The distance between homotopy classes of <Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript>-valued maps in multiply connected domains

Certain Sobolev spaces of S ¹-valued functions can be written as a disjoint union of homotopy classes. The problem of finding the distance between different homotopy classes in such spaces is considered. In particular, several types of one-dimensional and two-dimensional domains are studied. Lower bounds are derived for these distances. Furthermore, in many cases it is shown that the lower bounds are sharp but are not achieved. The first author’s work of was supported in part by NSF grant 0503887. The second author’s research of was supported by G.S. Elkin research fund.     

On the solid state of hydrogen fluoride: A self-consistent crystal field study

A recently developed self-consistent crystal field (SCCF ) method is applied to two suggested crystal structures of solid hydrogen fluoride, polar and nonpolar, respectively. Constrained geometry optimizations are performed and the results are compared with experiment and previous theoretical studies. Comparisons are also made with a previous SCCF study on hydrogen cyanide. The Pauli repulsion, dispersion, and “classical” crystal field contributions to the lattice energy are calculated. © 1993 John Wiley & Sons, Inc.     

Distinguishing sceneries by observing the scenery along a random walk path

LetG be an infinite connected graph with vertex setV. Ascenery onG is a map ξ :V → 0, 1 (equivalently, an assignment of zeroes and ones to the vertices ofG). LetS _{n n≥0} be a simple random walk onG, starting at some distinguished vertex v₀. Now let ξ and η be twoknown sceneries and assume that we observe one of the two sequences ξ(S _n) _n≥0 or {η(S _n)} _n≥0 but we do not know which of the two sequences is observed. Can we decide, with a zero probability of error, which of the two sequences is observed? We show that ifG = Z orG = Z², then the answer is “yes” for each fixed ξ and “almost all” η. We also give some examples of graphsG for which almost all pairs (ξ, η) are not distinguishable, and discuss some variants of this problem.     

Survival of the weak in hyperbolic spaces, a remark on competition and geometry

A simple competition model is presented. While in Euclidean spaces the weak will ``die out', in the presence of hyperbolicity, coexistence take place.

     

A theoretical study of CHx chemisorption on the Ni(100) and Ni(111) surfaces

Cluster model calculations have been performed for CH_x, x = 0−3, chemisorbed on Ni(100) and Ni(111). The predicted chemisorption energies, at the present level of theory, based on bond-prepared clusters for Ni(100) are for carbon 150 kcal/mol, for CH 136 kcal/mol, for CH₂ 91 kcal/mol and for CH₃ 46 kcal/mol. The corresponding energies for Ni(111) are for CH 120 kcal/mol, for CH₂ 88 cal/mol and for CH₃ 49 kcal/mol. These chemisorption energies lead to similar stabilities for all CH_x fragments on both Ni(100) and Ni(111). Large basis sets and multi-reference correlation treatments are found to be very important in particular for the multiply bonded species. The vibrational C-H stretching frequencies predicted for CH_x on Ni(111) are for CH 3054 cm⁻¹ (2980 cm⁻¹), for CH₂ 3204 cm⁻¹ and for CH₃ 2709 cm⁻¹ (2680 cm⁻¹), where the available experimental values are given in parent The predicted ionization spectra of adsorbed CH_x are also in general agreement with experimental findings.     

Inclusion complex formation in a particular geometry by a water-soluble paracyclophane in aqueous solution — NMR Studies —

NMR studies (¹H and ¹³C) demonstrating an inclusion complex formation in a particular geometry between a water-soluble paracyclophane, CP44, and hydrophobic substrates in acidic aqueous solution are described.     

Formulation design of an oral, fast-disintegrating dosage form containing taste-masked particles of famotidine

A fast-disintegrating dosage form has been developed as a user-friendly formulation that disintegrates in the mouth immediately. Patients can take it without water like a liquid formulation. In this study famotidine taste-masking technology was applied to the new fast-disintegrating tablet in an attempt to produce a novel, taste-masked, fast-disintegrating tablet. Partial granulation was found to be an effective and practical way to address content uniformity, however, oral disintegration time tended to become longer as content uniformity improved. The disintegration time was improved considerably by controlling ambient humidity during the compression process (>50% RH). Furthermore, since the new fast-disintegrating technology made it possible to use low compression force, there was no change in the structure or dissolution rate of the taste-masked particles after compression. Therefore, this system can produce a taste-masked fast-disintegrating tablet with satisfactory attributes.     

Bi-Lipschitz bijection between the Boolean cube and the Hamming ball

We construct a bi-Lipschitz bijection from the Boolean cube to the Hamming ball of equal volume. More precisely, we show that for all even n ∈ N there exists an explicit bijection ψ: {0, 1}ⁿ → {x ∈ {0, 1}ⁿ⁺¹ : |x| > n/2} such that for every x ≠ y ∈ {0, 1}ⁿ, \(\frac{1}{5} \leqslant \frac{{dis\tan ce\left( {\psi \left( x \right),\psi \left( y \right)} \right)}}{{dis\tan ce\left( {x,y} \right)}} \leqslant 4,\) where distance(·, ·) denotes the Hamming distance. In particular, this implies that the Hamming ball is bi-Lipschitz transitive.