1 citations · 1 across the 12 of their papers we have counts for
12 papers
The Euler characteristic of a triangulated manifold in terms of even-dimensional faces
Alexey V. Gavrilov
We give a formula for the Euler characteristic of a triangulated manifold of even dimension in terms of the numbers of even-dimensional faces only. The coefficients in this formula…
On the obstruction to extending a vector bundle from a submanifold
Alexey V. Gavrilov
For the first obstruction to extending a holomorphic vector bundle from a submanifold of a complex manifold found by Griffiths we give an explicit formula in terms of the Atiyah cl…
A steady Euler flow with compact support
A. V. Gavrilov
A nontrivial smooth steady incompressible Euler flow in three dimensions with compact support is constructed. Another uncommon property of this solution is the dependence between t…
Status of the Clausius inequality in classical thermodynamics
A. V. Gavrilov
We present an analysis of the foundations of the well known Clausius inequality. It is shown that, strictly speaking, the inequality is not a logical consequence of the Kelvin-Plan…
The Taylor series related to the differential of the exponential map
A. V. Gavrilov
In this paper we study the Taylor series of an operator-valued function related to the differential of the exponential map. For a smooth manifold with a torsion-free…
Is the Clausius inequality a consequence of the second law?
Alexey V. Gavrilov
We present an analysis of the foundations of the well known Clausius inequality. It is shown that, in general, the inequality is not a logical consequence of the Kelvin-Planck form…