The convexity of the range of three Hermitian forms and of the numerical range of sesquilinear forms

This note contains a demonstration of the convexity of the joint range of three Hermitian forms, and, as an immediate corollary, of the convexity of the numerical range of arbitrary sesquilinear forms.     

A test of a model t-matrix for direct reaction inelastic scattering

Differential cross sections and analyzing powers from the inelastic scattering of 65 MeV protons leading to the 1⁺T=0 (12.71 MeV) and 1⁺T = 1 (15.11 MeV) states in ¹²C have been analysed as tests of a model two-nucleon t-matrix.     

An efficient one—dimensional search procedure for barrier functions

In minimizing interior penalty functions, most of the computational time is spent on the one-dimensional search. This paper presents a method for performing this search on barrier functions which is significantly faster than current techniques. The method exploits the special structure of barrier functions. Comparative computational results are given for a set of six test problems.This research was partially supported by the National Aeronautics and Space Administration under Research Grant NSG 110-61 and by the Office of Naval Research under Grant No. N00014-67-A-0404-0010.     

Water partitioning in "dry" poly(ethylene oxide) alcohol (CmEn) nonionic surfactant--a proton NMR study

A proton NMR titration study is presented where in small increments quantities of water were added to "dry" CmEn nonionic surfactant. For a particular range of compositions, two resonances for the water/hydroxyl protons were observed that display large chemical shift increases as water content is increased indicating that water must partition between two chemical environments with a surprisingly slow chemical exchange rate. A detailed mechanism of how the increasing amounts of water are incorporated into the surfactant medium is presented accounting for all observed spectral changes.     

Synthesis of nanoscale NbSe2 materials from molecular precursors

This communication describes a new synthetic approach to one- (1D) and two-dimensional (2D) NbSe2 nanoscale materials using soft chemical methods. Our one-pot synthesis provides a direct route to control the morphology of nanostructures that can exhibit complex electronic properties, and can produce layered, nanocrystalline materials in high yield.     

Abiotic metallofoldamers as electrochemically responsive molecules

Described are the design, synthesis, and study of nonbiological molecules based on salophen and salen ligands that fold into single-stranded helices in the presence of either Ni(II) or Cu(II). X-ray diffraction studies show that the materials fold into helical structures in the solid state, and a series of NMR studies provide strong evidence that the folded structures are conserved in solution. Metal coordination is required for folding, as NMR and X-ray show that the free ligands do not adopt helical structures. Two of the racemic metallofoldamers spontaneously resolve during crystallization from CHCl3/acetonitrile, and CD spectroscopy and optical rotation show that the resolved, crystalline materials racemize quickly when dissolved at 5 degrees C. This shows that the secondary structures can reorganize easily and can, therefore, provide the basis for responsive materials. By comparison, an analogue from enantiomerically pure (R,R)-(-)-trans-cyclohexanediamine showed a strong CD signal and a large specific rotation. Electrochemical experiments show that a structural reorganization occurs upon metal-centered reduction of a Cu(II)-containing foldamer. When the reduction is carried out in the presence of coordinating ligands, it is proposed that apical binding of those ligands gives square pyramidal complexes. Semiempirical (AM1) calculations support that the helical structure would be disrupted by the reduction to Cu(I) with concomitant reorganization to a square pyramidal complex.