The PML equations for tsunami momentum, Eq. 2, were derived in the same manner as follows: begin{aligned}& beta_{(x)} frac{partial M}{partial t} + delta_{(x)} M = - ghfrac{partial eta }{partial x} & beta_{ y)} frac{partial N}{partial t} + delta_{ y)} N = - ghfrac{partial eta }{partial y}, end{aligned} (8 where we note that no further decomposition is required.
On the other hand, the BFT of the multipath signal with cross delay τ l from the previous symbol is derived in the same way as begin{aligned} text{BFT}&[r_{l}^(t)]approx & alpha_{l}^{primeprime}text{Sa}left[frac{tau_{l}^{2}}{2}left(beta-pi K_{m}-pi K_{m} 1-tau_{l} 1-tau_{lght)right] e^{jPsi_{l}/T_{s} } end{aligned} (28).
The net recharge map was derived in GIS using the formula as begin{gathered} {text{net recharge }} = {text{ precipitation }}left( {text{rainfall}} right), -, 0.0 5; times ;{text{precipitation }}left( {text{rainfall}} right), hfill - {text{ precipitation }}left( {text{rainfall}} right); times ;{text{run off coefficients}} hfill end{gathered}.
Late-night media reports Tuesday by The Washington Post and Politico confirmed what many have suspected from the beginning, namely that funding was derived in some fashion (at least after the Republican primaries had concluded) from the Clinton presidential campaign.
The quest for the real a term whose proliferating connotations in the musical seem derived, in equal measure, from postmodern literary theory and from hip-hop begins in Los Angeles in the 1970s.
That single four-letter monosyllable, derived from the Latin, beginning in "p" and ending in "b", is a word he insists he would not under any circumstances utter.
We begin with a BN model of the GF pathways as derived in [ 3].
Combination of low-eccentricity formulae of Equations (11) to (13) with the 1−e 2 dependence derived in Equations (14) to (16) gives begin{array}rcl@ leftlangle frac{da}{dt} rightrangle_{text{low}} &=& leftlangle frac{da}{dt} rightrangle_{1} (1-e^{2})^{-alpha + beta -3/2}, end{array} (33).
The three-parameter Birnbaum-Saunders distribution derived in Owen (2006) has PDF begin{array}rcl@ f_{1}(t) = frac{1}{sqrt{2 pi}} frac{1}{a sqrt{b} t^{kappa}} left(1 - kappa + frac{b kappa}{t} right) expleft[ -frac{(t - b)^{2}}{2 a^{2} b t^{2 kappa}} right],~~ t > 0, end{array} (8).
The probability density of these n×n dimensional complex matrices was recently derived in [6]: begin{aligned} p_{W}(mathbf{W} propto &e^{-a^{-1}text{tr}mathbf{W}} det(mathbf{W})^{n_{A}-n}×Psileft(n_{B},n_{A}+n_{B}+n;(b^{-1}mathbf{I}_{n} +a^{-1}mathbf{W} right). end{aligned} (12).
