Related papers: N-sphere chord length distribution
Elliptically contoured distributions can be considered to be the distributions for which the contours of the density functions are proportional ellipsoids. Kamiya, Takemura and Kuriki (2006) generalized the elliptically contoured…
We propose a projection-based class of uniformity tests on the hypersphere using statistics that integrate, along all possible directions, the weighted quadratic discrepancy between the empirical cumulative distribution function of the…
Superstring scattering from orientifold planes requires considering string amplitudes on world-sheets with crosscaps with the lowest order case (in string coupling constant) having the topology of the real projective plane. While amplitudes…
The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…
The distribution function of particles over clusters is proposed for a system of identical intersecting spheres, the centres of which are uniformly distributed in space. Consideration is based on the concept of the rank number of clusters,…
Helicity-dependent generalized parton distributions of the nucleon are derived from the overlap representation of generalized parton distributions using light-cone wave functions obtained in constituent quark models. Results from two…
The properties of the natural modes in a dispersive stratified N-layer medium are investigated. The focus is on the (over)completeness properties of these modes. Also the distribution of the natural frequencies is considered. Both the…
A geometrical method is presented for the calculation of the strand distribution functions for cable-in-conduit superconductors with simple and multiply connected cross-sections. The method is illustrated on different cable designs with…
In this paper, we derive a probability density function that generalizes the Burr XII distribution. The cumulative distribution function and the $n^{th}$ moment of the generalized distribution are obtained while the distribution of some…
A chord diagram refers to a set of chords with distinct endpoints on a circle. The intersection graph of a chord diagram $\cal C$ is defined by substituting the chords of $\cal C$ with vertices and by adding edges between two vertices…
Suspensions of hard core spherical particles of diameter $D$ with inter-core connectivity range $\delta$ can be described in terms of random geometric graphs, where nodes represent the sphere centers and edges are assigned to any two…
Statistical lattice ensembles of loops in three or more dimensions typically have phases in which the longest loops fill a finite fraction of the system. In such phases it is natural to ask about the distribution of loop lengths. We show…
We apply the scale-length method to several three dimensional samples of the Two degree Field Galaxy Redshift Survey. This method allows us to map in a quantitative and powerful way large scale structures in the distribution of galaxies…
We have investigated the spatial distribution of quasars and its relationship with redshift by using the two-point correlation function, the variance of cell counts and the conditional density as a function of redshift. By comparing our…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
In surface diffusion, one of the key observables is the so-called intermediate scattering function which is measured directly from the surface technique called Helium spin echo. In this work, we show that this function can be seen as a…
Let $M(\chi)$ denote the maximum of $|\sum_{n\le N}\chi(n)|$ for a given non-principal Dirichlet character $\chi \pmod q$, and let $N_\chi$ denote a point at which the maximum is attained. In this article we study the distribution of…
This paper investigates the rate-distortion function, under a squared error distortion $D$, for an $n$-dimensional random vector uniformly distributed on an $(n-1)$-sphere of radius $R$. First, an expression for the rate-distortion function…
By using the hybrid formalism, superstrings in four-dimensional NS-NS plane waves are studied in a manifest supersymmetric manner. This description of the superstring is obtained by a field redefinition of the RNS worldsheet fields and…
The main goal of this article is to understand how the length spectrum of a random surface depends on its genus. Here a random surface means a surface obtained by randomly gluing together an even number of triangles carrying a fixed metric.…