Related papers: Rational functions with maximal radius of absolute…

In this paper, we present several sharp upper bounds for the numerical radii of the diagonal and off-diagonal parts of the $2\times2$ block operator matrix $\begin{bmatrix}A&B\\ C&D\end{bmatrix}$. Among extensions of some results of…

When one wishes to numerically solve an initial value problem, it is customary to rewrite it as an equivalent first-order system to which a method, usually from the class of Runge-Kutta methods, is applied. Directly treating higher-order…

We study a stochastic control problem for continuous multidimensional martingales with fixed quadratic variation. In a radially symmetric environment, we are able to find an explicit solution to the control problem and find an optimal…

We present quadratically convergent algorithms to compute the extremal value of a real parameter for which a given rational transfer function of a linear time-invariant system is passive. This problem is formulated for both continuous-time…

We establish the existence of a finite-dimensional unitary realization for every matrix-valued rational inner function from the Schur--Agler class on a unit square-matrix polyball. In the scalar-valued case, we characterize the denominators…

We investigate the continuous non-monotone DR-submodular maximization problem subject to a down-closed convex solvable constraint. Our first contribution is to construct an example to demonstrate that (first-order) stationary points can…

Operator convex functions defined on the positive half-line play a prominent role in the theory of quantum information, where they are used to define quantum $f$-divergences. Such functions admit integral representations in terms of…

Let $S$ be a polynomial ring in $n$ variables over a field. Let $I$ be a homogeneous ideal in $S$ generated by forms of degree at most $d$ with $\text{dim}(S/I)=r$. In the first part of this paper, we show how to derive from a result of Hoa…

We consider a family of $(2,2)$-rational functions given on the set of complex $p$-adic field $\mathbb{C}_p$. Each such function has a unique fixed point. We study $p$-adic dynamical systems generated by the $(2,2)$-rational functions. We…

We present a practical algorithm to compute models of rational functions with minimal resultant under conjugation by fractional linear transformations. We also report on a search for rational functions of degrees 2 and 3 with rational…

In the paper, necessary and sufficient conditions are presented for a function involving a ratio of gamma functions to be logarithmically completely monotonic. This extends and generalizes the main result in [\emph{Inequalities and…

We prove new $\ell ^{p} (\mathbb Z ^{d})$ bounds for discrete spherical averages in dimensions $ d \geq 5$. We focus on the case of lacunary radii, first for general lacunary radii, and then for certain kinds of highly composite choices of…

Consider the general complex polynomial external field $$ V(z)=\frac{z^{k}}{k}+\sum_{j=1}^{k-1} \frac{t_j z^j}{j}, \qquad t_j \in \mathbb{C}, \quad k \in \mathbb{N}. $$ Fix an equivalence class $\mathcal{T}$ of admissible contours whose…

Let $\mathcal{A}$ denote the class of all analytic functions $f$ defined in the open unit disc $\mathbb{D}$ with the normalization $f(0)=0=f'(0)-1$ and let $P'$ be the class of functions $f\in\mathcal{A}$ such that ${\rm{Re}}\,f'(z)>0$,…

RRT* is one of the most widely used sampling-based algorithms for asymptotically-optimal motion planning. This algorithm laid the foundations for optimality in motion planning as a whole, and inspired the development of numerous new…

We propose an optimal approximation formula for analytic functions that are defined on a complex region containing the real interval $(-1,1)$ and possibly have algebraic singularities at the endpoints of the interval. As a space of such…

We establish the sharp growth order, up to epsilon losses, of the $L^2$-norm of the maximal directional averaging operator along a finite subset $V$ of a polynomial variety of arbitrary dimension $m$, in terms of cardinality. This is an…

In this paper we prove maximal regularity estimates in "square function spaces" which are commonly used in harmonic analysis, spectral theory, and stochastic analysis. In particular, they lead to a new class of maximal regularity results…

We consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…

We prove that Runge-Kutta (RK) methods for numerical integration of arbitrarily large systems of Ordinary Differential Equations are linearly stable. Standard stability arguments -- based on spectral analysis, resolvent condition or strong…