Chemistry of 1-Alkoxy-1-glycosyl Radicals: The Manno- and Rhamnopyranosyl Series. Inversion of alpha- to beta-Pyranosides and the Fragmentation of Anomeric Radicals

The formation and stereoselective quenching of 1-mannopyranosyl radicals by a tributyltin hydride-mediated intramolecular 1,5-hydrogen abstraction sequence is described. A competing process is 1,4-hydrogen atom abstraction leading principally to glucopyran-2-ulosides. Fragmentation of the anomeric radical resulting in the formation of ring opened products is a problem in certain series. The chemistry is dictated to a considerable extent by the nature of the protecting groups employed with the 4,6-benzylidene series and, for rhamnose, the Ley 3,4-dispiroketal, being particularly susceptible to the 1,4-hydrogen atom abstraction but less to the fragmentation. Photochemical conditions are described, in which these side reactions are practically eliminated, and applied to the inversion of an alpha- to a beta-mannoside in a disaccharide.     

Fermionic stochastic differential equations and the index of Fredholm operators

The index of a Fredholm operator associated to a-summable Fredholm module is expressed in terms of the vacuum expectation value of a unitary operator-valued stochastic process which satisfies a stochastic differential equation with unbounded coefficients driven by fermion noise.     

N-order direct form digital filters with integer arithmetic

For direct form digital filters with integer arithmetic, a characterization of the initial condition vector and state vectorX(), for a fixed, > 1, is established without the intermediate state vectors. This is used to determine initial conditions for stability and initial conditions for convergence to a limit cycle. Also, several properties of limit cycles are proven.     

LP modeling languages for personal computers: A comparison

The purpose of this paper is to compare and contrast the modeling capabilities of seven algebraic modeling languages (ML) available today, namely, AMPL, GAMS, LINGO, LPL, MPL, PC-PROG and XPRESS-LP. In general, these MLs do an excellent job of providing an interface with which the modeler can specify an algebraically formatted linear program (LP). That is, each ML provides a substantial improvement in time and convenience over the matrix generator/report writers of the last few decades. Further, each of the MLs provides: (1) significant flexibility in model specification, instantiation and modification, (2) effective and efficient conversion from algebraic to solver format, and (3) an understandable and, for the most part, self-documenting model representation. In addition, each of the MLs is constantly being updated and upgraded to provide additional capabilities sought by practitioners and users. However, as shown in the fifteen tables provided in the body of this paper, each ML has its own set of competitive advantages. For example, the most integrated environments (i.e. those integrating the modeling language with a full-screen editor, data import capabilities and a solver) are provided by LINGO and PC-PROG. The most user-friendly interfaces are provided by MPL and PC-PROG, both of which provide window-based interfaces to create models and pop-up windows to display error messages; MPL also uses pull-down menus to specify various operations, whereas PC-PROG uses function keys for operational control. Package costs are led by a current (March, 1991) introductory offer from LINGO. Modeling effectiveness, especially with respect to flexibility in specifying arithmetic statements, is led by GAMS and LPL. Model compactness, as measured by the number of lines required to specify a model, is led by AMPL, LPL, MPL and PC-PROG; LPL, MPL and PC-PROG also provide context sensitive editors which automatically position the cursor where the error was detected. And finally, the most comprehensive user documentation is provided by GAMS, whereas GAMS, LINGO and LPL provide extensive libraries of sample models for those users who learn by example.     

Why do clocks tick?

Drawing on recent developments in the matrix model approach to string theory and the causal set program for quantum gravity we address the question of the origin of time as one aspect of the phase transition from a topological quantum field theory to a quantum theory of gravity. We construct a model with two phases which can be interpreted as containing clocks which either do not tick or tick exactly once. This demonstrates that while a theory based on causal sets may appear to have inherent notions of time and causality, the existence of a phase transition means, that as Saint Augustine wrote in hisConfessions, the time, if such we may call it, when there was no time was not time at all.Received an Honorable Mention in the 1992 Gravity Research Foundation Essay Contest—Ed.     

Lattice size estimates for Gabor decompositions

It is shown that the Gabor frame operator for frames with lattice such thatab=1/N for some integerN1 is continuous on the modulation spaces ([9], [20]) whenever the basic functiong is a Schwartz function and (g, a, b) generates a frame forL ² (R). From this a sufficient condition on the lattice is given which guarantees that one has a Banach frame for the modulation spaces of Feichtinger.This work was supported by NSF grant # DMS-8916968 while the author was visiting Yale University.     

The reaction of allenylsilanes with α,β-unsaturated acylsilanes: new annulation approaches to five and six-membered carbocyclic compounds

The reaction of α,β-unsaturated acylsilanes with allenylsilanes can be directed to produce either five or six-membered carbocyclic compounds.     

Crystal structure of (1rs, 14sr, 17rs, 18rs)-2,20-dioxa-17-methyltricyclo [16,3,0,0] heneicosa-15-ene-3,19,21-trione; a macrocyclic lac

An X-ray study of the major product of the intramolecular Diels-Alder reaction of the diene-anhydride (2) has confirmed it as being the desired cytochalasan analogue (3). In particular the cyclisation has been regioselective, and has taken place via the endo transition state to generate the adduct with the correct relative configurations at the four chiral centres. Details of the conformational geometry of (3) are discussed.