The Ramifications of the Centres: Quantised Function Algebras at Roots of Unity

This paper continues the study of quantised function algebrasO[G] of a semisimple group G at an lth root of unity . Thesealgebras were introduced by De Concini and Lyubashenko in 1994,and studied further by De Concini and Procesi and by Gordon,amongst others. Our main purpose here is to increase understandingof the finite-dimensional factor algebras O[G](g), for g G.We determine the representation type and block structure ofthese factors, and (for many g) describe them up to isomorphism.A series of parallel results is obtained for the quantised Borelalgebras and . 2000 Mathematical Subject Classification: 16W35,17B37.     

Structure of adamantan-1-ammonium 1-adamantanecarboxylate

Adamantan-1-ammonium 1-adamantanecarboxylate, C₂₁H₃₃NO₂ (I) is a novel dispiro-type compound. Aminoadamantane derivatives, in which the spiro carbon atoms are part of heterocyclic rings, are of potential interest as biological active substances and antiviral agents. Complex (I) crystallizes in the centrosymmetric space group C2/c (No. 15) with eight molecules in the unit cell with a = 25.227(4), b = 6.527(1), c = 22.489(4) Å, and = 90.75(1)°. The two spiro units are a 1-adamantylammonium cation and a 1-adamantane carbonyloxy anion. The complex units are stabilized by a network of intermolecular carbonyloxy-to-amine hydrogen bonding and van der Waals cohesive forces. Germane bond lengths are: C—N = 1.479(9) and C—O (mean) = 1.25(2) Å.     

Thermodynamic calculations in relativistic finite-temperature quantum field theories

A Minkowski space formalism of finite-temperature quantum field theory is used to compute static thermodynamic quantities in the one- and two-loop approximation in an elegant and straightforward way using a generalization of Weinberg's tadpole method of calculating effective potentials. Systematic diagrammatic techniques for low- and high-temperature expansions are developed. Renormalizability by zero-temperature symmetric counterterms is proven for all orders in the loop expansion and demonstrated explicitly to two loops. Many useful computational techniques applicable to general finite temperature calculations are explained.     

Onp-absolutely summing constants of banach spaces

Given 1≦p<∞ and a real Banach spaceX, we define thep-absolutely summing constantμ _p(X) as inf{Σ _i ^=1/m |x*(x _i)|^p p Σ _i ^=1/m ‖x _i‖^p p]¹ p}, where the supremum ranges over {x*∈X*; ‖x*‖≤1} and the infimum is taken over all sets {x ₁,x ₂, …,x _m} ⊂X such that Σ _i ^=1/m ‖x _i‖>0. It follows immediately from [2] thatμ _p(X)>0 if and only ifX is finite dimensional. In this paper we find the exact values ofμ _p(X) for various spaces, and obtain some asymptotic estimates ofμ _p(X) for general finite dimensional Banach spaces. This is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Prof. A. Dvoretzky and Prof. J. Lindenstrauss.     

Magnetic moments of composite fermions

There have been a considerable number of papers proposing composite models for leptons and quarks. Recently, Glück and Lipkin have stated that reproducing the observed magnetic moments of these fermions presents a serious difficulty for these composite models. We show for a renormalizable theory that, in contrast to Glück's and Lipkin's nonrelativistic arguments, a deeply bound system (with heavy constituent particle masses m_c) of (total) spin $\text{1}\text{2}$, charge e and mass m has the magnetic moment $\text{(e/2m) [1 +}\text{“usual” (QED + QCD + weak) corrections +O}\text{(m/m}{}_{\mathrm{<mtext>c</mtext>}}\text{)}\text{“new” bindng corrections]}$. Although there remains the considerable dynamical problem of obtaining “light” bound fermions from heavy constituents, there is no separate, additional magnetic moment difficulty.     

The effect of non-orthogonality in the study of adsorption: Hydrogen on graphite

The effect of non-orthogonality between the localized orbitals of an adsorbed atom (or impurity atom) and those of the surrounding atoms of the substrate solid has been studied. The overlap matrix S takes in this case a simple form which enables us to calculate local densities of states and other local effects such as charges on the atoms by the continued fraction expansion. The method has been applied to a simplified model for the adsorption of hydrogen on graphite, and the results show an improvement with respect to calculations where the overlap is neglected.     

The infrared spectra of 2-aminomethylpyridine complexes of metal(II) ions

The infrared spectra (700–150 cm^?1) of twenty-six complexes of 2-aminomethylpyridine (amp) with first transition series metal(II) ions are discussed. The complexes include the tris(amp) complexes [M(amp)₃]²⁺ the bis(amp) compounds M(amp)₂X₂ and the mono(amp) complexes M(amp)X₂. Assignments of the NH₂ rocking modes, v(M-NH₂), v(M-py) and ligand modes are based on the effects of isotopic labelling of the amino group and the effects of substitution of the metal ion and halide. The structural implications of the spectra are discussed.     

Enumeration of coloured plane trees with a given type partition

Tutte's result for the number of planted plane trees with a given degree partition is rederived by a variety of methods and in particular by a simple piecewise construction technique. A theorem of Gordon and Temple is applied in order to give a general relationship between the number of planted plane trees and the number of rooted plane trees and the degree partition restriction is generalised to type partition. The piecewise construction method is successfully used to derive the number of planted plane trees with a given 2-colour degree partition, also derived by Tutte, and an algorithm for the k-coloured case is developed. This algorithm may be used to obtain more specific results. These models are relevant to the statistical mechanics of polymers and this is discussed briefly.