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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 ...
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:
The Marshall-Edgeworth index, credited to Marshall (1887) and Edgeworth (1925), [11] is a weighted relative of current period to base period sets of prices. This index uses the arithmetic average of the current and based period quantities for weighting. It is considered a pseudo-superlative formula and is symmetric. [12]
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 ″.
In mathematics, Fredholm operators are certain operators that arise in the Fredholm theory of integral equations.They are named in honour of Erik Ivar Fredholm.By definition, a Fredholm operator is a bounded linear operator T : X → Y between two Banach spaces with finite-dimensional kernel and finite-dimensional (algebraic) cokernel = / , and with closed range .
Index numbers are used especially to compare business activity, the cost of living, and employment. They enable economists to reduce unwieldy business data into easily understood terms. In contrast to a cost-of-living index based on the true but unknown utility function, a superlative index number is an index number that can be calculated. [1]
Given a function that accepts an array, a range query (,) on an array = [,..,] takes two indices and and returns the result of when applied to the subarray [, …,].For example, for a function that returns the sum of all values in an array, the range query (,) returns the sum of all values in the range [,].
CECEEUR – Central European Clearinghouses & Exchanges Index, Composit Index in Euro. Composed of Polish Traded Index (PTX), Czech Traded Index (CTX) and Hungarian Traded Index (HTX) by the Vienna Stock Exchange. UBS 100 Index - the 100 Swiss companies with the largest market capitalizations that are listed on the SIX Swiss stock exchange.