The group generated by the kinematic dynamo operator in the space of continuous divergence-free sections of the tangent bundle of a smooth manifold is studied. As shown in previous work, if the underlying Eulerian flow is ...

We give a formula for the tail of the distribution of the non-commutative Rademacher series, which generalizes the result that is already available in the commutative case. As a result, we are able to calculate the norm ...

Let X, Y and Z be Banach spaces, and let Πp(Y,Z) (1 ≤ p < ∞) denote the space of p-summing operators from Y to Z. We show that, if X is a £∞-space, then a bounded linear operator T:X⊗εY→Z is 1-summing if and only if a ...

We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper is to discuss the first way, due to ...

We obtain logarithmic improvements for conditions for regularity of the Navier-Stokes equation, similar to those of Prodi-Serrin or Beale-Kato-Majda. Some of the proofs make use of a stochastic approach involving Feynman-Kac ...

Differential equation based advection-diffusion models have been used in atmospheric science to mimic complex processes such as weather and climate. Differential and partial-differential equations (PDE's) have become popular ...

We establish upper bounds for the number of smooth values of the Euler function. In particular, although the Euler function has a certain “smoothing” effect on its integer arguments, our results show that, in fact, most ...

We give upper bounds for the number of solutions to congruences with the Euler function φ(n) and with the Carmichael function λ(n). We also give nontrivial bounds for certain exponential sums involving φ(n). Analogous ...

Notice that 1_2_3_4+1 = 52 , 2_3_4_5+1 = 112 , 3_4_5_6+1 = 192 , . . . . Indeed, it is well known that the product of any four consecutive integers always differs by one from a perfect square. However, a little experimentation ...

It is shown that the Fourier-Whittaker coefficients of Eisenstein series on the n-fold cover of GL(n) are L-functions, improving prior results of T. Suzuki.

We extend to the setting of polynomials over a finite field certain estimates for short Kloosterman sums originally due to Karatsuba. Our estimates are then used to establish some uniformity of distribution results in the ...

We establish upper bounds for multiplicative character sums and exponential sums over sets of integers that are described by various properties of their digits in a fixed base g ≥ 2. Our main tools are the Weil and ...

For an m × n matrix A with nonnegative real entries, Atkinson, Moran and Watterson proved the inequality s(A)3 ≤ mns(AAtA), where At is the transpose of A, and s(·) is the sum of the entries. We extend this result to finite ...

An RSA modulus is a product M = pl of two primes p and l. We show that for almost all RSA moduli M, the number of sparse exponents e (which allow for fast RSA encryption) with the property that gcd(e,φ(M)) = 1 (hence RSA ...

There is increasing interest in predicting ecological processes. Methods to accomplish such predictions must account for uncertainties in observation, sampling, models, and parameters. Statistical methods for spatio-temporal ...

In this paper we present a decoupling inequality that shows that multivariate U-statistics can be studied as sums of (conditionally) independent random variables. This result has important implications in several areas of ...

In a celebrated paper, Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of Hp spaces for 0 < p < ∞. In this paper, we show that their method extends to higher dimensions ...

The authors announce a general tail estimate, called a decoupling inequality, for a symmetrized sum of non-linear k-correlations of n > k independent random variables.

Let φ (n) and λ(n) denote the Euler and Carmichael functions, respectively. In this paper, we investigate the equation φ (n)r = λ(n)s, where r ≥ s ≥ 1 are fixed positive integers. We also study those positive integers n, ...

Boundary value problems are ubiquitous in the atmospheric and ocean sciences. Typical settings include bounded, partially bounded, global and limited area domains, discretized for applications of numerical models of the ...