On convergence analysis of space homeomorphisms

Various theorems on convergence of general spatial homeomorphisms are proved and, on this basis, theorems on convergence and compactness for classes of the so-called ring Q-homeomorphisms are obtained. In particular, it is established that a family of all ring Q-homeomorphisms f in ? ⁿ fixing two points is compact provided that the function Q is of finite mean oscillation. The corresponding applications have been given to mappings in the Sobolev classes W _loc ^1,p for the case p > n ? 1.     

Equicontinuity of homeomorphisms with unbounded characteristic

The article is devoted to the study of the boundary properties of homeomorphisms f: D → D′, D,D′ ? ? ⁿ , satisfying some geometric conditions responsible for the control of the measure of distortion of families of curves in D. Under additional requirements on the boundaries ?D and ?D′ of the domains, we prove that the family of all such homeomorphisms is equicontinuous in $\bar D$ .     

Biocompatibility of the Ti<Subscript>81</Subscript>Nb<Subscript>13</Subscript>Ta<Subscript>3</Subscript>Zr<Subscript>3</Subscript> Alloy

Titanium-based alloy with low-toxic metals such as niobium, tantalum and zirconium (TiNbTaZr) was manufactured. The primary weight percentages of elements used for fusion were: titanium, 65%; niobium, 20%, tantalum, 10%; and zirconium, 5%. The TiNbTaZr alloy had a yield strength of about 550 MPa, a tensile strength of about 700 MPa, and a Young’s modulus of about 50 GPa, that is, it was comparable with Nitinol. A primary study of the biocompatibility of the TiNbTaZr alloy using the SH-SY5Y cells showed that the alloy did not have significant short-term toxicicity towards the cells incubated on the alloy surface. The number of non-viable cells was 2.5 times lower on the TiNbTaZr alloy than on Nitinol. The biocompatibility of TiNbTaZr was more pronounced than that of the Nitinol reference sample.     

Influence of intrinsic defects on light-induced changes in the refractive index of lithium niobate crystals

3 crystals at continuous-wave illumination are reported. The investigation clearly indicates an increase in the photorefraction amplitude Δn_s (at saturation) with light intensity J for all crystals studied. The main result is a correlation between ∂(Δn_s)/∂J and the density N of intrinsic defects such as Nb_Li. This effect is independent of the accidental iron contamination. Therefore at low J, Δn_s decreases with an increase in N, whereas at high J the opposite dependence is observed. The threshold intensity value of such a transformation correlates with the optical quality of the crystal. It has been established that these photorefraction changes are connected with the light induced absorption of the secondary centers, caused by the existence of the metastable small polarons at room temperature during illumination. Received: 7 January 1997/Revised version: 7 February 1997     

Regular Nilpotent Elements and Quantum Groups

We suggest new realizations of quantum groups U _q (?) corresponding to complex simple Lie algebras, and of affine quantum groups. These new realizations are labeled by Coxeter elements of the corresponding Weyl group and have the following key feature: The natural counterparts of the subalgebras U(?), where ?⊂? is a maximal nilpotent subalgebra, possess non-singular characters. Received: 29 May 1998 / Accepted: 12 January 1999     

Reduction of Quantum Systems with Arbitrary First Class Constraints and Hecke Algebras

We propose a method for reduction of quantum systems with arbitrary first-class constraints. An appropriate mathematical setting for the problem is the homology of associative algebras. For every such algebra A and subalgebra B with augmentation ɛ there exists a cohomological complex which is a generalization of the BRST one. Its cohomology is an associative graded algebra Hk ^*(A,B) which we call the Hecke algebra of the triple (A,B,ɛ). It acts in the cohomology space H ^*(B,V) for every left A module V. In particular the zeroth graded component $Hk^{0}(A,B)$ acts in the space of B invariants of $V$ and provides the reduction of the quantum system. Received: 15 June 1998 / Accepted: 25 January 1999     

Estimation of Crystal Lattice Deformations with Depth of Proton-Exchanged Optical Waveguides on Lithium Niobate Single Crystal Substrates

Russian Physics Journal - A method for determining the crystal phase and estimating the crystal lattice deformations in HxLi1-xNbO3 proton-exchanged optical waveguides from an analysis of the Raman...     

An analogue of the operator curl for nonabelian gauge groups and scattering theory

We introduce a new perturbation for the operator curl relatedto connections with nonabelian gauge groups over ³. We alsoprove that the perturbed operator is unitarily equivalent tothe operator curl if the corresponding connection is close enoughto the trivial one with respect to a certain topology on thespace of connections.