Spectral method for matching exterior and interior elliptic problems

A spectral method is described for solving coupled elliptic problems on an interior and an exterior domain. The method is formulated and tested on the two-dimensional interior Poisson and exterior Laplace problems, whose solutions and their normal derivatives are required to be continuous across the interface. A complete basis of homogeneous solutions for the interior and exterior regions, corresponding to all possible Dirichlet boundary values at the interface, are calculated in a preprocessing step. This basis is used to construct the influence matrix which serves to transform the coupled boundary conditions into conditions on the interior problem. Chebyshev approximations are used to represent both the interior solutions and the boundary values. A standard Chebyshev spectral method is used to calculate the interior solutions. The exterior harmonic solutions are calculated as the convolution of the free-space Green's function with a surface density; this surface density is itself the solution to an integral equation which has an analytic solution when the boundary values are given as a Chebyshev expansion. Properties of Chebyshev approximations insure that the basis of exterior harmonic functions represents the external near-boundary solutions uniformly. The method is tested by calculating the electrostatic potential resulting from charge distributions in a rectangle. The resulting influence matrix is well-conditioned and solutions converge exponentially as the resolution is increased. The generalization of this approach to three-dimensional problems is discussed, in particular the magnetohydrodynamic equations in a finite cylindrical domain surrounded by a vacuum

Technology Interventions to Curb Obesity: A Systematic Review of the Current Literature

Abstract Obesity is a public health crisis that has reached epidemic proportions. Although intensive behavioral interventions can produce clinically significant weight loss, their cost to implement, coupled with resource limitations, pose significant barriers to scalability. To overcome these challenges, researchers have made attempts to shift intervention content to the Internet and other mobile devices. This article systematically reviews the recent literature examining technology-supported interventions for weight loss and maintenance among overweight and obese adults. Thirteen studies were identified that satisfied our inclusion criteria (12 weight loss trials, 1 weight maintenance trial). Our findings suggest that technology interventions may be efficacious at producing weight loss. However, several studies are limited by methodologic shortcomings. There are insufficient data to evaluate their efficacy for weight maintenance. Further research is needed that employs state-ofthe-art methodology, with careful attention being paid to adherence and fidelity to intervention protocols

London creditors and the fifteenth-century depression

Evidence of debts owed to Londoners, and contested before the royal Court of Common Pleas, allows an examination of the role of London creditors in the English depression of the fifteenth century and a reassessment of its causes. Here we examine four main issues. What is the nature of the Court of Common Pleas evidence (section I)? What were the three main forms of credit offered by Londoners –unsecured cash loans, sales of goods on credit, and written instruments called bonds (section II)? What is yielded by decadal analysis of Londoners’ extension of credit in the fifteenth century –making direct comparisons with Pamela Nightingale’s published Statute Merchant and Staple data (section III)? What defines, in modern economic terms, the claim of so called ‘monetarist’ historians that credit was actively withdrawn during the depression, and how is this verified by the actions of London creditors (section IV)? It is concluded that the records of the Court of Common Pleas provide the detailed evidence monetarist historians have previously lacked both to prove that Londoners actively withdrew credit during the fifteenth century and to demonstrate that they employed pure equilibrium credit rationing in order to do so

Homosexuellenunterdrückung in der bürgerlichen Gesellschaft

Homosexuellenunterdrückung in der bürgerlichen Gesellschaf

Siedeapparat (Hypsometer)

Der Ankauf erfolgte 1899 von der Firma Fuess in Steglitz. Es handelt sich um ein transportables Gerät, bestehend aus Dreibein, Wassergefäß, Spiritusbrenner und Thermometer. Es diente dazu, Siedepunktänderungen von Wasser zu messen und daraus den Luftdruck bzw. die Meereshöhe zu bestimmen. (K.R./P.G. 2011), UM HP 2