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Pennsylvania ( / ˌpɛnsɪlˈveɪniə / ⓘ, lit.'Penn's forest country' ), officially the Commonwealth of Pennsylvania [b] ( Pennsylvania Dutch: Pennsylvanie ), [7] is a state spanning the Mid-Atlantic, Northeastern, Appalachian, and Great Lakes regions of the United States.
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.
Zone 5 uses eight 2-digit codes (51–58) and two sets of 3-digit codes (50x, 59x) to serve South and Central America. Zone 6 uses seven 2-digit codes (60–66) and three sets of 3-digit codes (67x–69x) to serve Southeast Asia and Oceania. Zone 7 uses an integrated numbering plan; two digits (7x) determine the area served: Russia or Kazakhstan.
The Shapiro reaction or tosylhydrazone decomposition is an organic reaction in which a ketone or aldehyde is converted to an alkene through an intermediate hydrazone in the presence of 2 equivalents of organolithium reagent. [1] [2] [3] The reaction was discovered by Robert H. Shapiro in 1967. [4] The Shapiro reaction was used in the Nicolaou ...
The discography of Nas, an American rapper, consists of seventeen studio albums, one collaborative album, one group album, five compilations, four mixtapes, one extended play, and seventy-nine singles (including twelve collaboration singles and thirty-three as a featured artist). Nas has sold over 20 million records in the United States alone ...
The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...