Electronic and vibrational linear and nonlinear polarizabilities of Li@C60 and [Li@C60]+

Electronic and vibrational nuclear relaxation (NR) contributions to the dipole (hyper)polarizabilities of the endohedral fullerene Li@C(60) and its monovalent cation [Li@C(60)](+) are calculated at the (U)B3LYP level. Many results are new, while others differ significantly from those reported previously using more approximate methods. The properties are compared with those of the corresponding hypothetical noninteracting systems with a valence electron transferred from Li to the cage. Whereas the NR contribution to the static linear polarizabilities is small in comparison with the corresponding electronic property, the opposite is true for the static hyperpolarizabilities. A relatively small, but non-negligible, NR contribution to the dc-Pockels effect is obtained in the infinite frequency approximation.     

A Simple Linear-Time Recognition Algorithm for Weakly Quasi-Threshold Graphs

Weakly quasi-threshold graphs form a proper subclass of the well-known class of cographs by restricting the join operation. In this paper we characterize weakly quasi-threshold graphs by a finite set of forbidden subgraphs: the class of weakly quasi-threshold graphs coincides with the class of {P ₄, co-(2P ₃)}-free graphs. Moreover we give the first linear-time algorithm to decide whether a given graph belongs to the class of weakly quasi-threshold graphs, improving the previously known running time. Based on the simplicity of our recognition algorithm, we can provide certificates of membership (a structure that characterizes weakly quasi-threshold graphs) or non-membership (forbidden induced subgraphs) in additional ${{\mathcal O}(n)}$ time. Furthermore we give a linear-time algorithm for finding the largest induced weakly quasi-threshold subgraph in a cograph.     

Diagrammatic proof of the BCFW recursion relation for gluon amplitudes in QCD

We present a proof of the Britto–Cachazo–Feng–Witten tree-level recursion relation for gluon amplitudes in QCD, based on a direct equivalence between BCFW decompositions and Feynman diagrams. We demonstrate that this equivalence can be made explicit when working in a convenient gauge. We exhibit that gauge invariance and the particular structure of Yang–Mills vertices guarantee the validity of the BCFW construction.     

Minima of Trigonometric Polynomials

Let 0<n₁<n₂<...<n_N be N distinct integers, and leta₁, a₂, ..., a_N be complex numbers. We set [formula] and [formula] There are two well-known problems concerning the case a₁=a₂=...=a_N=1.1991 Mathematics Subject Classification 42A05.     

On the realization of symmetries in quantum mechanics

The aim of this paper is to give a simple, geometric proof of Wigner’s theorem on the realization of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several proofs exist already, it seems that the relevance of Wigner’s theorem is not fully appreciated in general. It is Wigner’s theorem which allows the use of linear realizations of symmetries and therefore guarantees that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical point of view in order to prove this theorem. It becomes apparent that Wigner’s theorem is nothing else but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics.     

Dissociation of 5-fluoro- and 3,5-dinitrosalicylic acids in water-methanol mixtures at 25 degrees

The association constants and molar conductivities, extrapolated to zero concentration, have been determined for 3,5-dinitrosalicylic and 5-fluorosalicylic acids in water-methanol mixtures at 25 degrees .     

Improvements of neutron activation techniques for the determination of fissile material concentrations

Certain experimental improvements, as variable sample size and irradiation position, automation and flexibility in radiation detection, broaden the measurable concentration range, increase the possible rate and accuracy of analysis and enlarge the application range of the home-made nuclear analyzer for fissile material analysis by delayed fission neutron counting and for short-lived multielement analysis by neutron activation gamma-ray spectrometry. Intercomparisons of results by various methods and laboratories show the need for regular checks of techniques to ensure reliable measurements.     

Intersecting M-branes

We present the magnetic duals of Güven's electric-type solutions of D = 11 supergravity preserving 1/4 or 1/8 of the D = 11 supersymmetry. We interpret the electric solutions as n orthogonal intersecting membranes and the magnetic solutions as n orthogonal intersecting 5-branes, with n = 2, 3; these cases obey the general rule that p-branes can self-intersect on (p − 2)-branes. On reduction to D = 4 these solutions become electric or magnetic dilaton black holes with dilaton coupling constant a = 1 (for n = 2) or (for n = 3). We also discuss the reduction to D = 10.