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 ...

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 ...

Abstract: The setting is that of vector-valued codes of length N. The background for this setting is our construction of new complex valued constant amplitude zero autocorrelation codes (off dc) - ...

ABSTRACT: The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function ; that ...

Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, Nouvelle Série, Vol. 52 (100), No. 3 (2009), pp. 211-226 (16 pages) We survey results on holomorphic functions (of one ...

We prove here that the Hardy space of $B$-valued functions $H^1(B)$ defined by using the conjugate function and the one defined in terms of $B$-valued atoms donot ...

Abstract: Definition of the weak Pareto improvement and the trap of weak Pareto improvement are given for noncooperative dynamical systems with vector-valued payoff functions. Specifically, we develop ...