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.     

Sand consolidation with calcium phosphate-polyelectrolyte composites

A new method for the consolidation of loose sand formations has been developed. The method involves in situ precipitation of a composite calcium phosphate-polyelectrolyte salt that binds together with loose sand grains, thus resulting to their consolidation. Three different polyelectrolytes (PE) were tested, i.e., polyacrylic acid (PAA), polyallylamine hydrochloride (PAH), and polyethylenimine (PEI). The effect of PE tested on the thermodynamics and the kinetics of precipitation of calcium phosphate salts was investigated. Three types of experiments were done. Investigation of the adsorption of PE on either hydroxyapatite (Ca(5)(PO(4))(3)OH, HAP) crystals or on sand grains. Measurement of the kinetics of heterogeneous nucleation of HAP on the solid substrates and the mechanical properties of the obtained crystals in batch experiments of low and high supersaturation solutions, respectively. Evaluation of the consolidation in sand packs in order to investigate the effectiveness of the method. The crystallization rates, R(p), on HAP crystals in the presence of the PE tested were found in the order R(p)(PAA)>R(p)(PEI)>R(p)(PAH), while nucleation and crystal growth on silicate sand took place only in the absence of adsorbed PE. PAH favored strongly the consolidation process, whereas PEI and PAA resulted in the formation of poorly consolidated grain agglomerates.     

Beyond the Navier-Stokes equation: Including random thermal fluctuations

Dissipation and fluctuation is analyzed in discretized systems with external and internal heat bath. Discretized and continuum dissipation and fluctuation theorems are derived for both cases. It is shown that the continuum limit of the internal heat bath case leads to the Navier-Stokes equation.