Exact Estimates for Double Dirichlet Series with Nonnegative Coefficients

We consider the double Dirichlet series

Nowhere monotone functions and functions of nonmonotonic type

We investigate the relationships between the notions of a continuous function being monotone on no interval, monotone at no point, of monotonic type on no interval, and of monotonic type at no point. In particular, we characterize the set of all points at which a function that has one of the weaker properties fails to have one of the stronger properties. A theorem of Garg about level sets of continuous, nowhere monotone functions is strengthened by placing control on the location in the domain where the level sets are large. It is shown that every continuous function that is of monotonic type on no interval has large intersection with every function in some second category set in each of the spaces , and .

     

A new method for spectral decomposition using a bilinear Bayesian approach

A frequent problem in analysis is the need to find two matrices, closely related to the underlying measurement process, which when multiplied together reproduce the matrix of data points. Such problems arise throughout science, for example, in imaging where both the calibration of the sensor and the true scene may be unknown and in localized spectroscopy where multiple components may be present in varying amounts in any spectrum. Since both matrices are unknown, such a decomposition is a bilinear problem. We report here a solution to this problem for the case in which the decomposition results in matrices with elements drawn from positive additive distributions. We demonstrate the power of the methodology on chemical shift images (CSI). The new method, Bayesian spectral decomposition (BSD), reduces the CSI data to a small number of basis spectra together with their localized amplitudes. We apply this new algorithm to a 19F nonlocalized study of the catabolism of 5-fluorouracil in human liver, 31P CSI studies of a human head and calf muscle, and simulations which show its strengths and limitations. In all cases, the dataset, viewed as a matrix with rows containing the individual NMR spectra, results from the multiplication of a matrix of generally nonorthogonal basis spectra (the spectral matrix) by a matrix of the amplitudes of each basis spectrum in the the individual voxels (the amplitude matrix). The results show that BSD can simultaneously determine both the basis spectra and their distribution. In principle, BSD should solve this bilinear problem for any dataset which results from multiplication of matrices representing positive additive distributions if the data overdetermine the solutions.     

A molecular mechanics force field for the cobalt corrinoids

A force field for the cobalt (III) corrinoids (derivatives of vitamin B₁₂) for use with a modified version of the molecular mechanics program 2(87) has been developed empirically around 19 cobalt corrinoid crystal structures. Bond lengths, bond angles and torsional angles are reproduced with r.m.s. differences of 0.01 Å, 2.4 °, and 4.2 °, respectively, within the standard deviation of the mean of these parameters found in the solid state. The axial ligand occupying the lower coordination site in the cobalamins, 5,6-dimethylbenzimidazole, is shown to have very limited rotational freedom and is constrained by the downward-pointing b and d propionamide side chains of the corrin ring. Strain-energy profiles for rotation of the side chains of the corrin ring show the existence of several local energy minima and this explains the observed variability in the orientations of these side chains in the solid state. The known change in conformation which occurs in the C ring when the e side chain is epimerized from the lower to the upper face of the corrin ring in cyano-13-epicobalamin is correctly predicted, provided the starting conformation of the C ring is unbiased. A study of cyano-8-epicobalamin indicates that an analogous conformational change does not occur in the B ring and the epimerized d side chain assumes an equatorial orientation relative to the corrin ring. Parameters for the Co---C bond in alkylcobalamins were developed and the structure of methyl- and adenosylcobalamin are accurately reproduced. An examination of the strain energy consequences of rotation of the adenosyl ligand about the Co---C bond identifies a number of low-energy conformations at least two of which, in which adenosyl lies over the “southern” and “eastern” portions of the corrin ring, respectively, have been previously deduced from NMR observations. Coordinated neopentyl in neopentylcobalamin is much more hindered to rotation about the Co---C bond and the lowest conformation finds two γ(C) atoms straddling the upwardly projecting C46 methyl group of the corrin.     

Hydrogen and carbon NMR data for aminoquinolines and aminoisoquinolines

Hydrogen and carbon chemical shifts and H? H and C? H couplings are reported for six aminoquinolines and six aminoisoquinolines in DMSO-d₆.     

An Initial-Value Problem for Fully Three-Dimensional Inflectional Boundary Layer flows

In a recent paper the present authors considered the effects of small cross-flow upon the nonlinear evolution of two oblique waves of unequal amplitude. The present analysis extends this work in two ways: (i) the cross-flow is increased to O(1) making it of comparable magnitude to the streamwise component and (ii) by taking the long-wavelength limit of Rayleigh's equation a whole spectrum of wave numbers can now be catered for. Thus (ii) allows a fairly general initial disturbance to be accommodated. Another significant effect due to the presence of a whole spectrum of wave numbers is that the critical layer jump is now forced by a quadratic, as opposed to the usual cubic, nonlinearity. Numerical solutions of the new nonlinear amplitude evolution equation are presented for a special class of initial disturbance. Received 7 January 1998 and accepted 15 September 1998     

A method to enhance porosity of micro-particles

The nuclear track technique (NTT) is used to enhance the porosity of silica micro-particles. The enhanced porosity is a result of the formation of surface and interior pores or tracks in the silica by the action of external and internal fission fragments. The fission tracks produced at the surface and within the interior of the micro-particles are a result of coating the particles with trace quantitities of uranium, instead of having trace quantities of uranium incorporated within the silica matrix.