Neighborhood unions and the cycle cover number of a graph

For several years, the study of neighborhood unions of graphs has given rise to important structural consequences of graphs. In particular, neighborhood conditions that give rise to hamiltonian cycles have been considered in depth. In this paper we generalize these approaches to give a bound on the smallest number of cycles in G containing all the vertices of G. We show that if for all x, y ? V(G), |N(x) ∩ N(y)| ≧ 2n/5 + 1, then V(G) is coverable by at most two cycles. Several related results and extensions to t cycles are also given.     

Parity violation at neutron p-wave resonances of238U and232Th and related questions

Parity violation effects have been studied at 40 neutron p-wave resonances of the even-even nuclei²³⁸U and²³²Th. Of these 11 show parity violation effects larger than 2 standard deviations, making parity violation a rather common phenomenon. Parity mixing up to 10% has been found. The root-mean squared matrix elements for parity violation derived from these resonances are M=0.58 (+0.50/-0.25) meV for²³⁸U, respectively 1.39 (+0.35/-0.38) meV for²³²Th.     

Sensitivity of trust-region algorithms to their parameters

In this paper, we examine the sensitivity of trust-region algorithms on the parameters related to the step acceptance and update of the trust region. We show, in the context of unconstrained programming, that the numerical efficiency of these algorithms can easily be improved by choosing appropriate parameters. Recommended ranges of values for these parameters are exhibited on the basis of extensive numerical tests. MSC classification: 65K05, 90C26, 90C30     

The Ideal Retraction Property for Idempotent Semigroups

A semigroup S is said to have the ideal retraction property provided each of its ideals is the image of an idempotent endomorphism of S. The main result of this work is a characterization of those bands which have the idempotent retraction property. All such bands are normal.     

Factors controlling the efficiencies of photoinduced electron-transfer reactions

The overall efficiencies of photoinduced electron transfer reactions in polar solvents are usually determined by the efficiency with which separated radical ions are formed from the initially formed geminate radical-ion pairs. These separation efficiencies are determined by the competition between retum electron transfer and separation within the geminate pairs. A method is described for determining whether variations in the quantum yields for formation of separated radical ions are due to changes in the reorganization parameters for the return electron transfer reactions, or to other factors. The use of the method is illustrated in studies of the effects of varying steric bulk and molecular size of the donors, and also in studies of the effect of using a charged sensitizer.     

Singlet-triplet interconversion of diphenylmethylene. Energetics,dynamics and reactivities of different spin states

A combination of picosecond and nanosecond laser spectroscopy measurements, chemical quenching experiments and triplet sensitization experiments has allowed the determination of the rapid singlet to triplet and slower triplet to singlet intersystem crossing rates for diphenylmethylene in fluid solution at room temperature. It is shown that under the conditions of the kinetic measurements, singlet and triplet diphenylmethylene (¹DPM and ³DPM, respectively) are in rapid equilibrium relative to reactions, so that knowledge of the values of k_ST and k_TS allows determination of the equilibrium constant and change in free energy for the ¹DPM 〈 ³DPM process. The absolute reactivity of ¹DPM toward a series of alcohols has been determined and is discussed in terms of other current investigations of carbene reactivity.     

A spin-dependent unitary group approach to many-electron systems

In this article we derive a segment-level formula for the matrix elements of the U(2n) generators in a basis symmetry adapted to the subgroup U(n) × U(2) (i.e., spin-orbit basis), for the representations appropriate to many-electron systems. This enables the direct evaluation of the matrix elements of spin-dependent Hamiltonians.     

Structure and dynamics of metallomacrocycles: recognition of zinc xylyl-bicyclam by an HIV coreceptor

As platforms for the design of metal-based therapeutic and diagnostic agents, macrocycles are rigid enough to provide strong metal binding sites and orient functional groups stereoselectively, yet flexible enough to accommodate structural changes required for induced-fit recognition of biological targets. We consider the recognition of the Zn(II) complex of the bis-tetraazamacrocycle xylyl-bicyclam, a potent anti-HIV agent, by the coreceptor CXCR4, a G-protein-coupled receptor used by HIV for membrane fusion and cell entry. NMR studies show that the macrocycles of Zn(II)(2)-xylyl-bicyclam perchlorate exist in aqueous solution as two major configurations, trans-I (nitrogen chirality R,S,R,S), and trans-III (S,S,R,R). Acetate addition induced a major structural change. X-ray crystallography shows that the acetate complex contains the unusual cis-V cyclam configuration (R,R,R,R and folded) with bidentate coordination of acetate to Zn(II) plus second-coordination-sphere double H-bond formation between diagonal NH protons on the opposite cyclam face and acetate carboxylate oxygens. Detailed 1D and 2D NMR studies show that the major configuration of Zn(II)(2)-xylyl-bicyclam acetate in aqueous solution is cis-V/trans-I. Molecular modeling shows that an analogous cis-V site can be formed when Zn(II)(2)-xylyl-bicyclam binds to CXCR4, involving the carboxylate groups of Asp262 (Zn(II) coordination) and Glu288 (double H-bonding). The second cyclam can adopt the trans-I (or trans-III) configuration with Zn(II) binding to Asp171. These interactions are consistent with the known structure-activity relationships for bicyclam anti-HIV activity and receptor mutation. Consideration of the anti-HIV activity of xylyl-bicyclam complexes of other metal ions suggests that affinity for carboxylates, configurational flexibility, and kinetic factors may all play roles in receptor recognition. For example, Pd(II) cyclam complexes interact only weakly with axial ligands and are inflexible and inactive, whereas Co(III) cyclams bind carboxylates strongly, are configurationally flexible, and yet have low activity. Our findings should aid the design of new generations of active macrocycles including highly specific chemokine receptor antagonists.