101 Ready-To-Use Excel Macros by Michael Alexander

By Michael Alexander

Shop time and be extra effective with this useful advisor to Excel macros!

While such a lot books approximately Excel macros provide basically minor examples, often aimed toward illustrating a selected subject, this worthwhile source provide you with the instruments had to successfully and successfully software Excel macros instantly. step by step directions assist you to create VBA macros and clarify find out how to customise your functions to seem and paintings precisely as you will have them to. through the tip of the e-book, you'll know the way every one featured macro works, be capable to reuse the macros integrated within the booklet and on-line, and adjust the macro for private use. indicates you the way to unravel universal issues of the featured macros, no matter if you lack large programming wisdom Outlines an issue that should be solved and gives the particular Excel macro, in addition to the downloadable code, to resolve the matter presents a proof of ways each one macro works and the place to exploit the macro.

With "101 Ready-to-Use Excel Macros," Microsoft MVP Michael Alexander is helping you retailer time, automate projects, and eventually be extra efficient.

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Extra info for 101 Ready-To-Use Excel Macros

Example text

Locally free OY -modules of finite ranks). Hence the assertion is obvious. 10. Note that Lf ∗ DY = DX→Y ⊗L f −1 DY = DX→Y . 2). We see from this that the functor Lf ∗ for f : X → Y does not necessarily send Dcb (DY ) to Dcb (DX ). We call Lf ∗ the inverse image functor on derived categories of D-modules. We will also use the shifted inverse image functor f † = Lf ∗ [dim X − dim Y ] : D b (DY ) → D b (DX ). defined by f † M · = Lf ∗ M · [dim X − dim Y ]. The shifted one will be more practical in considering the Riemann–Hilbert correspondence.

Sr contained in N −1 . Then i N = i −1 N −1 is generated as a DX -module by the sections s1 , . . , sr . The proof is complete. b,X b (D ) (resp. (DY ) (resp. Dcb,X (DY )) the subcategory of Dqc Denote by Dqc Y Dcb (DY )) consisting of complexes N˙ whose cohomology sheaves H ∗ (N˙) are supported by X. 2. For = qc or c the functor : D b (DX ) → D b,X (DY ) i gives an equivalence of triangulated categories. Its quasi-inverse is given by Ri = i † : D b,X (DY ) → D b (DX ). Proof. It is easily seen that i sends D b (DX ) to D b,X (DY ) and Ri sends D b,X (DY ) to D b (DX ).

Considering (X, π ∗ M) as a C× -module, we get its weight space decomposition (X, π ∗ M) = γ (M)(l) , l∈Z where z ∈ C× acts on γ (M)(l) by zl . In particular, (X, M) = γ (M)(0) . Now let us consider the Euler vector field θ = ni=0 xi ∂i (here {xi } is a linear coordinate system of V and ∂i = ∂/∂xi ) on V . If we define the action of θ on π ∗ M by θ ⊗ Id, we have γ (M)(l) = {u ∈ (X, π ∗ M) | θu = lu }. Moreover, we can easily check xi (γ (M)(l) ) ⊂ γ (M)(l+1) , ∂i (γ (M)(l) ) ⊂ γ (M)(l−1) . Set Z = {0} × Y ⊂ V × Y , and let j : X → V × Y and k : Z → V × Y be the embeddings.

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