相关论文: Groebner-Shirshov Bases: Some New Results
In this paper, we give a new realization of crystal bases for irreducible highest weight modules over $U_q(G_2)$ in terms of monomials. We also discuss the natural connection between the monomial realization and tableau realization.
Recent experimental results in charm and charmonium spectroscopy are reviewed.
Recently published formulas for the surface and regular solid spherical harmonics and for the expansion of the product of two normalized associated Legendre functions with different centers in ellipsoidal coordinates (Telhat Ozdogan, Metin…
Recent years have seen rapid developments in our knowledge and understanding of meson spectroscopy, especially in the charm quark sectors. In my invited overview I discussed some of these recent new developments, including theoretical…
The differential equation proposed by Frits Zernike to obtain a basis of polynomial orthogonal solutions on the the unit disk to classify wavefront aberrations in circular pupils, is shown to have a set of new orthonormal solution bases,…
A new homological symmetry condition is exhibited that extends and unifies several recently defined and widely used concepts. Applications include general constructions of tilting modules and derived equivalences, and characterisations of…
Motivated by better understanding the bideterminant (=product of minors) basis on the polynomial ring in $n \times m$ variables, we develop theory \& algorithms for Gr\"obner bases in not only algebras with straightening law (ASLs or Hodge…
We establish new connection formulae between Fibonacci polynomials and Chebyshev polynomials of the first and second kinds. These formulae are expressed in terms of certain values of hypergeometric functions of the type 2F1. Consequently,…
In this paper, we give a new proof of Hirose--Sato's formula for the expansion of $\zeta(\{2\}^{a_1-1},3,\dots,\{2\}^{a_r-1},3,\{2\}^{c-1},1,\{2\}^{b_1},\dots, 1,\{2\}^{b_s})$ in the Hoffman basis, using the drop 1 relation.
In his Ph.D. thesis, Sean Griffin introduced a family of ideals and found monomial bases for their quotient rings. These rings simultaneously generalize the Delta Conjecture coinvariant rings of Haglund-Rhoades-Shimozono and the cohomology…
This is a continuation of [15, 16]. We shall show that for type D_n the realization of crystal bases obtained from the decorated geometric crystals in [2] coincides with the polyhedral realizations of crystal bases.
We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…
Symmetry considerations are used in presenting a model of the electronic structure and the associated dynamics of the nitrogen-vacancy center in diamond. The model accounts for the occurrence of optically induced spin polarization, for the…
Schubert polynomials were introduced in the context of the geometry of flag varieties. This paper investigates some of the connections not yet understood between several combinatorial structures for the construction of Schubert polynomials;…
In this paper, a survey about recent progress on problems solved using graph amalgamations is presented, along with some new results with complete proofs, and some related open problems.
The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff-Love type, a detailed review of existing formulations of Kirchhoff-Love and Simo-Reissner…
Assuming sufficiently many terms of a n-dimensional table defined over a field are given, we aim at guessing the linear recurrence relations with either constant or polynomial coefficients they satisfy. In many applications, the table terms…
We present a systematic study of the performance of numerical pseudo-atomic orbital basis sets in the calculation of dielectric matrices of extended systems using the self-consistent Sternheimer approach of [F. Giustino et al., Phys. Rev. B…
We introduce the specialization map in Scholzes theory of diamonds. We consider v-sheaves that behave like formal schemes and call them kimberlites. We attach to them: a reduced special fiber, an analytic locus, a specialization map, a…
We report on the most recent experimental progress on $XYZ$ charmoniumlike meson states and their possible counterparts in the $s\overline{s}$ and $b\overline{b}$ systems.