Related papers: Vector Differential Operators in arbitrary coordin…
It is generally well understood the legitimate action of the Moisil-Theo\-do\-res\-co ope\-ra\-tor, over a quaternionic valued function defined on $\mathbb{R}^3$ (sum of a scalar and a vector field) in Cartesian coordinates, but it does not…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.
We consider a variable order differential operator on a graph with a cycle. We study the inverse spectral problem for this operator by the system of spectra. The main results of the paper are the uniqueness theorem and the constructive…
We exhibit a set of generating relations for the modular invariant ring of a vector and a covector for the two-dimensional general linear group over a finite field.
Symmetry is present in many tasks in computer vision, where the same class of objects can appear transformed, e.g. rotated due to different camera orientations, or scaled due to perspective. The knowledge of such symmetries in data coupled…
We suggest a new concept of functional-differential operators with constant delay on geometrical graphs that involves {\it global} delay parameter. Differential operators on graphs model various processes in many areas of science and…
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…
This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus,…
We define generalized vector fields, and contraction and Lie derivatives with respect to them. Generalized commutators are also defined.
In this article, discrete variants of several results from vector calculus are studied for classical finite difference summation by parts operators in two and three space dimensions. It is shown that existence theorems for scalar/vector…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
We give an algorithm to write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent…
The paper introduces a method of partial fractions with matrix coefficients and its applications to finding chains of generalized eigenvectors, to evaluation of matrix exponentials, and to solution of linear systems of ordinary differential…
Basic properties of Fourier integral operators on the torus are studied by using the global representations by Fourier series instead of local representations. The results can be applied to weakly hyperbolic partial differential equations.
We introduce a more general discrete fractional operator, given by convex linear combination of the delta and nabla fractional sums. Fundamental properties of the new fractional operator are proved. As particular cases, results on delta and…
We introduce basic aspects of new operator method, which is very suitable for practical solving differential equations of various types. The main advantage of the method is revealed in opportunity to find compact exact operator solutions of…
Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the…
This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemented with dual numbers. Directional derivatives are particular…
We study invariants under gauge transformations of linear partial differential operators on two variables. Using results of BK-factorization, we construct hierarchy of general invariants for operators of an arbitrary order. Properties of…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…