(3.6) If in (3.6) we substitute (3.3), compare even and odd parts, and then substitute (3.1), then we see that (3.6) is equivalent to a pair of lowering and raising differentiation formulas for Bessel functions (see [14], (10.6.2)): J_{alpha }'(x)- frac{alpha }{x} J_{alpha }(x)=-J_{alpha +1}(x),qquad J_{alpha +1}'(x)+frac{alpha +1}{x} J_{alpha +1}(x)=J_{alpha }(x).
But North Carolina is choosing a tried and true formula: raising payouts increases customer traffic.
Even his favorite formula — raising the "competitive metabolism" — could be read as a version of the old critique of the Times as slow and fustian.
Mr. Kerry is following the Clinton-era formula: raising taxes on the wealthy, spending more for health and education and restoring the spending ceilings and pay-as-you-go budget rules that along with the technology-driven economic surge helped turn the big deficits under Presidents Ronald Reagan and the first President Bush into surpluses.
They would cut benefits by: changing the benefit formula, raising retirement age and diminishing the cost-of-living adjustment COLAadjustment COLA
To bridge the gap, some colleges have begun revising their financial aid formulas, raising concerns about how campus diversity — both economic and racial — might be affected.
But he adamantly opposed any plans to change the formula on raising rents after renovations.
Initial tests conducted by Fonterra and a New Zealand government research institute had indicated the presence of Clostridium botulinum, raising fears that infant formula and sports drinks made from the product and widely exported could be dangerous.
She wasn't Marie Curie or Florence Nightingale, but she knew the formula for raising happy children and maintaining a thriving family.
More generally, if sm ∼ tn is false, then sm+k ∼ tn+k is false for all k ≥ 0. Formulas in the language of the typed theory with ∈ and ∼ have a monotonicity property: if φ is a generalized positive formula and one of its typed versions is false, then any version of the same formula obtained by raising types and refining the values of free variables in the formula will continue to be false.
