A Dominated Theorem on 5L(2, R) and Its Application

In this paper, we give the following dominated theorem: Let φ(g) ∈ L1(G//K),φε(t)=ε> 0, and the least radical decreasing dominatedfunction φ(t) = sup |φ(y)| ∈L1(G//K). If shtφ(t) is monotonically decreasingon (0, ∞), then for any f∈L1loc(G//K) , the following inequality holds:sup |φε * f(x)| ≤ Cmf(x),where mf(x) is the Hardy-Littlewood maximal function of f, and C = ||φ||1.An application of this dominated theorem is also given.     

A geometrical constraint for capillary jet breakup

The formation of thinning filaments is commonly observed previously to the break-up of a very viscous jet. This paper shows that a fluid under capillary forces cannot break-up through the uniform collapse of a filament.     

Attractors for 2D-Navier-Stokes models with delays

The existence of an attractor for a 2D-Navier-Stokes system with delay is proved. The theory of pullback attractors is successfully applied to obtain the results since the abstract functional framework considered turns out to be nonautonomous. However, on some occasions, the attractors may attract not only in the pullback sense but in the forward one as well. Also, this formulation allows to treat, in a unified way, terms containing various classes of delay features (constant, variable, distributed delays, etc.). As a consequence, some results for the autonomous model are deduced as particular cases of our general formulation.     

On the recognition problem of quasi-homogeneous locally nilpotent derivations in dimension three

We give a criterion to decide if a given w-homogeneous derivation on A?k[X₁,X₂,X₃] is locally nilpotent. We deduce an algorithm which decides if a k-subalgebra of A, which is finitely generated by w-homogeneous elements, is the kernel of some locally nilpotent derivation.     

Nonlinear Free Boundary Problems with Singular Source Terms

We prove the existence of solutions to nonlinear free boundary problem with singularities at given points.     

Berezin transform on¶compact Hermitian symmetric spaces

Let X=G ^* be a compact Hermitian symmetric space. We study the Berezin transform on L ²(X) and calculate its spectrum under the decomposition of L ²(X) into the irreducible representations of G ^*. As applications we find the expansion of powers of the canonical polynomial (Bergman reproducing kernel for the canonical line bundle) in terms of the spherical polynomials on X, and we find the irreducible decomposition of tensor products of Bergman spaces on X. Received: 10 September 1996 / Revised version: 10 September 1997     

Spline collocation for strongly elliptic equations on the torus

Summary We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4].     

Reaction of D2 with palladium fulleride C60Pd4.9

Fullerene deuteride was obtained by the reaction of deuterium with solid palladium fulleride C₆₀Pd_4.9 under fairly mild conditions. The compound was identified by FD-MS, UV-Vis and IR spectroscopies, and TLC.Translated from Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 483–484, February, 1996