The recently discovered nonequilibrium turbulence dissipation law implies the existence of axisymmetric turbulent wake regions where the mean flow velocity deficit decays as the inverse of the distance from the wake-generating body and the wake width grows as the square root of that distance. This behavior is different from any documented boundary-free turbulent shear flow to date. Its existenc...

We present a simple constructive proof of the existence of distinguished sum of squares representations for polynomials nonnegative over finite sets described by polynomial equalities and inequalities. A degree bound is directly obtained, as the cardinality of the support of the summands equals the number of points in the variety. Only basic results from commutative algebra are used in the cons...

Let K be a totally real cyclic number field of degree n that is the product of two distinct primes and such that the class number of the n-th cyclotomic field equals 1. We derive certain necessary and sufficient conditions for the existence of a Minkowski unit for K.

We consider a generalized hyperelastic-rod wave equation (or generalized Camassa– Holm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous semigroup of global weak solutions for any initial data from H1(R). We also present a “weak equals strong”uniqueness result.

Haiyang-2 scatterometers (HY-2A/B/C/D) have limitations in high wind speed retrieval due to the complexity of remote sensing mechanism and influence rainfall on radar cross section under conditions tropical cyclones. In this study, we focus evaluation Chinese scatterometer operational products from HY-2B/C/D over period July 2019 December 2021. are collocated with SMAP (Soil Moisture Active Pas...

A careful exposition of Zilber’s quasiminimal excellent classes and their categoricity is given, leading to two new results: the Lω1,ω(Q)definability assumption may be dropped, and each class is determined by its model of dimension א0. Boris Zilber developed quasiminimal excellent classes in [Zil05], in order to prove that his conjectural description of complex exponentiation was categorical. T...

We consider higher-order Camassa–Holm equations describing exponential curves of the manifold of smooth orientation preserving diffeomorphisms of the unit circle in the plane. We establish the existence of a strongly continuous semigroup of global weak solutions. We also present some invariant spaces under the action of that semigroup. Moreover, we prove a “weak equals strong” uniqueness result.