We prove a sharp pointwise estimate of the nonincreasing rearrangement of the fractional maximal function of f, M f, by an expression involving the nonincreasing rearrangement of f. This estimate is used to obtain necessary and suucient conditions for the boundedness of M between classical Lorentz spaces.

A new algorithm is introduced to estimate the number of distinct flows (or connections) in a data stream. The algorithm maintains an accurate estimate of the number of distinct flows over a sliding window. It is simple to implement, parallelizes optimally, and has a very good tradeoff between auxiliary memory and accuracy of the estimate: a relative accuracy of order 1/ √ m requires essentially...

We derive a weighted L-estimate of the Witten spinor in a complete Riemannian spin manifold (Mn, g) of non-negative scalar curvature which is asymptotically Schwarzschild. The interior geometry of M enters this estimate only via the lowest eigenvalue of the square of the Dirac operator on a conformal compactification of M .

Let x be a complex random variable with mean zero and bounded variance. Let Nn be the random matrix of size n whose entries are iid copies of x and M be an arbitrary matrix. We give a general estimate for the least singular value of the matrix Mn := M + Nn. In various special cases, our estimate extends or refines previous known results.

We give an estimate of the Gauss curvature for minimal surfaces in R m whose Gauss map omits more than m(m + 1)=2 hyperplanes in P m?1 (C).

Single epoch K-band photometry of 32 RR Lyrae stars in the young galactic globular cluster IC4499 is presented. The mean magnitudes have been estimated using the K-band template light-curves of Jones, Carney and Fulbright (1996). We derive an independent estimate of the distance and reddening for the cluster based on the new 〈MK〉 -log P –[Fe/H] relation from Bono et al.(2003) which has a zero-p...

Given a random sample of size n from an unknown distribution function F on R with finite derivatives and density f we wish to estimate θ = ∫ L(f) = ∫ L(f(x))dx for L a smooth function. Examples are ∫ f2, the differential entropy and the Kulback-Liebler distance. We estimate f by a kernel estimate f̂ based on a kernel of order p say. We show that {f̂(xi), i = 1, · · · , s} satisfy the Cornish-Fish...

The Burgess inequality is the best upper bound we have for the character sum Sχ(M,N) = ∑ M<n≤M+N χ(n). Until recently, no explicit estimates had been given for the inequality. In 2006, Booker gave an explicit estimate for quadratic characters which he used to calculate the class number of a 32-digit discriminant. McGown, used an explicit estimate to show that there are no Norm-Euclidean Galois ...

the major reason for the prediction of thermodynamic properties of mercury lies in the fact that itsintermolecular interactions highly depend on temperature and density. internal pressure is a good criterion toinvestigate the density dependence of the interatomic interactions. because its physical base is a forcetending to close together the molecules that is intermolecular interactions, and as...