22 research outputs found
Equidistribution of expanding translates of curves and Dirichlet's theorem on Diophantine approximation
We show that for almost all points on any analytic curve on R^{k} which is
not contained in a proper affine subspace, the Dirichlet's theorem on
simultaneous approximation, as well as its dual result for simultaneous
approximation of linear forms, cannot be improved. The result is obtained by
proving asymptotic equidistribution of evolution of a curve on a strongly
unstable leaf under certain partially hyperbolic flow on the space of
unimodular lattices in R^{k+1}. The proof involves ergodic properties of
unipotent flows on homogeneous spaces.Comment: 26 page
Discrete singular integrals in a half-space
We consider Calderon -- Zygmund singular integral in the discrete half-space
, where is entire lattice () in ,
and prove that the discrete singular integral operator is invertible in
) iff such is its continual analogue. The key point for
this consideration takes solvability theory of so-called periodic Riemann
boundary problem, which is constructed by authors.Comment: 9 pages, 1 figur
Relationship between solidification microstructure and hot cracking susceptibility for continuous casting of low-carbon and high-strength low-alloyed steels: A phase-field study
© The Minerals, Metals & Materials Society and ASM International 2013Hot cracking is one of the major defects in continuous casting of steels, frequently limiting the productivity. To understand the factors leading to this defect, microstructure formation is simulated for a low-carbon and two high-strength low-alloyed steels. 2D simulation of the initial stage of solidification is performed in a moving slice of the slab using proprietary multiphase-field software and taking into account all elements which are expected to have a relevant effect on the mechanical properties and structure formation during solidification. To account for the correct thermodynamic and kinetic properties of the multicomponent alloy grades, the simulation software is online coupled to commercial thermodynamic and mobility databases. A moving-frame boundary condition allows traveling through the entire solidification history starting from the slab surface, and tracking the morphology changes during growth of the shell. From the simulation results, significant microstructure differences between the steel grades are quantitatively evaluated and correlated with their hot cracking behavior according to the Rappaz-Drezet-Gremaud (RDG) hot cracking criterion. The possible role of the microalloying elements in hot cracking, in particular of traces of Ti, is analyzed. With the assumption that TiN precipitates trigger coalescence of the primary dendrites, quantitative evaluation of the critical strain rates leads to a full agreement with the observed hot cracking behavior. © 2013 The Minerals, Metals & Materials Society and ASM International
Difference equations and boundary value problems
We study multidimensional difference equations with a continual variable in the Sobolev-Slobodetskii spaces. Using ideas and methods of the theory of boundary value problems for elliptic pseudo-differential equations, we suggest to consider certain boundary value problems for such difference equation
Discreteness, periodicity, holomorphy, and factorization
The main topic of the paper is to establish some relations between the solvability of a special kind of discrete equations in certain canonical domains and holomorphy properties of their Fourier analogue