| Richard P. Stanley - Mathematics - 1997 - 600 pages
...(where « is a Laurent monomial in x\, . . . . xk) is a kind of "generalized noncommutative diagonal." **The main result of this section is given by the following theorem.** 6.7.1 Theorem. Let S = S(X, Y) be given by (6.52). Suppose that S(X, X~') is well-defined formally,... | |
| M. S. Agranovich - Mathematics - 2002 - 292 pages
...approximate y by y* € H* n BR. The operator Gi(X. Dmi u) can be studied similarly. The lemma is proved. D **The main result of this section is given by the following theorem. THEOREM** 7.9. Suppose that the operator F(x.D2m) is uniformly elliptic and that the Shapiro Lopatin.shi conditions... | |
| V. Lakshmikantham, S. Koksal - Mathematics - 2003 - 336 pages
...in the ordered interval [QO,/3O] formed by the lower and upper solutions c*o and /3o, respectively. **The main result of this section is given by the following theorem. Theorem** 6.5.1 Let hypotheses (Hl)-(H3) be satisfied. Then there exist monotone sequences (аn)^=i, (ßn)^=i... | |
| Sergei V. Petrovskii, Bai-Lian Li - Mathematics - 2005 - 242 pages
...is equivalent to assumption (6.26). That proves the theorem. 6.1.2 Exact solution and its properties **The main result of this section is given by the following theorem: Theorem** 6.3. Under constraints (6.10-6.11) and k > 2^/m, the system (6.8-6.9) has the following exact solution:... | |
| Vitaly Volpert - Differential equations, Elliptic - 2007 - 88 pages
...is formally adjoint to the operator L*. Therefore dim Ker(L) > dim Ker(L*). The corollary is proved. **The main result of this section is given by the following theorem. Theorem** 4.3. Suppose that the dimension of the kernel of the operator Ln equals fi and the codimension of the... | |
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