Graphic requirements for multistationarity

We discuss properties which must be satisfied by a genetic network in order for it to allow differentiation. These conditions are expressed as follows in mathematical terms. Let $F$ be a differentiable mapping from a finite dimensional real vector space to itself. The signs of the entries of the Jacobian matrix of $F$ at a given point $a$ define an interaction graph, i.e. a finite oriented finite graph $G(a)$ where each edge is equipped with a sign. Ren\'e Thomas conjectured twenty years ago that, if $F$ has at least two non degenerate zeroes, there exists $a$ such that $G(a)$ contains a positive circuit. Different authors proved this in special cases, and we give here a general proof of the conjecture. In particular, we get this way a necessary condition for genetic networks to lead to multistationarity, and therefore to differentiation. We use for our proof the mathematical literature on global univalence, and we show how to derive from it several variants of Thomas' rule, some of which had been anticipated by Kaufman and Thomas

On the arithmetic Chern character

We consider a short sequence of hermitian vector bundles on some arithmetic variety. Assuming that this sequence is exact on the generic fiber we prove that the alternated sum of the arithmetic Chern characters of these bundles is the sum of two terms, namely the secondary Bott Chern character class of the sequence and its Chern character with supports on the finite fibers. Next, we compute these classes in the situation encountered by the second author when proving a "Kodaira vanishing theorem" for arithmetic surfaces

Flight Tests to Determine the Effect of a Fixed Auxiliary Airfoil on the Lift and Drag of a Parasol Monoplane

Comparative flight tests were made with a small parasol monoplane in which the aerodynamic characteristics of the airplane were determined with the normal wing and with an auxiliary airfoil installed

Moments of inertia of several airplanes

This paper, which is the first of a series presenting the results of such measurements, gives the momental ellipsoids of ten army and naval biplanes and one commercial monoplane. The data were obtained by the use of a pendulum method, previously described. The moments of inertia are expressed in coefficient as well as in dimensional form, so that those for airplanes of widely different weights and dimensions can be compared

Land Quality and International Agricultural Productivity: A Distance Function Approach

Agricultural productivity measurement has been of great interest in recent years. Although analysts have long recognized that land quality plays an important role in agricultural productivity, land quality has been difficult to quantify and include in productivity models due to d ata limitations. Poor land quality, in the form of desertification, erosion, and poor soil quality, as well as climate and precipitation may limit growth in productivity over time. A Malmquist productivity index is proposed that decomposes productivity into efficiency change, technical change and land quality components and accounts for inter-country differences in land quality. The index is then applied to a 109-country data set covering 1980 to 2003. Many countries with lower productivity growth are limited by their resource endowment, and thus require policies and technology that reflect the needs of those environments.Land Economics/Use, Productivity Analysis,