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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.
As of 2010, 90.2% (10,710,239) of Pennsylvania residents age five and older spoke English at home as a primary language while 4.1% (486,058) spoke Spanish, 0.9% (103,502) spoke German including Pennsylvania Dutch, and 0.5% (56,052) spoke Chinese, which includes Mandarin of the population over the age of five.
Soap Opera Digest debuted in November 1975, co-founded by Angela Shapiro and Jerome Shapiro and featuring actors John Aniston, Ron Tomme, Audrey Peters, Birgitta Tolksdorf, Jerry Lacy, and Tudi Wiggins of Love of Life on its first cover. In the early 1990s, the magazine had up to 1.4 million subscribers. [citation needed]
The common law of business balance, often expressed as "you get what you pay for", is the principle that one cannot pay a little and get a lot. That is, paying a cheap price will not guarantee the buyer will receive a product of high quality value. In other words, a low price of a good may indicate that the producer compromised quality.
Measured year over year, producer prices rose by 2.2% in April, up from 1.8% in March and the biggest increase in a year. A measure of underlying inflation, which excludes the volatile food and ...
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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]
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