Electronic excitation and thermal effects in alkali-halide cluster anions

We have observed electronically excited states in alkali-halide cluster anions with one excess electron. Using photoelectron spectroscopy, we have found two narrow states in (KI)-2, (NaI)-2, and (NaCl)-2, consistent with a dipole-bound electron, while larger cluster anions exhibit a single broad excited state. In the larger systems, electronic excitation is often accompanied by vibrational excitation and thus a change in cluster temperature. Such temperature changes affect cluster structure and in some cases lead to rapid thermal isomerization.     

A practical one-pot synthesis of soluble hexa-peri-hexabenzocoronene and isolation of its cation-radical salt

A simple and practical synthesis of soluble hexa-peri-hexabenzocoronene (HBC) from readily available hexaphenylbenzene (HPB) is described. In this simple procedure, the substitution of the free para positions of the propeller-shaped HPB with tert-butyl groups and the oxidative cyclodehydrogenation to planar HBC is achieved in a one-pot reaction using ferric chloride both as a Lewis acid catalyst and as an oxidant in excellent yields. The ready availability of HBC allows the isolation of its pure cation-radical salt using a variety of chemical oxidants such as antimony pentachloride and triethyloxonium and nitrosonium hexachloroantimonate salts.     

Complexation with iron at sub-ppm levels in HPLC analyses of phospholipids

Gradient RP-HPLC analysis of a phospholipid, E5564, utilizing water, methanol and phosphoric acid occasionally results in the appearance of a broad unknown peak in the chromatogram before a well-resolved E5564 peak. This unknown peak does not elute in a reproducible fashion with regards to peak shape and retention time, and is not present in chromatograms resulting from injections of the diluent alone. Investigation of this phenomenon revealed that iron ions in sub-ppm levels in the HPLC mobile phase chelated E5564 and the resultant complex(es) comprised the broad peak. The iron source was identified as phosphoric acid, which was used as a mobile phase modifier. Further studies were conducted to characterize the nature of the phospholipid-iron association and resultant complex.     

Switchable catalysis: modular synthesis of functionalized Pyrimidinones via selective sulfide and halide cross-coupling chemistry

[reaction: see text] A general demonstration of orthogonal selectivity of the Liebeskind-Srogl cross-coupling protocol compared to the Suzuki-Miyaura and Stille variants is reported.     

Numerical differentiation procedures for non-exact data

The numerical differentiation of data divides naturally into two distinct problems:

1. the differentiation of exact data, and
2. the differentiation of non-exact (experimental) data.

In this paper, we examine the latter. Because methods developed for exact data are based on abstract formalisms which are independent of the structure within the data, they prove, except for the regularization procedure of Cullum, to be unsatisfactory for non-exact data. We therefore adopt the point of view that satisfactory methods for non-exact data must take the structure within the data into account in some natural way, and use the concepts of regression and spectrum analysis as a basis for the development of such methods. The regression procedure is used when either the structure within the non-exact data is known on independent grounds, or the assumptions which underlie the spectrum analysis procedure [viz., stationarity of the (detrended) data] do not apply. In this latter case, the data could be modelled using splines. The spectrum analysis procedure is used when the structure within the nonexact data (or a suitable transformation of it, where the transformation can be differentiated exactly) behaves as if it were generated by a stationary stochastic process. By proving that the regularization procedure of Cullum is equivalent to a certain spectrum analysis procedure, we derive a fast Fourier transform implementation for regularization (based on this equivalence) in which an acceptable value of the regularization parameter is estimated directly from a time series formulation based on this equivalence. Compared with the regularization procedure, which involvesO(n ³) operations (wheren is the number of data points), the fast Fourier transform implementation only involvesO(n logn).     

A Manpower Allocation Model of Job Specialization

A major copier machine company in Hong Kong presently faces the problem of providing effective servicing and repairing support to its four service regions. Due to the shortage of skilled technicians and the variety of jobs to be handled by technicians of differing skill levels, its Service Department appears to be understaffed, experiencing substantial daily backlogs. This study concentrates on a new perspective of operation: the assignment of technicians at each skill level to specialize in a single type of job in one of the four regions. The objective is to maximize the overall daily number of completed service calls. A mathematical model is developed to handle this specialized allocation problem, where the average travel time (forming part of the coefficient of one of the model's variables) of a technician servicing a type of job in a region is dependent on the decision variables – the composition of the whole team. This results in what we call a mixed integer non-linear programme with variable coefficients. An exact solution is obtained by an iterative algorithm with an overall dynamic programming approach. Sample numerical results are also reported.     

Orlik-Solomon Algebras and Tutte Polynomials

The OS algebra A of a matroid M is a graded algebra related to the Whitney homology of the lattice of flats of M. In case M is the underlying matroid of a hyperplane arrangement A in ^r , A is isomorphic to the cohomology algebra of the complement ^r A. Few examples are known of pairs of arrangements with non-isomorphic matroids but isomorphic OS algebras. In all known examples, the Tutte polynomials are identical, and the complements are homotopy equivalent but not homeomorphic.We construct, for any given simple matroid M ₀, a pair of infinite families of matroids M _n and M _n , n 1, each containing M ₀ as a submatroid, in which corresponding pairs have isomorphic OS algebras. If the seed matroid M ₀ is connected, then M _n and M _n have different Tutte polynomials. As a consequence of the construction, we obtain, for any m, m different matroids with isomorphic OS algebras. Suppose one is given a pair of central complex hyperplane arrangements A ₀ and A ₁ . Let S denote the arrangement consisting of the hyperplane {0} in ₁ . We define the parallel connection P(A ₀, A ₁), an arrangement realizing the parallel connection of the underlying matroids, and show that the direct sums A ₀ A ₁ and S P (A ₀, A ₁) have diffeomorphic complements.