A luminescence probe for measurements of electron-exchange rates in polymer films on electrodes

The effect of metal ions on the, reduction of 1,10-phenanthroline-5,6-quinone (1), 5,8-quinolinequinone (II) and 6,7-dichloro-5, 8-quinolinequinone (III) has been investigated in 50% dimethylsulfoxide+water solvent. 1 contains the 1,10-phenanthroline structure in both its quinone and hydroquinone forms, while II and III contain the 8-hydroxyquinoline structure in the hydroquinone forms. Complexation of the hydroquinones of II and III by metal ions causes positive shifts in the quinone half-wave potentials. These shifts have been used to calculate conditional formation constants for Pb²⁺(II) and Pb²⁺ and Zn²⁺(III). The quinone form of I binds strongly to Ni²⁺, Co²⁺ and Zn²⁺ but not to Ca²⁺. Mg²⁺. Mg₂₊. Mn²⁺ and Pb²⁺. With the latter four metals, binding to the hydroquinone from of I was detected and formation constants were determined. In addition to binding both the quinone and hydroquinone forms at the nitrogen atoms, Ni₂₊ Co²⁺ and Zn²⁺ formed complexes at the 1,2-dihydroxy site of the hydroquinone of I.     

The analysis of the near IR of some organic and organometallic compounds by photoacoustic spectroscopy

The photoacoustic spectrum (PAS) was measured in the near IR region (1000 to 2600 nm) for organic compounds (C₆H₆, C₆D₆, C₇H₈, and C₆H₁₂) and organometallic compounds (Cp₂Fe, Cp₂Fe₂(CO)₄, Cp₄Fe₄(CO)₄, Cp₄Fe₄S₄, C₆H₆Cr(CO)₃, CpCo(C₄Ph₄) and CpCo(CO)₂). Band assignments were made by comparison to the infrared spectra. The bands were assigned as the CH overtone stretch and combinations of CH and other IR fundamentals. These bands provide fingerprint spectra for these compounds.     

Investigation of the use of B3LYP zero-point energies and geometries in the calculation of enthalpies of formation

The use of B3LYP/6–31G^* zero-point energies and geometries in the calculation of enthalpies of formation has been investigated for the enlarged G2 test set of 148 molecules [J. Chem. Phys. 106 (1997) 1063]. A scale factor of 0.96 for the B3LYP zero-point energies gives an average absolute deviation nearly the same as scaled HF/6–31G^* zero-point energies for G2, G2(MP2), and B3LYP/6–311 + G(3df,2p) enthalpies. A scale factor of 0.98, which has been recommended in some studies, increases the average absolute deviation by about 0.2 kcal/mol. Geometries from B3LYP/6–31G^* are found to do as well as MP2/6–31G^* geometries in the calculation of the enthalpies of formation.     

An extension of the Dirac theory of constraints

Constructions introduced by Dirac for singular Lagrangians are extended and reinterpreted to cover cases when kernel distributions are either nonintegrable or of nonconstant rank, and constraint sets need not be closed.     

Total Variation Distance for Poisson Subset Numbers

Let n be an integer and A₀,..., A_k random subsets of {1,..., n} of fixed sizes a₀,..., a_k, respectively chosen independently and uniformly. We provide an explicit and easily computable total variation bound between the distance from the random variable , the size of the intersection of the random sets, to a Poisson random variable Z with intensity λ = EW. In particular, the bound tends to zero when λ converges and for all j = 0,..., k, showing that W has an asymptotic Poisson distribution in this regime. Received February 24, 2005     

Fourier series of half-range functions by smooth extension

This paper considers Fourier series approximations of one- and two-dimensional functions over the half-range, that is, over the sub-interval [0, L] of the interval [−L, L] in one-dimensional problems and over the sub-domain [0, L_x] × [0, L_y] of the domain [−L_x, L_x] × [−L_y, L_y] in two-dimensional problems. It is shown how to represent these functions using a Fourier series that employs a smooth extension. The purpose of the smooth extension is to improve the convergence characteristics otherwise obtained using the even and odd extensions. Significantly improved convergence characteristics are illustrated in one-dimensional and two-dimensional problems.     

Distributional Transformations,Orthogonal Polynomials,and Stein Characterizations

A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test functions higher order derivatives. The class includes the size and zero bias transformations, and when specializing to weighting by polynomial functions, relates distributional families closed under independent addition, and in particular the infinitely divisible distributions, to the family of transformations induced by their associated orthogonal polynomial systems. For these families, generalizing a well known property of size biasing, sums of independent variables are transformed by replacing summands chosen according to a multivariate distribution on its index set by independent variables whose distributions are transformed by members of that same family. A variety of the transformations associated with the classical orthogonal polynomial systems have as fixed points the original distribution, or a member of the same family with different parameter.     

Trivariate Cr Polynomial Macroelements

Trivariate C^r macroelements defined in terms of polynomials of degree 8r + 1 on tetrahedra are analyzed. For r = 1,2, these spaces reduce to well-known macroelement spaces used in data fitting and in the finite-element method. We determine the dimension of these spaces, and describe stable local minimal determining sets and nodal minimal determining sets. We also show that the spaces approximate smooth functions to optimal order.     

Super spline spaces of smoothnessr and degreed≥3r+2

The problem of computing the dimension of spaces of splines whose elements are piecewise polynomials of degreed withr continuous derivatives globally has attracted a great deal of attention recently. We contribute to this theory by obtaining dimension formulae for certain spaces of super splines, including the case where varying amounts of additional smoothness is enforced at each vertex. We also explicitly construct minimally supported bases for the spaces. The main tool is the Bernstein-Bézier method.Communicated by Klaus Höllig.