The cyclo-tetra-phosphate anion, [P(4)O(12)](4-), forms the title complex with cobalt(II) and quinolinium, {(C(9)H(8)N)(2)[Co(P(4)O(12))(H(2)O)(2)]·6H(2)O}(n). In the complex anion, the Co(II) ion, lying on an inversion center, is surrounded by four phosphate O atoms and two water mol-ecules in a slightly distorted octa-hedral geometry. The crystal structure consists of anionic ribbons of formu...

Parseval's formula and inversion formula for the S-transform are given. A relation between the S-transform and pseudodifferential operators is obtained. The S-transform is studied on the spaces S(ℝn) and S'(ℝn).

We give a new combinatorial interpretation of the noncommutative Lagrange inversion formula, more precisely, of the formula of Brouder-FrabettiKrattenthaler for the antipode of the noncommutative Faà di Bruno algebra.

In this note, we consider the minimum number of NOT operators in a Boolean formula representing a Boolean function. In circuit complexity theory, the minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f . In 1958, Markov determined the inversion complexity of every Boolean function and particularly proved that ⌈log 2 (n + 1)⌉ NO...

In two dimensions, the exponential X-ray transform has been wellstudied due to its applications of correcting attenuation effects in Single Photon Emission Computed Tomography (SPECT). Explicit inversion formulas have been known for over 15 years. The threedimensional (3D) case has not been as thoroughly examined, and inversion formulas are available for only a few of the wide range of possible...

In many numerical examples it has been demonstrated that the saddlepoint approximation for the cumulative distribution function of a general nor-malised statistic behaves better in comparison with the third order Edge-worth expansion. The eeect is especially pronounced in the tails. Here we are dealing with the inverse problem of quantile evaluation. The inversion 1 of the Lugannani-Rice approx...