'Necessarily distinct' presentation slideshows

Data Dependences and Parallelization

Data Dependences and Parallelization . Agenda. Introduction Single Loop Nested Loops Data Dependence Analysis. Motivation. DOALL loops: loops whose iterations can execute in parallel New abstraction needed Abstraction used in data flow analysis is inadequate

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Sets

Sets. Definition of a Set: NAME = {list of elements or description of elements} i.e. B = {1,2,3} or C = {x ? Z + | -4 < x < 4} Axiom of Extension: A set is completely defined by its elements i.e. {a,b} = {b,a} = {a,b,a} = {a,a,a,b,b,b}. Subset. A ?B ? ?x?U, x?A?x?B

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Every polynomial P(x) of degree n>0 has at least one zero in the complex number system.

N Zeros Theorem. Every polynomial P(x) of degree n>0 can be expressed as the product of n linear factors. Hence, P(x) has exactly n zeros, not necessarily distinct. The Fundamental Theorem of Algebra. Every polynomial P(x) of degree n>0 has at least one zero in the complex number system.

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Towards sustainable growth and full employment EU perspective

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