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It is our aim to establish a general analytic theory of asymptotic expansions of type f(x)=a_1 phi_1(x)+dots+ a_n phi_n(x)+o(phi_n(x)), x tends to x_0 (*), where the given ordered n-tuple of real-valued functions phi_1 dots,phi_n forms an…
We consider the minimization of integral functionals in one dimension and their approximation by $r$-adaptive finite elements. Including the grid of the FEM approximation as a variable in the minimization, we are able to show that the…
In this paper we consider the initial value problem for a family of shallow water equations on the line $\R$ with various asymptotic conditions at infinity. In particular we construct solutions with prescribed asymptotic expansion as…
Let $p_n$ denote the $n$-th prime. In 2000, Panaitopol established the inequality $p_1 \cdots p_n > p_{n+1}^{n - \pi(n)}$ for all $n \geq 2$, where $\pi(x)$ is the prime counting function. In 2021, Yang and Liao refined this by introducing…
Discrete-time affine processes are widely used in finance and economics and encompass count, positive, and nonnegative-valued processes. This paper develops near-unit-root asymptotic theory for this class of models. Unlike linear AR(1)…
Time Optimal Path Parametrization is the problem of minimizing the time interval during which an actuation constrained agent can traverse a given path. Recently, an efficient linear-time algorithm for solving this problem was proposed.…
We study the optimal partitioning of a (possibly unbounded) interval of the real line into $n$ subintervals in order to minimize the maximum of certain set-functions, under rather general assumptions such as continuity, monotonicity, and a…
In this paper asymptotic equalities are found for the least upper bounds of deviations in the uniform metric of de la Vallee Poussin sums on classes of 2\pi-periodic (\psi,\beta)-differentiable functions admitting an analytic continuation…
Uniform asymptotic expansions are derived for the zeros of the reverse generalized Bessel polynomials of large degree $n$ and real parameter $a$. It is assumed that $-\Delta_{1} n+\frac{3}{2} \leq a \leq \Delta_{2} n$ for fixed arbitrary…
We present an asymptotic formula for the number of line segments connecting q+1 points of an nxn square grid, and a sharper formula, assuming the Riemann hypothesis. We also present asymptotic formulas for the number of lines through at…
We consider the asymptotics of sums of the form $$ \frac1{F_n^\sigma} \sum_{m = 1}^{F_n-1} \frac{f(m/F_n)}{\left|{\sin(\pi m/F_n)}\right|^\sigma} \frac{f(F_{n-1}m/F_n)}{\left|{\sin(\pi F_{n-1}m/F_n)}\right|^\sigma} $$ where $(F_n)_{n \in…
This paper deals with inference in a class of stable but nearly-unstable processes. Autoregressive processes are considered, in which the bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with…
We consider the Random Euclidean Assignment Problem in dimension $d=1$, with linear cost function. In this version of the problem, in general, there is a large degeneracy of the ground state, i.e. there are many different optimal matchings…
In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
Asymptotic expansions are derived for Gegenbauer (ultraspherical) polynomials for large order $n$ that are uniformly valid for unbounded complex values of the argument $z$, including the real interval $0 \leq z \leq 1$ in which the zeros in…
The vertex isoperimetric number of a graph $G=(V,E)$ is the minimum of the ratio $|\partial_{V}U|/|U|$ where $U$ ranges over all nonempty subsets of $V$ with $|U|/|V|\le u$ and $\partial_{V}U$ is the set of all vertices adjacent to $U$ but…
The initial value problem of an integrable system, such as the Nonlinear Schr\" odinger equation, is solved by subjecting the linear eigenvalue problem arising from its Lax pair to inverse scattering, and, thus, transforming it to a matrix…
In this paper we present results on asymptotic characteristics of multivariate function classes in the uniform norm. Our main interest is the approximation of functions with mixed smoothness parameter not larger than $1/2$. Our focus will…
We consider time-dependent convection-diffusion problems with high P\'eclet number of order $\mathcal{O}(\varepsilon^{-1})$ in thin three-dimensional graph-like networks consisting of cylinders that are interconnected by small domains…