Utility functions and the ‘lin’ operation for convex sets

For an ℵ₀-dimensional spaceE of alternatives, there is described a preference relation ≿ such that (in a very strong sense)no information about ≿ can be expressed in terms of finite-dimensional linear transformations ofE. The same construction shows that for each countable ordinalβ, E contains a convex coneK such that lin ^β K =E but lin^β K ≡E forα<β.     

Strain aging in rock salt single crystals

Aging of plastically deformed rock salt single crystals resulted in an increased room temperature yield stress. This effect, which was found to be transient, was investigated as a function of aging time and temperature, prestrain and critical shear stress. The results suggest an interpretation in terms of Cottrell's theory of strain aging, the dislocation obstacles being represented by impurities, vacancies and their agglomerations. An estimation of the possible jump frequencies of the effective lattice defects from aging experiments yielded migration energies between 0.7 and 1.1eV.     

Thed-step conjecture for polyhedra of dimensiond<6

Two functions Δ and Δ _b , of interest in combinatorial geometry and the theory of linear programming, are defined and studied. Δ(d, n) is the maximum diameter of convex polyhedra of dimensiond withn faces of dimensiond−1; similarly, Δ _b (d,n) is the maximum diameter of bounded polyhedra of dimensiond withn faces of dimensiond−1. The diameter of a polyhedronP is the smallest integerl such that any two vertices ofP can be joined by a path ofl or fewer edges ofP. It is shown that the boundedd-step conjecture, i.e. Δ _b (d,2d)=d, is true ford≤5. It is also shown that the generald-step conjecture, i.e. Δ(d, 2d)≤d, of significance in linear programming, is false ford≥4. A number of other specific values and bounds for Δ and Δ _b are presented. This revised version was published online in November 2006 with corrections to the Cover Date.     

Hydrophobic Volume Effects in Albumin Solutions

Density measurements of aqueous albumin solutions as a function of concentration and temperature are reported. The solvents were H(2)O, D(2)O, and a physiological H(2)O-based buffer. An anomaly of the density at very small concentrations of albumin in D(2)O was found. Furthermore, the partial specific volume of albumin is remarkably different in D(2)O and H(2)O. We attribute both effects to structural differences of the solvents. Copyright 2001 Academic Press.     

A classification of the face numbers of Buchsbaum simplicial posets

The family of Buchsbaum simplicial posets generalizes the family of simplicial cell manifolds. The \(h'\) -vector of a simplicial complex or simplicial poset encodes the combinatorial and topological data of its face numbers and the reduced Betti numbers of its geometric realization. Novik and Swartz showed that the \(h'\) -vector of a Buchsbaum simplicial poset satisfies certain simple inequalities; in this paper we show that these necessary conditions are in fact sufficient to characterize the \(h'\) -vectors of Buchsbaum simplicial posets with prescribed Betti numbers.     

Synthesis and Characterization of New Block Copolymers with Poly(ethylene oxide) and Poly[3(S)‐sec‐butylmorpholine‐2,5‐dione] Sequences

Four different types of polydepsipeptide‐polyether block copolymers were synthesized via ring‐opening polymerization of 3(S)‐sec‐butylmorpholine‐2,5‐dione (BMD) in the presence of hydroxytelechelic poly(ethylene oxide) (PEO) with stannous octoate as a catalyst.The polymers were an AB block copolymer, an ABA block copolymer, an (A)₂B star shaped copolymer and an (A)₂B(A)₂ copolymer, where A is a poly[3(S)‐sec‐butylmorpholine‐2,5‐dione] (PBMD) and B a poly(ethylene oxide) block. The molar ratio of BMD to PEO was varied to obtain copolymers with different weight fractions of PBMD blocks ranging from 59.8 to 96.7 wt.‐%. The crystallinity of the PEO phase in the copolymers decreases in the following order: AB > (A)₂B > ABA > (A)₂B(A)₂ . The static contact angle θ decreases with increasing PEO content in the block copolymers.     

Appollonius Revisited: Supporting Spheres for Sundered Systems

When C is a ball in and S is the sphere , we say that S supports a convex body B if S intersects B and either (then S is a far support) or the interior of C is disjoint from B (then S is a near support). The focus here is on common supports for a system of d+1 bodies in such that for each way of selecting a point from each member of , the selected points are affinely independent and hence form the vertex-set of a d-simplex. The main result asserts that if is an arbitrary partition of , then there exists a unique Euclidean sphere that is simultaneously a near support for each member of and a far support for each member of . Received August 2, 1995, and in revised form November 30, 1995.     

The Rotational Spectrum of H2Te

In the present work, we study the spectrum of the H₂Te molecule in the submillimeter-wave and far infrared region. An important aim of this investigation is the further experimental characterization of the anomalous “four-fold cluster effect” exhibited by the rotational energy levels in the vibrational ground state of H₂Te. The spectrum in the region 90–472 GHz was measured with a source-modulated millimeter-wave spectrometer and that between 600 and 1600 GHz with a far-infrared sideband spectrometer. The far infrared spectrum from 30 to 360 cm⁻¹was measured with a Bruker IFS 120 HR interferometer attached to a 3 m long cell. We have assigned 224 submillimeter-wave lines and 1695 FIR lines. These observed data were supplemented by a large number of ground state combination differences derived from rotation–vibration bands of H₂Te, and the resulting large data set was analyzed by means of a modified Watson Hamiltonian. Accurate sets of rotational and centrifugal distortion constants for all eight tellurium isotopomers were obtained.