相关论文: Grobner fan for analytic D-modules with parameters
We apply Schmidt's Subspace Theorem to establish Arithmetic General Theorems for projective varieties over number and function fields. Our first result extends an analogous result of M. Ru and P. Vojta. One aspect to its proof makes use of…
A generalized criterion for signature related algorithms to compute Gr\"obner basis is proposed in this paper. Signature related algorithms are a popular kind of algorithms for computing Gr\"obner basis, including the famous F5 algorithm,…
We consider single particle Schrodinger operators with a gap in the en ergy spectrum. We construct a complete, orthonormal basis function set for the inv ariant space corresponding to the spectrum below the spectral gap, which are…
In this paper, we give a sufficient condition for a set $\mathal G$ of polynomials to be a Gr\"obner basis with respect to a given term-order for the ideal $I$ that it generates. Our criterion depends on the linkage pattern of the ideal $I$…
Given $p$ polynomials with coefficients in a commutative unitary integral ring $\mathcal{C}$ containing $\mathbb{Q}$, we define the notion of a generic Bernstein-Sato polynomial on an irreducible affine scheme $V \subset…
This article is partly a survey and partly a research paper. It tackles the use of Groebner bases for addressing problems of numerical semigroups, which is a topic that has been around for some years, but it does it in a systematic way…
For associative algebras in many different categories, it is possible to develop the machinery of Gr\"obner bases. A Gr\"obner basis of defining relations for an algebra of such a category provides a "monomial replacement" of this algebra.…
In this paper, we suggest a new efficient algorithm in order to compute S-polynomial reduction rapidly in the known algorithm for computing Grobner bases, and compare the complexity with others.
We apply convex geometry (cones, fans) to homological input (abelian categories, hearts of bounded t-structures) to construct a new invariant of an abelian category, its heart fan. This can be viewed as a `universal phase diagram' for…
The generalized Graetz problem refers to stationary convection-diffusion in uni-directional flows. In this contribution we demonstrate the ana-lyticity of generalized Graetz solutions associated with layered domains: either cylindrical…
In this talk I give an elementary introduction to the key algorithm used in recent applications of computational algebraic geometry to the subject of string phenomenology. I begin with a simple description of the algorithm itself and then…
Given n polynomials in n variables with a finite number of complex roots, for any of their roots there is a local residue operator assigning a complex number to any polynomial. This is an algebraic, but generally not rational, function of…
In this thesis we develop the foundations for a theory of analytic geometry over a valued field, uniformly encompassing the case when the base field is equipped with a non-archimedean valuation and the case when it has an archimedean one.…
We consider a differential algebra F of formal power series in infinitely many variables. We define the important notions of a normalized set of generators for an ideal of F and a regular quotient algebra. The concept of the passive…
We consider partially observed multiscale diffusion models that are specified up to an unknown vector parameter. We establish for a very general class of test functions that the filter of the original model converges to a filter of reduced…
For an ideal of a regular $\cc$-algebra, its Bernstein-Sato polynomial is the monic polynomial of the lowest degree satisfying an Bernstein-Sato functional equation. We generalize the notion of Bernstein-Sato functional equations to the…
We show that the Bernstein-Sato polynomial (that is, the b-function) of a hyperplane arrangement with a reduced equation is calculable by combining a generalization of Malgrange's formula with the theory of Aomoto complexes due to Esnault,…
In this paper we mainly study the necessary conditions for the existence of functionally independent generalized rational first integrals of ordinary differential systems via the resonances. The main results extend some of the previous…
Polynomial filters, a kind of Graph Neural Networks, typically use a predetermined polynomial basis and learn the coefficients from the training data. It has been observed that the effectiveness of the model is highly dependent on the…
Complete bases that are useful for beam propagation problems and that present the distinct property of being spatially confined at the initial plane are proposed. These bases are constructed in terms of polynomials of Gaussians, in contrast…