Infima and complements in the lattice of quasi-uniformities

We show that the infimum of any family of proximally symmetric quasi-uniformities is proximally symmetric, while the supremum of two proximally symmetric quasi-uniformities need not be proximally symmetric. On the other hand, the supremum of any family of transitive quasi-uniformities is transitive, while there are transitive quasi-uniformities whose infimum with their conjugate quasi-uniformity is not transitive. Moreover we present two examples that show that neither the supremum topology nor the infimum topology of two transitive topologies need be transitive. Finally, we prove that several operations one can perform on and between quasi-uniformities preserve the property of having a complement.     

Shape Optimization for Semi-Linear Elliptic Equations Based on an Embedding Domain Method

We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth domains in ℝ². A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in the case where the principal part of the differential operator is the Laplacian. Online publication 23 January 2004.     

Stable products of spheres in the non-linear coupling of oscillators or quasi-periodic motions

For generic families of vector fields or transformations, normally hyperbolic invariant products of spheres appear near partially elliptic rest points. To cite this article: M. Kammerer-Colin de Verdière, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

General covariance of the non-abelian DBI-action: checks and balances

We perform three tests on our proposal to implement diffeomorphism invariance in the non-abelian D0-brane DBI action as a base-point independence constraint between matrix Riemann normal coordinate systems. First, we show that T-duality along an isometry correctly interchanges the potential and kinetic terms in the action. Second, we show that the method to impose base-point independence using an auxiliary dN²-dimensional nonlinear sigma model also works for metrics which are curved along the brane, provided a physical gauge choice is made at the end. Third, we show that without alteration this method is applicable to higher order in velocities. Testing specifically to order 4, we elucidate the range of validity of the symmetrized trace approximation to the non-abelian DBI action.     

Solutions of the WDVV Equations and Integrable Hierarchies of KP Type

We show that reductions of KP hierarchies related to the loop algebra of SL_n with homogeneous gradation give solutions of the Darboux-Egoroff system of PDE's. Using explicit dressing matrices of the Riemann-Hilbert problem generalized to include a set of commuting additional symmetries, we construct solutions of the Witten– Dijkgraaf–E. Verlinde–H. Verlinde equations.     

Stopping rule for variable selection using stepwise discriminant analysis

Summary In general, when characterizing samples, such as ceramic samples or other types of samples, for first time by means of chemical elements, the analyst measures a large number of variables, many of which may not be very informative. In fact, some may even be unrelated to the issue at hand and blur the picture instead of making it clearer. In subsequent studies the analyst may wish to measure fewer variables for several reasons, such as being very time consuming; in cases where measurement time is important, such as on-line monitoring; in order to reduce cost or effort; etc. Therefore, the hope is to determine those variables that are most relevant without losing essential information and to remove the less productive information. The problem is how to perform this in an objective way and to capture crucial information using a multivariate analysis. This paper aims to describe and illustrate a stopping rule for the identification of redundant variables, and the selection of variable subsets, preserving multivariate data structure using stepwise discriminant analysis, selecting those variables that are in some senses adequate for discrimination purposes. One illustrative example using data sets obtained via INAA of ceramic samples from two archaeological sites is provided.     

Internal standardization for the determination of cadmium,cobalt, chromium and manganese in saline produced water from petroleum industry by inductively coupled plasma optical emission spectrometry after cloud point extraction

In the present paper a procedure is proposed for the determination of traces of Cd, Co, Mn and Cr in petroleum industry produced water by inductively coupled plasma optical emission spectrometry. The procedure is based on cloud point extraction of these metals, as their dithizonate complexes, into the surfactant-rich phase of octylphenoxypolyethoxyethanol surfactant (Triton X-114). Extractions were carried out in solutions with salinities between 10‰ and 70‰. Since residual salinity in the surfactant-rich phase caused differences in its transport to the plasma, yttrium was used as an internal standard to correct for this effect. The simultaneous metal extraction procedure was optimized by response surface methodology using a Doehlert design and desirability function. Enhancement factors of 21, 21, 9 and 19, along with limits of quantification of 0.093, 0.20, 0.73 and 1.2 μg L^− 1, and precision expressed as relative standard deviation (n = 8, 20.0 μg L^− 1) of 5.8, 1.2, 1.7 and 5.7% were obtained for Cd, Co, Mn and Cr, respectively. The accuracy was evaluated by spike recovery tests on the high salinity water samples with salinity of 40 and 63‰.     

Speed of adaptation in structured populations

Adaptation of populations takes place with the occurrence and subsequent fixation of mutations that confer some selective advantage to the individuals which acquire it. For this reason, the study of the process of fixation of advantageous mutations has a long history in the population genetics literature. Particularly, the previous investigations aimed to find out the main evolutionary forces affecting the strength of natural selection in the populations. In the current work, we investigate the dynamics of fixation of beneficial mutations in a subdivided population. The subpopulations (demes) can exchange migrants among their neighbors, in a migration network which is assumed to have either a random graph or a scale-free topology. We have observed that the migration rate drastically affects the dynamics of mutation fixation, despite of the fact that the probability of fixation is invariant on the migration rate, accordingly to Maruyama's conjecture. In addition, we have noticed a topological dependence of the adaptive evolution of the population when clonal interference becomes effective.