Simultaneous Pseudo-Timestepping for PDE-Model Based Optimization Problems

In this paper we present a new method for the solution of optimization problems with PDE constraints. It is based on simultaneous pseudo-time stepping for evolution equations. The new method can be viewed as a continuous reduced SQP method in the sense that it uses a preconditioner derived from that method. The reduced Hessian in the preconditioner is approximated by a pseudo-differential operator, whose symbol can be investigated analytically. We apply our method to a boundary control model problem. The new optimization method needs 3.2-times the overall computational effort of the solution of simulation problem alone.     

Single-server queues with spatially distributed arrivals

Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server's movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The service times are independent, but arbitrarily distributed. The model generalizes the continuous cyclic polling system (the diffusion coefficient of the Brownian motion is zero in this case) and can be interpreted as a continuous version of a Markov polling system. Using Tweedie's lemma for positive recurrence of Markov chains with general state space, we show that the system is stable if and only if the traffic intensity is less than one. Moreover, we derive a stochastic decomposition result which leads to equilibrium equations for the stationary configuration of customers on the circle. Steady-state performance characteristics are determined, in particular the expected number of customers in the system as seen by a travelling server and at an arbitrary point in time.     

A characterization of the \Sigma_1-definable functions of KP\omega + (uniform\; AC)

The subject of this paper is a characterization of the -definable set functions of Kripke-Platek set theory with infinity and a uniform version of axiom of choice: . This class of functions is shown to coincide with the collection of set functionals of type 1 primitive recursive in a given choice functional and . This goal is achieved by a G?del Dialectica-style functional interpretation of and a computability proof for the involved functionals. Received October 9, 1996     

Conformal field algebras with quantum symmetry from the theory of superselection sectors

According to the theory of superselection sectors of Doplicher, Haag, and Roberts, field operators which make transitions between different superselection sectors—i.e. different irreducible representations of the observable algebra—are to be constructed by adjoining localized endomorphisms to the algebra of local observables. We find the relevant endomorphisms of the chiral algebra of observables in the minimal conformal model with central chargec=1/2 (Ising model). We show by explicit and elementary construction how they determine a representation of the braid groupB which is associated with a Temperley-Lieb-Jones algebra. We recover fusion rules, and compute the quantum dimensions of the superselection sectors. We exhibit a field algebra which is quantum group covariant and acts in the Hilbert space of physical states. It obeys local braid relations in an appropriate weak sense.     

Extending the scope of enantiomer separation by capillary supercritical fluid chromatography on immobilized polysiloxane-anchored permethyl-β-cyclodextrin (Chirasil-Dex)

Immobilized polysiloxane-anchored permethyl-β-cyclodextrin (Chirasil-Dex) with a cyclodextrin content of approximately 30 % by weight, previously employed as a versatile chiral stationary phase for the separation of enantiomers by GC, has been used for the separation of enantiomers by capillary supercritical fluid chromatography (SFC). A considerable number of racemates could be resolved, e.g. aromatic alcohols, amino alcohols (TFA derivatives), and underivatized acids. Many pharmaceutical compounds were among those analyzed, including several NSAIDs (e.g. ibuprofen and ketoprofen), a steroidal drug (nor-gestrel), a barbiturate (hexobarbital), and others. Among the racemates resolved were many which cannot be analyzed by GC owing to low volatility or decomposition at elevated temperatures. For two racemates, analysis temperature and mobile phase density were systematically varied to give constant analysis times or capacity factors k. Low temperatures (ca 60 °C) yielded the best separation in term of separation factor, α, or resolution, R_s, even though higher densities had to be used. In comparison with GC, capillary SFC was able to furnish higher separation factors and similar resolution. The applicability of capillary SFC for the analysis of mixtures of cyclodextrin derivatives, e.g. those used in the synthesis of Chirasil-Dex, was, furthermore, demonstrated.     

Macrocyclization on the fullerene core: Direct regio- and diastereoselective multi-functionalization of [60]fullerene,and synthesis of fullerene-dendrimer derivatives

The macrocyclization between buckminsterfullerene, C₆₀, and bis-malonate derivatives in double Bingel reaction provides a versatile and simple method for the preparation of covalent bis-adducts of C₆₀ with high regio- and diastereoselectivity. A combination of spectral analysis, stereochemical considerations, and X-ray crystallography (Fig. 2) revealed that out of the possible in-in, in-out, and out-out stereoisomers, the reaction of bis-malonates linked by o-, m-, or p-xylylene tethers afforded only the out-out ones (Scheme 1). In contrast, the use of larger tethers derived from 1,10-phenanthroline also provided a first example, (±)- 19 (Scheme 2), of an in-out product. Starting from optically pure bis-malonate derivatives, the new bis-functionalization method permitted the diastereoselective preparation of optically active fullerene derivatives (Schemes 4 and 5) and, ultimately, the enantioselective preparation (enantiomeric excess ee > 97%) of optically active cis-3 bis-adducts whose chirality results exclusively from the addition pattern (Fig. 6). The macrocyclic fixation of a bis-malonate with an optically active, 9,9′-spirobi[9H-fluorene]-derived tether to C₆₀ under generation of 24 and ent- 24 with an achiral addition pattern (Scheme 4) was found to induce dramatic changes in the chiroptical properties of the tether chromophore such as strong enhancement and reversal of sign of the Cotton effects in the circular dichroism (CD) spectra (Figs. 4 and 5). By the same method, the functionafized bis-adducts 50 and 51 (Schemes 10 and 11) were prepared as initiator cores for the synthesis of the fullerene dendrimers 62 , 63 , and 66 (Schemes 12 and 13) by convergent growth. Finally, the new methodology was extended, to the regio- and diastereoselective construction of higher cyclopropanated adducts. Starting from mono-adduct 71 , a clipping reaction provided exclusively the all-cis-2 tris-adduct (±)- 72 (Scheme 14), whereas the similar reaction of bis-adduct 76 afforded the all-cis-2 tetrakis-adduct 77 (Scheme 15). Electrochemical investigations by steady-state voltammetry (Table 2) in CH₂Cl₂ (+0.1M Bu₄NPF₆) showed that all macroeyciic bis(methano)fullerenes underwent multiple reduction steps, and that regioisomerism was not much influencing the redox potentials, All cis-2 bis-adducts gave an instable dianion which decomposed during the electrochemical reduction. In CH₂Cl₂, the redox potential of the fullerene core in dendrimers 62, 63 , and 66 is not affected by differences in size and density of the surrounding poly(ether-amide) dendrons. The all-cis-2 tris- and tetrakis(meihano)fullercnes (±) -72 and 77 , respectively, are reduced at more negative potential than previously reported all-e tris- and tetrakis-adducts with methane bridges that are also located along an equatorial belt. This indicates a larger perturbation of the original fullerene π-chromophore and a larger raise in LUMO energy in the former derivatives.     

Ab initio calculations of small hydrides including electron correlation

Five different structures of CH₅ ⁺ and one structure of CH₅ ^– are calculated using a gaussian basis both in the SCF approximation and with the inclusion of electron correlation in the independent electron pair approximation (IEPA). While on SCF level the C _sstructure of CH₅ ⁺ has to lowest energy, the energy difference between the C _sand C _2vstructures becomes negligible if correlation is included. In contrast to this the approach of a proton to CH₄ at large and intermediate distances is most favorable towards a corner of the CH₄ tetrahedron which means a structure. The decomposition of CH₅ ⁺ into CH₃ ⁺ and H₂ requires 20kcal/mol on SCF level and 40 kcal/mol if correlation is included.