This paper studies the global well-posedness of the initial-value problem for the 2D Boussinesq-Navier-Stokes equations with dissipation given by an operator L that can be defined through both an integral kernel and a Fourier multiplier. When the symbol of L is represented by |ξ| a(|ξ|) with a satisfying lim|ξ|→∞ a(|ξ|) |ξ|σ = 0 for any σ > 0, we obtain the global well-posedness. A special cons...

where ξ is the central hyperplane in R perpendicular to ξ, and |B 2 | is the volume of the unit Euclidean ball in R. This inequality is sharp, and it generalizes the hyperplane inequality in dimensions up to four to the setting of arbitrary measures in place of volume. In order to prove this inequality, we first establish stability in the affirmative case of the Busemann-Petty problem for arbit...

we classify the paracontact riemannian manifolds that their rieman-nian curvature satisfies in the certain condition and we show that thisclassification is hold for the special cases semi-symmetric and locally sym-metric spaces. finally we study paracontact riemannian manifolds satis-fying r(x, ξ).s = 0, where s is the ricci tensor.

It is proved that a Riemannian manifold M isometrically immersed in a Sasakian space form˜M(c) of constant ϕ-sectional curvature c < 1, with the structure vector field ξ tangent to M, satisfies Chen's basic equality if and only if it is a 3-dimensional minimal invariant submanifold. 1. Introduction. Let˜M be an m-dimensional almost contact manifold endowed with an almost contact structure (ϕ,ξ,...

We study the decomposition of the Riemannian curvature R tensor of an almost quaternion-Hermitian manifold under the action of its structure group Sp(n)Sp(1). Using the minimal connection, we show that most components are determined by the intrinsic torsion ξ and its covariant derivative ∇̃ξ and determine relations between the decompositions of ξ ⊗ ξ, ∇̃ξ and R. We pay particular attention to the...

This text is devoted to simultaneous approximation to ξ and ξ by rational numbers with the same denominator, where ξ is an irrational non-quadratic real number. We focus on an exponent β0(ξ) that measures the regularity of the sequence of all exceptionally precise such approximants. We prove that β0(ξ) takes the same set of values as a combinatorial quantity that measures the abundance of palin...

Abstract. The complex zeros of the Riemannn zeta-function are identical to the zeros of the Riemann xi-function, ξ(s). Thus, if the Riemann Hypothesis is true for the zetafunction, it is true for ξ(s). Since ξ(s) is entire, the zeros of ξ(s), its derivative, would then also satisfy a Riemann Hypothesis. We investigate the pair correlation function of the zeros of ξ(s) under the assumption that ...

Dzhaparidze and van Zanten (2004, 2004b) proved an explicit series expansion of the multi-parameter fractional Brownian sheet. We extend their results to a certain class of isotropic Gaussian random fields with homogeneous increments, In particular, this class contains the multi-parameter fractional Brownian motion. Let ξ(x) be a centred mean-square continuous Gaussian random field with homogen...

This text is devoted to simultaneous approximation to ξ and ξ by rational numbers with the same denominator, where ξ is a non-quadratic real number. We focus on an exponent β0(ξ) that measures the quality of such approximations (when they are exceptionally good). We prove that β0(ξ) takes the same set of values as a combinatorial quantity that measures the abundance of palindrome prefixes in an...

This paper continues our earlier investigations into the inversion of random functions in a general (abstract) setting. In Section 2 we investigate a concept of invertibility and the invertibility of the composition of random functions. In Section 3 we resolve some questions concerning the number of samples required to ensure the accuracy of parametric maximum likelihood estimation (MLE). A dir...