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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.
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 ″.
Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices.
Edexcel and AQA both offer completely different courses, with Edexcel including the calculation of solids formed through integration, [5] and AQA not including integration. AQA's syllabus mainly offers further algebra, with the factor theorem and the more complex algebra such as algebraic fractions.
Examples of determining indices for a plane using intercepts with axes; left (111), right (221) There are two equivalent ways to define the meaning of the Miller indices: [1] via a point in the reciprocal lattice, or as the inverse intercepts along the lattice vectors. Both definitions are given below.
In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms.Dedicated to the discrete logarithm in (/) where is a prime, index calculus leads to a family of algorithms adapted to finite fields and to some families of elliptic curves.
Sample of a well maintained data [clarification needed]. In statistics and research design, an index is a composite statistic – a measure of changes in a representative group of individual data points, or in other words, a compound measure that aggregates multiple indicators.
5] Where: is a complexity factor; is a unit capacity; is a capacity of crude distillation unit; is a number of all units; The NCI assigns a complexity factor to each major piece of refinery equipment based on its complexity and cost in comparison to crude distillation, which is assigned a complexity factor of 1.0.