APPLICATIONS OF MULTICOMPONENT ASSEMBLY PROCESSES TO THE FACILE SYNTHESES OF DIVERSELY FUNCTIONALIZED NITROGEN HETEROCYCLES

Several multicomponent assembly processes have been developed for the synthesis of intermediates that may be elaborated by a variety of cyclizations to generate a diverse array of highly functionalized heterocycles from readily-available starting materials. The overall approach enables the efficient preparation of libraries of small molecules derived from fused, privileged scaffolds.     

Distinctive field dependence of the longitudinal muon polarization for Mu* in polycrystalline silicon

A distinctive longitudinal magnetic field dependence of the muon polarization for anomalous muonium in polycrystalline semiconductor targets has been predicted. The polarization exhibits a cusp,i.e., a discontinuous jump in the slope from negative to positive. Measurements of the longitudinal polarization for polycrystalline silicon in fields up to 0.5 T, and temperatures 53 and 200 K have been made at LAMPF. A cusp in the field dependence indeed occurs at 0.345 T, in excellent agreement with the prediction. No cusp is observed at 200 K because Mu^* has been thermally ionized.     

Thermodynamics of black holes in anti-de Sitter space

The Einstein equations with a negative cosmological constant admit black hole solutions which are asymptotic to anti-de Sitter space. Like black holes in asymptotically flat space, these solutions have thermodynamic properties including a characteristic temperature and an intrinsic entropy equal to one quarter of the area of the event horizon in Planck units. There are however some important differences from the asymptotically flat case. A black hole in anti-de Sitter space has a minimum temperature which occurs when its size is of the order of the characteristic radius of the anti-de Sitter space. For larger black holes the red-shifted temperature measured at infinity is greater. This means that such black holes have positive specific heat and can be in stable equilibrium with thermal radiation at a fixed temperature. It also implies that the canonical ensemble exists for asymptotically anti-de Sitter space, unlike the case for asymptotically flat space. One can also consider the microcanonical ensemble. One can avoid the problem that arises in asymptotically flat space of having to put the system in a box with unphysical perfectly reflecting walls because the gravitational potential of anti-de Sitter space acts as a box of finite volume.     

The alternating semigroups: Generators and congruences

The idea of an even permutation has recently been generalized, via path notation, to one-one partial transformations (charts) in the symmetric inverse semigroupsC _n. The even charts form the alternating semigroupA _n ^c ⊂C _n . Generators ofA _n ^c are identified: It then follows that forn≥5,A _n ^c is the collection of restrictions of the even permutations (of rankn). Like theC _n case, the congruences ofA _n ^c form a chain. Part of this research was supported by a Mary Washington College faculty development grant.     

(2 + 1) Resonance enhanced multiphoton ionization of hydrogen chloride in a pulsed supersonic jet: Vacuum wavenumbers of rotational lines with detailed band analysis for excited electronic states of HCl

A comprehensive study of the excited electronic states of HCl is reported. Using resonance enhanced multiphoton ionization ((2 + 1) REMPI) and time-of-flight mass spectrometry (TOFMS) over 120 band systems are analyzed. Supersonic jet techniques are used to prepare rotationally cold species for laser spectroscopy in the 77 000 to 96 000 cm⁻¹ region. At least 50 new electronic states are characterized as well as several features only tentatively assigned previously. A long vibrational progression consisting of 29 vibrational levels of the deeply bound V¹Σ⁺(0⁺) valence/ion-pair state is studied. We also extend the identification and analysis to high vibrational levels of low-lying Rydberg states. The assignments of [²Π_i] Rydberg state complexes are evaluated in terms of spin-orbit coupling and united-atom calculations. In several band systems, the spectra exhibit anomalous rotational line intensities and broadened linewidths which are consistent with predissociation. Multiphoton ionization with mass spectrometry permits the investigation of isotope effects as well as the appearance of fragment species associated with repulsive potential curves.     

The explicit construction of irreducible polynomials over finite fields

For a finite field GF(q) of odd prime power order q, and n 1, we construct explicitly a sequence of monic irreducible reciprocal polynomials of degree n2 ^m (m = 1, 2, 3, ...) over GF(q). It is the analog for fields of odd order of constructions of Wiedemann and of Meyn over GF(2). We also deduce iterated presentations of GF (q ⁿ 2).     

Local minima for indefinite quadratic knapsack problems

We consider the complexity of finding a local minimum for the nonconvex Quadratic Knapsack Problem. Global minimization for this example of quadratic programming is NP-hard. Moré and Vavasis have investigated the complexity of local minimization for the strictly concave case of QKP; here we extend their algorithm to the general indefinite case. Our main result is an algorithm that computes a local minimum in O(n(logn)²) steps. Our approach involves eliminating all but one of the convex variables through parametrization, yielding a nondifferentiable problem. We use a technique from computational geometry to address the nondifferentiable problem.Supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research, Department of Energy, under contract W-31-109-Eng-38, in part by a Fannie and John Hertz Foundation graduate fellowship, and in part by Department of Energy grant DE-FG02-86ER25013.A000.