*Correspondence: [email protected] Institute of Mathematics, Brno University of Technology, Technická 2, Brno, 616 69, Czech Republic Abstract The paper deals with stability regions of a certain discretization of a linear differential equation with constant delay. The main aim of the paper is to analyze the regions of asymptotic stability of the modified midpoint method applied to a li...

In this paper, we examine the question of the boundary controllability of the one-dimensional nonisentropic Euler equation for compressible polytropic gas, in the context of weak entropy solutions. We consider the system in Eulerian coordinates and the one in Lagrangian coordinates. We obtain for both systems a result of controllability toward constant states (with the limitation γ < 5 3 on the...

We suggest an algorithm for the calculation of large-amplitude traveling water waves in irrotational flows and in flows with constant and nonconstant vorticity, respectively. The algorithm is based on a quite general partial differential equation constrained optimization formulation, maximizing the wave amplitude subject to the PDE constraint that the Euler equations hold. Numerical examples il...

Given an array of n real numbers A = (a1; a2; : : : ; an), de ne MIN(i; j) = minfai; : : : ; ajg. The range minima problem consists of preprocessing array A such that queries MIN(i; j), for any 1 i j n, can be answered in constant time. Range minima is a basic problem that appears in many other important problems such as lowest common ancestor, Euler tour, pattern matching with scaling, etc. In...

Let T be the triangle with vertices (1,0), (0,1), (1,1). We study certain integrals over T , one of which was computed by Euler. We give expressions for them both as a linear combination of multiple zeta values, and as a polynomial in single zeta values. We obtain asymptotic expansions of the integrals, and of sums of certain multiple zeta values with constant weight. We also give related expre...

We present a non-diffusive and contact discontinuity capturing scheme for linear advection and compressible Euler system. In the case of advection, this scheme is equivalent to the Ultra-Bee limiter of [20], [24]. We prove for the Ultra-Bee scheme a property of exact advection for a large set of piecewise constant functions. We prove that the numerical error is uniformly bounded in time for suc...

Curvature-Invariant de Sitter spin currents mediating between spaces of different constant curvature are assigned to special holographic twistorial/gyro angular density patterns on low-dimensional AdS/dS surfaces. The corresponding curvature-invariant geodetic impedance and matching condition for spin currents are given by a conformal Gudermannian mapping between surfaces of different constant ...

Given the anomalous magnetic moments of electrons and positrons in the one-loop approximation, we calculate the exact Lagrangian of an intense constant magnetic field that replaces the HeisenbergEuler Lagrangian in traditional quantum electrodynamics (QED). We have established that the derived generalization of the Lagrangian is real for arbitrary magnetic fields. In a weak field, the calculate...

We consider some fundamental constants from the point of view of the duality symmetry. Our analysis of duality is focused on three issues: the maximum radiated power of gravitational waves, the cosmological constant, and the Hydrogen atom energy. We show that the maximum radiated power of gravitational waves implies that the Planck time is a minimal time. Furthermore, we prove that duality impl...

We study the divergence of large-order perturbation theory in the worldline expression for the two-loop Euler-Heisenberg QED eeective Lagrangian in a constant magnetic eld. The leading rate of divergence is identical, up to an overall factor, to that of the one-loop case. From this we deduce, using Borel summation techniques, that the leading behaviour of the imaginary part of the two-loop eeec...