Muonium in bulk fused quartz: Test case for RAHD relaxation theory

Muonium (μ ⁺ e ⁻) in bulk fused quartz is a unique system in that theμ ⁺ spin polarization (in the muonium state) relaxes almost entirely via random anisotropic hyperfine distortions (RAHD). As such, this system provides an excellent test case for a new RAHD spin relaxation theory. This theory is quantitatively compared to static zero field data and the functional characteristics in both the high field and dynamic limits are considered as well.     

Reactions of cyclic oxalyl compounds, 43: Synthesis and thermolysis of fused 1‐arylaminopyrrolones

Fused N‐(di)arylamino‐pyrrol‐2,3‐diones 1 are reacted with diphenylketene, thiosemicarbazide or 1,2‐diaminobenzene to afford the 3‐diphenylmethylene pyrrolones 2 , the thiosemicarbazones 4 or the quinoxaline derivatives 5 as well as 6 , respectively. Thermolysis of 2b,c,e,f,6b and the pyrrolo‐quinoxaline 8 afford the corresponding N‐deaminated products 3, 7 and 9 . Rearrangements into diazapropellanes following a thermally initiated Fischer ‐ indolization as originally expected do not occur.     

Thermal stability of brominated poly(isobutylene‐co‐isoprene)

The thermal stability of brominated isobutylene–isoprene rubber (BIIR) was investigated through studies of the elastomer and a model compound that accurately represented the reactive functionality within the polymer. An analysis of commercial BIIR and reaction products of brominated 2,2,4,8,8‐pentamethyl‐4‐nonene (BPMN) by NMR demonstrated that bromination of isobutylene–isoprene rubber by 1,3‐dibromo‐5,5‐dimethylhydantoin yielded a kinetically favored exomethylene substitution product, 3‐bromo‐6,6‐dimethyl‐2‐(2,2‐dimethylpropyl)‐1‐heptene ( 2 ), as opposed to the more stable endo‐isomer, (E,Z)‐4‐(bromomethyl)‐2,2,8,8‐tetramethyl‐4‐nonene ( 3 ). The exposure of BIIR and the brominated model compound BPMN to vulcanization temperatures led to the isomerization of 2 to 3 at a rate strongly dependent on HBr concentration. The elimination of HBr from these allylic bromides to produce exo‐ and endo‐conjugated dienes proceeded concurrently with isomerization, and the kinetics of these processes could be rationalized on the basis of a polar reaction mechanism. The product distributions obtained from both the model system and BIIR were consistent, thereby justifying an extension of the model compound approach to an analysis of BIIR vulcanization chemistry. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2019–2026, 2001     

Lattices with large minimal extensions

This paper characterizes those finite lattices which are a maximal sublattice of an infinite lattice. There are 145 minimal lattices with this property, and a finite lattice has an infinite minimal extension if and only if it contains one of these 145 as a sublattice. Received October 5, 1998; accepted in final form May 19, 1999.     

Positive polynomials on compact sets

The aim of this note is to give short algebraic proofs of theorems of Handelman, Pólya and Schmüdgen concerning the algebraic structure of polynomials being positive on certain subsets of ℝ ⁿ . The main ingredient of the proofs is the representation theorem of Kadison–Dubois. The proof of the latter is elementary and algebraic but tricky. Received: 6 February 1999 / Revised version: 28 August 2000     

Bound states of D(2p)–D0 systems supersymmetric p-cycles

We discuss some issues related to D(2p)–D0-branes with background magnetic fluxes, respectively, in a T-dual picture, Dp–Dp-branes at angles. In particular, we describe the nature of the supersymmetric bound states appearing after tachyon condensation. We present a very elementary derivation of the conditions to be satisfied by such general supersymmetric gauge configurations, which are simply related by T-duality to the conditions for supersymmetric p-cycles in .     

A relation between structure and pair potential for liquid metals

We emphasize the importance of considering the relationship between the structure of a liquid and the interatomic potential directly from the point of view of wave vector space (k space). Although the Ornstein-Zernike equation was not originally derived from this point of view, this equation when transformed into the k-space representation has direct physical content, when coupled with a normal mode representation according to the approaches of Pines and Bohm (1952), and Percus and Yevick (1958). These normal modes are defined isothermally, and the relation to the dynamical modes of the liquid is discussed. The use of a simple k-space relationship between the transform of the Ornstein-Zernike direct correlation function and the transform, V_k , of the interatomic potential is explored. This leads to a correspondingly simple relationship between the structure factor and the interatomic potential. It is equivalent to a generalized Debye-Hückel equation and is expected to be valid only under special circumstances; namely, where the potential is long range in a particular sense and the small k behaviour of V_k is dependent mainly upon this long-range behaviour and relatively insensitive to details of the potential at short distances. It is noted that these conditions appear to be met reasonably well for the liquid alkali metals. The comparison of theory and experiment is somewhat uncertain because of incomplete experimental data on the structure factor as well as unresolved theoretical issues.     

The triplet spectrum of tetramethyl-1,3-cyclobutanedione

The low-temperature single-crystal spectrum of TMCBD has revealed a low-lying triplet state at 25 718 cm^-1 (72·5 kcal/mol). The observed band is ascribed to a ³ A_u (³ A ₂) ← ¹ A_g nπ* transition on the basis of its small singlet-triplet splitting, its polarization behaviour, and its vibrational structure. The ³ A_u state is first-order spin-orbit coupled to either or both of the ¹ B _2u or ¹ B _3u states. No evidence for two or more nπ* transitions was found. Several multi-membered progressions in the carbonyl wagging mode indicate the presence of a distorted excited state, in which the carbonyl carbons attain a pyramidal conformation. Analysis of the site symmetry shows that TMCBD is distorted to a boat-shaped C _2v structure in its triplet nπ* state.