A natural extension of the classical envelope theorem in vector differential programming

The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, according to changes of any of the parameters which appear in the constraints. We show that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity.

Validation of a mobility item bank for older patients in primary care

Background: To develop and validate an item bank to measure mobility in older people in primary care and to analyse differential item functioning (DIF) and differential bundle functioning (DBF) by sex. Methods: A pool of 48 mobility items was administered by interview to 593 older people attending primary health care practices. The pool contained four domains based on the International Classification of Functioning: changing and maintaining body position, carrying, lifting and pushing, walking and going up and down stairs. Results: The Late Life Mobility item bank consisted of 35 items, and measured with a reliability of 0.90 or more across the full spectrum of mobility, except at the higher end of better functioning. No evidence was found of non-uniform DIF but uniform DIF was observed, mainly for items in the changing and maintaining body position and carrying, lifting and pushing domains. The walking domain did not display DBF, but the other three domains did, principally the carrying, lifting and pushing items. Conclusions: During the design and validation of an item bank to measure mobility in older people, we found that strength (carrying, lifting and pushing) items formed a secondary dimension that produced DBF. More research is needed to determine how best to include strength items in a mobility measure, or whether it would be more appropriate to design separate measures for each construct.

Characterization of the instability mechanisms affecting slopes on carbonatic Flysch: Alicante (SE Spain), case study

The studied Flysch sequence of Alicante occupies a widely populated area crossed by main communication routes. The slopes existing on this area usually suffer slope instabilities that cause substantial damage and a very high maintenance cost. In order to assess the type of instability mechanisms affecting these heterogeneous carbonatic slopes, in this paper a wide inventory of 194 Flysch rock slopes has been performed, reporting the existing lithologies, their competence and their relative arrangement and the geometrical relationship between bedding and the slope and the associated instability mechanism. All these data have been jointly used for performing an instability mechanisms characterization. For systematically characterizing the wide type of complex rock exposures existing in the study area, they are divided into basic units referred as lithological pattern columns to which the different observed instability mechanisms are associated. Inventoried instability mechanisms are diverse and sometimes are combined with each other. Rockfalls are a very common instability mechanism associated to the differential weathering and sapping of the marly lithologies which are present in a wide number of geometrical combinations. The other instability mechanisms closely depend on the combination of the geometrical and lithological parameters. Therefore, this work provides a new basic tool which can be easily used during preliminary project stages for knowing the instability mechanisms which can affect rock slopes excavated on carbonatic Flysch heterogeneous geological formations.