Causality structure and the Weierstrass theorem

In a recent paper P. M. Prenter has shown that the Weierstrass theorem can be lifted up to a real separable Hilbert space H. In this paper H is equipped with an identity resolving orthoprojector chain. The Weierstrass type result of Prenter, namely, if ? is any continuous function on H, then there exists a finite order approximating polynomic operator on every compact K ? H, is sharpened by the extension: if ? is strictly causal (strictly anticausal) then the polynomic approximation can also be strictly causal (strictly anticausal). Other extensions in the same spirit are developed and the results are interpreted in the setting of Volterra operators on L₂.     

A polynomial energy-gap model for molecular linewidths

A simple phenomenological model for predicting high-temperature linewidths is described. The rotationally inelastic relaxation time is calculated by using a polynomial inverse-energy-gap model. From this time, the linewidths may be calculated and ambient pressure linewidths may then be used to determine the polynomial coefficients and predict high-temperature linewidths. A detailed comparison with known nitrogen linewidths is given. The relaxation rates obtainable from the model may also be used to calculate pressure-narrowing effects for vibrational Q branches.     

Molecular interactions in polystyrene cosolvent systems

Studied here are miscible binary cosolvents for polystyrene, for which polystyrene is insoluble in either of the individual solvents. Polymer-solvent interactions in solutions of atactic polystyrene in acetone/diethyl ether and in methylcyclopentane (MCP)/acetone binary cosolvents have been investigated using nuclear magnetic resonance (NMR) spectroscopy. Polystyrene ¹³C chemical shifts were measured as a function of miscible binary solvent compositions and temperature. The NMR data were used to calculate “association constants” as a measure of specific interactions of the solvent components with all sites on the polymer. In mixtures of acetone and diethyl ether, ¹³C-NMR indicates a weak interaction between the polystyrene phenyl ring and the diethylether solvent component. In the polystyrene/MCP/acetone system, present NMR data reveal no preferential interactions. Additional NMR measurements were performed on polystyrene in mixtures of CCl₄/acetone. From these results, it is concluded that although preferential polymer-solvent interactions are present in some cosolvent systems, they are not a prerequisite for such behavior.     

Uniaxial drawing of poly(ethyleneoxide)/poly(methyl methacrylate) blends by solid-state extrusion

Ultradrawn ribbons of solution-cast blends of poly(ethylene oxide) (PEO)/poly(methyl methacrylate) (PMMA) have been prepared by a solid-state coextrusion in a capillary rheometer. An increase of noncrystallizable PMMA in the blends drastically decreased the drawability from a draw ratio of 36 for pure PEO to 5 for a mixture of PEO/PMMA 40/60% by weight. A low crystallinity and depression of melting temperature for PEO were observed with increasing draw. The Flory-Huggins theory for melting temperature depression has been used to derive the binary interaction parameter for these blends.     

Tolanes derivatives

The phase behavior for each of two linear thermotropic liquid crystalline polyesters with a corresponding low molecular weight liquid crystal of similar structure have been investigated. Two distinct types of phase diagrams have been obtained for binary mixtures of a polymer, one containing an in-chain azoxybenzene moiety mixed with para-azoxyanisole and one containing a naphthalene unit mixed with a dimethylester liquid crystal. These phase diagrams were studied by DSC, polarized light microscopy and x-ray diffraction. From this understanding of the physical mixtures a transesterification reaction incorporating the bifunctional low molecular weight liquid crystal by a solid-state reaction into the naphthalene-containing polyester was undertaken. This reaction may be viewed as a potential new processing technique for polymers. The thermal stability of an interreacted blend was shown to be superior to that of either individual component by thermogravimetric analysis. Thus, the potential new processing technique features a lower melting, lower viscosity blend followed by the incorporation of the dimethylester liquid crystal into the polyester main chain producing a more rigid, more stable polymer backbone.     

The coupling of bem and fem for the two-dimensional viscous flow problem

In this paper we propose a numerical scheme for treating the problem of sJow viscous flow past an obstacle in the plane. This scheme is a combination of boundary element and finite element methods. By introducing an auxiliary boundary curve, we divide the region under consideration into two subregions, an inner and an outer region. In the inner region, we employ a finite element method (FEM) for solving a system of simplified field equations with proper natural boundary conditions. In the outer region, the solution is expressed in the form of a simple-layer potential with density function satisfying a system of modified integral equations of the first kind. The latter are solved by a boundary element method (BEM). Both solutions are matched on the common auxiliary boundary curve. Error estimates in suitable function spaces are derived in terms of the mesh widths as well as the small parameters, the Reynolds numbers