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In this paper we study the embedding of Riemannian manifolds in low codimension. The well-known result of Nash and Kuiper [21, 20] says that any short embedding in codimension one can be uniformly approximated by C isometric embeddings. This statement clearly cannot be true for C embeddings in general, due to the classical rigidity in the Weyl problem. In… (More)

Discrete spectral analysis and synthesis study the description of translation invariant function spaces over discrete Abelian groups. The basic building bricks are the exponential monomials. A remarkable result of R. J. Elliot in 1965 claimed that spectral synthesis holds on any Abelian group, which means that the exponential monomials span a dense linear… (More)

It is known since the pioneering works of Scheffer and Shnirelman that there are nontrivial distributional solutions to the Euler equations which are compactly supported in space and time. Obviously these solutions do not respect the classical conservation law for the total kinetic energy and they are therefore very irregular. In recent joint works we have… (More)

We prove the weak-strong uniqueness for measure-valued solutions of the incompressible Euler equations. These were introduced by R.DiPerna and A.Majda in their landmark paper [10], where in particular global existence to any L initial data was proven. Whether measure-valued solutions agree with classical solutions if the latter exist has apparently remained… (More)

Exponential polynomials are the building bricks of spectral synthesis. In some cases it happens that exponential polynomials should be extended from subgroups to whole groups. To achieve this aim we prove an extension theorem for exponential polynomials which is based on a classical theorem on the extension of homomorphisms.

The problem of spectral synthesis on arbitrary Abelian groups is solved in the negative. 2003 Elsevier Inc. All rights reserved.

In this note we prove that if K is a compact set of m×n matrices containing an isolated point X with no rank-one connection into the convex hull of K \ {X}, then the rank-one convex hull separates as K = ( K \ {X} )rc ∪ {X}. This is an extension of a result of P. Pedregal, which holds for 2× 2 matrices.

- A Lapat, László Székelyhidi, István Hornyák
- Biomedical chromatography : BMC
- 1997

RDX is one of the most important military explosives. It is a component of some plastic explosives which are frequently used in terrorist attacks. Two fluorimetric methods have been described for the quantitative determination of RDX which are based on the detection of nitrite ions. After a basic decomposition of RDX the nitrite ion can be detected by… (More)

The purpose of this article is to give a survey of recent results on the construction of elliptic equations and systems with critical regularity properties. The constructions are based on the method of convex integration, combined with a careful analysis of oscillations in the spirit of compensated compactness. Our aim is to emphasize the approach which… (More)

Here e2 = (0, 1) T , v is the velocity vector, p is the pressure, θ is a scalar function. The Boussinesq equations arises from many geophysical flows, such as atmospheric fronts and ocean circulations (see, for example, [25],[27]). To understand the turbulence phenomena in fluid mechanics, one needs to go beyond classical solutions. The pair (v, p, θ) on… (More)