Chronic paroxysmal hemicrania Chronic paroxysmal hemicrania Chronic paroxysmal hemicrania (CPH), also known as Sjaastad syndrome, is a severe debilitating unilateral headache usually affecting the area around the eye. It normally consists of multiple severe, yet short, headache attacks affecting only one side of the cranium. It is more commonly diagnosed in women than in men, but, unlike a migraine, has no neurological symptoms associated with it. CPH headaches are treated through the use of non-steroidal anti-inflammatory drugs, with indomethacin found to be usually effective in eliminating symptoms. Paroxysmal hemicrania is classified by the frequency and duration of attacks experienced by patients. Episodic paroxysmal
Formally smooth map equivalent to usual notion of smoothness. Formally smooth map In algebraic geometry and commutative algebra, a ring homomorphism formula_1 is called formally smooth (from French: "Formellement lisse") if it satisfies the following infinitesimal lifting property: Suppose "B" is given the structure of an "A"-algebra via the map "f". Given a commutative "A"-algebra, "C", and a nilpotent ideal formula_2, any "A"-algebra homomorphism formula_3 may be lifted to an "A"-algebra map formula_4. If moreover any such lifting is unique, then "f" is said to be formally étale. Formally smooth maps were defined by Alexander Grothendieck in "Éléments de géométrie algébrique" IV. For