相关论文: Multivector Functions of a Real Variable

In this article we discuss an important students' misconception about derivatives, that the expression of the derivative of the function contains the information as to whether the function is differentiable or not where the expression is…

Suppose that we are given a formal power series of many variables with coefficients in $\mathbb{R}$ (or $\mathbb{C}$) and we want to compute its $n$-th (multiplicative) root. As can be expected coefficients of the root have to satisfy a…

This is the first part of a work devoted to the study of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence. We prove two main results concerning systems that are regular singular at…

What does it mean to ``add'' velocities relativistically -- clarification of the conceptual problems, new derivations of the related formulas, and identification of the source of the non-associativity of the standard vector version of the…

We extend many theorems from the context of solid angle sums over rational polytopes to the context of solid angle sums over real polytopes. Moreover, we consider any real dilation parameter, as opposed to the traditional integer dilation…

There are given conditions for represention of a function of many arguments as the difference of convex functions.

Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than $ 1 $ are derived. An application in coding theory is illustrated by showing that multispace…

How do we take repeated derivatives of composed multivariate functions? for one-dimensional functions, the common tools consist of the Fa\'a di Bruno formula with Bell polynomials; while there are extensions of the Fa\'a di Bruno formula,…

These notes are about ridge functions. Recent years have witnessed a flurry of interest in these functions. Ridge functions appear in various fields and under various guises. They appear in fields as diverse as partial differential…

Differential Calculus is a staple of the college mathematics major's diet. Eventually one becomes tired of the same routine, and wishes for a more diverse meal. The college math major may seek to generalize applications of the derivative…

This note examines linear combinations of multi-indexed sequences and derives the multivariate generating function of such a linear combination in terms of the original sequence's m.g.f. Applications include finding distributions and…

We quantize the Maxwell theory in the presence of a electric charge in a "dual" Loop Representation, i.e. a geometric representation of magnetic Faraday's lines. It is found that the theory can be seen as a theory without sources, except by…

This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a…

This paper proves that in Size Theory the comparison of multidimensional size functions can be reduced to the 1-dimensional case by a suitable change of variables. Indeed, we show that a foliation in half-planes can be given, such that the…

This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter…

We use a lifting trick to show that the Beurling-Malliavin multiplier theorem extends to radial functions in several variables in a straightforward way. This simplifies an argument of Vasilyev and also answers a question of Vasilyev on the…

Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…

The possibility of physics in multiple time dimensions is investigated. Drawing on recent work by Walter Craig and myself, I show that, contrary to conventional wisdom, there is a well-posed initial value problem--deterministic, stable…

This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…

Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note we consider the analytic properties of diversities, in particular the generalizations of uniform…