We build upon recent advances on the distributional aspect of Stein’s method to propose a novel and flexible technique for computing Stein operators for random variables that can be written as products of independent random variables. We show that our results are valid for a wide class of distributions including normal, beta, variance-gamma, generalized gamma and many more. Our operators are kt...

It is well-known that distributional solutions to the Cauchy problem for ut +(b(t, x)u)x = 0 with b(t, x) = 2H(x− t), where H is the Heaviside function, are non-unique. However, it has a unique generalized solution in the sense of Colombeau. The relationship between its generalized solutions and distributional solutions is established. Moreover, the propagation of singularities is studied.

Degree distribution is a fundamental property of networks. While mean degree provides a standard measure of scale, there are several commonly used shape measures. Widespread use of a single shape measure would enable comparisons between networks and facilitate investigations about the relationship between degree distribution properties and other network features. This paper describes five candi...

M. H. Al-Abbadi and M. Darus 2009 recently introduced a new generalized derivative operator μ λ1 ,λ2 , which generalizedmany well-known operators studied earlier by many different authors. In this present paper, we shall investigate a new subclass of analytic functions in the open unit disk U {z ∈ C : |z| < 1} which is defined by new generalized derivative operator. Some results on coefficient ...

This paper is devoted to the identification of the unknown smooth coefficient c entering the hyperbolic equation c x ∂t u − Δu 0 in a bounded smooth domain in R from partial on part of the boundary dynamic boundary measurements. In this paper, we prove that the knowledge of the partial Cauchy data for this class of hyperbolic PDE on any open subset Γ of the boundary determines explicitly the co...

We present an algorithm that generates networks in which the skewness of the degree distribution is tuneable by modifying the preferential attachment step of the Barabási-Albert construction algorithm. Skewness is linearly correlated with the maximal degree of the network and, therefore, adequately represents the influence of superspreaders or hubs. By combining our algorithm with work of Holme...