In order to rewrite Equation 13 in terms of (r1, θ1), the necessary coordinate transformation from (r2, θ2) to (r1, θ1) is accomplished via Graf's addition formula for Bessel functions (section 11.3, p 360, Equation 2 in Watson1966), which is recast in an appropriate form as follows: J n k 2 r 2 cos n θ 2 + φ = ∑ m = 0 ∞ J m k 2 r 1 F m, n C cos m θ 1 + F m, n S sin m θ 1, (14).
This case, which is recast as a logic AND relationship between the genes k 1 and k 2, can be enforced by the following set of constraints: (3) { w k 1. L B j ≤ v j ≤ w k 1. U B j w k 2. L B j ≤ v j ≤ w k 2. U B j Note that based on these equations, if at least one of w k 1 or w k 2 is zero, then the flux through reaction j is forced to zero.
"Travelers are seeking to bring back experiences and memories," said Dan Vinh, vice president for marketing at Renaissance in Bethesda, Md., which is recasting its concierges as "navigators," a change that is underlined by a microsite, renaissancenavigator.com, in both online and mobile versions.
The popular 1980s detective show "Remington Steele" is getting a modern-day make-over thanks to NBC, which is recasting the show as a half-hour comedy.
Nationwide, the walks -- which were recast as marches, with flags replacing corporate banners -- raised 15percentt more than they did a year ago, she said.
The bell, which was recast twice in its early days, is predominantly copper but contains nine other elements, including gold and arsenic, along with "cracks, fissures and air bubbles," Ms. Diethorn said.
The variational inflation mechanics problem yields the governing equations and boundary conditions, which are recast as a nonlinear two-point boundary value problem in a suitable form for efficient computation.
There is a ring of eight bells, six of which were recast in 1925 by Taylor's of Loughborough from the metal of the previous four 17th-century bells.
In the end, though, these are points of distinction that do not detract from the pleasures of the new record, and which in fact help it in its central mission, which is to recast Armstrong and Jones as conservators of the past and send listeners back to "Songs Our Daddy Taught Us".
The findings suggest that people with low self-esteem may be resistant to their friends' efforts to help them feel better about themselves, particularly a strategy called positive reframing, which is a recasting of a situation in a positive light.
This sharing of parts goes to the heart of the "real" Jaguar question, which might be recast: "Isn't it really a Ford?" -- as if that would make it louche and low-rent.
