English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In the theory of distributions, there is a general lack ofdefinitions for products and powers of distributions.  In physics(Gasiorowicz (1967), page 141), one finds the need to evaluateδ2 when calculating the transition rates of certainparticle interactions and using some products such as(1/x)⋅δ.  In 1990, Li and Fisher introduced acomputable delta sequence in an m-dimensional space to obtaina noncommutative neutrix product of r−k and Δδ (Δ denotes the Laplacian) for anypositive integer k between 1 and m−1 inclusive. Cheng andLi (1991) utilized a net δϵ(x) (similar to theδn(x)) and the normalization procedure of μ(x)x+λ to deduce a commutative neutrix product ofr−k and δ for any positive real number k. The objectof this paper is to apply Pizetti's formula and the normalizationprocedure to derive the product of r−k and ∇δ (∇ is the gradient operator) on ℝm. The nice propertiesof the δ-sequence are fully shown and used in the proof ofour theorem

international journal of mathematics and mathematical sciences

The product of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$r^{-k}$" id="E1"><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 xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\nabla\delta$" id="E2"><mml:mo>∇</mml:mo><mml:mi>δ</mml:mi></mml:math>on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$\mathbb{R}^{m}$" id="E3"><mml:msup><mml:mi>ℝ</mml:mi><mml:mrow><mml:mi>m</mml:mi></…

The product ofr−kand∇δonℝm