Subscripts, repeated

The summation sign has been included for emphasis. In the first line of (6.30) there do not appear to be any repeated subscripts, but that is because they have been subsumed in the abbreviated notation. If the stiffness tensor elements are written out in full, as in (6.24), this is immediately apparent. The selection rules in (6.30) correspond directly to the components of stress and strain that are related by each of the three stiffness constants. 

Summation over repeated subscripts is again implied, in this case over the subscript j. Fi are body forces (such as gravity), which will be neglected. 

Note that we use the shorthand notation Fx etc. Also for convenience, we denote dF/dxre5 by Ft to save repeated subscripts.)... 

Constants with repeated subscripts refer to pure compounds, i.e., BoM = B0l> and the order of the subscripts is immaterial, i.e, BoI2 = Ba2i- The coefficients with dissimilar subscripts, such as Bo 2, arise from the interaction of unlike molecules and are called interaction coefficients or binary interaction coefficients. 

Summation over repeated subscripts from 1,..., n is implied. Compare this result with Eqs. (4.11) and (4.12) (van Kampen, 1992). 

Repeated subscript indices imply summation over all allowed values of the indices. The practical necessity of employing cartesian tensor notation here forces us to adopt a notation differing in some other respects from that employed elsewhere in the book (for example, the use of superscript K to identify species). 

If the Einstein summation convention is used, whereby any expression is summed over every repeated subscript, this becomes... 

Trie Tree data structure employing (1) repeated subscripting, and (2) different numbers of node successors. A data structure that is particularly useful for multiway search structure from information retrieval useful means for search of linguistic data. 

A trie is a data structure that uses repeated subscripting and is used to enable multiway search. The term comes from the word re/r/eval. It originated in the field of information retrieval and has developed in part because of machine translation. The benefit of using the trie approach is that it helps reduce the number of ways to search. It does this by eliminating impossible cases. (For example, in English words, a q is never followed by anything but a space [Iraq] or the letter u . That involves a considerable reduction from 26 or 27 other letters or space symbol.) Entries in the nodes of a trie are instructions that describe how to proceed further in a symbol-by-symbol search. 

The notation of sum over repeating subscript is used, such as QijQji = QijQft- Note that... 

Equation 6.26 uses the summation convention on repeated subscripts. 

Here, the functions = — (VaVjg... Vv

Cartesian components and the repeated subscripts imply summation over x, y, and z). In particular, is the... 

Free index non-repeated subscripts are called free subscripts since they are free to take on any value in 3D space. The count of the free indices on a variable indicates the order of the tensor, e.g. Fj is a vector (first order tensor), Oy is a second order tensor. 

Dummy index repeated subscripts are called dummy subscripts, since they can be changed freely to another letter with no effect on the equation. 

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