In this paper, we give a new realization of crystal bases for irreducible highest weight modules over Uq(G2) in terms of monomials. We also discuss the natural connection between the monomial realization and tableau realization. Introduction In 1985, the quantum groups Uq(g), which may be thought of as q-deformations of the universal enveloping algebras U(g) of Kac-Moody algebras g, were introd...

We comment on the implementation of various algorithms in multivariate polynomial theory. Specifically, we describe a modular computation of triangular sets and possible applications. Next we discuss an implementation of the F4 algorithm for computing Gröbner bases. We also give examples of how to use Gröbner bases for vanishing ideals in polynomial and rational function interpolation.

Any configuration of lattice vectors gives rise to a hierarchy of higher-dimensional configurations which generalize the Lawrence construction in geometric combinatorics. We prove finiteness results for the Markov bases, Graver bases and face posets of these configurations, and we discuss applications to the statistical theory of log-linear models.

ONIOM calculation is carried out to estimate the acidity of five aliphatic alcohols before and after adsorbing on the tip of (8,0) single-walled carbon nanotube. The ONIOM method is performed using a combination of density functional theory and AM1 semiemperical method for alcohols and their corresponding conjugated bases. Deprotonation Gibbs free energies of alcohols are calculated and compare...

A comprehensive treatment of the theory of Gröbner bases is far beyond the scope of this tutorial. The reader is reffered to [1], [2], [3] for a more detailed discussion. Gröbner bases offers a powerful algorithmic criterion for the existence of solutions to a system of algebraic equations over algebraically closed fields. While the theory is rich and builds on the theory of Ideals and Varietie...

The photoelectron properties of DNA and RNA bases are studied using many-body perturbation theory within the GW approximation, together with a recently developed Lanczos-chain approach. Calculated vertical ionization potentials, electron affinities, and total density of states are in good agreement with experimental values and photoemission spectra. The convergence benchmark demonstrates the im...

In this paper we consider parametric ideals and introduce a notion of comprehensive involutive system. This notion plays the same role in theory of involutive bases as the notion of comprehensive Gröbner system in theory of Gröbner bases. Given a parametric ideal, the space of parameters is decomposed into a finite set of cells. Each cell yields the corresponding involutive basis of the ideal f...

A construction of bases for cell modules of the Birman–Murakami–Wenzl (or B–M–W) algebra Bn(q, r) by lifting bases for cell modules of Bn−1(q, r) is given. By iterating this procedure, we produce cellular bases for B–M–W algebras on which a large Abelian subalgebra, generated by elements which generalise the Jucys–Murphy elements from the representation theory of the Iwahori–Hecke algebra of th...

The theory of Amalgamated Knowledge' Bases [7] represents a formal logical foundation for heterogeneous databases. In an Amalgamated Knowledge Base, data sources are modeled by generalized annotated logic. Moreover, an Amalgamated Knowledge Base is equipped with a supervisor acting as a mediator for amalgamating knowledge from the local databases. Even if the framework is quite appealing, it do...