The Two-Body Interaction with a Circle in Time

We complete our previous^{(1, 2)} demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation,⁽⁴⁾ including fine structure. We complete our previous derivation⁽²⁾ of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.     

Potent New Heterogeneous Asymmetric Catalysts

A set of new, air‐stable, Rh^I‐based heterogeneous asymmetric hydrogenation catalysts have been synthesised, characterised, and tested. Individual members of this new family all exhibit good enantioselectivity.     

High-resolution infrared spectra of NCCN and NCCN

High-resolution spectra of ¹⁵N¹²C¹²C¹⁵N and ¹⁴N¹³C¹³C¹⁴N have been measured and analyzed from 200 to 3600 cm⁻¹. All the vibrational levels below 900 cm⁻¹ have been observed and characterized. The Fermi resonance between ν₂ and 2ν₄ has been studied and the resonance constant has been determined for several cases. Several Σ⁻ states have been directly observed for the first time for each isotopomer, the (0001111)0f, (0011111)0f, and (0002222)0f states. The pattern of the energy levels for clusters of l-type resonance coupled levels, such as 0001131,3, has been determined for cyanogen for the first time. Among other things this involved the determination of the vibrational l-type resonance constant, r₄₅. Many of the power series constants, α_i and x_ij, and higher order constants have been determined.     

Mechanism in homogeneous catalysis; NMR as a prime mover

An overview of the contribution of NMR to the development of our understanding of homogeneous catalysis is presented, with an emphasis on work from the author’s research group.     

Active-constraint variable ordering for faster feasibility of mixed integer linear programs

The selection of the branching variable can greatly affect the speed of the branch and bound solution of a mixed-integer or integer linear program. Traditional approaches to branching variable selection rely on estimating the effect of the candidate variables on the objective function. We present a new approach that relies on estimating the impact of the candidate variables on the active constraints in the current LP relaxation. We apply this method to the problem of finding the first feasible solution as quickly as possible. Empirical experiments demonstrate a significant improvement compared to a state-of-the art commercial MIP solver.     

Unique satisfiability of Horn sets can be solved in nearly linear time

If a Horn set I has a single satisfying truth assignment or model then that model is said to be unique for I. The question of determining whether a unique model exists for a given Horn set I is shown to be solved in O((L)*L) time, where L is the sum of the lengths of the clauses in I and is the inverse Ackermann function. It is also shown that if LA*log (A) where A is the number of distinct proposition letters then unique satisfiability can be determined in O(L) time.     

An efficient palladium catalyzed synthesis of 2-arylbenzothiazoles

A novel and convergent palladium catalyzed synthesis of 2-arylbenzothiazoles has been investigated. The key step in the synthesis is a Suzuki biaryl coupling of 2-bromobenzothiazole with aryl boronic acids to provide a variety of 2-arylbenzothiazole derivatives in good yield. The synthetic utility of this methodology is demonstrated by the synthesis of 2-(4-aminophenyl)-6-methoxybenzothiazole, a PET probe precursor for the in vivo imaging of Alzheimer's disease.     

13C and 1H NMR analysis of the nitration products of 2-amino-4-oxo-(3H)-5-trifluoromethylquinazoline and 2-amino-4-oxo-(3H)-5-fluoroquinazoline

Nitration of 2-amino-4-oxo-(3H)-5-trifluoromethylquinazoline is shown to occur exclusively at C⁶ as determined from an analysis of long range ¹H and ¹⁹F scalar couplings to ring carbons. Nitration of 2-amino-4-oxo-(3H)-5-fluoroquinazoline is found to occur both at C⁶ and C⁸ as evident from an analysis of the ¹⁹F and ¹H couplings of the ring protons.