相关论文: Fluid varieties
Algebraic varieties which are locally isomorphic to open subsets of affine space will be called {\em plain}. Plain varieties are smooth and rational. The converse is true for curves and surfaces, and unknown in general. It is shown that…
Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.
A distinguished variety is a variety that exits the bidisk through the distinguished boundary. We show that Ando's inequality for commuting matrix contractions can be sharpened to looking at the maximum modulus on a distinguished variety,…
We review some recent results on the equilibrium shapes of charged liquid drops. We show that the natural variational model is ill-posed and how this can be overcome by either restricting the class of competitors or by adding penalizations…
In this article, we study the invariant differential forms which a correspondence of curves admits. We also try to classify the correspondences of $\mathbb{P}^1$ that admits such invariant differential forms.
For an orbifold, there is a notion of an orbifold embedding, which is more general than the one of sub-orbifolds. We develop several properties of orbifold embeddings. In the case of translation groupoids, we show that such a notion is…
We consider linear systems on toric varieties of any dimension, with invariant base points, giving a characterization of special linear systems. We then make a new conjecture for linear systems on rational surfaces.
The development of microfluidic devices has recently revived the interest in "old" problems associated with transport at, or across, interfaces. As the characteristic sizes are decreased, the use of pressure gradients to transport fluids…
We give a criterion of factoriality of a suspension. This allows to construct many examples of flexible affine factorial varieties. In particular, we find a homogeneous affine factorial 3-fold that is not a homogeneous space of an algebraic…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the…
The physical foundation of the main mathematical concepts in the nonstandard analysis theory of turbulence are presented and discussed. The basic fact is that there does not exist the absolute zero fluid-volume. Therefore, the corresponding…
A correspondence between scalar field fluctuations and generalized fluctuations in a hydrodynamic approximation of fields is obtained. The results presented here are of interest to field-fluid correspondences and form part of theoretical…
We consider impulsive semiflows defined on compact metric spaces and deduce a variational principle. In particular, we generalize the classical notion of topological entropy to our setting of discontinuous semiflows.
This note provides a detailed proof of the fact that a linear vector field on a vector bundle has a flow by vector bundle isomorphisms. It implies then easily the existence of global solutions to linear non-autonomous ODE's, with a standard…
Despite of remarkable successes the theory of superfluidity, until now we have no a physical explanation of an opportunity of existence of viscousless flow of liquid helium in viscous medium. The existence of superfluid flow becomes…
Variational flows allow practitioners to learn complex continuous distributions, but approximating discrete distributions remains a challenge. Current methodologies typically embed the discrete target in a continuous space - usually via…
We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.
We define and study the invariance properties of homological units. Some applications are given to the derived invariance of Hodge numbers. In particular, we prove that if X and Y are derived equivalent smooth projective varieties of…
This paper surveys results found by the authors in the previous papers (see for example, A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for spherical layer flows of a viscid fluid, Journal of Geometry and Physics, 130,…