm converges if the temperatureT(t) goes to zero no faster thanC/log(t/t ₀) ast+, with a computable constantC andt ₀ the initial time. The bias and the variance of the sample-means estimator in the annealing algorithm go to zero likeO(t^–1+) for some 0<1, with =0 only in very special circumstances. Our results concerning the convergence of the annealing algorithm, and the rate of convergence to zero of the bias and the variance of the sample-means estimator, provide a rigorous procedure for choosing the optimal annealing schedule. This optimal choice reflects the competition between two physical effects: (a) The adiabatic effect, whereby if the temperature is loweredtoo abruptly the system may end up not in a ground state but in a nearby metastable state, and (b) the super-cooling effect, whereby if the temperature is loweredtoo slowly the system will indeed approach the ground state(s) but may do so extremely slowly.     

Host-guest interactions in aqueous media withp-tert.-butylcalix[4]arene bearing polyoxyethylene chains

The interactions ofp-tert.-butylcalix[4]arene bearing polyoxyethylene chains (C3) with pyrene (Py), 1-anilino-8-naphthalenesulfonate (ANS) andN-phenyl-naphthylamine (NPN) in aqueous solution were studied by absorption and fluorescence measurements. Absorption spectral changes and fluorescence enhancements reveal that C3, which has a hydrophobic cavity, can include organic molecules and ions in aqueous solution and form 11 host-guest complexes with ANS and NPN. C3 forms inclusion complexes with Py at different stoichiometries depending on the host: guest molar ratio. Binding constants of 2.2×10⁴, 2.0×10⁴ and 3.6×10⁵ dm³ mol^–1 were calculated for the C3Py, C3ANS and C3NPN complexes (11), respectively, based on the Benesi-Hildebrand equation.Author for correspondence.     

Effect of carbonate incorporation on the structural and superconducting properties of the double chain compound Y2Ba4Cu7O15−x

Structural investigations on powder samples of Y₂Ba₄Cu₇O_15–x with different carbonate content have been performed. Powder x-ray Rietveld refinements showed the remarkable influence of carbonate incorporation on the lattice parameters. Most important is the decrease of T_c with increasing carbonate content. We assign these effects to an incorporation of the carbonate ion into the crystal lattice, copper vacancies at the Cu(1) position and a possible misorientation of the copper oxygen single chains. No change of the structure (e. g. superstructure) could be found.     

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.     

The effect of fluorination: a crystallographic and computational study of mesogenic alkyl 4-[2-(perfluorooctyl)ethoxy]benzoates

The series of alkyl 4-[2-(perfluorooctyl)ethoxy]benzoates (F8-n) shows a systematic change of crystal structures depending on the length of the alkyl chain: separate packing of perfluorooctyl (Rf) and alkyl (Rh) chains from each other for shorter (n=2) and longer (n=11) members, alternate packing of Rf and Rh chains for middle (n=6,7) members, and an intermediate type of packing for n=4. Semiempirical MO calculations show slightly repulsive interactions between the Rf chains, and attractive ones between Rf and Rh chains and between Rh and the core of a molecular pair. It is concluded that fluorination determines the molecular shape of the crystal structures by making the chain rigid. It is confirmed that the interactions between Rf chains are small compared with those between other moieties and that they are forced to aggregate owing to the exclusion from other moieties. Thus, the effect is dependent on the geometries and intermolecular interactions of the other moieties.     

Proton transfer reactions from N-H acid [5,10,15,20-tetrakis(pentafluorophenyl)-21-H, 23-H-porphyrin] to strong bases in acetonitrile

Deprotonation of 5,10,15,20-tetrakis(pentafluorophenyl)-21-H, 23-H-porphyrin (PhF₅PorH₂) by various bases has been studied by ¹H NMR and kinetic methods. The kinetic parameters in acetonitrile were defined for proton transfer reactions yielding [NH]⁺ protonated bases and [NHN]⁻ anions with intramolecular hydrogen-bonded chains.