In this letter we present an idea which reconciles a homogeneous and isotropic Friedmann universe with a fractal distribution of galaxies. We use two observational facts: The flat rotation curves of galaxies and the (still debated) fractal distribution of galaxies with fractal dimension D = 2. Our idea can also be interpreted as a redefinition of the notion of bias.

In this paper we establish existence and uniqueness results for equilibria in systems with an infinite number of agents and with local and global social interactions. We also examine the structure of the equilibrium distribution and derive a “Markov”property for the equilibrium distribution of a class of spatially homogeneous systems.

Applications of multi-state approach to the reliability evaluation of systems composed of independent components are considered. The main emphasis is on multi-state systems with degrading components because of the importance of such an approach in safety analysis, assessment and prediction, and analysing the effectiveness of operation processes of real technical systems. The results concerned w...

Counts of galaxies as a function of apparent magnitude are among the most time-honored observations in cosmology. In this Letter, we focus on some statistical properties of these counts which are fundamental in order to characterize the large scale correlations in the galaxy spatial distribution. There are, in fact, no longer doubts since two decades of the existence of very large scale structu...

Homogeneous traffic flows are believed to be better in absorbing disturbances, raise capacity and stimulate traffic safety. Measures to make traffic more homogeneous are therefore often taken to increase capacity. This paper shows that the ability of a traffic flow to deal with traffic coming from an on-ramp reduces when the through flow becomes more homogeneous. A motorway was modelled in the ...

We investigate the evolution of the velocity distribution function of a granular gas composed of viscoelastic particles in the homogeneous cooling state, i.e. before clustering occurs. The deviation of the velocity distribution function from the Maxwellian distribution is quantified by a Sonine polynomials expansion. The first non-vanishing Sonine coefficient a2(t), reveals a complex time depen...

In the present study the distribution of morphogenetic, behavioural and serological traits have been reported among three schedule castes viz. Bhagat, Mahasha and Batwal of Jammu and Kashmir. For the purpose, a survey was conducted and frequencies of different traits were calculated. It was observed that the frequency distribution of various traits among the studied populations shows the homoge...

Present investigations provide baseline data on the distribution of morphogenetic traits: ear lobe attachment, nose tip and chin fissure; behavioural traits: hand clasping, arm folding, handedness, leg folding and tongue rolling among five endogamous groups of Haryana i.e. Kumhar, Nai, Luhar, Saini and Bania. Among these traits, hand clasping, leg folding and tongue rolling showed homogeneous d...

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

An evolutionary distribution z (x, t) is a distribution of the density of organisms along the values of adaptive traits x at time t. Predator and prey evolutionary distributions with competition, assortative mating and mutations display dynamics that include cyclic waves and other esoteric phenomena. Such phenomena depend on the parameter space, on the instability of the predator–prey dynamics,...