We prove a characterization theorem for the test functions in a CKS-space. Some crucial ideas concerning the growth condition are given.

{ For 2 ? 1 n < p < n we prove existence of a distributional solution u of the p-harmonic system ? div(jruj p?2 ru) = in ,

The Weibull function is widely used to describe skew distributions observed in nature. However, the origin of this ubiquity is not always obvious to explain. In the present paper, we consider the well-known Galton-Watson branching process describing simple replicative systems. The shape of the resulting distribution, about which little has been known, is found essentially indistinguishable from...

Volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, volatility is unobservable and only the price is known. Diffusion theory has many common points with the research on volatility, the key of the analogy being that volatility is a time-dependent...

In many natural situations, one observes a local system with many competing species that is coupled by weak immigration to a regional species pool. The dynamics of such a system is dominated by its stable and uninvadable (SU) states. When the competition matrix is random, the number of SUs depends on the average value and variance of its entries. Here we consider the problem in the limit of wea...

To understand the multiple relations between developers and projects on GitHub as a whole, we model them as a multilayer bipartite network and analyze the degree distributions, the nearest neighbors’ degree distributions and their correlations with degree, and the collaborative similarity distributions and their correlations with degree. Our results show that all degree distributions have a pow...

Efficient, Reliable, and Secure Content Delivery

Recent years have witnessed significant efforts in deriving and embedding semantic information in content for improved content retrieval, adaptation, and distribution. Relatively little work considers leveraging this semantic information in the infrastructure to better serve the needs of clients and achieve better cost-effectiveness of infrastructure resources. In this paper, we identify semant...

In contrast to the classical goal of group testing, we consider the problem of finding m defective elements out of D (m ≤ D). We analyze two different test functions. We give adaptive strategies and present lower bounds for the number of tests and show that our strategy is optimal for m = 1. DOI: 10.1134/S0032946012020068