delta sequenceDirac-delta functionHeaviside functionHadamard finite partneutrix limitregular sequencecompositiondistributionThe symbol [equation] for an infinitely differentiable function f having a simple root is meaningless in the theory of Schwartz distributions. In this work we first of all give meaning...
Under any reflection or rotationρ, the delta function is invariant: As in the one-variable case, it is possible to define the composition of δ with a bi-Lipschitz function[23] g : Rn→ Rn uniquely so that the identity for all compactly supported functions ƒ. Using the coarea formula...
Results on compositions involving Dirac-delta function The distributional composition δ~((r))(x_+~λ) for λ = 0, in other words, the composition δ~((r))(H(x)) is defined as the neutrix limit of the regular s... E Ozcag - Application of Mathematics in Technical & Natural Sciences...
A result on the neutrix composition of the delta function where [([[PHI].sup.*]).sup.n] is the convolution of [PHI] with itself n times, [([[PHI].sup.*]).sup.0] = [[delta].sub.0] by convention with [[delta].sub.0] is the Dirac distribution at 0. Large deviations properti...
Series of Dirac delta functions, Proceedings of the International Conference on Differential Equations, Edinburg,Texas,1991; in: Partial Differential Equations,... R Estrada,R Estrada,R Estrada - International Conference on Differential Equations 被引量: 0发表: 1991年 Ergodicity of Markov semigroups ...
Based on the crystallographic features given above, we chose a Ba-rich composition (Ba is 40% and the others are 15% each) aiming to create a polar high-entropy phase. We note that this composition still has a large configurational entropy (≃1.50R; R is the universal gas constant), ...
. the function \(t \mapsto \text {im}\, ( f_{\pm , t} | d_{\omega ,\lambda } f_{\pm , t} )\) is continuous and converges to zero for \(t \rightarrow \infty \) , so for every \(\epsilon \in ]0, \delta ]\) there exists \(t \ge t_0\) such that \(\...
\Delta M\propto -{B}^{\gamma }{R}_{{\rm{T}}}{R}_{{\rm{D}}}{\mathrm{{sin}}}\left[2\pi \times \left(\frac{F}{B}-\frac{1}{2}+\beta +\delta \right)\right] (1) whereRT = (λTμ/B)/sinh(λTμ/B),RD = exp(−λTDμ/B) andλ = (2π2kBm...
The distributional composition δ~((r))(x_+~λ) for λ = 0, in other words, the composition δ~((r))(H(x)) is defined as the neutrix limit of the regular sequence {δ_n~((r))(x_+~λ)} and the expressions [δ~((r))(x)]~(-k) and [δ_+~((r))(x)]~(-k) are ...
Dirac-delta functionNeutrixNeutrix limitNeutrix composition of distributionIn [1], Koh and Kuan defined the powers of the Dirac-delta distribution for positive integers. Here we extend their definition for negative integers. Also, we give meaning to the distribution δ − k +....