Vibrational and high pressure conformational studies of 1,1,2-trichloroethane

The infrared spectra of 1,1,2-trichloroethane were recorded from 4000 to 50 cm^?1 in the vapour and liquid states. Additional spectra above 200 cm^?1 of the low temperature crystal and of two crystalline solids, prepared by compressing the sample in a diamond anvil cell, were obtained. Also, infrared spectra of the liquid and of the compound dissolved in CS₂ were recorded at increased pressures. Raman spectral data of the liquid (including polarization measurements) and of the low temperature crystal were obtained.The fundamental frequencies for each of the two conformers, C₁ and C_s, were assigned and the results checked by normal coordinate analysis. The same diagonal and off-diagonal force constants were employed for the two conformers and the force fields were derived by means of a least squares refinement, including data for chloroethane, 1,1-dichloroethane and various deuterated species. A standard deviation of 3 % was obtained in the final fit.From the changes in relative intensities for infrared bands belonging to the C₁ and C_s conformers with increasing pressure, the volume differences (ΔV¯between the conformers were determined in CS₂ solution and in the pure liquid.     

Local structure of graphs with λ=μ=2,a 2=4

Several properties of graphs with ==2,a ₂=4 are studied. It is proved that such graphs are locally unions of triangles, hexagons or heptagons. As a consequence, a distance regular graph with intersection array (13,10,7;1,2,7) does not exist.     

Spencer cohomologies and symmetry groups

We propose the construction of a spectral sequence converging to Spencer cohomologies. By using symmetry groups of differential equations systems, we manage to unify computations by reduction to the invariant systems over a homogeneous space. The conditions of coincidence of Spencer cohomologies with the cohomologies of an invariant Spencer complex we obtain from the arithmetic of a -characteristic manifold with respect to fundamental weights of the homogeneous space.     

Growth functions for semi-regular tilings of the hyperbolic plane

This paper studies the growth function, with respect to the generating set of edge identifications, of a surface group with fundamental domainD in the hyperbolic plane ann-gon whose angles alternate between /p and /q. The possibilities ofn,p andq for which a torsion-free surface group can have such a fundamental polygon are classified, and the growth functions are computed. Conditions are given for which the denominator of the growth function is a product of cyclotomic polynomials and a Salem polynomial.This work was supported in part by NSF Research Grants.     

The invertibility of the product of unbounded Toeplitz operators

In this note I give necessary and sufficient conditions on outer functionsf andg for the operator to be bounded and invertible on H². I also discuss the relationship of this question to two open questions in operator theory and weighted norm inequalities.     

On nonnegative solvability of linear operator equations

LetE be a Banach lattice having order continuous norm. Suppose, moreover,T is a nonnegative reducible operator having a compact iterate and which mapsE into itself. The purpose of this work is to extend the previous results of the authors, concerning nonnegative solvability of (kernel) operator equations on generalL ^p-spaces. In particular, we provide necessary and sufficient conditions for the operator equation x=T x+y to possess a nonnegative solutionxE wherey is a given nonnegative and nontrivial element ofE and is any given positive parameter.     

Incomplete idempotent Schröder quasigroups and related packing designs

Summary In this paper it is proved that, for any positive integern 2, 3 (mod 4),n 7, there exists an incomplete idempotent Schröder quasigroup with one hole of size two IISQ(n, 2) except forn = 10. It is also proved that for any positive integern 0, 1 (mod 4), there exists an idempotent Schröder quasigroup ISQ(n) except forn = 5 and 9. These results completely determine the spectrum of ISQ(n) and provide an application to the packing of a class of edge-coloured block designs.Research supported by NSERC grant A-5320.Research supported by NSFC grant 19231060-2.     

Brownian confinement and pinning in a Poissonian potential. II

Summary We continue our study ofd-dimensional Brownian motion in a soft repulsive Poissonian potential over a long time interval [0,t]. We prove here a pinning effect: for typical configuratons, with probability tending to 1 ast tends to , the particle gets trapped close to locations of near minima of certain variational problems. These locations lie at distances growing almost linearly witht from the origin, and the particle gets pinned within distance smaller than any positive power oft of one such location. In dimension 1, we can push further our estimates and show that in a suitable sense, the particle gets trapped with high probability, within time t and within distance (logt)²⁺ from a suitable location at distance of ordert/(logt)³ from the origin.This article was processed by the author using the LATEX style filepljour1m from Springer-Verlag     

Processes of flats induced by higher dimensional processes III

Stationary processes of k-flats in ^d can be thought of as point processes on the Grassmannian _k ^d of k-dimensional subspaces of ^d . If such a process is sampled by a (d–k+ j)-dimensional space F, it induces a process of j-flats in F. In this work we will investigate the possibility of determining the original k-process from knowledge of the intensity measures of the induced j-processes. We will see that this is impossible precisely when 1<k<d–1 and j=0,...,2[r/2]–1, where r is the rank of the manifold _k ^d . We will show how the problem is equivalent to the study of the kernel of various integral transforms, these will then be investigated using harmonic analysis on Grassmannian manifolds.The research of the first and third authors was supported in part by NSF grants DMS-9207019 and DMS-9304284. The research of the second author was supported in part by NFR contract number R-RA 4873-306 and the Swedish Academy of Sciences.     

A note on “small representations of finite distributive lattices as congruence lattices”

G. Grätzer, H. Lakser, and E. T. Schmidt proved that every distributive lattice with n join-irreducible elements can be represented as the congruence lattice of a small lattice L, that is, a lattice L with O(n ² ) elements. G. Grätzer, I. Rival, and N. Zaguia proved that, for any <2, O(n ² ) can not be improved to O(n ). In this note we show that the theorem about small representation can be improved further to get a more delicate result.