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David Shapiro (born November 25, 1946) is an American economist at the Pennsylvania State University. He joined the Penn State faculty [1] in 1980. He is a leading academic in the field of Economic Demography , specializing in fertility transition in sub-Saharan Africa and in the study of children's schooling in Africa.
Statement of the inequality. Suppose is a natural number and are positive numbers and: Then the Shapiro inequality states that. where and . For greater values of the inequality does not hold, and the strict lower bound is with . The initial proofs of the inequality in the pivotal cases [2] and [3] rely on numerical computations.
Career [ edit] Shapiro was a leading mathematician and computer scientist at the RAND Corporation think tank from 1959 until 1999. In the late 1960s and early 1970s Shapiro was the lead designer of one of the first computer-based mapping and cartography systems. In the 1970s Shapiro co-designed the MH Message Handling System. [3]
Mel Shapiro is an American theatre director and writer, college professor, and author . Trained at Carnegie-Mellon University, Shapiro began his professional directing career at the Pittsburgh Playhouse and then as resident director at Arena Stage in Washington, D.C. He was co-producing director at the Guthrie Theater in Minneapolis and has ...
North Center is one of the 77 community areas of Chicago, Illinois, located in the city's North Side. North Center is bordered on the north by Montrose Avenue, on the south by Diversey Parkway, on the west by the Chicago River and on the east by Ravenswood Avenue; it includes the neighborhoods of North Center, Roscoe Village, St. Ben's, and ...
James S. Shapiro (born 1955) is Professor of English and Comparative Literature at Columbia University who specializes in Shakespeare and the Early Modern period. Shapiro has served on the faculty at Columbia University since 1985, teaching Shakespeare and other topics, and he has published widely on Shakespeare and Elizabethan culture .