例句與造句

1. The Fredholm alternative can be applied to solving linear elliptic boundary value problems.
2. This example has the same essential properties as all other elliptic boundary value problems.
3. The analysis of elliptic boundary value problems requires some fairly sophisticated tools of functional analysis.
4. Existence of the solution and spectral properties then follow from the theory of compact operators; in particular, an elliptic boundary value problem on a bounded domain has infinitely many isolated eigenvalues.
5. He studied mathematics at the University of Bonn gaining his PhD in 1980 with the title " Infinitely Many Solutions for Superlinear, Anticoercive Elliptic Boundary Value Problems without Oddness ".
6. It's difficult to find elliptic boundary value problem in a sentence. 用elliptic boundary value problem造句挺難的
7. However, whereas the spectral method is based on the eigendecomposition of the particular boundary value problem, the spectral element method does not use that information and works for arbitrary elliptic boundary value problems.
8. In the 1950s Schwarz's method was generalized in the theory of partial differential equations to an iterative method for finding the solution of a elliptic boundary value problem on a domain which is the union of two overlapping subdomains.
9. An important example of a compact operator is compact embedding of Sobolev spaces, which, along with the G錼ding inequality and the Lax Milgram theorem, can be used to convert an elliptic boundary value problem into a Fredholm integral equation.
10. For second order elliptic boundary value problems, piecewise polynomial basis function that are merely continuous suffice ( i . e ., the derivatives are discontinuous . ) For higher order partial differential equations, one must use smoother basis functions.
11. Because of the good properties we have enumerated ( as well as many we have not ), there are extremely efficient numerical solvers for linear elliptic boundary value problems ( see finite element method, finite difference method and spectral method for examples .)
12. By the mid 1960s the theory of singular integrals was firmly established by Calder髇's contributions to the theory of differential equations, including his proof of the " uniqueness in the Cauchy problem " using algebras of singular integral operators, his reduction of elliptic boundary value problems to singular integral equations on the boundary ( " the method of the Calder髇 projector " ), and the crucial role played by algebras of singular integrals ( through the work of Calder髇 s student R . Seeley ) in the " initial proof of the Atiyah-Singer Index Theorem ", see also the Commentary by Paul Malliavin . and Calder髇 s proof of the " boundedness of the  first commutator ".