We have now calculated additional terms in the asymptotic expansions, yielding relatively simple approximations for P and Q that are valid for crack-like pores having aspect ratios as high as 0.3, needle-like pores having aspect ratios as low as 3, and nearly spherical pores.
Mr. Pyburn said the workers were disciplined for valid reasons, like leaving work stations without permission.
The permits, which are issued by states, should be valid nationwide like a driver's license, Trump said.
The law bars retaliation, but states that as long as an employer has a "valid reason," like a prolonged absence, the firing is legitimate.
One was asked about his poor timekeeping and said he was only ever late when he had a valid excuse, "like when the police break down your door and are all over the place looking for drugs".
That year, 49,000 students without an officially valid excuse, like an illness, did not take the English test, and 67,000 did not sit for the math test, according to the State Education Department.
A new series of passports was being printed, but the Ministry of the Interior had ordered only around twenty thousand copies, an Iraqi official told me, far too few to meet the need which meant that obtaining a valid passport, like buying gas or heating oil, would become subject to black-market influences.
A new series of passports was being printed, but the Ministry of the Interior had ordered only around twenty thousand copies, an Iraqi official told me, far too few to meet the need — which meant that obtaining a valid passport, like buying gas or heating oil, would become subject to black-market influences.
Ms. Caproni also said that even though the F.B.I. manual says agents can open assessments "proactively," they still must always have a valid reason — like a tip that is not solid enough to justify a more intensive level of investigation but should still be checked out.
That is, we still make valid formulae like p ⊰ (q ⊰ q).
