M1-E2 interference in the Zeeman effect of the 461.5 nm line of Bi I

Studies of the interference effect in the mixed-type forbidden line 461.5 nm are reported. A special computer program considering the M1-E2 interference was designed to obtain the predicted contour of the Zeeman structure of the line. By variation of free parameters, describing the line shape and the electric-quadrupole admixture, the calculated profiles were fitted into the recorded spectra. The E2 admixture found is (7.4± 0.4)%. Our result is compared with recent theories and other experiments.     

Overlap number of graphs

An overlap representation of a graph G assigns sets to vertices so that vertices are adjacent if and only if their assigned sets intersect with neither containing the other. The overlap number φ(G) (introduced by Rosgen) is the minimum size of the union of the sets in such a representation. We prove the following: (1) An optimal overlap representation of a tree can be produced in linear time, and its size is the number of vertices in the largest subtree in which the neighbor of any leaf has degree 2. (2) If δ(G)?2 and G≠K₃, then φ(G)?|E(G)| ? 1, with equality when G is connected and triangle‐free and has no star‐cutset. (3) If G is an n‐vertex plane graph with n?5, then φ(G)?2n ? 5, with equality when every face has length 4 and there is no star‐cutset. (4) If G is an n‐vertex graph with n?14, then φ(G)?n²/4 ? n/2 ? 1, with equality for even n when G arises from K_{n/2, n/2} by deleting a perfect matching. © 2011 Wiley Periodicals, Inc. J Graph Theory     

Detection of determinism and randomness in time series: A method based on phase space overlap of attractors

The space overlap of an attractor reconstructed from a time series with a similarly reconstructed attractor from a random series is shown to be a sensitive measure of determinism. Results for the time series for Henon, Lorenz and Rössler systems as well as a linear stochastic signal and an experimental ECG signal are reported. The overlap increases with increasing levels of added noise, as shown in the case of Henon attractor. Further, the overlap is shown to decrease as noise is reduced in the case of the ECG signal when subjected to singular value decomposition. The scaling behaviour of the overlap with bin size affords a reliable estimate of the fractal dimension of the attractor even with limited data.     

Multisite bond and overlap treatment of polymer‐chain band structure

The usual tight‐binding (TB) approximation, employed in electronic structure calculations, is extended to include the more‐distant neighbor sites than the first. In doing so, a simple power law is adopted to describe the bond and overlap contributions, which enables the energy dispersion relation to be obtained in a closed analytic form. The resulting energy band structure has markedly different features from its TB counterpart to which it reduces in the appropriate limits. In particular, local extrema always occur at the TB stationary values, although these may not both be band edges. Another intermediate critical point may arise, which is one of the band edges, the other being located at one of the TB extrema. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 341–346, 2003     

Bechtold-Jacobs generalized model for shift scheduling with extraordinary overlap

In constructing working shifts, the classical Dantzig (Operation Research 2:339–341, 1954) set covering model uses a great number of variables which makes computation very complicated for some cases that incorporate a high degree of break-placement flexibility. Bechtold and Jacobs (Management Science 36:1339–1351, 1990) proposed an implicit model under the assumption that there is no extraordinary overlap, which considerably reduced the number of variables. In this paper we give a generalization that is valid without this hypothesis by adding a minimal set of constraints. Also, in some cases where there is extraordinary overlap we reduce our constraint set to a subset with the same number or less than that of Bechtold and Jacobs. I. Addou’s current address is Département de Mathématiques et Statistique, Université de Montréal, Succ. Centre-ville, Montréal, Québec, Canada, H3C2J7; e-mail: addou@dms.umontreal.ca.     

Extended basis NDDO calculations on diatomic molecules

The ab initio NDDO method as described by Roby has been investigated for a range of diatomic species, using symmetric orthonormalization and various basis set sizes. No limiting behaviour is observed with basis set extension.     

Interionic forces in AgF,AgCl and AgBr crystals

An interionic force model has been used in which the short range nearest neighbour and the next nearest neighbour repulsive interactions and the van der Waals’ interactions are balanced by the long range electrostatic forces. The nearest neighbour and the next nearest neighbour interactions are derived from the overlap integrals for outer shell electrons. The van der Waals’ interactions are estimated from the Slater-Kirkwood variational method. The cohesive energy, the bulk modulus and its pressure dependence for AgF, AgCl and AgBr crystals have been calculated and compared with experimental data.     

S2O‾自由基光电子能谱的Franck-Condon分析

本文考虑多振动模混合和热带效应,凭借谐振子模型,推得计算两维-四振动模Franck-Condon重叠积分的解析表示,且应用于S2O‾ 自由基光电子能谱的理论研究。对于S2O( 1A′) – S2O‾( 2A″) 光脱附过程,结合分子轨道从头算和密度泛函理论,计算Franck-Condon因子,从而得到电子跃迁振动谱线的相对强度,理论上得到的光电子能谱与实验上观测到的能谱达到较好的一致;进一步在光谱模拟过程中,拟合实验能谱得到可靠的负离子自由基S2O‾电子态（ 2A″）的几何结构参数：键长R(SS) = 2.008 +/-0.005Å 和 R(SO) = 1.519+/-0.005Å.     

CALORIMETRIC STUDY OF THERMOCHROMIC COMPLEXES. 2. HEAT CAPACITY AND PHASE TRANSITION OF BIS(N,N‐DIETHYLETHYLENEDIAMINE)COPPER(II) PERCHLORATE

Abstract

The thermochromic phase transition of bis(N,N-diethylethylenediamine) copper(II) perchlorate has been studied by adiabatic calorimetry in the 12–359 K temperature range. A large heat capacity anomaly was observed at 317.64 K with a long heat-capacity tail extending down to ～200 K. The enthalpy and entropy of the phase transition were found to be δ_trs H = 17.43 kJ mol^?1 and δ_trs S = 55.21 J K^?1 mol^?1, respectively. Together with a calorimetric study of a homologous thermochromic complex, bis(N,N-diethylethylenediamine)copper(II) tetrafluoroborate (J. Phys. Chem. Solids, 55, 99 (1994)), the nature of the present thermochromic phase transition is well described by a puckering motion of the copper-ligand chelate rings and a change in the ligand-field strength estimated on the basis of the angular overlap model. The correlation between structures, electronic spectra and thermal properties is discussed.