The Riesz decomposition of finely superharmonic functions

This paper answers a question of Fuglede about minimal positive harmonic functions associated with irregular boundary points. As a consequence, an old and central problem of fine potential theory, concerning the Riesz decomposition, is resolved. Namely, it is shown that, on certain fine domains, there exist positive finely superharmonic functions which do not admit any positive finely harmonic minorant and yet are not fine potentials.     

Unified Interactive Multiple Objective Programming: An Open Architecture For Accommodating New Procedures

It has previously been shown that nine of the most prominent procedures of interactive multiple objective programming can be considered as special cases of a common procedure called the unified algorithm. In this paper, we show how four additional procedures can be similarly included in the unified approach. Also, the paper presents a procedure-switching matrix that depicts the possibilities for switching from one procedure to another, one iteration to the next, in the unified algorithm if so directed by a user.     

The effect of dissipation on coherent quantum tunnelling in a double-well system: Two-level model using an adjoint equation approach

We examine the effect of dissipation on coherent quantum tunnelling between the two lowest levels of a double-well system using an adjoint equation approach developed previously in the treatment of quantum-optical problems. Dissipation is modelled by a linear coupling to a bath of harmonic oscillators. The high frequency portion of the bath is adiabatically eliminated using a cumulant expansion technique, which generates frequency renormalisation terms. Making a low temperature assumption, an approximate two-level model is developed in the form of three coupled stochastic differential equations. With a decorrelation approximation, the two-level equations can be solved to yield familiar results. However, the adjoint equation also permits the use of direct stochastic simulation as a means of solution, and simulations are carried out for a range of parameters. A comparison with the decorrelation approximation is made.     

Solid State Structures and Solution Dynamics of Unsolvated and Diethyl Ether Solvated Dilithium N,N'-Bis(trimethylsilyl)ethylenediamide Complexes

The lithiation of N,N'-bis(trimethylsilyl)ethylenediamine, 1, by 2 equiv of methyllithium in diethyl ether yields the dimeric diethyl ether adduct [{Li[N(SiMe(3))CH(2)CH(2)NSiMe(3)]Li.OEt(2)}(2)], 2. Recrystallization of 2 from benzene gives quantitatively the unsolvated trimer [{Li[N(SiMe(3))CH(2)CH(2)NSiMe(3)]Li}(3)], 3. The solution dynamics of 2 and 3 in toluene have been investigated using variable temperature multinuclear NMR spectroscopy. In solution, 2 is undergoing a rapid exchange process involving an equilibrium between unsolvated and diethyl ether solvated dimers, whereas compound 3 exists in a temperature dependent equilibrium of dimeric and trimeric species, of which the trimer is fluxional and exchanges inequivalent ligands by an intramolecular distortion of the Li(6)N(6) cage structure. Crystals of 2 are monoclinic, of space group P2(1)/n (No. 14), with a = 10.692(9) ?, b = 16.192(2) ?, c = 24.04(4) ?, beta = 101.16(5) degrees, V = 4083(8) ?(3), and Z = 4. Crystals of 3 are trigonal, of space group R&thremacr;m(No. 166), a = 17.765(1) ?, c = 13.394(1) ?, V = 3660.5(5) ?(3), Z = 3.