Related papers: Signed Chord Length Distribution. II
Signed graphs have their edges labeled either as positive or negative. Here we introduce two types of signed distance matrix for signed graphs. We characterize balance in signed graphs using these matrices and we obtain explicit formulae…
The number of positive and negative carries in the addition of two independent random signed digit expansions of given length is analyzed asymptotically for the $(q, d)$-system and the symmetric signed digit expansion. The results include…
Data uniformity is a concept associated with several semantic data characteristics such as lack of features, correlation and sample bias. This article introduces a novel measure to assess data uniformity and detect uniform pointsets on…
In this paper we obtain the density function and the distribution function of the distance between two uniformly and independently distributed random points in any right-angled triangle. The density function is derived from the chord length…
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…
We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and…
In the first half of the paper we consider interaction between the small amplitude travelling waves ("sound") and the shock waves in the transmission line containing both nonlinear capacitors and nonlinear inductors. We calculate the…
Dense distributions of string-like objects in material media are considered in terms of continuum field theory. The strings are assumed to carry a quantized abelian topological charge, such as the Burgers vector of dislocations in solids or…
In recent work, we have proposed a theory for the derivation of an exact nonlinear dispersion relation for elastic wave propagation which here we consider for a thin rod (linearly nondispersive) and a thick rod (linearly dispersive). The…
We generalize the invariant imbedding theory of the wave propagation and derive new invariant imbedding equations for the propagation of arbitrary number of coupled waves of any kind in arbitrarily-inhomogeneous stratified media, where the…
An analytical theory of non-uniformly doped or shaped PN-junction diodes submitted to large-signals at high frequencies is presented. The resulting expressions can be useful to evaluate the performance of semiconductor device modeling…
Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…
The elastic string (rod) of a large mass M is considered, the left end of which is fixed to a body of a small mass m. The second body of mass m is fixed to the right end of the string. The force of the delta-function form is applied to the…
In the past two decades, geometric phases have provided a powerful new way of looking at quantum mechanical systems, manifesting themselves in subtle but observable ways. Here, we use them to define a versatile function ("distribution of…
This paper addresses the problem of coding a continuous random source correlated with another source which is only available at the decoder. The proposed approach is based on the extension of the channel coding concept of syndrome from the…
A new set of discrete ordinates is proposed for one-dimensional radiative transfer in spheres with central symmetry. The set is structured with un-normalized circular functions. This resulted in a conservative and closed set of discrete…
Some conjectures on partition hook lengths, recently stated by the author, have been proved and generalized by Stanley, who also needed a formula by Andrews, Goulden and Jackson on symmetric functions to complete his derivation. Another…
Periodic configurations of electrodes, in particular of microelectrodes, have been of interest since the advent of microfabrication. In this report, theory which is common to any periodic cell (or any cell that can be extended periodically)…
In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent…
Stern's diatomic sequence is a well-studied and simply defined sequence with many fascinating characteristics. The binary signed-digit (BSD) representation of integers is used widely in efficient computation, coding theory and other…