Single Machine Group Scheduling with Two Ordered Criteria

The problem of scheduling jobs on a single machine is considered. It is assumed that the jobs are classified into several groups and the jobs of the same group have to be processed contiguously. A sequence independent set-up time is incurred between each two consecutively scheduled groups. A schedule is specified by a sequence for the groups and a sequence for the jobs in each group. The quality of a schedule is measured by two critera ordered by their relative importance. The objective is to minimize the maximum cost, the secondary criterion, subject to the schedule is optimal with respect to total weighted completion time, the primary criterion. A polynomial time algorithm is presented to solve this bicriterion group scheduling problem. It is shown that this algorithm can also be modified to solve the single machine group scheduling problem with several ordered maximum cost criteria and arbitrary precedence constraints.     

Germanium carboxylates: the first X‐ray diffraction study of germanium(II) dicarboxylate and germanium(IV) tetracarboxylate

Germanium(II) dipropionate (1) has been synthesized and its crystal structure, as well as that of germanium(IV) tetrapropionate (2), has been determined. By contrast to monomeric 2 with monodentate propionate ligands, compound 1 is associated, forming a cyclotetramer [Ge(O₂CEt)₂]₄ (1a) via intermolecular dative C?O → Ge interactions. Copyright © 2005 John Wiley & Sons, Ltd.     

Non-parametric estimation from simultaneous degradation and failure time dataEstimation non-paramétrique à partir de données de dégradation et de défaillances

The paper considers degradation and failure time models with multiple failure modes. Dependence of traumatic failure intensities on the degradation level are included into the models. Non-parametric estimators of various reliability characteristics are proposed. Theorems on simultaneous asymptotic distribution of random functions characterizing degradation and intensities of traumatic events are proposed. To cite this article: V. Bagdonavi?ius et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 183–188.     

Gradient-like flows and self-indexing in stratified Morse theory

We develop the idea of self-indexing and the technology of gradient-like vector fields in the setting of Morse theory on a complex algebraic stratification. Our main result is the local existence, near a Morse critical point, of gradient-like vector fields satisfying certain “stratified dimension bounds up to fuzz” for the ascending and descending sets. As a global consequence of this, we derive the existence of self-indexing Morse functions.     

Unbiased Estimation for a Multivariate Exponential whose Components have a Common Shift

It is shown that for independent and identically distributed random vectors, for which the components are independent and exponentially distributed with a common shift, we can construct unbiased estimators of their density, derived from the Uniform Minimum Variance Unbiased Estimator (UMVUE) of their distribution function. As direct applications of the UMVUEs of the density functions we present a Chi-square goodness of fit test of the model, and give two tables of the UMVUEs of some commonly used functions of the unknown parameters of the multivariate exponential model considered in this paper.     

Thermooptical detection in microchips: from macro- to micro-scale with enhanced analytical parameters

In this paper, we compared the methods of photothermal spectroscopy used in different spatial scales, namely thermal-lens spectrometry (TLS) and thermal-lens microscopy (TLM) to enhance the performance parameters in analytical procedures. All of the experimental results were confirmed by theoretical calculation. It was proven that the design for both TLM and TLS, despite a different scale for the effect, is governed by the same signal-generating and probing conditions (probe beam diameter at the sample should be equal to the diameter of the blooming thermal lens), and almost does not depend on the nature of the solvent. Theoretical and experimental instrumental error curves for thermal lensing were coincident. TLM obeys the same law of instrumental error as TLS and shows better repeatability for the same levels of thermal-lens signals or absorbances. TLS is more advantageous for studying low concentrations in bulk, while TLM shows much lower absolute LODs due to better repeatability for low amounts. The behavior of the thermal-lens signal with different flow rates was studied and optimum conditions, with the minimum contribution to total error, were found. These conditions are reproducible, are in agreement with the existing theory of the thermal response in thermal lensing, and do not significantly affect the design of the optimum scheme for setups. TLM showed low LODs in solvent extraction (down to 10(-8) M) and electrokinetic separation (10(-7) M), which were shown to be governed by discussed instrumental regularities, instead of by microchemistry.