On the (non)existence of best low-rank approximations of generic IxJx2 arrays

Several conjectures and partial proofs have been formulated on the (non)existence of a best low-rank approximation of real-valued IxJx2 arrays. We analyze this problem using the Generalized Schur Decomposition and prove (non)existence of a best rank-R approximation for generic IxJx2 arrays, for all values of I,J,R. Moreover, for cases where a best rank-R approximation exists on a set of positive volume only, we provide easy-to-check necessary and sufficient conditions for the existence of a best rank-R approximation

A Century of Brickmaking at Berlin Junction: A History of the Alwine Brick Company

The Alwine family name had been associated with brickmaking in York and Adams Counties at least since the early 1850s, when Peter Samuel Alwine started his first brickyard on a farm in Paradise Township of York County.1 He learned the trade of brickmaking during his youth and by the age of seventeen had become a skilled artisan. He learned how to make bricks by working in the spring and summer months at a brickmaking operation in Peach Bottom Township, located in the southeastern corner of York County. He did not set up his own brickyard until later, and following his marriage to Catharine Dahlhammer in 1860, he moved his brickmaking facilities to the farm where they settled in Paradise Township, near the Borough of Berwick (now Abbottstown) in Adams County. During that time, Mr. Alwine also engaged for varying periods as a schoolteacher, country merchant, and farmer. Later, he established a brickyard at Spring Grove in York County, and eventually another at Berlin Junction, near New Oxford in Adams County. Over the years, he attained a reputation as a man of considerable learning and sound business judgment. After his death, in 1895, his sons William and Lewis Alwine continued the business under the name Alwine Brothers Brickyard, and later William’s son Charles Emory Alwine would become president of the firm. Following Charles Alwine’s retirement, and three generations of Alwine leadership, ownership of the company was transferred in 1978 to the Glen-Gery Corporation of Reading. This article chronicles the history of the Alwine Brick Company from its beginnings to its final years, including more than a century at Berlin Junction, Adams County, Pennsylvania. [excerpt

The marginated pool

The pulmonary circulation harbors a large intravascular reservoir of leukocytes refered to as the Marginated Pool. This marginated pool is balanced by propeling and retaining forces acting on leukocytes during their passage through the pulmonary circulation. The present paper discusses these factors and their underlying mechanisms. Copyright (C) 2002 S. Karger AG, Basel