In this paper, weakly homogeneous generalized functions in the special Colombeau algebras are determined up to equality in the sense of generalized distributions. This yields characterizations that are formally similar to distribution theory. Further, we give several characterizations of equality in the sense of generalized distributions in these algebras.

Let f be a C∞ function on R and P be a quadratic form defined by P (x) = P (x1, x2, · · · , xm) = x1+· · ·+xp−xp+1−· · ·−xp+q with p+q = m. In this paper, we mainly show that

As a sequel to [1], the position of the maximum in a geometrically distributed sample is investigated. Samples of length n are considered, where the maximum is required to be in the first d positions. The probability that the maximum occurs in the first d positions is sought for d dependent on n (as opposed to d fixed in [1]). Two scenarios are discussed. The first is when d = αn for 0 < α ≤ 1,...

Many authors have modeled regional earthquake interevent times using a gamma distribution, whereby data collapse occurs under a simple rescaling of the data from different regions or time periods. We show, using earthquake data and simulations, that the distribution is fundamentally a bimodal mixture distribution dominated by correlated aftershocks at short waiting times and independent events ...

The market for music products has recently been subject to dramatic forces for change. We propose a model and theoretical perspective for understanding the transformation of the market structure in the recorded music industry value chain due to new forms of digital distribution. We take into account the traditional music industry’s value chain and distribution network, and the product character...

In [1], R. A. Kunze has presented a notion of generalized Fourier transform of functions on locally compact abelian groups. The point of this paper is to extend this idea in the direction of distribution theory and to present some initial results on this generalized Fourier transform of distributions. In a later paper we hope to investigate in detail the domain, range, and kernel of this transf...

This article provides a contemporary exposition at amoderately quantitative level of the distribution theory associated with the matching and the birthday problems. A large number of examples, many not well known, are provided to help a reader have a feeling for these questions at an intuitive level. © 2004 Elsevier B.V. All rights reserved.

Individuals may join groups for several reasons, one of which is the possibility of sharing information about the quality of a foraging area. Sharing information in a patch-foraging scenario gives each group member an opportunity to make a more accurate estimate of the quality of the patch. In this paper we present a mathematical model in which we study the effect of group size on patch-leaving...

exists. The function f is continuously differentiable when it is differentiable and f ′ is continuous. A k-times continuously differentiable function is C, and a continuous function is C. A V -valued function f is weakly C when for every λ ∈ V ∗ the scalar-valued function λ◦ f is C. This sense of weak differentiability of a function f does not refer to distributional derivatives, but to differe...

this paper presents a mathematical model that could assist in measuring, monitoring and controlling tem-perature variation in cold and ‘red-hot’ metal working conditions of machining. a numerical analysis tech-nique of the temperature distribution, based on the theory of complex applied potential, was carried out using the principles of relationship analysis between the paths of heat supply in ...