The use of vector-valued martingales in risk theory

A completely dependent risk process with perturbation and phase-type distributed claim sizes is analyzed. Claim arrivals are modeled by a Markovian arrival process. Using a vector-valued martingale, the Laplace transform of the time to ruin is derived algorithmically. The conditional memoryless property of the phase-type distribution yields the distribution of the deficit at ruin as a corollary.     

A Facile Route to Metal Nitride Clusterfullerenes by Using Guanidinium Salts: A Selective Organic Solid as the Nitrogen Source

Using guanidinium salts 1 and 2 as the new nitrogen sources, metal nitride clusterfullerenes (NCFs) based on a variety of metals (Dy, Sc, Y, Gd, Lu, and mixed metals Sc/Dy, Sc/Gd, Sc/Lu, and Lu/Ce) have been synthesized based on a new “selective organic solid” (SOS) route. The synthesis of Dy‐NCFs by using Dy/ 1 was studied in detail, and the optimum molar ratio of 1 /Dy/C has been determined to be 2.5:1:10. For several representative metals such as Sc, Y, Gd, Dy, and Sc/Dy, we quantitatively compared the yield of M₃N@C₈₀ synthesized by the SOS route with the reported “reactive gas atmosphere” route, thereby indicating that the yield of M₃N@C₈₀ by using 1 could be comparable to that obtained by the reactive gas atmosphere route. Three other nitrogen sources ( 3 – 5 ) were also studied for comparison, which were mixed with Dy metal but did not result in the formation of Dy‐NCF. A possible reaction scheme for the solid‐state reaction of 1 , metal, and graphite is proposed. The SOS route appears to be a general route for the synthesis of NCFs that promises both high selectivity of NCFs and high reproducibility of the fullerene yield. Another advantages of the SOS route compared to the reported “trimetallic nitride template” (TNT) process and the reactive gas atmosphere route is that no additional heating pretreatment is needed, thus simplifying the procedure and being much more facile.     

Crystallization of niobium germanosilicate glasses

Niobium germanosilicate glasses are potential candidates for the fabrication of transparent glass ceramics with interesting non-linear optical properties. A series of glasses in the (Ge,Si)O₂-Nb₂O₅-K₂O system were prepared by melting and casting and their characteristic temperatures were determined by differential thermal analysis. Progressive replacement of GeO₂ by SiO₂ improved the thermal stability of the glasses. Depending on the composition and the crystallization heat-treatment, different nanocrystalline phases—KNbSi₂O₇, K₃Nb₃Si₂O₁₃ and K_3.8Nb₅Ge₃O_20.4 could be obtained. The identification and characterization of these phases were performed by X-ray diffraction and Raman spectroscopy.The 40 GeO₂-10 SiO₂-25 Nb₂O₅-25 K₂O (mol%) composition presented the higher ability for volume crystallization and its nucleation temperature was determined by the Marotta's method. An activation energy for crystal growth of ∼529 kJ/mol and a nucleation rate of 9.7×10¹⁸ m⁻³ s⁻¹ was obtained, for this composition. Transparent glass ceramics with a crystalline volume fraction of ∼57% were obtained after a 2 h heat-treatment at the nucleation temperature, with crystallite sizes of ∼20 nm as determined by transmission electron microscopy.     

Multiple orthogonal polynomials applied to matrix function evaluation

Multiple orthogonal polynomials generalize standard orthogonal polynomials by requiring orthogonality with respect to several inner products. This paper discusses an application to the approximation of matrix functions and presents quadrature rules that generalize the anti-Gauss rules proposed by Laurie.