s-Stable Laws in Insurance and Finance and Generalization to Nilpotent Lie Groups

s-stable laws on Hilbert spaces, associated with some nonlinear transformations, were introduced by Jurek.^{(16, 18)} Here, we interpret certain s-stable motions as limits of total amount of claims processes (up to a deterministic reserve) of a portfolio of (nontraded) excess-of-loss reinsurance contracts and show that they lead to Erlang's model. We also give explicit formulas for the price of perpetual American options in case the logarithm of the price of the underlying asset is an s-stable motion. Furthermore, we generalize the concept of s-stability to simply connected nilpotent Lie groups. For step 2-nilpotent Lie groups we characterize the Lévy measure and the s-domain of attraction of nongaussian s-stable convolution semigroups.     

Phosphate diester hydrolysis by mono- and dinuclear lanthanum complexes with an unusual third-order dependence

A series of mono- and dinuclear lanthanum complexes of 15,31-dimethyl-3,11,19,27,33,35-hexaazapentacyclo[27.3.1.1.(5,9)1,(13,17). 1(21,25)]hexatriaconta-5,7,9(33),13,15,17(34),21,23,25(35),29,31, 1(36)-dodecaene-34,36-diol (24RBPyBC, L) have been defined in solution. Their ability to hydrolyze bis(4-nitrophenyl) phosphate, a phosphate diester, was studied. The various metal-coordinated hydroxide nucleophiles that form in solution attack the substrate in the hydrolysis reaction. The dihydroxo dilanthanum complex, L-2La-2(OH), is the most effective catalyst. Its rate constant is 75 times larger than the rate constant for the monohydroxo dilanthanum complex, L-2La-OH. The mononuclear complexes are not as successful as the dinuclear complexes because they have fewer metal ions per complex to act as Lewis acids. They also cannot generate hydroxide nucleophiles at low pH values like the dinuclear complexes can. The reaction has an unusual third-order dependence on the catalyst concentration which is valid for the dinuclear complexes as well as the mononuclear complexes. This implies a mechanism where a metal-coordinated hydroxide nucleophile attacks the phosphorus of the substrate on the side opposite the negatively charged oxygens.     

Preliminary calculations confirming that anomalous muonium in diamond and silicon is bond-centered interstitial muonium

The model of anomalous muonium as bond-centered interstitial muonium has been examined by approximate ab-initio Hartree-Fock calculations in diamond and silicon and found to be in excellent agreement with experiment.     

First-principles calculations of pseudolocal vibrational modes: the case of Cu and Cu pairs in Si

Pseudolocal vibrational modes (pLVMs) are defect-related vibrational modes which are localized despite being below the phonon maximum. Such modes are sometimes seen as phonon replicas in photoluminescence spectra. The pLVMs associated with two copper-related defects are calculated from first-principles density-functional theory in periodic supercells. The localization of the pLVMs is quantified using the magnitude of the eigenvectors of the dynamical matrix.     

A differential method for calculation of aspherical surfaces using polynomial approximation

A simple method is described for the correction of the spherical aberration using one aspherical surface represented by a polynomial approximation. The same principle is useful for the design of aplanatic systems containing two aspherical surfaces.Finally, the author wishes to convey his thanks to Mr. J. Vondich (Institute of Physics, Czechoslovak Academy of Sciences) for performing the calculations.     

Grazing-incidence aplanatic mirror systems

In this paper the author adapts his own as well as other authors' results concerning aplanatic mirror systems to the condition of grazing-incidence, systematically taking account of extraparaxial constants.