Zobrazeno 1 - 10
of 527
pro vyhledávání: '"13N10"'
Solving systems of partial differential equations (PDEs) is a fundamental task in computational science, traditionally addressed by numerical solvers. Recent advancements have introduced neural operators and physics-informed neural networks (PINNs) t
Externí odkaz:
http://arxiv.org/abs/2411.16663
Autor:
Puthenpurakal, Tony J.
Let $K$ be a field and let $R = K[X_1, \ldots, X_m]$ with $m \geq 2$. Give $R$ the standard grading. Let $I$ be a homogeneous ideal of height $g$. Assume $1 \leq g \leq m -1$. Suppose $H^i_I(R) \neq 0$ for some $i \geq 0$. We show (1) $H^i_I(R)_n \ne
Externí odkaz:
http://arxiv.org/abs/2411.13090
We revisit the concept of special algebras, also known as \textit{purely inseparable ring extensions}. This concept extends the notion of purely inseparable field extensions to the more general context of extensions of commutative rings. We use diffe
Externí odkaz:
http://arxiv.org/abs/2407.01056
Autor:
Steiner, Avi
We provide an alternative definition for the familiar concept of regular singularity for meromorphic connections. Our new formulation does not use derived categories, and it also avoids the necessity of finding a special good filtration as in the for
Externí odkaz:
http://arxiv.org/abs/2406.14253
Let $K$ be a field of characteristic 0 and $S=K[x_1,\ldots,x_m]/I$ be an affine domain. Consider $R=S_P$ where $P\in Spec(S)$ such that $R$ is regular. In this paper we construct a field $F$ which is contained in $R$ such that (1) The residue field o
Externí odkaz:
http://arxiv.org/abs/2406.05390
Autor:
Shi, Quan, Zuo, Huaiqing
We prove the multiplicative Thom-Sebastiani rule for Bernstein-Sato polynomials, answering the longstanding questions of Budur and Popa. We generalize the result to the tensor of two effective divisors on the product of two arbitrary non-singular com
Externí odkaz:
http://arxiv.org/abs/2406.04121
Autor:
Bavula, V. V.
The class of $\D$-locally nilpotent algebras (introduced in the paper) is a wide generalization of the algebras of differential operators on commutative algebras. Examples includes all the rings $\CD (A)$ of differential operators on commutative alge
Externí odkaz:
http://arxiv.org/abs/2406.07569
Autor:
Delgado, Rafael, Heredero, Rafael Hernández, Jiménez-Pastor, Antonio, Rueda, Sonia L., Zurro, Maria-Angeles
Almost commuting operators were introduced in 1985 by George Wilson to present generalizations the Korteweg-de Vries hierarchy, nowadays known as Gelfand-Dikey (GD) hierarchies. In this paper, we review the formal construction of the vector space of
Externí odkaz:
http://arxiv.org/abs/2405.05421
Autor:
Mukhopadhyay, Alapan, Smith, Karen E.
Let $k$ be an arbitrary field. We construct examples of regular local $k$-algebras $R$ (of positive dimension) for which the ring of differential operators $D_k(R)$ is trivial in the sense that it contains {\it no} operators of positive order. The ex
Externí odkaz:
http://arxiv.org/abs/2404.09184
Autor:
Levin, Alexander
We generalize the Gr\"obner basis method for free D-modules to the case of several term orderings induced by a partition of the set of basic variables. Using this generalized Gr\"obner basis technique we prove the existence and give a method of compu
Externí odkaz:
http://arxiv.org/abs/2404.02069