It would be interesting to verify in examples that this is the case in at least the majority of the differential equations which are known to be integrable in finite terms.
Lie has determined all distinct types of continuous groups of orders three or four; and all types of non-integrable groups (a term which will be explained immediately) of orders five and six (cf.
If G is an integrable group of order r, the infinitesimal operations X1, X2, .
It is easily soluble in the common organic solvents, and crystallizes in plates or tables melting at 238 deg.
Caraways are, however, more extensively consumed entire in certain kinds of cheese, cakes and bread, and they form the basis of a popular article of confectionery known as caraway comfits.
The essential oil is largely obtained by distillation for use in medicine as an aromatic stimulant and carminative, and as a flavouring material in cookery and in liqueurs for drinking.
It is also obtained as a decomposition product of brucine or strychnine, when these alkaloids are distilled with zinc dust.
It distils unchanged, even when the operation is carried out in the presence of zinc dust.
These limitations on the nature of the function are known as Dirichlet's conditions; it follows from them that the function is integrable throughout the interval.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "integrable" in a variety of sentences. We hope that you will now be able to make sentences using this word.
