The solid-phase synthesis and use of N-monosubstituted piperazines in chemical library synthesis

An efficient solid-phase synthesis of mono-N-substituted piperazines is presented. The key transformation involves a selective borane amide bond reduction in the presence of a carbamate resin linkage. This synthetic route takes advantage of the large diverse pool of commercially available carboxylic acids, acid chlorides, and sulfonyl chlorides. The solid-phase approach facilitates parallel processing by eliminating the need for column chromatography after each synthetic step. The N-monosubstituted piperazines were shown to react with polymeric activated tetrafluorophenol (TFP) reagents to generate arrays of amides and sulfonamides in good purity for biological testing.     

A generalization of a theorem on biseparating maps

In J. Math. Anal. Appl. 12 (1995) 258–265, Araujo et al. proved that for any linear biseparating map  from C(X) onto C(Y), where X and Y are completely regular, there exist ω in C(Y) and an homeomorphism h from the realcompactification vX of X onto vY, such that

The compact version of this result was proved before by Jarosz in Bull. Canad. Math. Soc. 33 (1990) 139–144. In Contemp. Math., Vol. 253, 2000, pp. 125–144, Henriksen and Smith asked to what extent the result above can be generalized to a larger class of algebras. In the present paper, we give an answer to that question as follows. Let A and B be uniformly closed Φ-algebras. We first prove that every order bounded linear biseparating map from A onto B is automatically a weighted isomorphism, that is, there exist ω in B and a lattice and algebra isomorphism ψ between A and B such that

(a)=ωψ(a) for all aA.

We then assume that every universally σ-complete projection band in A is essentially one-dimensional. Under this extra condition and according to a result from Mem. Amer. Math. Soc. 143 (2000) 679 by Abramovich and Kitover, any linear biseparating map from A onto B is automatically order bounded and, by the above, a weighted isomorphism. It turns out that, indeed, the latter result is a generalization of the aforementioned theorem by Araujo et al. since we also prove that every universally σ-complete projection band in the uniformly closed Φ-algebra C(X) is essentially one-dimensional.     

Toeplitz Operators Associated to Unimodular Algebras

We introduce a class of function algebras, that we call unimodular, and study Toeplitz operators on the Hardy spaces associated to representing measures on these algebras.We show that our class of function algebras is very extensive and that a number of important results for Toeplitz operators and their associated C*-algebras extend to the very general setting we consider. Submitted: July 1. 2001.     

Parallel connections over symmetric spaces

Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated vector bundle of a canonical principal bundle, with the connection inherited from the principal bundle. The problem of finding Riemannian (or unitary) vector bundles with parallel curvature then reduces to finding representations of the structure group of the canonical principal bundle.     

Synthesis of multiply substituted, ion channel forming octi(p-phenylene)s: theme and variations

[reaction: see text] To facilitate the access to unique models for biological processes, we examined six different synthetic routes to octi(p-phenylene) rods with lateral and terminal substituents R(L) and R(T). This systematic study allowed us to increase to overall yield for the synthesis of a new class of oligo(p-phenylene) ionophores about 20 times and to provide general insights into the practicability of synthetic routes to multiply substituted molecular rods.     

Synthesis, spectroscopy, and X-ray structure of the polymer catena-[bis(azido-N)-copper(II)-μ-bis(2-benzimidazolyl)butane]

The title compound, catena-[bis(azido-N)-copper(II)-(bis(2-benzimidazolyl)butane), [Cu(C₁₈H₁₈N₄)(N₃)₂]_n, was obtained from the reaction of the ligand bis(2-benzimidazolyl)butane and Cu(N₃)₂. The x-ray crystal structure is reported. The compound crystallizes in the monoclinic space group P2₁/c with a = 8.2524(10), b = 12.765(5), c = 9.1125(15) Å, = 106.423(12)°, Z = 2. The Cu(II) ions are square-planar coordinated with trans-oriented end-on binding azido ligands. The structure is a polynuclear chain with the benzimidazole bridging at each end. In addition a N_(ligand)-H···N_(azido) H-bridge [N_(ligand)···N_(azido) = 2.994(7) Å] is present, resulting in a pseudo 2-dimensional lattice. The characteristic azido infrared vibrations are found at 2060 and 2077 cm^–1 (_as(N₃)) and 1284 and 1297 cm^–1 ((N₃)).     

Low temperature scanning force microscopy of the Si(111)-(7x7) surface

A low temperature scanning force microscope (SFM) operating in a dynamic mode in ultrahigh vacuum was used to study the Si(111)- (7x7) surface at 7.2 K. Not only the twelve adatoms but also the six rest atoms of the unit cell are clearly resolved for the first time with SFM. In addition, the first measurements of the short range chemical bonding forces above specific atomic sites are presented. The data are in good agreement with first principles computations and indicate that the nearest atoms in the tip and sample relax significantly when the tip is within a few A of the surface.