On the direct sum conjecture

We prove the direct sum conjecture for various sets of systems of bilinear forms. Our results depend on a priori knowledge of the complexity of at least one of the direct summands and its underlying algebraic structure. We also briefly survey some previous results concerning the complexity and structure of minimal algorithms for various direct sum systems.     

The maximal eigenvalue of 0–1 matrices with prescribed number of ones

We determine the maximum spectral radius for 0–1 matrices with m² + l ones for l=2m, 2m ? 3 for all m and for a fixed l and m> M(l). Similar results are obtained for symmetric 0–1 matrix with zero diagonal. In all cases, equality is characterized.     

Perturbation of embedded eigenvalues in the generalizedN-body problem

We discuss the perturbation of continuum eigenvalues without analyticity assumptions. Among our results, we show that generally a small perturbation removes these eigenvalues in accordance with Fermi's Golden Rule. Thus, generically (in a Baire category sense), the Schrödinger operator has no embedded non-threshold eigenvalues.Supported in part by NSF Grant DMS 8602826     

Study of the formation of Cs inclusions in refractory bcc metals by133Xe(Cs) Mössbauer resonance

The formation and properties of Cs inclusions in Mo and W are observed through a preimplanted¹³³Xe(Cs) local probe, which is found to reside in three sites: a substitutional site, an interfacial one and a further site which is not detectable directly, but the presence of which can be inferred from the Mössbauer measurements. The location of the probe at the interface of small Cs inclusions is characterized by large Debye temperatures of around 200 K, a quadrupole interaction of +1.86(15) mms^–1, which is close to known surface site values, and an isomer shift of –0.33(12) mms^–1. From the latter value an approximate local pressure of 5 GPa is deduced. In W the site populations are followed as a function of Cs dose. The observed interchange of populations in the low dose range is thought to represent the initial formation of the second phase inclusions.     

Propellanes. Part LXXXII. Preparation and Labelling of [20.3.3]Propellane-24,27-dione

The title diketone has been prepared by a synthetic sequence beginning with decane-1,10-dicarboxylic acid.     

Mixed magnesium and nickel nitrate hexahydrates: an unexpected restructuring

Single crystals of the congruently melting equimolar mixture of magnesium nitrate hexahydrate and nickel nitrate hexahydrate have been grown. The compound crystallizes in a structure foreign to both components, namely in the monoclinic cobalt nitrate hexahydrate structure. The cations are located at random on the cation sub-lattice of the latter crystalline structure.     

An equivariant Novikov conjecture

We discuss and formulate the correct equivariant generalization of the strong Novikov conjecture. This will be the statement that certain G-equivariant higher signatures (living in suitable equivariant K-groups) are invariant under G-maps of manifolds which, nonequivariantly, are homotopy equivalences preserving orientation. We prove this conjecture for manifolds modeled on a complete Riemannian manifold of nonpositive curvature on which G (a compact Lie group) acts by isometries. We also use the theory of harmonic maps to construct (in some cases) G-maps into such model spaces.Dedicated to Alexander GrothendieckPartially supported by NSF Grants DMS 84-00900 and 87-00551.Partially supported by NSF Grant DMS 86-02980, a Presidential Young Investigator Award, and a Sloan Foundation Fellowship.     

Charge separation in ground-state 1,2,4,5-tetra-substituted benzene derivatives

The conditions required for a formal biradical to exist in a zwitterionic form in the ground state are discussed following the recent experimental observation of zwitterionic structure in the ground state of a quinoid molecule (di-tert-butyl derivative of 2,5-diamino-1,4-benzoquinonediimine, I). A unique characteristic of molecules of this class is the fact that they may be considered as being formed by the union of two radicals, each having an odd number of pi electrons. In the case of I, one fragment carries the two amino group having 7 pi electrons; it acts as the electron donor. The other fragment carries the two oxygen atoms (carrying 5 pi electrons) and acts as an electron acceptor. A model that predicts the properties of these systems is presented, based on previous work on non-Kekule hydrocarbons(2,3) and on the electron donating and attracting properties of the donor and acceptor groups, respectively. The zwitterion is formed by an electron transfer leading to two subunits carrying 6 pi electrons each and may become more stable than the triplet biradical even in the gas phase (i.e., in the absence of an external field) if the ionization potential of the donor is small (of the order of 3-4 eV). In some cases solvation in a polar solvent is required to make the zwitterionic form the lowest energy species on the ground-state surface. The 'spacer' between the donor and acceptor groups (which need not be necessarily derived from an aromatic structure) can be varied and influences the overall dipole moment that is calculated in some cases to be quite large (over 20 D in the gas phase).