Entropy function spaces and interpolation

We associate to every function space, and to every entropy function E, a scale of spaces Λp,q(E) similar to the classical Lorentz spaces Lp,q. Necessary and sufficient conditions for they to be normed spaces are proved, their role in real interpolation theory is analyzed, and a number of applications to functional and interpolation properties of several variants of Lorentz spaces and entropy spaces are given.     

Studying links via closed braids IV: composite links and split links

Summary The main result concerns changing an arbitrary closed braid representative of a split or composite link to one which is obviously recognizable as being split or composite. Exchange moves are introduced; they change the conjugacy class of a closed braid without changing its link type or its braid index. A closed braid representative of a composite (respectively split) link is composite (split) if there is a 2-sphere which realizes the connected sum decomposition (splitting) and meets the braid axis in 2 points. It is proved that exchange moves are the only obstruction to representing composite or split links by composite or split closed braids. A special version of these theorems holds for 3 and 4 braids, answering a question of H. Morton. As an immediate Corollary, it follows that braid index is additive (resp. additive minus 1) under disjoint union (resp. connected sum).Oblatum 29-XI-1988 & 25-I-1990Partially supported by NSF Grant #DMS-88-05672     

Poly(epichlorohydrin) modified with 3,4,5‐tris(dodecyloxy)benzoate: The structure and dynamics of the aliphatic side chains in the columnar mesophase

We investigated the dynamics and structure of the aliphatic side chains of a randomly grafted copolymer, obtained through the chemical modification of poly(epichlorohydrin) with potassium 3,4,5‐tris(dodecyloxy)benzoate, with solid‐state ¹³C NMR. Below 283 K, the aliphatic chains partially crystallized in an all‐anti conformation. The calorimetric data were compatible with an orthorhombic packing. Below 323 K, the polymer exhibited a columnar mesophase. Spin–lattice relaxation times were determined in this temperature range and at 333 K, that is, in the isotropic phase. In the liquid‐crystalline state, some carbons exhibited a double decay in the spin–lattice relaxation, and this was attributed to presence of the liquid‐crystalline phase. This hypothesis was supported by a conformational analysis performed by molecular modeling. The activation energies of the relaxation processes in the mesophase were also estimated. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2099–2111, 2005     

Mixed fluoroamine complexes of chromium(III)

Summary Mixed difluoro(diamine)(diamme)chromium(III) complexes have been synthesized with ethylenediamine (en), 1,3 propanediamine(tn) and 1,2-cyclohexanediamine(chxn):trans-[CrF₂(aa)(bb)]Br (aa=en, bb=tn; aa=tn, bb= chxn) andcis-[CrF₂(aa)(bb)]Br (aa=en, bb=chxn). The corresponding fluoroaqua(diamine) (diamine)chromium(III) complexes have been prepared by acid hydrolysis as perchlorate or iodide salts. All have been characterized by chemical analysis, electronic and i.r. spectra and conductivity measurements.     

Testing Departures from Gamma, Rayleigh and Truncated Normal Distributions

This paper provides necessary and sufficient conditions for a solution to likelihood equations for an exponential family of distributions, which includes Gamma, Rayleigh and singly truncated normal distributions. Furthermore, the maximum likelihood estimator is obtained as a limit case when the equations have no solution. These results provide a way to test departures from Rayleigh and singly truncated normal distributions using the likelihood ratio test. A new easy way to test departures from a Gamma distribution is also introduced.