![]() ![]() The COUNTA() function counts all cells that are NOT empty whereas the COUNT() function only counts the cells that have numbers in them. If you are in Excel 2007 and later you can use the COUNTA() function instead of the COUNT() function. Dynamic Ranges that Include Text and More This way, the entire column will be referenced. If you use Excel 2007 or later, just use A:A as the argument for the COUNT() function, as shown in the first dynamic example above. The range reference that you use for the COUNT() function should be large enough to hold any size list that you could have in the future so it does not need to be changed. The COUNT() function counts all cells in the range that have a number. Change A:A to whatever column contains your list of data. Then, we need to use the COUNT() function as the 4th argument for the OFFSET() function in order to figure out how big our range should be. To use the OFFSET() function to return a dynamic range we simply need to put the first cell in the range as the first argument, A2 in this case.
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The authors study the compatibility conditions needed for reconstruction. The reduced variational problem has a nice geometrical interpretation in terms of connections. It is known that the quotient manifold (J1P)/G can be identified with the bundle of connections of π:P→M. Let l:(J1P)/G→R be the reduced Lagrangian. The Lagrangian is assumed to be invariant under the natural action of G on J1P. ![]() In the paper under review, the authors extend the idea of the Euler-Poincaré reduction to a Lagrangian L:J1P→R defined on the first jet bundle of an arbitrary principal bundle π:P→M with structure group G. These equations are known as the Euler-Poincaré equations. As is well known, the Euler-Lagrange equations defined by L for curves on G are equivalent to a new kind of equation for l for the reduced curves in the Lie algebra g. ![]() ![]() Then L induces a function l:(TG)/G≅g→R called the reduced Lagrangian, g being the Lie algebra of G. 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