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With view on the context of convex thermomechanics, we propose tools based on the concept of Bregman divergence, a notion introduced in the 1960s and used in learning and optimization as well. This study is motivated by the need of "discrepancy measures" between physically constrained fields that are used both in traditional algorithms, analysis methods and data driven modelling or applications as well. We give also a characterization of symmetrical Bregman divergences through their generating functions which can only be quadratic forms. Some properties of the Bregman divergence and the introduced concept of Bregman Gap between couples of dual quantities are given, and some existing errors in thermomechanics are recovered. Exploiting the framework of Standard Generalized Materials, we give a set of generating functions for a large range of applications, including coupled multi-physics. Finally some results useful for computational geometry are detailed. [ABSTRACT FROM AUTHOR]

The article presents the discussion on underscoring the significance of data collection techniques in enhancing OSINT practices across various domains, including intelligence analysis, cybersecurity, market research, and journalism.

The article focuses on the transformations that teachers imprint to didactic situations of mathematics associated with a socio-constructive didactic approach. The case of two educators working with the topic of Data Analysis in preschool is studied. Methodologically, we consider this study a Didactic Development Engineering (Perrin Glorian, 2011). The analysis was carried out from a double theoretical perspective: the didactic situations are characterized and analyzed from the Theory of Didactic Situations (Brousseau, 1998), while, for the analysis of teaching practices, the double didactic/ergonomic approach was mainly considered (Robert y Rogalski, 2002) and the ethnographic perspective (Rockwell & Mercado, 2003). Although the transformations identified are different from each other, in both cases, the essentials of the didactic purposes were preserved. This is expressive of the need and feasibility of appropriation processes. The main contribution of the text is the identification of factors that underlie these transformations, of the needs to which they respond and of the tensions they create in decision-making in the classroom. [ABSTRACT FROM AUTHOR]

Abstract: Data processing for NMR velocimetry of fast flow: a numerical study of ‘Couette’ rheo-NMR measurements. NMR velocimetry in Couette rheo-NMR experiments is known to be accurate within the limit that the fluid undergoes small displacements during the sequence. In this work, it is shown that even when this last requirement can not be fulfilled, some good-quality measurements may however be extracted from raw data. A data processing method is developed, which increases the range of measurable velocity by a factor of 10, without any necessary change in the sequence. The method is validated on simulated, noise-free, NMR data. The simulation method, which takes into account coherence pathway selection, is also described. To cite this article: H. Kassem, S. Rodts, C. R. Chimie 9 (2006) . [Copyright &y& Elsevier]