We consider the subharmonicity property of logarithm Azukawa pseudometrics pseudoconvex domains under variations. prove that such a holds for variation balanced domains. also give non-balanced example. The relation volume indicatrix and estimate in Ohsawa–Takegoshi [Formula: see text]-extension theorem is discussed.

In this study, we first investigate the intersection of two different ruled surfaces in R^3 for tangential spherical indicatrix curves on DS^2 using E. Study mapping. The conditions these are expressed by theorems with bivariate functions. Secondly, considering principal normal DS^2, examine Similarly, indicated Thirdly, mapping, explore binormal DS^2. Likewise, denoted Fourthly, pole study sam...

Single crystals of GdCa4O(BO3)3 were examined to determine their thermal properties. Samples were grown by the Czochralski pulling technique. There were three types of samples: a pure crystal, the crystal doped with neodymium (4 at.% of Nd), and the third one doped with ytterbium (7 at.% of Yb). All samples were rectangular prisms with edges parallel to the axes of the optical indicatrix X, Y ,...

The objective of this article is to build up a general theory of geometrical optics for spinning light rays in an inhomogeneous and anisotropic medium modeled on a Finsler manifold. The prerequisites of local Finsler geometry are reviewed together with the main properties of the Cartan connection used in this work. Then, the principles of Finslerian spinoptics are formulated on the grounds of p...