The following theorem provides a formula that can be programmed into a computer algebra package in order to calculate the number of distinct shuffles of two permutations. Maple 11.0 running on a 2008 laptop can quickly handle calculations up to length 13. For example, #sh(id13, 789 10 11 12 13

Hyperbolic systems of conservation laws in one-space dimension

The possibility of reversion of the inequality in the Second Main Theorem of Cartan in the theory of holomorphic curves in projective space is discussed. A new version of this theorem is proved that becomes an asymptotic equality for a class of holomorphic curves defined by solutions of linear

In [S, Ch. IV, §18] the Main Theorem of complex multiplication is proved in a manner that uses some adelic formalism. However, [S] uses a framework for algebraic geometry that has long been abandoned, so many of the beautiful ideas there are somewhat shrouded in mystery for the reader who

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In this paper, we consider the defect (also called ramification deficiency) of finite extensions of valued fields. For a valued field (K,v), we will denote its value group by vK and its residue field by K or by Kv. An extension of valued fields is written as

[2] Preliminary considerations

Conclusion ◮ Network coding is a theory for communicating information across networks more efficiently.

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