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Laws of Indices's dam Sampers showed modest racing ability, winning three minor races at Dundalk Racecourse in a thirteen-race career. [4] She was a granddaughter of the Prix de Malleret winner Privity, who was in turn a daughter of the Princess Royal Stakes winner Sylph, a full sister to the Irish St. Leger winner Leading Counsel. [5]
Miller indices of a plane (hkl) and a direction [hkl].The intercepts on the axes are at a/ h, b/ k and c/ l. The International Union of Crystallography (IUCr) gives the following definition: "The law of rational indices states that the intercepts, OP, OQ, OR, of the natural faces of a crystal form with the unit-cell axes a, b, c are inversely proportional to prime integers, h, k, l.
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:
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 ...
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A subgroup H of finite index in a group G (finite or infinite) always contains a normal subgroup N (of G), also of finite index. In fact, if H has index n, then the index of N will be some divisor of n! and a multiple of n; indeed, N can be taken to be the kernel of the natural homomorphism from G to the permutation group of the left (or right ...
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In the 1930s through early 1950s, Bond developed a new theory of comminution that introduced an index, called the 'Bond Work Index', which relates power consumption in crushing and grinding to the feed and product size distribution. [1] His theory and index were introduced in a widely cited 1952 journal article. [2]