Wiener integrals, Malliavin calculus and covariance measure structure

We introduce the notion of covariance measure structure for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of variations and we make Gaussian assumptions only when necessary. Our main examples are finite quadratic variation processes with stationary increments and the bifractional Brownian motion.     

Investigation on the physicochemical properties of La-doped Er0.05Y1.95O3 nanopowders

Journal of Thermal Analysis and Calorimetry - A series of high-purity Er0.05Y1.95O3 nanopowders with different lanthanum content was prepared by modification of the Pechini sol–gel method...     

On Multimode Nonlinear Vibrations of Filled Cylindrical Shells

A technique is proposed to study the multimode nonlinear vibrations of circular shells fully filled with a perfect incompressible liquid. This technique is used to study the basic laws of modal interaction at nonlinear, including sub-harmonic resonances     

Synthesis of ordered and disordered silicas with uniform pores on the border between micropore and mesopore regions using short double-chain surfactants.

Silica molecular sieves with uniform pores on the borderline between micropore (diameter <2 nm) and mesopore (from 2 to 50 nm) ranges were synthesized by a novel method using judiciously chosen mixtures of short double-chain alkylammonium surfactants. These silicas were characterized using X-ray diffraction (XRD), thermogravimetry, and nitrogen and argon adsorption. The calcined materials exhibited either 2-dimensional (2-D) hexagonal or disordered structures with XRD interplanar spacing from 2.51 to 2.93 nm, including the value of as small as 2.69 nm for highly ordered 2-D hexagonal silica. The dependence of the pore size and surfactant content on the surfactant chain length provided strong evidence for supramolecular templating being operative in the formation of small-pore silicas, even for the surfactant chain length of six carbon atoms. Both hexagonally ordered and disordered calcined samples were shown to exhibit narrow pore size distributions with maxima in the range from 1.96 to 2.61 nm (reliably evaluated on the basis of the unit-cell dimension and pore volume for 2-D hexagonal materials, and calculated using a properly calibrated procedure), tailored by the surfactant chain length. The samples exhibited primary pore volumes from 0.28 to 0.54 cm(3) g(-1) and specific surface areas from 730 to 930 m(2) g(-1). Because of their small yet uniform pore size and large specific surface area, the silicas reported herein promise to be useful in applications in adsorption and catalysis. Adsorption studies of these materials provided a unique new insight into the pore-filling mechanism for small-pore materials. Moreover, the approach proposed herein is expected to facilitate the synthesis of not only small-pore silicas but also materials with other framework compositions, thus largely contributing to bridging the gap in attainable pore sizes between micropore and mesopore ranges.     

Photorefractive light scattering in lithium niobate crystals doped with Mg2+, B3+, Y3+, and Ta5+

We have investigated the photorefractive (photoinduced) light scattering in lithium niobate single crystals: LiNbO₃, LiNbO₃:B, LiNbO₃:Y(0.46 mas %), LiNbO₃:Y(0.24):Mg(0.63 mas %), and LiNbO₃:Ta(1.13):Mg(0.0109 mas %) that were grown from congruent melts. We have found that the shape of the speckle structure of this scattering and the kinetics of the development of its indicatrix depend substantially on the type of the impurity dopant in the lithium niobate crystal. We have observed that, upon laser irradiation of crystals doped with Y³⁺, Ta⁵⁺:Mg²⁺, and Y³⁺:Mg²⁺, the shape of their scattering indicatrix changes with time. At the same time, the LiNbO₃:B crystal is characterized by a complete absence of time changes in its speckle structure, which indicates that the photorefractive effect in this crystal is substantially lowered.     

Interaction of a pulsating spherical body and an infinite cylindrical shell in an incompressible liquid

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 31, No. 11, pp. 17–24, November, 1995.