Rheological and physical properties of aliphatic hyperbranched polyesters

The effects of the size (pseudo‐generation number) and nature of end groups on physical and rheological properties were investigated for a series of hyperbranched polyesters based on an ethoxylated pentaerythritol core and 2,2‐bis‐(hydroxymethyl)propionic acid repeat units. The observed linear dependence of the melt viscosity on the molar mass in the high pseudo‐generation‐number limit indicated that entanglement effects were substantially absent. Moreover, the marked influence of end capping of the end groups on the physical and rheological properties suggested that intermolecular interactions were dominated by contacts between the outer shells of the molecules, in which the end groups were assumed to be concentrated. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1218–1225, 2004     

On the Representation of Band-Dominant Functions on the Sphere Using Finitely Many Bits

A band-dominant function on the Euclidean sphere embedded in R ^q+1 is the restriction to this sphere of an entire function of q+1 complex variables having a finite exponential type in each of its variables. We develop a method to represent such a function using finitely many bits, using the values of the function at scattered sites on the sphere. The number of bits required in our representation is asymptotically the same as the metric entropy of the class of such functions with respect to any of the L ^p norms on the sphere.     

Studies on Rare-Earth/Iron and Actinide/Iron Multilayers

Hyperfine Interactions - Multilayers of Ce/Fe and U/Fe were fabricated by sputtering and studied by X-ray diffraction and reflectivity, Mössbauer spectroscopy and polarised neutron...     

Rank-one completions of partial matrices and completely rank-nonincreasing linear functionals

We obtain necessary and sufficient conditions for the existence and the uniqueness of rank-one completions of a partial matrix, and we verify a conjecture of Hadwin and Larson concerning the nature of completely rank-nonincreasing linear functionals defined on pattern subspaces.

     

Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting

In this paper we discuss Sobolev bounds on functions that vanish at scattered points in a bounded, Lipschitz domain that satisfies a uniform interior cone condition. The Sobolev spaces involved may have fractional as well as integer order. We then apply these results to obtain estimates for continuous and discrete least squares surface fits via radial basis functions (RBFs). These estimates include situations in which the target function does not belong to the native space of the RBF.

     

Contour lines of the optical functions for solids

The well-known equations for the optical functions of reflectance, transmittance and phase changes on reflection and transmission for a solid material have been rearranged into the form of simple geometric figures in the u, v (n, k) plane. The curves for F_p show a singularity on the n-axis.     

Rapid multielemental analysis of Chinese reference soils by laser ablation inductively coupled plasma-source mass spectrometry

Summary Laser ablation inductively coupled plasma-source mass spectrometry has been used to determine thirty elements (Na, Mg, Al, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, As, Rb, Sb, Cs, Ba, La, Ce, Nd, Sm, Eu, Dy, Ho, Yb, Hf, Ta, W, Th, U) in seven Chinese reference soils. The Surrey prototype spectrometer was employed with sample ablation by a free-running ruby laser. Concentrations in the soils (GSS-2 to GSS-8) were calculated from elemental responses and sensitivities derived from another soil in the series, namely GSS-1. Comparisons with previous neutron activation analyses are made. Rapid semiquantitative analyses are proved feasible. About eighty percent of the LA-ICP-MS determined concentrations were within a factor of two of the concentrations measured by INAA, and many were considerably closer than this. Precisions were typically in the range 2–10% RSD, but some were considerably poorer for elements present at trace levels.     

OR turnaround: looking at problem areas

This is the fourth in a series on management strategies for "turning around an OR." The first three articles appeared in the January, April, and June issues of OR Manager.