相关论文: On Two Kinds of Differential Operators on General …

Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questions and employing different methodologies. It is the purpose…

We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…

This paper considers steady surface waves `riding' a Beltrami flow (a three-dimensional flow with parallel velocity and vorticity fields). It is demonstrated that the hydrodynamic problem can be formulated as two equations for two scalar…

We study some canonical differential operators on vector bundles over smooth, complete Riemannian manifolds. Under very general assumptions, we show that smooth, compactly supported sections are dense in the domains of these operators.…

In this paper we consider a slab of viscous incompressible fluid bounded above by a free boundary, bounded below by a flat rigid interface, and acted on by gravity. The unique equilibrium is a flat slab of quiescent fluid. It is well-known…

These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the…

In this paper we provide a definition of fractional gradient operators, related to directional derivatives. We develop a fractional vector calculus, providing a probabilistic interpretation and mathematical tools to treat multidimensional…

The aim of this paper is twofold. On the one hand, the study of gradient Schr\"{o}dinger operators on manifolds with density $\phi$. We classify the space of solutions when the underlying manifold is $\phi-$parabolic. As an application, we…

We investigate the functional determinant of the laplacian on piece-wise flat two-dimensional surfaces, with conical singularities in the interior and/or corners on the boundary. Our results extend earlier investigations of the determinants…

This manuscript, titled Differential Geometry of Curves and Surfaces in Three-dimensional Euclidean Space, is intended for undergraduate students of mathematics and other sciences with the need of use of Euclidean differential geometry. We…

The divergence-like operator on an odd symplectic superspace which acts invariantly on a specially chosen odd vector field is considered. This operator is used to construct an odd invariant semidensity in a geometrically clear way. The…

We present a method for calculating the results of operation of differential operators operating on components of vector in generalized coordinates not restricted to orthogonal one. For this we use the relationships between covariant,…

This paper deals with sheaves of differential operators on noncommutative algebras. The sheaves are defined by quotienting a the tensor algebra of vector fields (suitably deformed by a covariant derivative) to ensure zero curvature. As an…

Invited talk at the International Symposium on Generalized Symmetries in Physics at the Arnold-Sommerfeld-Institute, Clausthal, Germany, July 26 -- July 29, 1993. This talk reviews results on the structure of algebras consisting of…

If a one-variable function is sufficiently smooth, then the limit position of secant lines its graph is a tangent line. By analogy, one would expect that the limit position of secant planes of a two-variable smooth function is a plane…

There are several types of Laplacians of a vector field on a Riemannian manifold. These include the Bochner and the Hodge Laplacian. The Gauss formula for the Levi-Civita connection relates the extrinsic connection to the intrinsic…

We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…

We give a complete description of differential operators generating a given bracket. In particular we consider the case of Jacobi-type identities for odd operators and brackets. This is related with homotopy algebras using the derived…

Let $\Delta$ be a linear differential operator acting on the space of densities of a given weight $\lo$ on a manifold $M$. One can consider a pencil of operators $\hPi(\Delta)=\{\Delta_\l\}$ passing through the operator $\Delta$ such that…

In this paper, autonomous differential equations type delta of order one on integral domains are defined. For this we will use the autonomous ring defined on the Hurwitz expansion ring of exponential generating functions with coefficients…