Outage Probability for Multi-Cell Processing under Rayleigh Fading

Multi-cell processing, also called Coordinated Multiple Point (CoMP), is a very promising distributed multi-antennas technique that uses neighbour cell's antennas. This is expected to be part of next generation cellular networks standards such as LTE-A. Small cell networks in dense urban environment are mainly limited by interferences and CoMP can strongly take advantage of this fact to improve cell-edge users' throughput. This paper provides an analytical derivation of the capacity outage probability for CoMP experiencing fast Rayleigh fading. Only the average received power (slow varying fading) has to be known, and perfect Channel State Information (CSI) is not required. An optimisation of the successfully received data-rate is then derived with respect to the number of cooperating stations and the outage probability, illustrated by numerical examples

The Effect of Market Structure on Pest Resistance Buildup

In this paper we present a continuous time optimal control analysis of resistance buildup in agricultural chemicals when the supplier is a monopolist. We compare the monopolistic, competitive and socially optimal solutions after establishing the stability of each equilibrium. The central finding is that with a monopolistic supplier, resistance buildup is lower than socially optimal. This directly opposes the standard result in the resistance literature. This implies that policies to manage resistance should vary with the age of the chemical, with no intervention during the lifetime of a patent and an optimal tax once the patent expires.Research Methods/ Statistical Methods,

Determination of the degree of substitution (DS) of mixed cellulose esters by elemental analysis

Equations for transforming the results of elemental analysis (EA) into degree of substitution (DS) values for aliphatic cellulose esters were developed. The equations allow to determine the DS of cellulose derivatives bearing not only one but also two different acyl substituents. Error transmission studies revealed that the accuracy of the DS-values for a pure sample depends on both the number of carbon atoms in the substituents and on the uncertainty of the EA, especially from the hydrogen content. This method provides accurate DS-values (± 0.10 in most cases) if H-content determinations are within ± 0.1

Bi-acylation of cellulose: determining the relative reactivities of the acetyl and fatty-acyl moieties

The global reaction between acetic anhydride and a fatty acid yields, at equilibrium, an asymmetric acetic-aliphatic anhydride in a medium containing finally: acetic-fatty anhydride, acetic anhydride, fatty acid, acetic acid and fatty anhydride. No solvent or catalyst was used to evaluate the impact of the actual reactivity of the anhydrides. The competition between the formation of acetyl and fatty acyl ester functions was evaluated by determining the ratio of acetyl/fatty acyl groups grafted on solid cellulose. The influence of temperature, reaction time, and length of fatty chain on the total degree of substitution and on the ratio of acetyl/fatty acyl ester functions was investigated. For the first time, a correlation has been established between esterification and the length of the aliphatic chain of the fatty acid. Reactivity of the medium decreased with the number of carbons in the fatty acid, raised to the power 2.37

Interactions with water of mixed acetic-fatty cellulose esters

Cellulose powder was acylated with mixtures containing acetic, fatty and acetic-fatty anhydrides to form acetic-fatty cellulose esters. The total degree of substitution (DS) of the mixed cellulose esters (MCE) ranged from 2x10-2 to 2.92. MCE were characterized by their interactions with water. Static contact angles with water were measured on a regular smooth surface. The values found were dependent on the fatty acyl content and independent of the acetyl content. In the case of acetic-oleic cellulose esters, the minimum DS of the oleoyl moiety required to obtain permanent water repellency was 3x10-4. The microporosity of the samples may account for this exceptional hydrophobic character. Nevertheless, water vapor adsorption measurements on powder samples revealed only a limited increase in hydrophobicity of the MCE compared to cellulose acetate with the same acetyl content. It was thus demonstrated that water repellency and vapor water adsorption are not correlated

Backward blow-up estimates and initial trace for a parabolic system of reaction-diffusion

In this article we study the positive solutions of the parabolic semilinear system of competitive type \left\{\begin{array} [c]{c}% u_{t}-\Delta u+v^{p}=0, v_{t}-\Delta v+u^{q}=0, \end{array} \right. in $\Omega\times\left(0,T\right)$, where $\Omega$ is a domain of $\mathbb{R}^{N},$ and $p,q>0,$ $pq\neq1.$ Despite of the lack of comparison principles, we prove local upper estimates in the superlinear case $pq>1$ of the form $$u(x,t)\leqq Ct^{-(p+1)/(pq-1)},\qquad v(x,t)\leqq Ct^{-(q+1)/(pq-1)}$$ in $\omega\times\left(0,T_{1}\right) ,$ for any domain $\omega \subset\subset\Omega$ and $T_{1}\in\left(0,T\right) ,$ and $C=C(N,p,q,T_{1}$ For $p,q>1,$ we prove the existence of an initial trace at time 0, which is a Borel measure on $\Omega.$ Finally we prove that the punctual singularities at time $0$ are removable when $p,q\geqq1+2/N

Local and global properties of solutions of quasilinear Hamilton-Jacobi equations

We study some properties of the solutions of (E) \;-\Gd_p u+|\nabla u|^q=0 in a domain \Gw \sbs \BBR^N, mostly when $p\geq q>p-1$. We give a universal priori estimate of the gradient of the solutions with respect to the distance to the boundary. We give a full classification of the isolated singularities of the positive solutions of (E), a partial classification of isolated singularities of the negative solutions. We prove a general removability result in expressed in terms of some Bessel capacity of the removable set. We extend our estimates to equations on complete non compact manifolds satisfying a lower bound estimate on the Ricci curvature, and derive some Liouville type theorems.Comment: to appear J. Funct. Ana

Large solutions of elliptic systems of second order and applications to the biharmonic equation

In this work we study the nonnegative solutions of the elliptic system \Delta u=|x|^{a}v^{\delta}, \Delta v=|x|^{b}u^{\mu} in the superlinear case \mu \delta>1, which blow up near the boundary of a domain of R^{N}, or at one isolated point. In the radial case we give the precise behavior of the large solutions near the boundary in any dimension N. We also show the existence of infinitely many solutions blowing up at 0. Furthermore, we show that there exists a global positive solution in R^{N}\{0}, large at 0, and we describe its behavior. We apply the results to the sign changing solutions of the biharmonic equation \Delta^2 u=|x|^{b}|u|^{\mu}. Our results are based on a new dynamical approach of the radial system by means of a quadratic system of order 4, combined with nonradial upper estimates