In the present day, nonlinear variational problems or partial differential equation based optimal control problems are not only important but also very challenging problems which usually involve high storage requirements, hard optimization and solution techniques.
With an ageing population, war, and sports related injuries there is an ever-expanding requirement for hard tissue replacement such as bone.
Currently, these two requirements are hard to reconcile: they require either that effects of disease on geometry are negated naturally (by compensatory remodelling) or removed artificially (by hard-to-validate 'virtual' techniques), or that longitudinal studies are carried out over periods at least for human disease of many years.
They either leak, can't be washed properly or end up not meeting airport requirements (how hard is it, for goodness sake?).
Mr. Kass said there are "no refrigeration requirements for hard cheeses," because "their water content is not conducive to bacterial growth".
The complaints boil down to "If you don't win, blame the rules," or "Give us an A for effort instead of results, because the requirements are hard".
But cost-benefit requirements are hard to apply coherently to financial regulation, as the Harvard law professor John Coates IV has argued — because it's rarely possible to get "precise, reliable, quantified" measures there.
Rob Caviness, a guitar teacher at Backbeat Music Studios in Denver, tells Mr. Manjoo that some of his students, veterans of Guitar Hero, have been disappointed when confronted with the real-world requirements of hard work and delayed gratification.
"I'm also glad to see that Co-op Bank hasn't gone down the increasingly common route of introducing daily or monthly agreed overdraft fees as these hit customers with short-term and lower borrowing requirements particularly hard".
