相关论文: Multiple mixing, 75 years of Rokhlin's problem

Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject had been collected in author's book [Total mean curvature and sub manifolds of finite type, World Scientific, NJ, 1984]. A…

We give a partial account of some problems concerning cohomological invariants and metric properties of complex non-K\"ahler manifolds.

In this paper, we prove multiplicity of solutions for a class of quasilinear problems in $ \mathbb{R}^{N} $ involving variable exponents and nonlinearities of concave-convex type. The main tools used are variational methods, more precisely,…

A new method is proposed to numerically integrate a dynamical system on a manifold such that the trajectory stably remains on the manifold and preserves first integrals of the system. The idea is that given an initial point in the manifold…

We present a simple analysis of k-means|| (Bahmani et al., PVLDB 2012) -- a distributed variant of the k-means++ algorithm (Arthur and Vassilvitskii, SODA 2007). Moreover, the bound on the number of rounds is improved from $O(\log n)$ to…

Lie symmetry method is applied to investigate symmetries of the combined KdV-nKdV equation, that is a new integrable equation by combining the KdV equation and negative order KdV equation. Symmetries which are obtained in this article, are…

Odd index pairings of $K_1$-group elements with Fredholm modules are of relevance in index theory, differential geometry and applications such as to topological insulators. For the concrete setting of operators on a Hilbert space over a…

A new approach to the construction of difference schemes of any order for the many-body problem that preserves all its algebraic integrals is proposed. We introduced additional variables, namely, distances and reciprocal distances between…

T. Coulhon introduced an interesting reformulation of the usual Sobolev inequalities. We characterize Coulhon type inequalities in terms of rearrangement inequalities.

The non-conservation of entanglement, when two or more particles interact, sets it apart from other dynamical quantities like energy and momentum. It does not allow the interpretation of the subtle dynamics of entanglement as a flow of this…

Simple semitoric systems were classified about ten years ago in terms of a collection of invariants, essentially given by a convex polygon with some marked points corresponding to focus-focus singularities. Each marked point is endowed with…

This survey covers some of the results contained in the papers by Costantino, Geer and Patureau (https://arxiv.org/abs/1202.3553) and by Blanchet, Costantino, Geer and Patureau (https://arxiv.org/abs/1404.7289). In the first one the authors…

We investigate the metric and cohomological properties of higher dimensional analogues of Inoue surfaces, that were introduced by Endo and Pajitnov. We provide a solvmanifold structure and show that in the diagonalizable case, they are…

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented…

This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…

We investigate the equivariant and Hopf-cyclic cohomology of module algebras over Hopf algebroids and derive their Morita invariance. For this, we use the tools developed by McCarthy for $k$-linear categories and subsequently by Kaygun and…

The existence and uniqueness of the numerical invariant measure of the backward Euler-Maruyama method for stochastic differential equations with Markovian switching is yielded, and it is revealed that the numerical invariant measure…

It is shows that some aspects of classic KPP-problem (1937) can be extended to some fourth and sixth-order quasilinear parabolic equations.

The problem of combining the evidence concerning an unknown, contained in each of $k$ Bayesian inference bases, is discussed. This can be considered as a generalization of the problem of pooling $k$ priors to determine a consensus prior.…

First ideas of neutrino masses, mixing and oscillations proposed by Bruno Pontecorvo in 1957 and later development of these ideas are considered in some details. Original ideas of the two-neutrino mixing proposed by Maki, Nakagawa and…