Gauge-invariant correlation functions for the Ising-gauge Ising-Higgs system in 2 dimensions

We use recent calculations of correlation functions of the 2-dimensional Ising model in the presence of a magnetic field to study the Z₂-gauge Z₂-Higgs system in 2 dimensions. We study both the correlation of two plaquettes and the gauge-invariant correlation of Higgs fields. From these we are able to discuss criteria for confinement in the presence of matter.     

Olefin group selectivity in non-aqueous reversed-phase LC

Summary The effects of mobile phase composition upon olefin group selectivity (the ratio of the retention factor of a n-alkane to 1-olefin of equal carbon number) has been examined for non-aqueous reversed-phase liquid chromatorphy. Under time-normalized conditions, large variations in olefin group selectivities were noted as the mobile phase constitutents were changes. However, methylene group selectivities were found to be insensitive to the nature of the mobile phase under these conditions. Mobile phases containing alcohols demonstrated low olefin group selectivities compared to those containing acetonitrile as weak solvent. The results of this study explain variations previously observed in the LC separation of olive oil triglycerides that differ in the number of methylene groups and double bonds.     

Decomposition of the photoabsorption continuum underlying the Schumann-Runge bands of 16O2—II. Role of the 1 3Πg state and collision-induced absorption

Measurements are presented of molecular oxygen photoabsorption cross-sections and pressure coefficients taken at selected minima between rotational lines of the Schumann-Runge band system. Both room-temperature and liquid-nitrogen-temperature results are presented from 1760–1980 Å, and corrections are applied for the effect of the wings of the rotational lines. Absorption into the B³∑^?_u and A³∑⁺_u⁺ and is found to be insufficient to account for the total observed cross-section, and it is proposed that transitions to the 1³Π_g valence state account for the remainder. The pressure dependence of the cross-sections is consistent with collision-induced enhancement of the intensities of the forbidden transitions X³∑^?_g → A³∑⁺_g and $\text{X}{}^3\text{∑}{}^{\mathrm{?}}{}_{\mathrm{g}}\text{→ 1}{}^3\text{Π}{}_{\mathrm{g}}$, while the temperature dependence of the pressure coefficients is not consistent with absorption due to stable (O₂)₂ dimers.     

Evidence of multiexciton complexes bound to neutral acceptors in GaAs

The first observation of six sharp photoluminescence lines with energies less than the energies of the lines associated with a radiative recombination of a single exciton bound to a neutral acceptor in high purity epilayers of GaAs at liquid helium temperature is reported. It is proposed that these lines arise as a result of a radiative recombination of an exciton in a multiexciton complex bound to a neutral acceptor.     

Non-linear partial difference equations for the two-spin correlation function of the two-dimensional Ising model

For all temperatures, the two-point function of the two-dimensional Ising model is shown to be expressible in terms of the solution of a non-linear partial difference equation on the lattice. From this difference equation, the known results for the two-point function of the Ising field theory are regained by taking the scaling limit.     

Bounds on cost effective domination numbers

A vertex υ in a set S is said to be cost effective if it is adjacent to at least as many vertices in V\S as it is in S and is very cost effective if it is adjacent to more vertices in V\S than to vertices in S. A dominating set S is (very) cost effective if every vertex in S is (very) cost effective. The minimum cardinality of a (very) cost effective dominating set of G is the (very) cost effective domination number of G. Our main results include a quadratic upper bound on the very cost effective domination number of a graph in terms of its domination number. The proof of this result gives a linear upper bound for hereditarily sparse graphs which include trees. We show that no such linear bound exists for graphs in general, even when restricted to bipartite graphs. Further, we characterize the extremal trees attaining the bound. Noting that the very cost effective domination number is bounded below by the domination number, we show that every value of the very cost effective domination number between these lower and upper bounds for trees is realizable. Similar results are given for the cost effective domination number.     

Screening of protein kinases by ATP-STD NMR spectroscopy

ATP-STD NMR takes advantage of Mg2+ binding to ATP to adjust the ATP affinity for protein kinases permitting a wide range of Ki's to be determined for ATP competitive ligands. Substituting Mn2+ for Mg2+ creates a paramagnetic probe (MnATP) from which the proximity of non-ATP competitive ligands can be inferred. Internal standards and references are used to reduce false positives due to protein or compound degradation. Use of the natural ATP ligand confers active site-specificity that is not available a priori from other ligand binding experiments.