Complexité et circuits eulériens dans les sommes tensorielles de graphes

The paper starts from two general remarks about the spectra of tensorial products and tensorial sums of square matrices. Since some classical results about spanning trees and Eulerian circuits may be reformulated in terms of eigenvalues of (what is called here) the second associated matrix, the initial remark about tensorial sums of matrices leads to natural applications to the enumeration of spanning trees and Eulerian circuits in tensorial sums (sometimes simply called “products”) of graphs. Examples and numerical results are given, in particular for the complexity of tensorial sums of chains and/or cycles and for the enumeration of the Eulerian circuits of the tensorial sum of two circuits.     

Enthalpie de dissolution a 298 K des fluorures de potassium et de cesium dans l'acide fluorhydrique et le fluorure d'hydrogene

A calorimetric cell designed for studies of reaction in anhydrous hydrogen fluoride has been constructed. Enthalpies of solution of KF and CsF in aqueous solution of HF (from 0 to 100 % HF) have been measured.     

K-Theory Contents of Volume 23

Volume Contents

K-Theory Contents of Volume 23     

Spectrofluorimetric determination of formaldehyde in maple syrup

A quick and simple method was developed for determination of formaldehyde in maple syrup. In this method, formaldehyde reacts with Fluoral P to form a complex which is chemically extracted by isobutanol and determined by spectrofluorimetry. Performance, as gauged by the limits of detection (0.16 mg/kg) and quantitation (0.21 mg/kg), recovery (>79%), and variability (1.9-16.1%, depending on fortification level and class of syrup) were superior to the current official AOAC standard method.     

Transition on a slender cone in hypervelocity flow

 An experimental exploratory study of laminar, transitional and turbulent boundary layers on a slender, sharp cone at zero incidence in hypervelocity flow was conducted in the shock tunnel T5, whose high operating pressure permits achieving the necessary high Reynolds numbers at high total enthalpy. Surface heat transfer rate and resonantly enhanced flow visualization were used to determine transition location and flow structure. Results suggest that the transition mechanism at the conditions tested is via the Tollmien–Schlichting instability, but since no detailed information about the noise spectrum in the facility is available, a definite conclusion is not possible. A strong, gas-dependent increase of the transition Reynolds number evaluated at the reference temperature on specific total enthalpy was observed. This effect increases monotonically with decreasing the dissociation energy of the gas. Received: 1 February 1996/Accepted: 28 June 1996     

Optimum blank design by using the FEM based on inverse motion in orthotropic elasto-plasticity

Inverse form finding aims to determine the optimum blank design of a workpiece whereby the desired end configuration that is obtaining after a forming process, the boundary conditions and the applied loads are known. Inputting the optimal initial configuration a subsequent computation with the Finite Element Method (FEM) then has to result in exactly the nodal coordinates of the desired deformed workpiece. Germain et al. [1] recently presented a new form finding strategy for isotropic elasto-plasticity, see also Landkammer et al. [2] for orthotropic plasticity. The corresponding algorithm uses the inverse mechanical formulation (also denoted as inverse finite element method) in addition to the common direct formulation in a recursive way. Switching between the direct and the inverse mechanical formulation, while fixing the internal plastic variables in the inverse step, uniquely detects the undeformed configuration iteratively. This contribution demonstrates within an example that the developed recursive algorithm even works with combinations of orthotropic elastic and orthotropic plastic material parameters without affecting the nearly linear convergence rate of the form finding algorithm. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)