Biaxial monogenic functions from Funk‐Hecke's formula combined with Fueter's theorem

Funk‐Hecke's formula allows a passage from plane waves to radially invariant functions. It may be adapted to transform axial monogenics into biaxial monogenics that are monogenic functions invariant under the product group SO(p)× SO(q). Fueter's theorem transforms holomorphic functions in the plane into axial monogenics, so that by combining both results, we obtain a method to construct biaxial monogenics from holomorphic functions.     

Thermo-elastic properties of heterogeneous materials with imperfect interfaces: Generalized Levin's formula and Hill's connections

We study the thermo-elastic properties of heterogeneous materials containing spherical particles or cylindrical fibres. The interface between the matrix and second-phase inhomogeneity is imperfect with either the displacement or the stress experiencing a jump across it. We relate the effective coefficient of thermal expansion (CTE) to the effective elastic moduli and thereby generalize Levin's formula, and reveal two connections among the effective elastic moduli, thereby generalizing Hill's connections. In contrast to the classical results, the effective CTE in the presence of an imperfect interface is strongly dependent on the size of the inhomogeneity, besides the interface elastic and thermo-elastic properties. This size dependence has been accurately captured by simple scaling laws.     

Integration by Parts Formula and Applications for SDEs Driven by Fractional Brownian Motions

By using coupling by change of measures, the Driver-type integration by parts formula is established for a class of stochastic differential equations driven by fractional Brownian motions. As applications, (log) shift Harnack inequalities and estimates on the distribution density of the solutions are presented.     

An integral formula for the total mean curvature matrix

The notion of total mean curvature matrix of a submanifold in ${\mathbb{R}}^n$ is defined. A kinematic integral formula for the total mean curvature matrix is proved.     

Asymptotic properties of neutral stochastic differential delay equations

This paper discusses asymptotic properties, especially asymptotic stability of neutral stochastic differential delay equations. New techniques are developed to cope with the neutral delay case, and the results of this paper are more general than the author's earlier work within the delay equations     

Dimethyltin Dichloride-Dibenzyl Sulfoxide, a Compound Crystallizing with Seven Molecules in the Asymmetric Unit

Dimethyltin dichloride-dibenzyl sulfoxide,((CH3)2SnCl2·O=S(CH2C6H5)2),crystallizes in the orthorhombic space group P212121 with a superstructure of dimensions a = 11.9290(1),b = 19.50490(1),c = 55.7390(6) ; Z = 28. The geometry of the five-coordinated tin atom in each of the seven independent adduct molecules is a square pyramid that is displaced towards a cis-trigonal bipyramid; the extent of displacement along the Berry pseudorotation pathway ranges from 20 to 45%.