Drainage hydraulics: about the equivalent depth formulae

Equivalent formulae for the supremum and stability of weighted pseudoinverses

During recent decades, there have been a great number of research articles studying interior-point methods for solving problems in mathematical programming and constrained optimization. Stewart and O’Leary obtained an upper bound for scaled pseudoinverses sup W∈P ‖(W 12X)+W 2 ‖2 of a matrix X where P is a set of diagonal positive definite matrices. We improved their results to obtain the suprem...

Size-Depth Tradeoffs for Boolean Formulae

We present a simplified proof that Brent/Spira restructuring of Boolean formulas can be improved to allow a Boolean formula of size n to be transformed into an equivalent log depth formula of size O(nα) for arbitrary α > 1.

Size-Depth Tradeoffs for Algebraic Formulae

Size-Depth Tradeo s for Algebraic Formulae

We prove some tradeoos between the size and depth of algebraic formulae. In particular, we show that, for any xed > 0, any algebraic formula of size S can be converted into an equivalent formula of depth O(log S) and size O(S 1+). This result is an improvement over previously-known results where, to obtain the same depth bound, the formula-size is (S), with 2.

Equivalent forcing depth in tropical oceans

The forcing efficiency for the first and the second baroclinic modes by the wind stress in tropical oceans has been discussed by calculating equivalent forcing depth from annual mean, seasonal, and pentadal density profiles of the observational data. In the annual mean field, the first mode is forced preferentially in the western Pacific and the Indian Ocean, whereas the second mode is more str...