Zur Wertverteilung approximativ analytischer Funktionen

Ohne Zusammenfassung     

Parallel information-based complexity

We develop the theory of information-based complexity from a parallel point of view. For a model of computation with p processors, each being capable of arithmetic operations and decisions, we analyze the complexity of function approximation, numerical integration, and solution of Fredholm integral equations. We obtain tight bounds on the complexity, considered as a function of three variables simultaneously: the number of processors, the required precision, and (in the case of approximation and integral equations) the number of points, in which the approximate solution is to be determined.     

Zinkkomplexe eines neuen N,N, O‐Liganden

Zinc Complexes of a New N, N, O Ligand The tridentate ligand N, N(2‐dimethylaminoethyl)‐3, 5‐di‐tert.‐butyl‐salicylaldimine ( L H) results from the corresponding salicylic aldehyde and N, N‐dimethyl ethylenediamine. With zinc salts it forms the mononuclear halide complexes [ L ZnCl ˙ CH₃OH] ( 1 ) and [ L ZnI ˙ CH₃OH] ( 2 ) and the presumably polymeric acetate [ L ZnOCOCH₃] ( 3 ). With diethyl zinc and diphenylphosphoric acid it yields the phosphate complex [ L Zn‐OPO(OPh)₂ ˙ CH₃OH] ( 4 ). The coordination of the complexes, which is between trigonal bipyramidal and square pyramidal, and the character of the five donors in the phosphate complex represent the transition state of a hydrolytic substrate cleavage in a zinc enzyme.     

Method for Simultaneously Improving the Thermal Stability and Mechanical Properties of Poly(lactic acid): Effect of High-Energy Electrons on the Morphological, Mechanical, and Thermal Properties of PLA/MMT Nanocomposites

Nanocomposites derived from poly(lactic acid) (PLA) and organically modified montmorillonite (oMMT) have been cross-linked by high-energy electrons in the presence of triallyl cyanurate (TAC). The morphology of untreated and cross-linked PLA/MMT nanocomposites was characterized by wide-angle X-ray scattering (WAXS) and transmission electron microscopy (TEM). This treatment can improve both the thermal stability and the glass-transition temperatures of the PLA nanocomposites (e.g., PLA-MMT-TAC 30kGy, 50kGy, and 70kGy) because of the formation of cross-linking structures in the nanocomposites that will considerably reduce the mobility of polymers. Interestingly, at relatively low irradiation doses (e.g., 30 and 50 kGy) a good balance between tensile strength and elongation at break for the PLA nanocomposites could be achieved. These mechanical properties are superior to those of pure PLA. Therefore, combining nanotechnology and electron beam cross-linking is a promising new method of simultaneously improving the mechanical properties (toughness and tensile strength) and thermal stability of PLA.     

A Study on Transreactions of PET/PEN Reactive Blending in a Twin‐Screw Extruder Using an Axial Dispersion Model

Transreactions of PET and PEN melt‐mixed in a twin‐screw extruder are investigated. The extruder is modeled and characterized in the frame of a tubular system of closed type. The kinetic modeling is based on a modified second‐order reversible reaction equation, which allows the dispersion equation to be solved analytically. The analysis shows a good agreement between the model and experiment. The axial dispersion model is employed to predict the extent of transesterification reactions (X) and degree of randomness (RD). ¹H NMR measurements are performed to estimate X and RD. Theoretical and experimental data are in good agreement. The model can thus be exploited to describe the effects of processing parameters, mixing time, mixing temperature, and blend composition on X and RD.