1. Fréchet space C∞[a, b] 2. Fréchet space of smooth functions E = C∞(Rn) 3. Fréchet space of Schwartz functions S on R 4. LF-space of test functions D on R 5. Generalized functions (distributions) D∗, S ∗, E∗ as linear functionals 6. Generalized functions D∗, S ∗, E∗ as completions of D 7. Fourier transforms of tempered distributions 8. Distributions supported at a point 9. Appendix: weak dual...

The Lagrangian velocity statistics of dissipative drift-wave turbulence are investigated. For large values of the adiabaticity (or small collisionality), the probability density function of the Lagrangian acceleration shows exponential tails, as opposed to the stretched exponential or algebraic tails, generally observed for the highly intermittent acceleration of Navier-Stokes turbulence. This ...

In this paper we present two novel reflectance measurement procedures that requiresampling

To understand the natural numbers, we must first understand the primes. Yet the behavior of the primes remains for the most part a mystery. For example, despite the efforts of many great mathematicians over hundreds of years, we still know very little about how the primes are distributed (scattered) throughout the natural numbers. The results and conjectures pertaining to the distribution of th...

We study the asymptotical behavior of the p-adic singular Fourier integrals Jπα,m;φ(t) = 〈 fπα;m(x)χp(xt), φ(x) 〉 = F [ fπα;mφ ] (t), |t|p → ∞, t ∈ Qp, where fπα;m ∈ D ′(Qp) is a quasi associated homogeneous distribution (generalized function) of degree πα(x) = |x| α−1 p π1(x) and orderm, πα(x), π1(x), and χp(x) are a multiplicative, a normed multiplicative, and an additive characters of the fi...

Recently, commentators have suggested that the distributional form of cost data should be explicitly modelled to gain efficiency in estimating the population mean. We perform a series of simulation experiments to evaluate the usual sample mean and the mean estimator of a lognormal distribution, in the context of both theoretical distributions and three large empirical datasets. The sample mean ...

Recently, a novel technique called coded cache have been proposed to facilitate the wireless content distribution. Assuming the users have the identical cache size, prior works have described the fundamental performance limits of such scheme. However, when heterogenous user cache sizes is taken into account, there remains open questions regarding the performance of the cache. In this work, for ...

The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools and procedures to analyse the statistical properties of networks defined by arbitrary degree distributions and other constraints. Doing so reveals the highly ...

Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability Pa or deleting a node with the probability Pd = 1−Pa at each time step, where Pa and Pd are determined by the Logistic population equation, topological properties of networks are studied. All the fat-tailed degree distributions observed in ...