Modeling of L-lactide Polymerization by Reactive Extrusion

The kinetics of L-lactide ring-opening polymerization initiated by stannous octoate and triphenylphosphine was investigated in a batch apparatus (Haake Rheocord Mixer). Based on the experimental data, a kinetic model is developed, considering a coordination-insertion mechanism. Reactive extrusion experiments were further conducted for the same polymerization process, on a co-rotating twin screw extruder. The melted material flow and mixing was described by using the Ludovic® commercial simulator. Based on the developed kinetic model and simulated flow of L-lactide polymerization mixture, a mathematical model of reactive extrusion process is formulated, describing the evolutions of monomer conversion and average molecular weight along the extruder. The model is predicting with a reasonable good accuracy the experimental data.     

Regularized Traces and Taylor Expansions for the Heat Semigroup

The coefficients in asymptotics of regularized traces and associatedtrace (spectral) distributions for Schrödinger operatorswith short and long range potentials are computed. A kernelexpansion for the Schrödinger semigroup is derived, anda connection with non-commutative Taylor formulas is established.     

Defect‐induced ferrimagnetism in the half‐metallic Co2CrAl and Co2CrSi compounds

Co₂CrAl and Co₂CrSi are amongst the most studied Heusler alloys due to their half‐metallic character. These compounds are also well‐known to present ferromagnetism with high Curie temperatures. We show using first‐principles calculations that the creation of Cr antisites (Cr atoms at the Co sites) induces ferrimagnetism in these compounds without destroying the half‐metallic character of these alloys. The reduction of the total spin moment causes lower external fields and thus smaller energy losses in realistic magnetoelectronic, also known as spintronic, devices. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exact inequalities for sums of asymmetric random variables, with applications

Let be independent identically distributed random variables each having the standardized Bernoulli distribution with parameter . Let if and . Let . Let f be such a function that f and f′′ are nondecreasing and convex. Then it is proved that for all nonnegative numbers one has the inequality where . The lower bound on m is exact for each . Moreover, is Schur-concave in . A number of corollaries are obtained, including upper bounds on generalized moments and tail probabilities of (super)martingales with differences of bounded asymmetry, and also upper bounds on the maximal function of such (super)martingales. Applications to generalized self-normalized sums and t-statistics are given.      

A Study of L-Lactide Ring-Opening Polymerization Kinetics

Summary: The paper presents an experimental study of L-lactide polymerization in molten state using as initiator the Stannous Octoate. The experiments were performed in a Haake mixer. The operating temperatures were between 170 and 195°C, the reaction time up to 60 min and monomer to initiator initial molecular ratio between 10² and 5 · 10³. The conversion was determined by using ¹H NMR and the molecular weights distributions by SEC. A preliminary mathematical modeling study was also performed, based on experimental data and a previously published reaction scheme.     

Linearity of Space-Time Transformations¶Without the One-to-One, Line-onto-Line, or Constancy-of-Speed-of-Light Assumptions

Using a version of the fundamental theorem of geometry without the 1-to-1 assumption, recently obtained by the authors, the following is proved: Let n≥ 2 and T be a mapping ofℝ ⁿ onto itself which maps every timelike lineℓ into an arbitrary line so that the image of every future ray ofℓcontains at least two distinct points or the same holds for every past ray ofℓ. Then T is affine. A version of the Pappus theorem under minimal assumptions is also given, which is then used as a tool in this paper. Related results have been obtained by Borchers and Hegerfeldt. Received: 3 May 1999 / Accepted: 7 July 2000     

Heat invariants of Riemannian manifolds

We calculate heat invariants of arbitrary Riemannian manifolds without boundary. Every heat invariant is expressed in terms of powers of the Laplacian and the distance function. Our approach is based on a multidimensional generalization of the Agmon-Kannai method. An application to computation of the Korteweg-de Vries hierarchy is also presented.