A mass spectrometric study of the pyrolysis of gibberellic acid

The behaviour of gibberellic acid (GA₃) under electron impact and chemical ionization conditions has been examined. The tendency of GA₃ to undergo pyrolysis by the loss of the elements of water and carbon dioxide has been identified. Two methods of sample introduction can be used to minimize the occurrence of this pyrolysis. Accurate mass measurement allows the composition of the pyrolysis product to be determined and metastable techniques confirm the structure of this product to be epi-allogibberic acid rather than its isomer allogibberic acid. This result corrects a misconception in the literature and illustrates the advantage of metastable methods compared with accurate mass measurements, for the determination of small structural differences within a molecule.     

Constrained near-minimax approximation by weighted expansion and interpolation using Chebyshev polynomials of the second,third, and fourth kinds

Well known results on near-minimax approximation using Chebyshev polynomials of the first kind are here extended to Chebyshev polynomials of the second, third, and fourth kinds. Specifically, polynomial approximations of degreen weighted by (1–x ²)^1/2, (1+x)^1/2 or (1–x)^1/2 are obtained as partial sums of weighted expansions in Chebyshev polynomials of the second, third, or fourth kinds, respectively, to a functionf continuous on [–1, 1] and constrained to vanish, respectively, at ±1, –1 or +1. In each case a formula for the norm of the resulting projection is determined and shown to be asymptotic to 4^–2logn +A +o(1), and this provides in each case and explicit bound on the relative closeness of a minimax approximation. The constantA that occurs for the second kind polynomial is markedly smaller, by about 0.27, than that for the third and fourth kind, while the latterA is identical to that for the first kind, where the projection norm is the classical Lebesgue constant _n . The results on the third and fourth kind polynomials are shown to relate very closely to previous work of P.V. Galkin and of L. Brutman.Analogous approximations are also obtained by interpolation at zeros of second, third, or fourth kind polynomials of degreen+1, and the norms of resulting projections are obtained explicitly. These are all observed to be asymptotic to 2^–1logn +B +o(1), and so near-minimax approximations are again obtained. The norms for first, third, and fourth kind projections appear to be converging to each other. However, for the second kind projection, we prove that the constantB is smaller by a quantity asymptotic to 2^–1log2, based on a conjecture about the point of attainment of the supremum defining the projection norm, and we demonstrate that the projection itself is remarkably close to a minimal (weighted) interpolation projection.All four kinds of Chebyshev polynomials possess a weighted minimax property, and, in consequence, all the eight approximations discussed here coincide with minimax approximations when the functionf is a suitably weighted polynomial of degreen+1.     

Nonabelian orbifolds and the boson-fermion correspondence

For a positive integerl divisible by 8 there is a (bosonic) holomorphic vertex operator algebra (VOA) associated to the spin lattice _l . For a broad class of finite groupsG of automorphisms of we prove the existence and uniqueness of irreducibleg-twisted -modules and establish the modular-invariance of the partition functionsZ(g, h, ) for commuting elements inG. In particular, for any finite group there are infinitely many holomorphic VOAs admittingG for which these properties hold. The proof is facilitated by a boson-fermion correspondence which gives a VOA isomorphism between and a certain fermionic construction, and which extends work of Frenkel and others.Supported by NSA grant MDA904-92-H-3099.Supported by NSF grant DMS-9122030.     

The Landau-Lifshitz equation,elliptic curves and the ward transform

The Landau-Lifshitz (LL) equation is studied from a point of view that is close to that of Segal and Wilson's work on KdV. The LL hierarchy is defined and shown to exist using a dressing transformation that involves parameters ₁, ₂, ₃ that live on an elliptic curve . The crucial role of the groupK ₂ × ₂ of translations by the half-periods of and its non-trivial central extension is brought out and an analogue of Birkhoff factorisation for -equivariant loops in is given. This factorisation theorem is given two treatments, one in terms of the geometry of an infinite-dimensional Grassmannian, and the other in terms of the algebraic geometry of bundles over . Further, a Ward-like transform between a class of holomorphic vector bundles on the total spaceZ of a line-bundle over and solutions of LL is constructed. An appendix is devoted to a careful definition of the Grassmannian of the Frechet spaceC (S ¹).     

Time variations in environmental pollution

Two programmes of work are described involving the measurement of environmental pollution over periods from two hours to many years. The long period measurements are deduced from neutron activation analysis of whole wood samples taken from individual tree rings for trees grown in various locations, and some results for cadmium, antimony and germanium levels are reported. In a second series of experiments the concentration of airborne particulate matter is being measured using a moving filter (streak sampler) technique to give a continuous record with two hour resolution. The filter samples are being analysed by proton induced X-ray emission (PIXE) and preliminary data is presented.     

The temperature dependence of the d-electron dipole strengths of cobalt(II) tetrahalides

The dipole strengths of the ⁴A₂ → ⁴T₁(F), ⁴T₁(P), d-electron transitions of the cobalt(II) tetrahalides are found to decrease with an increase in temperature, in agreement with a dynamic ligand-polarisation model for the absorption mechanism. The reduction in dipole strength is accounted for by a decrease in the coulombic coupling between the quadrupole moment of the d-electron transition of the metal ion and the transient electric dipole moment induced in the ligands, due to the anharmonic increase in the mean bond length and the progressively larger mean-square amplitudes of the bending modes of the complex ion in its ground electronic state as the temperature is raised.     

Electronic absorption and MCD spectra for Pt(AuPPh3)8(2+) and Au(AuPPh3)8(3+) cluster complexes in poly(methyl methacrylate) thin films at 295 and 10 K

Electronic absorption and 8 T magnetic circular dichroism (MCD) spectra are reported for nitrate salts of Pt(AuPPh3)8(2+) and Au(AuPPh3)8(3+) in poly(methyl methacrylate) (PMM) thin films at 295 and 10 K in the vis-UV region from 1.6 to 3.6 microm(-1) (1 microm(-1) = 10(4) cm(-1). Enhanced resolution is observed at low temperature, especially for Pt(AuPPh3)8(2+), which emphasizes the differences in the nature of the low-energy excited configurations and states between Pt(AuPPh3)8(2+) and Au(AuPPh3)8(3+). The absorption and MCD spectra for Pt(AuPPh3)8(2+) are interpreted in terms of a combination of excitations from filled Pt 5d orbitals to empty Au framework 6s orbitals and intraframework Au8(2+) (IF) transitions, whereas the spectra for Au(AuPPh3)8(3+) are ascribed entirely to Au IF transitions.     

Cooperative hydrogen-bonding effects in a water square: a single-crystal neutron and partial atomic charges and hardness analysis study

Four isomorphous complexes of formula [M(L)(4)(H(2)O)(2)]SO(4).2H(2)O (M = Co, 1a; Ni, 1b; Cu, 1c; Zn, 1d) have been isolated and characterized by single-crystal X-ray diffraction and neutron diffraction using the quasi-Laue diffractometer VIVALDI at the Institut Laue-Langevin as well as by thermogravimetric analysis. The structures contain a discrete, strongly hydrogen-bonded water tetramer which causes a significant distortion of the metal coordination sphere in each case. Partial atomic charges and hardness analysis (PACHA) calculations reveal that the shortest hydrogen bonds are not the strongest in this constrained, cyclic solid-state structure and show that the distortion at the metal center is caused by the drive to maintain the integrity of the water tetramer. The system undergoes a disorder-order transition on slow cooling that provides insight into the nature of communication between water squares.