Laplace\u2019s Method of Integration in the Path Integral Approach for the Probabilistic Response of Nonlinear Systems

In this paper the response of nonlinear systems under stationary Gaussian white noise excitation is studied. The Path Integral (PI) approach, generally employed for evaluating the response Probability Density Function (PDF) of systems in short time steps based on the Chapman-Kolmogorov equation, is here used in conjunction with the Laplace\u2019s method of integration. This yields an approximate analytical solution of the integral involved in the Chapman-Kolmogorov equation. Further, in this manner the repetitive integrations, generally required in the conventional numerical implementation of the procedure, can be circumvented. Application to a nonlinear system is considered, and pertinent comparisons with stationary analytical solutions are presented, demonstrating the efficiency and accuracy of the proposed approach

An integrated micromorphological and phytolith study of urban soils and sediments from the Gallo‐Roman town Atuatuca Tungrorum, Belgium

Tongeren is the only Roman administrative capital within the borders of present-day Belgium. It developed in the first century A.D. and became an important civitas. Many excavations in the center of town have uncovered complex stratigraphic sequences, including dark earths, dating to Roman as well as early medieval times. Their interpretation, based on traditional archaeological methods, often remains problematic. A large-scale excavation at Vermeulenstraat in 2014 is the first occasion where a geoarchaeological study was conducted using both micromorphology and the study of phytoliths in thin sections. The aim was to evaluate the impact of depositional and post-depositional processes, to gain an understanding of the formation of the dark earths encountered on the site, to characterize the deposits between and underneath them, and to identify and differentiate human activities and natural phenomena. The results show a range of different activities and events, such as cultivation, construction (including floor preparation), destruction, waste dumping, and gardening. Their different formation histories illustrate the evolution of the area, and their analysis provides an important precedent for the further geoarchaeological study of this town.SCOPUS: ar.jDecretOANoAutActifinfo:eu-repo/semantics/publishe

A systematic survey of floral nectaries

The construction of classifications, as well as the understanding of biological diversity, depends upon a careful comparison of attributes of the organisms studied (Stuessy, 1990). It is widely known that data from diverse sources showing differences from taxon to taxon are of systematic significance. Dur-ing the 20th century, systematists have emphasized that their discipline involves a synthesis of all knowledge (Stevens, 1994) or, in other words, the variation of as many relevant characters as possible should be incorporated into the natural system to be constructed. The extent to which particular characters are constant or labile will determine their usefulness to syste-matics. In general, more conservative characters will be valuable in defining families and orders, whereas more labile characters may be useful at the ge-neric and specific levels (Webb, 1984). There is no doubt that floral characters are among the most used in the classification of flowering plants. At the same time, they constitute essential features in diagnostic keys to taxa in both taxonomic treatments and Floras (Cronquist, 1981, 1988).Fil: Bernardello, Gabriel Luis Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto Multidisciplinario de Biología Vegetal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto Multidisciplinario de Biología Vegetal; Argentin