Deformation retracts and the Hochschild homology of polynomial rings

We assume given a ringA with unit, and a subcomplex of the reduced bar complex ofA. We assume that this subcomplex is a deformation retract of the whole complex and thus has homology equal to the Hochschild homology ofA, but it will typically be smaller and easier to calculate with. We use these to construct (accordingly small) deformation retracts for the reduced bar complexes ofA[t] andA[t,t ⁻¹]. WhenA is a Banach algebra, we also do this construction forC ^∞(S¹;A). Partially supported by N.S.F. Grant No. DMS 92-03398.     

Passive linear stationary dynamical scattering systems with continuous time

In this paper we consider systems with the separable Hilbert inner, input and output spacesX, $\mathfrak{N}^ - $ , $\mathfrak{N}^ + $ of the form $$\frac{{dx(t)}}{{dt}} = \hat Bx(t) + L\varphi ^ - (t),\varphi ^ + (t) = N(x(t),\varphi ^ - (t)),x(0) = a$$ with some natural restrictions on the coefficients which have been proposed by Yu.L. Shmuljan. For each system the concepts of simple, minimal, passive scattering, conservative scattering, optimal passive scattering ones are introduced. We realize any $[\mathfrak{N}^ - ,\mathfrak{N}^ + ]$ valued function θ(p) which is holomorphic with contractive values in the right half plane as the transfer function (t.f.) of a simple conservative scattering system and also as the t.f. of a minimal optimal passive scattering system. Both these realizations are defined by θ(p) uniquely up to unitary similarity. Reduction of the problem to the corresponding problems for systems with discrete time via Cayley transform is used.     

New Insights into the Chemistry of Lithium Carbamoyls: Characterization of an Adduct (R(2)NC(O)CLi(OLi)NR(2))

Studies of the reaction of lithium dicyclohexylamide with N,N-dibutylformamide, 1-formylpiperidine, and 4-formylmorpholine indicate that the equilibria resulting from these compounds are shifted toward the formation of an adduct, which quickly collapses to dicyclohexylamine and the lithiated carbamoyl anion derived from the initial disubstituted formamide. Further reactions of the lithium carbamoyl lead to a new adduct where a lithiated carbon is bounded to N, O, and a carbonyl functionality. The (13)C NMR analysis of the reaction mixtures showed the presence of similar intermediates in all cases: adducts of this type have not been reported before. These dilithiated intermediates were trapped with methyl iodide giving the corresponding doubly methylated derivatives. Isolation of substituted glyoxylamides and quantitative determination of the products yields constitute further evidence of the whole reaction scheme proposed.     

Mass spectra of o-aminobenzophenones

The electron impact induced fragmentation of chlorine substituted o-aminobenzophenones has been examined. All the compounds show ions formed by α-cleavage on either side of the carbonyl group. The relative intensity of the resulting ions is predictable from the quasi-equilibrium theory. The most important features of the mass spectra of these compounds are, however, intense [M? H]⁺ ions for the primary amines and [M – OH]⁺ ions for the N-methylated compounds. These and other less intense peaks as well as some metastable ions allows structural elucidation.     

Coxeter cochain complexes

We define the Coxeter cochain complex of a Coxeter group (G, S) with coefficients in a ?[G]-module A. This is closely related to the complex of simplicial cochains on the abstract simplicial complex I(S) of the commuting subsets of S. We give some representative computations of Coxeter cohomology and explain the connection between the Coxeter cohomology for groups of type A, the (singular) homology of certain configuration spaces, and the (Tor) homology of certain local Artin rings.     

Hydroxy-1-aminoindans and derivatives: preparation, stability, and reactivity

The chemical stability and reactivity of hydroxy-1-aminoindans and their N-propargyl derivatives are strongly affected by the position of the OH group and its orientation relative to that of the amino moiety. Thus, the 4- and 6-OH regioisomers were found to be stable, while the 5-OH analogues were found to be inherently unstable as the free bases. The latter, having a para orientation between the OH and the amino moieties, could be isolated only as their hydrochloride salts. 7-Hydroxy-1-aminoindans and 7-hydroxy-1-propargylaminoindans represent an intermediate case; while sufficiently stable even as free bases, they exhibit, under certain experimental conditions, unexpected reactivity. The instability of the 5- and 7-hydroxy-aminoindans is attributed to their facile conversion to the corresponding, reactive quinone methide (QM) intermediates. The o-QM obtained from 7-hydroxy-aminoindans was successfully trapped with ethyl vinyl ether via a Diels-Alder reaction to give tricyclic acetals 32a,b.     

The higher connectivity of intersections of real quadrics

A linear system of real quadratic forms defines a real projective variety. The real non-singular locus of this variety (more precisely of the underlying scheme) has a highly connected double cover as long as each non-zero form in the system has sufficiently high Witt index.