相关论文: Remarks on basic calculus in hyperboloidal foliati…
We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a…
Given the growing quantity of proposals and works of basic hypergeometric functions in the scope of $q$-calculus, it is important to introduce a systematic classification of $q$-calculus. Our aim in this article is to investigate certain…
A general method for calculating or constructing lower central factors of groups is presented. {\it Relative basic commutators} are defined.
We present the basic theory of calculus on dual real numbers, and prove the counterpart of the ordinary fundamental theorem of calculus in the context of dual real numbers.
A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators,…
We establish Fourier extension estimates for compact subsets of the hyperbolic hyperboloid in three dimensions via polynomial partitioning.
We give a combinatorial interpretation for the hypergeometric functions associated with tuples of rational numbers.
We give an overview of how calculus of the embedding functor can be used for the study of long knots and summarize various results connecting the calculus approach to the rational homotopy type of spaces of long knots, collapse of the…
In this article we review the basics of the phasor formalism in a rigorous way, highlighting the physical motivation behind it and presenting a hyperbolic counterpart of the phasor addition formula.
In this paper we use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus and we introduce and study certain operators generalizing the classical umbral…
In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.
In this article we give an approach to define continuous functional calculus for bounded quaternionic normal operators defined on a right quaternionic Hilbert space.
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without…
We present an analysis of some constructions and arguments from the universe of T. G. Goodwillie's Calculus, in a general model theoretic setting.
The central structure in various versions of noncommutative geometry is a differential calculus on an associative algebra. This is an analogue of the calculus of differential forms on a manifold. In this short review we collect examples of…
A Compact Introduction to Fractional Calculus is presented including basic definitions, fractional differential equations and special functions.
These notes present elementary introduction to tractors based on classical examples, together with glimpses towards modern invariant differential calculus related to vast class of Cartan geometries, the so called parabolic geometries.
This paper summarizes the core definitions and results regarding the chain differential for functions in locally convex topological vector spaces. In addition, it provides a few elementary calculus rules of practical interest, notably for…
An overview of some basic notions is given, especially with an eye towards somewhat "fractal" examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids.