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.

The first Gröbner basis algorithm was constructed by Buchberger in 1965; thus it bears his name to this day – Buchberger’s algorithm.[9] Though Buchberger’s algorithm looks relatively simple, it can take a very large amount of time. The step that creates 0 h via a normal form calculation is computationally very difficult. This is particularly frustrating (and wasteful) if the normal form calcul...

Let M (f) denote the midpoint rule and T (f) the trapezoidal rule for estimating ∫ b a f(x) dx. Then Simpson’s rule = M (f) + (1 − )T (f), where = 3 . We generalize Simpson’s rule to multiple integrals as follows. Let Dn be some polygonal region in R; let P0; : : : ; Pm denote the vertices of Dn, and let Pm+1 equal the center of mass of Dn. De4ne the linear functionals M (f) =Vol(Dn)f(Pn+1), wh...

For a class of cubic differential systems, Kukles established necessary and sufficient conditions for the existence of a centre. This paper presents a particular system that shows that either Kukles' conditions are incomplete, or the multiplicity of the origin as a focus is greater than or equal to 9. The second author described in [6] a mechanical procedure based on Poincare's classic method, ...

In this paper, it is proved that any algehraicgeometr ic code can be expressed as a cross section of an extended multidimensional cyclic code. Both algebraic-geometric codes and multidimensional cyclic codes are descr ibed by a unified theory of l inear block codes def ined over point sets: algebraic-geometric codes are def ined over the points of an algebraic curve, and an m-dimensional cyclic...

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...

Quadratization is a transform of system ODEs with polynomial right-hand side into at most quadratic via the introduction new variables. It has been recently used as pre-processing step for model order reduction methods, so it important to keep number variables small. Several algorithms have designed search quadratization being monomials in original To understand limitations and potential ways i...

This article investigates the forward kinematics problem formulation and resolution specifically applied to spatial parallel manipulators which allow only for translationnal displacements of the end-effector. The translation manipulator is usually constituted of three to six kinematics chains with three actuators usually located on the base. These mechanisms are designed to prevent any rotation...

In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$  which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...