In this research communication on commutative algebra it was proposed to deal with Grobner Bases and its applications in signals and systems domain.This is one of the pioneering communications in dealing with Cryo-EM Image Processing application using multi-disciplinary concepts involving thermodynamics and electromagnetics based on first principles approach. keywords: Commutative Algebra/HOL/S...

We prove an automorphic analogue of Deligne's conjecture for symmetric fourth L-functions Hilbert modular forms. extend the result Morimoto [41] based on generalization and refinement results Grobner Lin [18] to cohomological irreducible essentially conjugate self-dual cuspidal representations GL2 GL3 over CM-fields.

New formulas for the n moment μn(a, b, c, d; q) of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and staircase tableaux. A related positivity theorem is given and another one is conjectured. Résumé. Nous présentons de nouvelles formules pour les n-moments μn(a, b, c, d...

In this extended abstract, we give a complete description and enumeration of smooth and rationally smooth Schubert varieties in finite type. In particular, we show that rationally smooth Schubert varieties are in bijection with a new combinatorial data structure called staircase diagrams. Résumé. Dans ce résumé étendu, nous donnons une description complète et le dénombrement de variétés lisses ...

The Gröbner fan of an ideal I ⊂ k[x1, . . . , xn], defined by Mora and Robbiano, is a complex of polyhedral cones in Rn. The maximal cones of the fan are in bijection with the distinct monomial initial ideals of I as the term order varies. If I is homogeneous the Gröbner fan is complete and is the normal fan of the state polytope of I. In general the Gröbner fan is not complete and therefore no...

pn(xi,...,xn) = 0 for x = (x\,... ,xn). This problem is very common in many fields of science and engineering, such as formula construction, geometric intersection problems, inverse kinematics, power flow problems with PQ-specified bases, computation of equilibrium states, etc. Elimination theory-based methods, most notably the Buchberger algorithm (Buchberger 1985) for constructing Grobner bas...

The concept of comprehensive Grobner bases was introduced by Weispfenning. Montes has proposed an efficient algorithm for computing these bases. But he has not explicitly used Buchberger's criteria in his algorithm. In this paper we prove that we can apply these criteria on Montes algorithm. We propose a modified version of Montes algorithm and evaluate its performance via some examples.