Now showing items 1-20 of 62
The annular hull theorems for the kinematic dynamo operator for an ideally conducting fluid
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 ...
The Distribution of Non-Commutative Rademacher Series
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 ...
p-summing operators on injective tensor products of spaces
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 ...
A counterexample to the smoothness of the solution to an equation arising in fluid mechanics
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 ...
Conditions implying regularity of the three dimensional Navier-Stokes equation
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 ...
A Hierarchical Bayesian Non-linear Spatio-temporal Model for the Spread of Invasive Species with Application to the Eurasian Collared-Dove
(Environmental and Ecological Statistics, 2007)
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 ...
Multiplicative Structure of Values of the Euler Function
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 ...
Congruences and Exponential Sums with the Euler Function
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 ...
Squares from products of integers
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 ...
Whittaker-Fourier Coefficients of Metaplectic Eisenstein Series
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.
Short Kloosterman Sums for Polynomials over Finite Fields
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 ...
Character Sums over Integers with Restricted g-ary Digits
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 ...
Matrix inequalities with applications to the theory of iterated kernels
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 ...
On the Number of Sparse RSA Exponents
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 ...
Hierarchical Bayesian Models for Predicting The Spread of Ecological Processes
(Ecological Society of America, 2003)
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 ...
Decoupling inequalities for the tail probabilities of multivariate u-statistics
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 ...
On a weak type (1, 1) inequality for a maximal conjugate function
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 ...
Bounds on the tail probability of u-statistics and quadratic forms
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.
Values of the Euler Function in Various Sequences
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, ...
Hierarchical Bayesian Approach to Boundary Value Problems with Stochastic Boundary Conditions
(American Meteorological Society, 2003)
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 ...