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  2. Raising and lowering indices - Wikipedia

    en.wikipedia.org/wiki/Raising_and_lowering_indices

    It is common convention to use greek indices when writing expressions involving tensors in Minkowski space, while Latin indices are reserved for Euclidean space. Well-formulated expressions are constrained by the rules of Einstein summation: any index may appear at most twice and furthermore a raised index must contract with a lowered index ...

  3. Frobenius method - Wikipedia

    en.wikipedia.org/wiki/Frobenius_method

    Some solutions of a differential equation having a regular singular point with indicial roots = and .. In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a linear second-order ordinary differential equation of the form ″ + ′ + = with ′ and ″.

  4. Index (economics) - Wikipedia

    en.wikipedia.org/wiki/Index_(economics)

    It either understates or overstates cost-of-living increases. This is the limitation of the CPI that is described as the index number problem. There is no theoretically ideal solution to this problem. In practice for retail price indices, the "basket of goods" is updated incrementally every few years to reflect changes.

  5. Ricci calculus - Wikipedia

    en.wikipedia.org/wiki/Ricci_calculus

    The free indices in a tensor expression always appear in the same (upper or lower) position throughout every term, and in a tensor equation the free indices are the same on each side. Dummy indices (which implies a summation over that index) need not be the same, for example:

  6. Hilbert's second problem - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_second_problem

    In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic is consistent – free of any internal contradictions. Hilbert stated that the axioms he considered for arithmetic were the ones given in Hilbert (1900) , which include a second order completeness axiom.

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    mail.aol.com

    Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!

  8. Worked-example effect - Wikipedia

    en.wikipedia.org/wiki/Worked-example_effect

    "A worked example is a step-by-step demonstration of how to perform a task or how to solve a problem". [8]: 190 Worked examples are designed to support initial acquisition of cognitive skills through introducing a formulated problem, solution steps and the final solution. [2] [page needed] Studying worked examples is an effective instructional ...

  9. 50Languages - Wikipedia

    en.wikipedia.org/wiki/50Languages

    50Languages, formerly Book2, is a set of webpages, downloadable audio files, mobile apps and books for learning any of 56 languages. Explanations are also available in the same 56 languages. Explanations are also available in the same 56 languages.