Stochastic grid bundling method for backward stochastic differential equations

ABSTRACT

In this work, we apply the Stochastic Grid Bundling Method (SGBM) to numerically solve backward stochastic differential equations (BSDEs). The SGBM algorithm is based on conditional expectations approximation by means of bundling of Monte Carlo sample paths and a local regress-later regression within each bundle. The basic algorithm for solving the backward stochastic differential equations will be introduced and an upper error bound is established for the local regression. A full error analysis is also conducted for the explicit version of our algorithm and numerical experiments are performed to demonstrate various properties of our algorithm.     

What is a crystal to the new chemical crystallographer,after that first,automated structure analysis?

This educational review postulates the importance of maintaining an adequate level of crystallographic education among structure-dependent scientists whose interests are not primarily in crystallography, at a time when automation and validation have made it possible to obtain high-quality structure analyses in many cases with a minimum of crystallographic background. The topics addressed are intended to form a second round of crystallographic education for a novice user whose first round involved hands-on experience with structure solution and an introduction to elementary concepts. The specific topics, chosen for their relevance as basic knowledge and their lack of emphasis in many formal treatments, are (1) crystallographic reference frames and the utility of the reciprocal cell in geometrical calculations; (2) the relationship between the two concepts that constitute our model of the crystal, namely the unit cell and the lattice; (3) the manner in which an atom is represented in concept and in practice; (4) the importance of interleaved symmetry elements required by the presence of additional symmetry on a lattice; (5) the harnessing of the natural properties of the crystalline state for the potential manipulation of properties of synthetic crystals; and (6) useful terminology for navigating a crystal structure.     

TRACES OF THE TERRITORY IN SPANISH PHOTOGRAPHY SINCE THE 1990s

This paper proposes a reading of the cultural and social aspects associated with sundry notions of territory through Spanish photography at the end of the twentieth century and the beginning of the twenty-first. An analysis of a series of case studies reveals a new awareness of the common space through the concept of trace, being understood beyond the material imprint, as it falls under the influence of the cultural aspects that clarify the account of the conflict and consciousness of the suburbs and peripheries. Contemporary ruins arising from unbridled urban growth, or the invisible wounds associated with certain places, converge in a series of images that have their own tradition in the conceptual experiments of the 70s and the aesthetics of the “non-site” displayed in the 90s. As background, the economic and political avatars of recent years in Spain – also linked to a global crisis – are manifested in a series of photographic musings whose images portray the scenarios of a premature ruin linked to property speculation and the traces of a collective memory.     

Research on corrosion performance of 6061 aluminum alloy in salt spray environment

Salt spray corrosion test was carried out on 6061 aluminum alloy, and quasi-static tensile test at room temperature was carried out on the sample with universal testing machine. The effect of salt spray corrosion on the mechanical properties of 6061 aluminum alloy was studied by scanning electron microscope (SEM), energy dispersive spectrometer (EDS) and electrochemistry. The corrosion rate of 6061 aluminum alloy was quantitatively characterized by different corrosion parameters. It was found that local corrosion of 6061 aluminum alloy occurred in salt spray environment, mainly pitting corrosion and intergranular corrosion. With the increase of corrosion time, the polarization resistance of 6061 aluminum alloy decreases, and the corrosion rate significantly increases. The average corrosion rate and the maximum corrosion rate of 6061 aluminum alloy were characterized by corrosion weight loss and corrosion pit depth. And they can be transformed into each other. The mechanical properties of 6061 aluminum alloy were mainly affected by the depth of corrosion pit. With the increase of corrosion time, the tensile strength and fracture strain decreased, resulting in poor plasticity of the sample. At the same time, the change of elongation of 6061 aluminum alloy can be accurately predicted by the depth of corrosion pit.     

An evaluation of Acacia mearnsii tannin as an aluminum corrosion inhibitor in acid,alkaline, and neutral media

The electrochemical behavior of aluminum in tannin from Acacia mearnsii bark was evaluated by potentiodynamic polarization curves and electrochemical impedance spectroscopy (EIS) in media under three different pH conditions: acid, alkaline, and neutral. A relationship among pH, polymerization grade (PG), zeta potential, surface, and electrochemical properties was observed in the inhibition performance of the tannin. At high pH, the oligomer structure of the tannin was affected, resulting in a low PG (4) and high zeta potential (−75 mV), and consequently, the inhibition efficiency decreased (68%) in comparison with that in acid (99%) and neutral media (96%). The values obtained indicate a physisorption mechanism for the aluminum corrosion inhibition in the studied conditions.     

Mine inonoations

The paper describes the types of inundations affecting underground mining operations together with their safety, operational, and stability implications. A critical analysis has highlighted three major causes of inundations. These have been classified as event controlled, accidental or spontaneous. The event controlled inundations are associated with the development of fracture zones around a longwall working and followed by main and periodic roof falls in caved mine workings, particularly in coal mines. An approximate theory to predict the event of main and periodic roof falls in the goaf behind the long wall face is given. These types of inundations have been illustrated with several case histories.