Reduced Functions, Gradients and Hessians from Fixed-Point Iterations for State Equations

In design optimization and parameter identification, the objective, or response function(s) are typically linked to the actually independent variables through equality constraints, which we will refer to as state equations. Our key assumption is that it is impossible to form and factor the corresponding constraint Jacobian, but one has instead some fixed-point algorithm for computing a feasible state, given any reasonable value of the independent variables. Assuming that this iteration is eventually contractive, we will show how reduced gradients (Jacobians) and Hessians (in other words, the total derivatives) of the response(s) with respect to the independent variables can be obtained via algorithmic, or automatic, differentiation (AD). In our approach the actual application of the so-called reverse, or adjoint differentiation mode is kept local to each iteration step. Consequently, the memory requirement is typically not unduly enlarged. The resulting approximating Lagrange multipliers are used to compute estimates of the reduced function values that can be shown to converge twice as fast as the underlying state space iteration. By a combination with the forward mode of AD, one can also obtain extra-accurate directional derivatives of the reduced functions as well as feasible state space directions and the corresponding reduced or projected Hessians of the Lagrangian. Our approach is verified by test calculations on an aircraft wing with two responses, namely, the lift and drag coefficient, and two variables, namely, the angle of attack and the Mach number. The state is a 2-dimensional flow field defined as solution of the discretized Euler equation under transonic conditions.     

Systèmes aromatiques à 10 électrons π dérivés de l'aza-3a pentalène. IX—etude par RMN de l'équilibre azide/tetrazole dans le cas du tetrazolo [5,1-b] benzothiazole

Azido-tetrazole equilibrium is observed in the case of a solution of tetrazolo [5,1-b] benzothiazole in CDCl₃, using proton magnetic resonance at 250 MHz. Analysis of the spectra obtained yields the chemical shifts and the coupling constants of the two tautomeric forms.     

Photoisomerization processes in the IR-140 laser dye

The photoisomerization processes in the well known IR-140 laser dye and in the closest relevant DTTC model have been investigated by a mode-locked laser spectroscopy in order to observe the influence of a partial rigidization of the polymethine chain. The kinetic, spectral and thermodynamic parameters have been measured; the correlations between the transient quantum yields and the laser efficiency under flash-lamped pumping are discussed. Evidence is given for a surprising solvent effect upon the photoisomerization process.     

Intercomparisons and development of reference materials for short-term mutagenicity testing

Summary Every new product to be put on the market must be checked by a range of testing procedures so as to assess its toxicity (directive 67/548/EEC). Results from the prescribed reverse mutation assay (Ames test) are part of the consideration of whether the introduction of the product into trade is allowed. Using the above test, European testing laboratories achieved different results for the same substances, false negative and false positive results being obtained. The Community Bureau of Reference (BCR) was requested to undertake a project on short-term mutagenicity testing in order to harmonize results at the European level. The results obtained by a first intercomparison using four direct mutagens showed that further work in this field is necessary. Before starting a second intercomparison using two indirect mutagens, a preliminary study was initiated in order to examine the influence of several important parameters. The aim of this project is to certify highly purified 2-aminoanthracene and benzo(a)pyrene for their mutagenic activity.     

Etudes par la RMN du carbone-13 de quelques dérivés cyclopropaniques: Déplacements chimiques et paramètres structuraux

Measurements of the ¹³C chemical shifts of monosubstituted cyclopropanes (C₃H₅X, X = CH₃, Br, ? C?CH) enabled us to determine the direct additivity parameters which depend solely on the nature of the substituent. In the case of polysubstituted derivatives, complementary effects due to pairwise contributions of the substituents superpose upon the direct effects. A systematic study of cyclopropanes polysubstituted by bromine atoms, and methyl and ethynyl groups shows these different contributions and permits us to propose a simple interpretation for the majority of cases. Pairwise interaction has been ascribed either to electron transfer or to symmetric or dissymmetric steric interactions between the different substituents, as is shown by the comparison of the theoretical with the experimental shift values.     

Oxygen-17 nuclear magnetic resonance study of some oxirane derivatives

The ¹⁷O chemical shifts of seventeen variously substituted oxiranes have been measured in CDCI₃ solution. Deviations of δ_o from additivity have been interpreted in terms of steric effects and loss of conjugation. Moreover, in the case of certain cis- and trans-dimethyl-substituted compounds, ¹⁷O NMR allows a differentiation between the different molecular configurations.