A practical synthesis of (+/-)-alpha-isosparteine from a tetraoxobispidine core

[reaction: see text] The title alkaloid was synthesized in racemic form from 3,7-diallyl-2,4,6,8-tetraoxo-3,7-diazabicyclo[3.3.1]nonane (7) by a regioselective diallylation reaction followed by double ring-closing olefin metathesis and exhaustive reduction. Tetraoxobispidine 7 was itself prepared in three simple operations from dimethyl malonate. The entire sequence to alpha-isosparteine was conducted on a multigram scale and proceeded without recourse to chromatography.     

Superstructures of donor packing arrangements in a series of molecular charge transfer salts

Three conducting BEDT-TTF charge-transfer salts with tris(oxalato)metallate anions have unit cells containing both[small alpha] and [small beta][double prime] donor packing motifs.     

Synthesen von Carotinen mit ψ-Endgruppen und (Z)-Konfiguration an terminalen konjugierten Doppelbindungen

Syntheses of Carotenes with ψ-End Groups and (Z)-Configuration at Terminal Conjugated Double Bonds Five carotenes bearing (5Z)-ψ-end groups were synthesized and carefully characterized: (5Z)-lycopene ( 6 ), (5Z5′Z)-lycopene ( 7 ), (5′Z)-neurosporene ( 8 ), (5′Z)-β,ψ-carotene ( 12 ), and (5′Z)-ε,ψ-carotene ( 14 ).     

Homomorphisms on some function algebras

In this note we prove, for some classes of real locally convex spacesE including all complete Schwartz spaces, that every non-zero homomorphism on the algebraC (E) ofC -functions onE is given by a point evaluation at some point ofE.     

Vector—valued fractal interpolation functions and their box dimension

Summary We introduce continuous functions f: 1 $$ " align="middle" border="0"> , whose graphs are the attractors of certain iterated function systems, and which interpolate a given set of data or interpolation points ={(t _j ,x _j ):j = 0, 1, , M; M >1} according tof(t _j ) =x _j . The box dimension of the graph of these functions is in general non-integral. We present a formula for this dimension. Applications to the approximation of complicated self-affine functions are indicated.     

The number oft-wise balanced designs

We prove that the number oft-wise balanced designs of ordern is asymptotically , provided that blocks of sizet are permitted. In the process, we prove that the number oft-profiles (multisets of block sizes) is bounded below by and above by for constants c₂>c₁>0.     

Comparison methods for a class of function valued stochastic partial differential equations

Summary A comparison theorem is derived for a class of function valued stochastic partial differential equations (SPDE's) with Lipschitz coefficients driven by cylindrical and regular Hilbert space valued Brownian motions. Moreover, we obtain necessary and sufficient conditions for the positivity of the mild solutions of the SPDE's where the sufficiency follows from the comparison theorem. Thereby it is, e.g., possible to identify a class of SPDE's, which can serve as stochastic space-time models for the density of particles. As a consequence we can construct unique mild solutions of SPDE's on the cone of positive functions with non-Lipschitz drift parts including the case of arbitrary polynomialsR(x) withR(O)O and leading negative coefficient.This research was supported by a grant from ONR     

Experiments in Solving Mixed Integer Programming Problems on a Small Array of Transputers

The time-consuming process of solving large-scale Mixed Integer Programming problems using the branch-and-bound technique can be speeded up by introducing a degree of parallelism into the basic algorithm. This paper describes the development and implementation of a parallel branch-and-bound algorithm created by adapting a commercial MIP solver. Inherent in the design of this software are certain ad hoc methods, the use of which are necessary in the effective solution of real problems. The extent to which these ad hoc methods can successfully be transferred to a parallel environment, in this case an array of at most nine transputers, is discussed. Computational results on a variety of real integer programming problems are reported.     

Smoothed cross-validation

Summary For bandwidth selection of a kernel density estimator, a generalization of the widely studied least squares cross-validation method is considered. The essential idea is to do a particular type of presmoothing of the data. This is seen to be essentially the same as using the smoothed bootstrap estimate of the mean integrated squared error. Analysis reveals that a rather large amount of presmoothing yields excellent asymptotic performance. The rate of convergence to the optimum is known to be best possible under a wide range of smoothness conditions. The method is more appealing than other selectors with this property, because its motivation is not heavily dependent on precise asymptotic analysis, and because its form is simple and intuitive. Theory is also given for choice of the amount of presmoothing, and this is used to derive a data-based method for this choice.Research of the second author was done while on leave from the University of North Carolina. That of both the second and third was partially supported by National Science Foundation Grants DMS-8701201 and DMS-8902973