Sentence examples for cup product from inspiring English sources
We use the latter realization to implement the duality between the derived functor modules and the Beilinson-Bernstein modules, as cup product between local cohomology group followed by evaluation over the fundamental cycle.
In the blank design of square cup stamping, the backward tracing program can produce an appropriate blank configuration which forms a sound net-shape cup product without requiring machining after forming.
Since Galois conjugation gives an isomorphism of natural cohomology groups, which respects the cup product, as for instance the Dolbeault cohomology groups ( H^p(Omega ^q_X)), we obtain interesting consequences in the direction of question A) above.
These Kodaira fibred surfaces S are very interesting topological objects: they were constructed by Kodaira [251] as a counterexample to the conjecture that the index (of the cup product in middle cohomology) would be multiplicative for fibre bundles.
end{aligned}Equivalently, the operator L given by cup product with the cohomology class (h in H^2 (X, {mathbb {Z}})) of a hyperplane, ( L :H^i (X, {mathbb {Z}}) rightarrow H^{i+2} (X, {mathbb {Z}})), induces an isomorphism begin{aligned} L^j :H^{n-j} (X, {mathbb {Q}}) rightarrow H^{n+j} (X, {mathbb {Q}}), quad forall j le n. end{aligned}.
The idea of proof is to use the fact that the first cohomology group (H^1 X, {mathbb {C}})) carries a nondegenerate skew-symmetric form, obtained simply from the cup product in 1-dimensional cohomology multiplied with the ((n-1))-th power of the Kähler class.
The number of customers purchasing World Cup products does not diminish even a little bit.
Hulseman also distributed free Dora Hall records with Solo Cup products.
FIFA has launched more than 600 legal actions around the world to protect its trademarks and copyright, going after unofficially branded World Cup products and counterfeit souvenirs.
(77) 購買世界杯相關產品的顧客一點也沒減少 [Chinese Gigaword] gòumǎi__shìjièbēi__xiāngguān__chǎnpǐn__de__gùkè__[yì__diǎn] purchase__World Cup__related__products__REL__customer__one__dot yě__méi__jiǎnshǎo FOC__NEG__diminish The number of customers purchasing World Cup products does not diminish even a little bit.
The company behind paper bags, pizza boxes, paper coffee cups, cleaning product supplies, meat packaging and toilet roll deliveries said the recession was hitting its customers but that did not necessarily mean a fall in business for Bunzl.
