In this Discussion we shall reflect on various aspects of the recently published paper by Elaiw and Ibrahim (2008). Their paper considers the onset of convective instabilities of a mixed convection boundary layer induced by the combined presence of a hot horizontal surface in an unbounded porous medium and an externally-imposed uniform horizontal forced convective flow. These authors also adopt...

Let (xn) ⊂ R d be a uniformly separated sequence which forms a Fourier frame for PWB2 , the space of square-integrable functions on R d whose Fourier transforms vanish outside the Euclidean unit ball B2. Given λ > 0 and f ∈ PWB2 , there is a unique sequence (aj) in l2 such that the function Iλ(f)(x) := X aje −λ‖x−xj‖ 2 2 , x∈R d , is continuous and square integrable on R, and satisfies the inte...

An innovative approach to non-uniform sampling is proposed in this research paper specifically two engineering methods to sampling are proposed. Using results from statistics literature, an “optimal sampling” scheme is discussed. Information theoretic approach to nonuniform sampling formulated.

A novel method for aliasing detection and resolving in the estimation of polynomialphase signal (PPS) parameters is presented. Aliasing is detected using two high-order ambiguity functions (HAFs) of a uniformly sampled PPS embedded in noise. If aliasing occurred, we propose a way of recovering the true parameters from their aliased positions. To that end, a closed-form expression for the true p...

We examine the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples. This sampling scheme, which has been studied previously, has an interesting optimality property that uniform sampling lacks: one can sample and reconstruct the class ( ) of multiband signals with spectral support , at rates arbitrarily close to the Landau minimum rate equal to t...

Karp and Lipton introduced advice-taking Turing machines to capture nonuniform complexity classes. We study this concept for automata-like models and compare it to other nonuniform models studied in connection with formal languages in the literature. Based on this we obtain complete separations of the classes of the Chomsky hierarchy relative to advices.

How iceberg shape affects melting is investigated in a combined experimental and numerical study of ice warm salt water. Experiments show that, contrast to previous models, highly nonuniform---side melt rates can be up 3 times larger than bottom rates, vary significantly within each face. Numerical simulations reveal that vortices accelerate at high flow speeds, double diffusive effects matter ...

Abstract: The exact description of the overall behavior of composites with nonlinear dissipative phases requires an infinity of internal variables. Approximate models involving only a finite number of those can be obtained by considering a decomposition of the microscopic anelastic strain field on a finite set of transformation fields. The Transformation Field Analysis of Dvorak (1992) correspo...

We review mathematical methods for the treatment of a system of Bose particles with nonuniform density. Common pitfalls are pointed out.

We propose a new way to model conditional independence in Markov models. The central feature of our nonuniform Markov model is that it makes predictions of varying lengths using contexts of varying lengths. Experiments on the Wall Street Journal reveal that the nonuniform model performs slightly better than the classic interpolated Markov model of Jelinek and Mercer (1980). This result is somew...