In the title complex, [Ni(C(10)H(6)NO(2))(2)(CH(3)OH)(2)], the Ni(II) ion lies on an inversion center and is coordinated by two quinoline-2-carboxyl-ate ligands in the equatorial sites and two axial methanol ligands, forming a distorted octa-hedral environment. In the crystal, mol-ecules are linked via O-H⋯O hydrogen bonds into a two-dimensional network parallel to (10[Formula: see text]).

In this note, we give the exact distribution of a scaled condition number used by Demmel to model the probability that matrix inversion is difficult. Specifically, consider a random matrix A and the scaled condition number kd{A) = \\A\\f \\A~l\\. Demmel provided bounds for the condition number distribution when A has real or complex normally distributed elements. Here, we give the exact formula.

1. Introduction. The Lagrange inversion formula is one of the fundamental results of enumerative combinatorics. It expresses the coefficients of powers of the compositional inverse of a power series in terms of the coefficients of powers of the original power series. G. Labelle [10] extended Lagrange inversion to cycle index series, which are equivalent to symmetric functions. Although motivate...

In [3] we described a technique for solving certain linear operator equations by studying the operator power series de…ned by the system. Essential for obtaining explicit solutions is a Lagrange inversion formula for power series with coe¢ cients in an integral domain K. Such a formula can be found in “Recursive Matrices and Umbral Calculus”by Barnabei, Brini and Nicoletti [1]. J. F. Freeman’s ...

We derive a (/-analogue of the classical formula for the number of derangements of an n element set. Our derivation is entirely analogous to the classical derivation, but relies on a descent set preserving bijection between the set of permutations with a given derangement part and the set of shuffles of two permutations. A classical application of binomial inversion (more generally the principl...

This talk first introduces the m-arithmetic triangle — a generalization of Pascal’s triangle, and then presents an explicit formula for the numbers of the m-arithmetic triangle; we have found some asymptotic expansions for these numbers. With a new formula for inversion of analytic functions, which we introduced recently, we get inversion formulas, in which new special numbers An appear. We pre...

Carbonate reservoirs exhibit complex pore structure, which significantly affects the elastic properties and seismic response, as well prediction of physical parameters. As one main factors impacting fluid prediction, structure parameter directly involves in few inversion methods. In order to predict inversion, a novel quantitative reflection coefficient formula is proposed, that integrate Russe...

Inverting the exponential Radon transform has a potential use for SPECT (single photon emission computed tomography) imaging in cases where a uniform attenuation can be approximated, such as in brain and abdominal imaging. Tretiak and Metz derived in the frequency domain an explicit inversion formula for the exponential Radon transform in two dimensions for parallel-beam collimator geometry. Pr...

In the title complex, [Ni(C(4)H(3)N(2)O(2))(2)(H(2)O)(2)], the Ni(II) ion is located on an inversion center and shows a distorted octa-hedral geometry, defined by two N,O-bidentate 1H-imidazole-4-carboxyl-ate ligands in the equatorial plane and two water mol-ecules in the axial positions. Inter-molecular N-H⋯O hydrogen bonds link the complex mol-ecules into layers parallel to (10[Formula: see t...