Singular terms of helicity amplitudes at one loop in QCD and the soft limit of the cross sections of multi-parton processes

We describe a general method that enables us to obtain all the singular terms of helicity amplitudes of n-parton processes at one loop. The algorithm uses helicity amplitudes at tree level and simple color algebra. We illustrate the method by calculating the singular part of the one-loop helicity amplitudes of all 2 → 3 parton subprocesses. The results are used to derive the soft gluon limit of the cross sections of all 2 → 4 parton scattering subprocesses which provide a useful initial condition for the angular ordering approximation to coherent multiple soft gluon emission, incorporated in existing Monte Carlo simulation programs.     

Globally Linked Pairs of Vertices in Equivalent Realizations of Graphs

A two-dimensional framework (G,p) is a graph G = (V,E) together with a map p: V → ℝ². We view (G,p) as a straight line realization of G in ℝ². Two realizations of G are equivalent if the corresponding edges in the two frameworks have the same length. A pair of vertices {u,v} is globally linked in G if %and for all equivalent frameworks (G,q), the distance between the points corresponding to u and v is the same in all pairs of equivalent generic realizations of G. The graph G is globally rigid if all of its pairs of vertices are globally linked. We extend the characterization of globally rigid graphs given by the first two authors [13] by characterizing globally linked pairs in M-connected graphs, an important family of rigid graphs. As a byproduct we simplify the proof of a result of Connelly [6] which is a key step in the characterization of globally rigid graphs. We also determine the number of distinct realizations of an M-connected graph, each of which is equivalent to a given generic realization. Bounds on this number for minimally rigid graphs were obtained by Borcea and Streinu in [3].     

Variational extension of the mean spherical approximation to arbitrary dimensions

We generalize a variational principle for the mean spherical approximation for a system of charged hard spheres in 3D to arbitrary dimensions. We first construct a free energy variational trial function from the Debye-Hückel excess charging internal energy at a finite concentration and an entropy obtained at the zero-concentration limit by thermodynamic integration. In three dimensions the minimization of this expression with respect to the screening parameter leads to the mean spherical approximation, usually obtained by solution of the Ornstein-Zernike equation. This procedure, which interpolates naturally between the zero concentration/coupling limit and the high-concentration/ coupling limit, is extended to arbitrary dimensions. We conjecture that this result is also equivalent to the MSA as originally defined, although a technical proof of this point is left for the future. The Onsager limitT ΔS ^MSA /ΔE ^MSA → 0 for infinite concentration/coupling is satisfied for all d ≠ 2, while ford=2 this limit is 1. On leave from Department of Physics, University of Puerto Rico, Mayagüez Campus, Mayagüez, Puerto Rico, 00681.     

Directed paths with random phases

Directed Feynman paths in 1 + 1 dimensions that acquire random phases are examined numerically and analytically. This problem is relevant for the behavior of the conductance in two-dimensional amorphous insulators in the variable-range-hopping regime. Large-scale numerical simulations were performed on a model with short-range correlations. For the scaling of the transverse fluctuations ( t^ν), we obtain ν = 0.68 ± 0.025; and for the r.m.s free-energy fluctuations ( t^ω), we obtain ω = 0.335 ± 0.01. Up to 100 000 random samples were used for times as large as 2000. These results seem to exclude a recent conjecture that ν = 3/4 and ω = 1/2. Two versions of a model with long-range correlations are solved and shown to yield ν = 1/2; a physical explanation is given.     

Synthesis of cephalosporins carrying isoxazolyl acetamido and related side chains

Starting from 3,5-dimethylisoxazole the carboxylic acids I and V, the amino acids VIII (L-) and IX (D-), and the ureido acids X (L-) and XI (D-) were prepared, which were used for the synthesis of the new cephalosporins XVIIb, XXa-c (L-), and XXIb (D-). Thein vitro antibacterial activity of these semi-synthetic antibiotics was studied. The resorption of XVIIb was investigated in mice.Research Group for Antibiotics of the Hungarian Academy of Sciences, H-4010 Debrecen, P.O. Box 70, Hungary. Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1524–1535, November, 1998.     

Configurational assignment of fragment ions by CID. Stereochemistry and mechanism of retro-Diels–Alder fragmentation accompanied by hydrogen transfer in gas-phase cations

Low energy CID mass spectra of m/z 173, C₈H₁₃O₄⁺, obtained from the diethyl ester of cis,syn,cis-l,2,3,3a,4,5,5a,6,7,8-decahydroindacene-4,5-dicarboxylic acid and cis,syn,cis-l,2,3,4,5,6,7,8,8a,9,10,10a-dodecahydrophenanthrene-9,10-dicarboxylic acid indicate they have the structure of protonated diethyl maleate. This finding together with previous deuterium labelling results suggest that the formation of this ion from both precursors takes place by migration of a hydrogen atom from an allylic δ-position followed by the concerted cleavage of two allylic C? C bonds in analogy to the ground state retro-Diels–Alder fragmentation.     

Anisotropy parameters for molecules excited by electron impact

Rotationally resolved excitation of the a¹Δ_g and b¹∑ _g ⁺ states of O₂ is considered. Results for the relevant state multipoles are given. The anisotropy produced by electron impact is visualised by figures of the angular distribution of the molecular axes in the excited states.