In this paper, we prove the degenerations of Schubert varieties in a minusculeG/P, as well as the class of Kempf varieties in the flag varietySL(n)/B, to (normal) toric varieties.
As a consequence, we obtain that determinantal varietes degenerate to (normal) toric varieties.
If the additive group of complex numbers acts algebraically on a normal affine variety, then the associated ring of invariants need not be finitely generated, but is an ideal transform of some normal affine algebra (Theorem 1).
We investigate such normal affine algebras in the case of a locally trivial action on a factorial variety.
On the other hand, there is a locally trivialGa-action on a normal affine variety with nonfinitely generated ring of invariants (Theorem 2).
Tilting modules for classical groups and howe duality in positive characteristics
We use the theory of tilting modules for algebraic groups to propose a characteristic free approach to "Howe duality" in the exterior algebra.
In our paper [KR] we began a systematic study of representations of the universal central extension[InlineEquation not available: see fulltext.] of the Lie algebra of differential operators on the circle.
This study was continued in the paper [FKRW] in the framework of vertex algebra theory.
In the present paper we study the remaing nontrivial case, that of a negative central charge-N.
Using the Bayesian method, for certain choices of the prior distribution, several forms of estimators of the parameters in the normal stress Weibull distribution and the inverse power law model are derived.
In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y/x) are studied.
Some simulation results indicate that the method performs better than the normal approximation method in term of coverage accuracies.
These revealed that the inhibiting cells discharged more quantity of heat than the normal growing cells.
A tapped-inductor is used to replace the normal output filter inductor, so that the circulating current in the zero-state can be reset to zero.
Some applications are given to control theory for partial differential equations.
Thus, PPARα/γ dual agonists may provide superior therapy to the current PPARγ-selective agonists, due to the additional lipid control afforded by the PPARα component.
Study subjects were divided into three groups: subjects in group 1 were microalbuminuric diabetic (n = 33), in group 2 subjects were normoalbuminuric diabetic group (n = 32), and group 3 was formed from nondiabetic healthy control subjects (n = 18).
Serum VEGF concentrations were significantly higher in the diabetic groups than in the control group even at the normoalbuminuric stage.
Compound IVc indicated the best antibacterial activity compared with the control drug ampicillin (CAS 69-53-4).