标题：The product of <mml:math alttext="$r^{-k}$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>r</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:msup></mml:math> and <mml:math alttext="$\nabla\delta$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>∇</mml:mo><mml:mi>δ</mml:mi></mml:math> on
<mml:math alttext="$\mathbb{R}^{m}$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>ℝ</mml:mi><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msup></mml:math>
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2000
卷号：24
DOI：10.1155/S0161171200004233
出版社：Hindawi Publishing Corporation
摘要：In the theory of distributions, there is a general lack of
definitions for products and powers of distributions. In physics
(Gasiorowicz (1967), page 141), one finds the need to evaluate
δ2 when calculating the transition rates of certain
particle interactions and using some products such as
(1/x)⋅δ. In 1990, Li and Fisher introduced a
“computable” delta sequence in an m-dimensional space to obtain
a noncommutative neutrix product of r−k and Δδ (Δ denotes the Laplacian) for any
positive integer k between 1 and m−1 inclusive. Cheng and
Li (1991) utilized a net δϵ(x) (similar to the
δn(x)) and the normalization procedure of μ(x)x
