Examining the balance between efficiency and resilience in closed-loop supply chains

Central European Journal of Operations Research - We study a hybrid system where the demand of customers can be satisfied by both manufacturing new products and remanufacturing used products. To...     

Random rotations of the Wiener path

Summary Let (W, H, ) be an abstract Wiener space and letR(w) be a strongly measurable random variable with values in the set of isometries onH. Suppose that Rh is smooth in the Sobolev sense and that it is a quasi-nilpotent operator onH for everyhH. It is shown that (R(w)h) is again a Gaussian (0, |h| _H ² )-random variable. Consequently, if (e _i ,i)W ^* is a complete, orthonormal basis ofH, then defines a measure preserving transformation, a rotation, onW. It is also shown that if for some strongly measurable, operator valued (onH) random variableR, (R(w+k)h) is (0, |h| _H ² )-Gaussian for allk, hH, thenR is an isometry and Rh is quasi-nilpotent for allHH. The relation between the stochastic calculi for these Wiener pathsw and , as well as the conditions of the inverbibility of the map are discussed and the problem of the absolute continuity of the image of the Wiener measure under Euclidean motion on the Wiener space (i.e. composed with a shift) is studied.The research of the second author was supported by the Fund for the Promotion of Research at the TechnionDedicated to the memory of Albert Badrikian     

Spectrophotometric determination of zinc in copper-base alloys with TAN

TAN reacts with zinc(II) forming a red complex with composition 1:2 Zn(II)-TAN and absorption maximum at 582 nm. Zinc can be determined with this reagent in the presence of Triton X-100, in the pH range 6.20-8.00 with a molar absorptivity of 4.5×10⁴ l/mol/cm Beer's Law was obeyed up to least 1.55 g/ml. Copper interference was eliminated with a mixture of thiosulfate and ascorbic acid and nickel separated by precipitation with dimethylglyoxime. The proposed method was used for zinc determination in several copper-base alloys and the results of analysis in comparison with certified values indicated that the procedure was accurate and precise. A derivative procedure is also proposed, allowing zinc determination with high sensitivity (5-400 ng/ml).     

Temperature dependence of the Mössbauer spectra of amorphous and nanocrystallized Fe86Zr7Cu1B6

Mössbauer measurements have been performed on amorphous and nanocrystalline alloy ribbons of nominal composition Fe₈₆Zr₇Cu₁B₆. The nanocrystalline samples were obtained by annealing the as-quenched alloy at different temperatures in the range between 650 and 870 K. Mössbauer spectra of the as-quenched amorphous sample have been recorded at 77 K, room temperature and above the Curie temperature (330 K) at 360 K. We have also performed Mössbauer measurements at room temperature in the nanocrystalline alloys to characterize the phases that appear after the annealing and their relative concentration. The as-quenched sample spectra reveal the existence of two inequivalent sites for Fe. Such a feature is also observed in the remaining amorphous phase of the annealed samples. In the first steps of crystallization, -Fe precipitates and its concentration increases with the annealing temperature. The experimental results suggest that the composition of the whole amorphous phase does not suffer large changes during crystallization.