regular singularities造句
例句與造句
- This shows the need to restrict to flat connections with regular singularities in the Riemann Hilbert correspondence.
- In particular, when " X " is compact, the condition of regular singularities is vacuous.
- This equation has regular singularities at 0 and " in the projective line "'P "'1.
- Such a result was proved for algebraic connections with regular singularities by Pierre Deligne ( 1970 ) and more generally for regular holonomic D-modules by Masaki Kashiwara ( 1980, 1984 ) and Zoghman Mebkhout ( 1980, 1984 ) independently.
- Riemann showed that the second-order differential equation for 2 " F " 1 ( " z " ), examined in the complex plane, could be characterised ( on the Riemann sphere ) by its three regular singularities.
- It's difficult to find regular singularities in a sentence. 用regular singularities造句挺難的
- This has two regular singularities at t =-1, 1 and one irregular singularity at infinity, which implies that in general ( unlike many other special functions ), the solutions of Mathieu's equation " cannot " be expressed in terms of hypergeometric functions.
- On the other hand, if we work with holomorphic ( rather than algebraic ) vector bundles with flat connection on a noncompact complex manifold such as " A " 1 = "'C "', then the notion of regular singularities is not defined.
- The condition of regular singularities means that locally constant sections of the bundle ( with respect to the flat connection ) have moderate growth at points of " Y " X ", where " Y " is an algebraic compactification of " X ".
- In fact more is true : Schwarz's list underlies all second-order equations with regular singularities on compact Riemann surfaces having finite monodromy, by a pullback from the hypergeometric equation on the Riemann sphere by a complex analytic mapping, of degree computable from the equation's data.
- "' Riemann Hilbert correspondence "'( for regular holonomic D-modules ) : there is a functor " DR " called the de Rham functor, that is an equivalence from the category of holonomic D-modules on " X " with regular singularities to the category of perverse sheaves on " X ".
- The wider importance of the table, for general second-order differential equations in the complex plane, was shown by Felix Klein, who proved a result to the effect that cases of finite monodromy for such equations and regular singularities could be attributed to changes of variable ( complex analytic mappings of the Riemann sphere to itself ) that reduce the equation to hypergeometric form.
- Since these solutions do not have polynomial growth on some sectors around the point " in the projective line "'P "'1, the equation does not have regular singularities at " . ( This can also be seen by rewriting the equation in terms of the variable " w " : = 1 / " z ", where it becomes