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We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…
We compute some asymptotic limits for solutions of Burgers equation with Cauchy data in $L^1(R)$.
We introduce a new approach to the the asymptotic iteration method (AIM) by means of which we establish the standard AIM connection with the continued fractions technique and we develop a novel termination condition in terms of the…
We present an asymptotic study of the Dirichlet to Neumann map of high contrast composite media with perfectly conducting inclusions that are close to touching. The result is an explicit characterization of the map in the asymptotic limit…
We study right limits of the Bergman Shift matrix. Our results have applications to ratio asymptotics, weak asymptotic measures, relative asymptotics, and zero counting measures of the orthogonal and orthonormal polynomials.
In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…
Let $(M,\omega)$ be a symplectic manifold and $U\subseteq M$ an open subset. We study the natural inclusion of the compactly supported Hamiltonian group of $U$ in the compactly supported Hamiltonian group of $M$. The main result is an upper…
We study a generalization of deduplication, which enables lossless deduplication of highly similar data and show that standard deduplication with fixed chunk length is a special case. We provide bounds on the expected length of coded…
We consider the infinite symmetric group and its infinite index subgroup given as the stabilizer subgroup of one element under the natural action on a countable set. This inclusion of discrete groups induces a hyperfinite subfactor for each…
A sufficient condition for a cluster point of a planar harmonic function to be an asymptotic value is given, based on a partitioning into regions of constant valence. A sufficient condition for the cluster set of a planar harmonic function…
We give asymptotic formulas for the number of balanced words whose slope $\alpha$ and intercept $\rho$ lie in a prescribed rectangle. They are related to uniform distribution of Farey fractions and Riemann Hypothesis. In the general case,…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
An asymptotic formula for the number of partitions into p-cores is derived. As a byproduct some integer valued trigonometric sums are found
This brief note aims at condensing some results on the 32-point approximate DFT and discussing its arithmetic complexity.
As the conclusion of a line of investigation undertaken in two previous papers, we compute asymptotic frequencies for the values taken by numerators of differences of consecutive Farey fractions with denominators restricted to lie in…
Several asymptotic expansions and formulas for cubic exponential sums are derived. The expansions are most useful when the cubic coefficient is in a restricted range. This generalizes previous results in the quadratic case and helps to…
The omega limit sets plays a fundamental role to construct global attractors for topological semi-dynamical systems with continuous time or discrete time. Therefore, it is important to know when omega limit sets become nonempty compact…
This is the second of two papers on the uniform asymptotics for real double Hurwitz numbers with triple ramification. Using the modified tropical correspondence theorem established in the first paper of this series, we introduce a…
In this paper we study the asymptotic behaviour of two relatively new complexity functions defined on infinite words and their relationship to periodicity. Given a factor $u$ of an infinite word $x$, we say $u$ is closed if it is a letter…
In a paper in the American Mathematical Monthly, the corresponding author asks for an asymptotic of a gcd-sum function \begin{align}\sum_{ab\leq N}\tau(\gcd(a,b))\label{eqn:taugcdsum}\end{align} We extensively study generalizations of the…