On defining the distributions δ r $\delta^{r}$ and ( δ ′ ) r $(\delta ^{\prime})^{r}$ by conformable derivatives

THE PRODUCT OF r−k AND ∇δ ON Rm

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 ob...

Significant Differences in the Electrochemical Behavior of the r-, !-, γ-, and δ-Tocopherols (Vitamin E)

R-, !-, γ-, and δ-Tocopherols can be oxidized in dry CH2Cl2 or CH3CN by one electron to form cation radicals that deprotonate to form the neutral phenoxyl radicals, which are then immediately further oxidized by one electron to the phenoxonium cations (an ECE electrochemical mechanism, where E signifies an electron transfer and C represents a chemical step, with the electrochemical mechanism ha...

On δ-Quasi Armendariz Modules

δ-Small Submodules and δ-Supplemented Modules

Multiplication of Distributions in one dimension: possible approaches and applications to δ-function and its derivatives

We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our theory to study a certain number of examples, involving products between Dirac delta functions and its successive derivatives.