A Gelfand-Cetlin polytope is a convex polytope obtained as an image of certain completely integrable system on a partial flag variety. In this paper, we give an equivalent description of the face structure of a GC-polytope in terms of so called the face structure of a ladder diagram. Using our description, we obtain a partial differential equation whose solution is the exponential generating fu...

Groebner–Shirshov Basis and Gelfand–Kirillov dimension of the Leavitt path algebra are derived.

11. Geoffroy, M., Lambolez, B., Audinat, E., Hamon, B., Crepe], F., Rossier, J. and Kado, R. T. (1991) Mol. Pharmacol. 39,587-591 12. Lambolez, B., Audinat, E., Bochet, P., Crepe], F. and Rossier, J. (1992) Neuron 9,247-258 Gilliland, G., Perrin, S. and Bunn, F. H. (1990) in PCR Protocols (Innis, M. A., Gelfand, D. H., Sninsky, J. J. and White, T. G., eds.), pp. 60-69, Academic Press, NY Wang, ...

This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as Koszul and Lie algebra methods, homological techniques, and the Bernstein-Gelfand-Gelfand correspondence, all illustrated with concrete calculations. We also...

We study Translation functors and Wall-Crossing functors on inn-nite dimensional representations of a complex semisimple Lie algebra using D-modules. This functorial machinery is then used to prove the Endomorphism-theorem and the Structure-theorem; two important results were established earlier by W. Soergel in a totally diierent way. Other applications to the category O of Bernstein-Gelfand-G...

K e y w o r d s S e c o n d o r d e r impulsive differential system, Singular boundary value problem, Semilinear elliptic problem, Positive solution, Radial solution, Upper solution, Lower solution, Fixed-point index. 1. I N T R O D U C T I O N In this paper , we prove the existence of mul t ip le posi t ive solut ions for a s ingular Gel fand type b o u n d a r y value p rob lem of the followi...

Let sn(T ) denote the nth approximation, isomorphism, Gelfand, Kolmogorov or Bernstein number of the Hardy-type integral operator T given by

We study the supersymmetric Gelfand-Dickey algebras associated with the superpseu-dodifferential operators of positive as well as negative leading order. We show that, upon the usual constraint, these algebras contain the N=2 super Virasoro algebra as a subal-gebra when the leading order is odd. The decompositions of the coefficient functions into N=1 primary fields are then obtained by covaria...