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 ...
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 ...
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 ...
Abstract: Kernel methods are among the most popular techniques in machine learning. From a regularization theory perspective, they provide a natural choice for the hypotheses space and the ...
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 ...
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If the space of all real-valued functions of bounded variation on a real closed interval is endowed with the topology of simple convergence, then every bounded subset which is bounded for the values ...
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 ...
What I'm trying to do is dimensionality reduction of a set of m log files containing n time-related signals. They are all physical signals so they are all related to time t. where all the fnm are ...