We point out a certain class of functions f and g for which random variables f(X1,...,Xm) and g(Xm+1,...,Xk) are non-negatively correlated for any symmetric jointly stable random variables Xi. We also show another result ...

Let Sk be the k-th partial sum of Banach space valued independent identically distributed random variables. In this paper, we compare the tail distribution of ∥Sk∥ with that of ∥Sj∥, and deduce some tail distribution maximal ...

The purpose of this article is to summerize some recent results of the author about Orlicz-Lorentz spaces - function spaces that provide a common generalization of Orlicz spaces and Lorentz spaces.

We study evolutionary semigroups generated by a strongly continuous semi-cocycle over a locally compact metric space acting on Banach fibers. This setting simultaneously covers evolutionary semigroups arising from ...

Laplace transform is used to solve the problem of heat conduction over a finite slab. The temperature and heat flux on the two surfaces of a slab are related by the transfer functions. These relationships can be used to ...

This paper considers how to measure the magnitude of the sum of independent random variables in several ways. We give a formula for the tail distribution for sequences that satisfy the so called Lévy property. We then give ...

Let (fn) be a mean zero vector valued martingale sequence. Then there exist vector valued functions (dn) from [0,1]n such that ∫01 dn(x1,...,xn) dxn = 0 for almost all x1,...,xn-1, and such that the law of (fn) is the same ...

In this paper, we extend the basic transference theorem for convolution operators on Lp spaces of Coifman and Weiss to H1 spaces.

We discuss some conjectural inequalities concerning a problem from the calculus of variations, namely that rank 1 convex functions are quasi-convex. An affirmative answer would also give the best constants for the ...

Let G be a locally compact abelian group whose dual group Γ contains a Haar measurable order P. Using the order P we define the conjugate function operator on Lp(G), 1 ≤ p < ∞, as was done by Helson. We will show how to ...

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 develop a spatial modeling framework for count data that is efficient to implement in high-dimensional prediction problems. We consider spectral parameterizations for the spatially varying mean of the Poisson model. The ...

Accomodation of important sources of uncertainty in ecological models is essential to realistically predicting ecological processes. The purpose of this project is to develop a robust methodology for modeling natural ...

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 ...

We show that the canonical embedding C(K) to LΦ(μ) has Gaussian cotype p, where μ is a Radon probability measure on K, and Φ is an Orlicz function equivalent to tp(log t)p/2 for large t.

This paper provides a new approach to proving generalizations of the F.&M. Riesz Theorem, for example, the result of Helson and Lowdenslager, the result of Forelli (and de Leeuw and Glicksberg), and more recent results of ...

Hardy martingales were introduced by Garling and used to study analytic functions on the N-dimensional torus TN, where analyticity is defined using a lexicographic order on the dual group ZN. We show how, by using basic ...