Variable-Energy Photoelectron Spectroscopy of (eta(5)-C(5)H(5))NiNO: Molecular Orbital Assignment and Xalpha-SW Calculations

Variable-energy valence and inner-valence photoelectron spectra have been recorded for the CpNiNO complex (Cp = eta(5)-C(5)H(5)) between 21.2 and 100 eV, using He I radiation and synchrotron radiation. The ground state electronic structure has been calculated by using the Xalpha-SW method. Photoionization cross sections (sigma) have also been calculated for the valence ionizations using the Xalpha-SW method. The theoretical branching ratios (sigma(i)/ summation operatorsigma) have been compared with the observed branching ratios (A(i)()/ summation operatorA) between 21.2 and 100 eV. The assignment of the photoelectron spectrum based on the analysis of intensity variations and width of vibrational peaks is consistent with the ion state orbital ordering 5e(1)(1) < 7a(1)(2) < 3e(2)(3) < 4e(1)(4) (band numbers are in parentheses) and is inconsistent with another recently proposed ordering 5e(1)(1), 5e(1)(2) < 7a(1), 3e(2)(3) < 4e(1)(4), which takes the 5e(1) vibronic effects into consideration. The experimental branching ratio results indicate a Ni 3p resonance effect around 75 eV in the photoionization process. The inner-valence spectrum has also been assigned with the aid of the Xalpha-SW calculations.     

Self-intersections of curves on surfaces

Let M be a compact orientable surface with nonempty boundary (x(M)<0) and fundamental group . Let be a geodesic on M (with a fixed hyperbolic structure), and let W be a (cyclically reduced) word in a fixed set of generators of which represents . In this paper, we give an algorithm to count the number of self-intersections of in terms of W, generalizing a result of Birman and Series, where an algorithm was given to decide if was simple. Some applications of the algorithm to surfaces with one boundary and the Markoff spectrum are also given.     

Optimal linear estimators of the unknown mean of a random field observed on a cross

Explicit formulas of minimum-variance linear unbiased estimators of the unknown mean are derived for homogeneous random fields with correlation functions observed on the set (a cross).Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 116–121, 1988.