Alexandre M. Vinogradov

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Indwelling prostheses and subcutaneous delivery devices are now routinely and indispensably employed in medical practice. However, these same devices often provide a highly suitable surface for bacterial adhesion and colonization, resulting in the formation of complex, differentiated, and structured communities known as biofilms. The University of(More)
The solutions of vacuum Einstein's field equations, for the class of Riemannian metrics admitting a non Abelian bidimensional Lie algebra of Killing fields, are explicitly described. They are parametrized either by solutions of a transcendental equation (the tortoise equation), or by solutions of a linear second order differential equation in two(More)
We discuss several aspects of singularities of the solutions of the partial differential equations of Klein–Gordon, Schrödinger and Dirac. In particular we analyze the fold type singularity, of the first and higher orders, and the related characteristic equations. We also consider the field equations as reduction of homogenous equations in higher(More)
If K is a commutative ring and A is a K-algebra, for any sequence σ of positive integers there exists [Vi2] an higher order analogue dR σ of the standard de Rham complex dR ≡ dR (1,...,1,..) , which can also be defined starting from suitable (=differentially closed) subcategories of A − Mod. The main result of this paper is that the cohomology of dR σ does(More)
Some new results on geometry of classical parabolic Monge-Ampere equations (PMA) are presented. PMAs are either integrable, or nonintegrable according to integrability of its characteristic distribution. All integrable PMAs are locally equivalent to the equation u xx = 0. We study nonintegrable PMAs by associating with each of them a 1-dimensional(More)
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