A CONTIN-Based Approach Towards the Data Analysis of Particle Sizing Experiments by Centrifugal Photosedimentometry

In order to analyse the output data of centrifugal photosedimentation experiments using CONTIN software, a mathematical model has been derived. This model is based on Fick's second law and describes the sedimentation behaviour of monomodal particles in a centrifugal field: it predicts that the extinction at the detection point decays exponentially until the particles are sedimented past the detection point, which gives a sharp drop of the curves to the baseline. In practice, however, a more fluently decaying profile was obtained. Simulations revealed that the polydispersity of the sample was responsible for this behaviour. When centrifugal photosedimentation data for effective monomodal and bimodal samples of fairly monodispersed PMMA lattices were analysed with CONTIN, using the model proposed, accurate particle size distributions were obtained, provided that the sample cell was completely filled. This was imperative in order to minimize the deviations of the practical application as compared with the theoretical model.     

Distributions vectorielles homogènes sur une algèbre de Jordan

We study distributions on a Euclidean Jordan algebra V with values in a finite dimensional representation space for the identity component G of the structure group of V and homogeneous equivariance condition. We show that such distributions exist if and only if the representation is spherical, and that then the dimension of the space of these distributions is r+1 (where r is the rank of V). We give also construction of these distributions and of those that are invariant under the semi-simple part of G.     

Statistical mechanics of hard spheres: validity of the basic relations of the scaled particle theory for frozen structures

In a previous article (J. Math. Phys. 36(201),1995), an equation of state for a hard sphere system was derived from the basic relations of the scaled particle theory without making use of some specific properties of the fluid state; they were only involved in the calculation of the two parameters which appear in that equation. In a later article (Z. f. Phys. B 102(255), 1997) it was therefore used to describe the glassy states, assuming tacitly that the basic relations of the scaled particle theory not only hold for the fluid state, but also for frozen structures. That assumption shall now be discussed in more detail and it will be shown that the basic relations are valid for all possible states of the system.     

Polynomial-time algorithms for regular set-covering and threshold synthesis

A set-covering problem is called regular if a cover always remains a cover when any column in it is replaced by an earlier column. From the input of the problem - the coefficient matrix of the set-covering inequalities - it is possible to check in polynomial time whether the problem is regular or can be made regular by permuting the columns. If it is, then all the minimal covers are generated in polynomial time, and one of them is an optimal solution. The algorithm also yields an explicit bound for the number of minimal covers. These results can be used to check in polynomial time whether a given set-covering problem is equivalent to some knapsack problem without additional variables, or equivalently to recognize positive threshold functions in polynomial time. However, the problem of recognizing when an arbitrary Boolean function is threshold is NP-complete. It is also shown that the list of maximal non-covers is essentially the most compact input possible, even if it is known in advance that the problem is regular.     

An Optimal Congestion and Cost-sharing Pricing Scheme for Multiclass Services

We study in this paper a social welfare optimal congestion-pricing scheme for multiclass queuing services which can be applied to telecommunication networks. Most of the literature has focused on the marginal price. Unfortunately, it does not share the total cost among the different classes. We investigate here an optimal Aumann–Shapley congestion-price which verifies this property. We extend the work on the Aumann–Shapley price for priority services, based on the results on the marginal price: instead of just determining the cost repartition among classes for given rates, we obtain the rates and charges that optimize the social welfare.     

A new “one flask” preparation of 2-alkylamino-4-chloroquinazolines from ortho aminobenzonitriles and phosgeniminium salts

Phosgeniminium salts $\text{7}$ react easily with ortho amino-benzonitriles $\text{6}$ to give, selectively and quantitatively the corresponding 2-dialkylamino-4-chloroquinazolines $\text{5}$.     

Zero-flee regions for a rational function with applications

In this paper, we study a rational function which plays an important role in several problems of interest (eigenvalue problems, linear control theory, ... ). Our main interest is to determine zero-free regions. We also derive upper and lower bounds for this function. Communicated by T.L. Freeman