For many, the INDEX-XMATCH combination in Excel is the go-to method for retrieving a value from a dataset. However, you can also use this dynamic duo to perform two-way lookups, returning a value at ...

Originally, Excel was not designed to be a real database. Its early database functions were limited in quantity and in quality. And because every record in an Excel database is visible on the screen ...

Functions are the driving force of any Microsoft Excel spreadsheet, generating a single value or an array of results based on certain arguments you input. However, combining—or nesting—functions ...

We prove the formulae conjectured by the first author for the index of K-theory classes over the moduli stack of algebraic G-bundles on a smooth projective curve. The formulae generalize E. Verlinde's ...

The Atiyah-Singer index theorem gives a topological formula for the index of an elliptic differential operator. The topological index depends on a cohomology class that is constructed from the ...