We prove a quantitative version of Hilbert's irreducibility theorem for function fields: If $f(T_1,\ldots, T_n,X)$ is an irreducible polynomial over the field rational functions finite $\mathbb{F}_q$ characteristic $p$, then proportion $n$-tuples $(t_1,\ldots, t_n)$ monic polynomials degree $d$ which $f(t_1,\ldots, t_n,X)$ reducible out all $O(dq^{-d/2})$.

In the present study, a modified Structure Function was introduced. In this modified Structure Function model, the coefficient of model was computed dynamically base on the coherent structure in the flow field. The ability of this Modified Structure Function was investigated for complex flow over a square cylinder in free stream and a low aspect ratio cylinder confined in a channel. The Results...

We prove long time diffusive behavior (homogenization) for convec-tion-diffusion in a turbulent flow that it incompressible and has a stationary and square integrable stream matrix. Simple shear flow examples show that this result is sharp for flows that have stationary stream matrices. Contents 1 Introduction 279 2 Outline of the paper 286 3 Abstract framework 288 4 Variational principles 294 ...

This paper considers the problem of reconstructing raw signals from random projections in the context of time-of-flight imaging with an array of sensors. It presents a new signal model, coined as multi-channel pulse-stream model, which exploits pulse-stream models and accounts for additional structure induced by inter-sensor dependencies. We propose a sampling theorem and a reconstruction algor...

denote the open ball of radius a centred on the origin in IR. If the function ~g : Ba → IR d obeys there is a constant G < 1 such that ‖~g(~x)− ~g(~y)‖ ≤ G ‖~x− ~y‖ for all ~x, ~y ∈ Ba (H1) ‖~g(~0)‖ < (1−G)a (H2) then the equation ~x = ~g(~x) has exactly one solution. Discussion of hypothesis (H1): Hypothesis (H1) is responsible for the word “Contraction” in the name of the theorem. Because G <...