your healthyliving Facebook “f ” Logo The UK’s number 1 free in-store natural health magazine

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ON THE GLOBAL ROOT NUMBERS OF GL(n) × GL(m) DIPENDRA PRASAD AND DINAKAR RAMAKRISHNAN To Professor G. Shimura 1. Introduction Let F be a number field, n, m ≥ 1, and π = ⊗0v πv , π 0 = ⊗0v πv0 cuspidal, unitary

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ON THE CIRCULAR SUMMATION OF THE ELEVENTH POWERS OF RAMANUJAN’S THETA FUNCTION Ken Ono Appearing in the Journal of Number Theory Abstract. Let f (a, b) denote Ramanujan’s theta series. In his “Lost Notebook”, Ram

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“ . . . We n o w v i e w e d t h e m t h r o u g h a p r i s m o f r e a l i t y. ” -Ronald Reagan Prism of Reality Issue Number 1 Summer 2012

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translates between real-world situations and number sentences. 466 Meets the Standard Knows division facts; multiplies multi-digit numbers; solves multiplication Partially Meets the Standard Knows basic multiplication f

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N U ME R I C A L R E L A TED o F

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• Mathematics
• Algebra
• Abstract algebra
• Commutative algebra
• Analytic number theory
• Elliptic curve
• Group theory
• Birch and Swinnerton-Dyer conjecture
• Curve
• Complex multiplication
• Integral element
• Supersingular elliptic curve

PHYSICS OF FLUIDS 24, Reynolds number effect on the velocity increment skewness in isotropic turbulence Wouter J. T. Bos,1 Laurent Chevillard,2 Julian F. Scott,1 and Robert Rubinstein3

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F U N D E D R E S E A R C H P R O J E C T SYOUR DONATIONS AT WORK Every year Wings for Life receives a large number of applications ­promise in helping us to find a cure for spinal cord injury. The spec-

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An Open Letter about Firearms at AAR-SBL Annual Meetings in 2016 and Beyond From John F. Kutsko (Executive Director, SBL) and Jack R. Fitzmier (Executive Director, AAR) In recent weeks we have received a number of reques

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AN ALTERNATIVE PROOF OF THE LINEARITY OF THE SIZE-RAMSEY NUMBER OF PATHS ANDRZEJ DUDEK AND PAWEL PRALAT Abstract. The size-Ramsey number rˆ(F ) of a graph F is the smallest integer m such that there exists a graph G on

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