| 1. |
- Brahme, Anders, et al.
(författare)
-
Solution of an integral equation encountered in rotation therapy
- 1982
-
Ingår i: Physics in Medicine and Biology. - : IOP Publishing. - 0031-9155 .- 1361-6560. ; 27:10, s. 1221-1229
-
Tidskriftsartikel (refereegranskat)abstract
- An integral equation relating the lateral absorbed dose profile of a photon beam to the resultant absorbed dose distribution during single-turn rotating-beam therapy has been set up and solved for the case of a cylindrical phantom with the axis of rotation coinciding with the axis of symmetry of the cylinder. In the first approximation the results obtained are also valid when the axis of rotation is somewhat off-centred, even in a phantom that deviates from circular symmetry, provided the rotation is performed in both clockwise and counter clockwise directions. The calculated dose profiles indicate that improved dose uniformity can be achieved using a new type of non-linear wedge-shaped filter, which can easily be designed using the derived general analytic solution to the integral equation.
|
|
| 2. |
- Roos, Jan-Erik, 1935-
(författare)
-
Three-Dimensional Manifolds, Skew-Gorenstein Rings and their Cohomology.
- 2010
-
Ingår i: Journal of Commutative Algebra. - Tempe, AZ : Rocky Mountain Mathematics Consortium. - 1939-0807. ; 2:4, s. 473-499
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra). We present some applications of the homological theory of these graded skew-commutative rings. In particular we find compact oriented 3-manifolds without boundary for which the Hilbert series of the Yoneda Ext-algebra of the cohomology ring of the fundamental group is an explicit transcendental function. This is only possible for large first Betti numbers of the 3-manifold (bigger than - or maybe equal to - 11). We give also examples of 3-manifolds where the Ext-algebra of the cohomology ring of the fundamental group is not finitely generated.
|
|
| 3. |
|
|
| 4. |
|
|
| 5. |
|
|
| 6. |
- Roos, Jan-Erik
(författare)
-
Détermination de la dimension homologique globale des algèbres de Weyl. (French)
- 1972
-
Ingår i: Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences. Séries A et B. - 0151-0509. ; 274:1, s. A23-A26
-
Tidskriftsartikel (refereegranskat)abstract
- (Review by Rinehart):Let An be the algebra obtained from a field K by adjoining variables x_1, · · · , x_n, y_1, · · · , y_nsubject to the relations x_iy_j −y_jx_i =\delta ij . If K has characteristic 0, the reviewer showed [Proc.Amer. Math. Soc. 13 (1962), 341–346; MR0137747 (25 #1196)] that A_1 has global dimension 1.For larger n there followed an inequality, but the problem of a precise determination has remainedopen until now. The author shows that A_n has global dimension n in characteristic 0. His result isindependent of (and includes) the reviewer’s. His proof for general n is considerably simpler thanthat of the reviewer for n = 1, although this fact may be obscured by his deduction of the resultfrom general considerations involving Gabriel’s localizations. The only localizations that arise inthis case involve passage from A_n to A_n \otimes_{K[x_n]} K(x_n) (with the evident ring structure), and asimilar one for y_n. These rings are easily seen to have dimension at most n (using an inductivehypothesis), and the author shows that it follows readily that the weak dimension of A_n is at mostn. This suffices, since An is Noetherian.Reviewed by G. S. Rinehart
|
|
| 7. |
|
|
| 8. |
|
|
| 9. |
|
|
| 10. |
|
|
