In this chapter, we will describe the curves in $\mathbb{R}^2$ or $\mathbb{R}^{3}$ as the image of a function. $$\vec{r}(t) = \big(r_{1}(t), r_{2}(t),\dots ,r_{n}(t ...

In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and ...

Abstract: We provide two extensions of Halanay’s inequality, where the scalar function in the usual Halanay’s inequality is replaced by a vector valued function, under a Metzler condition. We provide ...

Abstract: We provide two extensions of Halanay’s inequality, where the scalar function in the usual Halanay’s inequality is replaced by a vector valued function, under a Metzler condition. We provide ...

This paper covers the concept of a conservative vector field, and its application in vector physics and Newtonian mechanics. Conservative vector fields are defined as the gradient of a scalar-valued ...

Course Description: Calculus of functions of several variables: calculus of vector-valued functions, partial differentiation, multiple integrals. Perform calculus operations on vector‐valued functions ...

The code of Vector-valued Control Variates (vvCVs) is in the folder Vector-valued-Control-Variates-Code/src/src_vvCV_MDMP/. This includes the most generalised version ...