Related papers: Rayleigh's Stretched String
We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively…
How does the amplitude of a wiggle on a string change when the string is stretched? We answer this question for both longitudinal and transverse wiggles and for arbitrary equation of state, {\it i.e.}, for arbitrary relation between the…
For the quadratic Lagrange interpolation function, an algorithm is proposed to provide explicit and verified bound for the interpolation error constant that appears in the interpolation error estimation. The upper bound for the…
This paper provides the first criteria for the linear independence of multiple polylogarithm values over algebraic number fields. In particular, we derive novel results regarding the linear independence of products of polylogarithms at…
We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and…
This work deals with the large time behaviour of the spatially homogeneous Landau equation with Coulomb potential. Firstly, we obtain a bound from below of the entropy dissipation $D(f)$ by a weighted relative Fisher information of $f$ with…
We prove some upper bounds for the Dirichlet eigenvalues of a class of fully nonlinear elliptic equations, namely the Hessian equations
We study for several compact strictly convex disjoint obstacles the length spectrum $\mathcal L$ formed by the lengths of all primitive periodic reflecting rays. We prove the existence of sequences $\{\ell_j\},\: \{m_j\}$ with $\ell_j \in…
A rigorous way to obtain sharp bounds for Stokes constants is introduced and illustrated on a concrete problem arising in applications.
We provide a complete description of realizable period representations for meromorphic differentials on Riemann surfaces with prescribed orders of zeros and poles, hyperelliptic structure, and spin parity.
We consider a strongly damped semilinear wave equation with initial data prescribed as $(\varrho\phi,\varrho h)$, where the profiles are fixed and only the amplitude $\varrho>0$ is allowed to vary. The question addressed here is how this…
Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…
A Particle Tracking Velocimetry experiment has been performed in a turbulent flow at intermediate Reynolds number. We present experimentally obtained stretching rates for particle pairs in the inertial range. When compensated by a…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous…
We prove a formula for the $n$-th derivative of the period function $T$ in a period annulus of a planar differential system. For $n = 1$, we obtain Freire, Gasull and Guillamon formula for the period's first derivative \cite{FGG}. We apply…
Intrinsic and extrinsic geometric properties of string world sheets in curved space-time background are explored. In our formulation, the only dynamical degrees of freedom of the string are its immersion coordinates. Classical equation of…
We consider the topic of linearization of finite elasticity for pure traction problems. We characterize the variational limit for the approximating sequence of rescaled nonlinear elastic energies. We show that the limiting minimal value can…
Using adiabatic expansions formalism, upper bounds for interband transitions for Bloch electrons in slowly varying in time electric fields are obtained. These bounds imply the validity of one-band approximation on long time scales.
We consider difference equations with several non-monotone deviating arguments and nonnegative coefficients. The deviations (delays and advances) are, generally, unbounded. Sufficient oscillation conditions are obtained in an explicit…
Let $S$ be a finite set of points in the Euclidean plane. Let $D$ be a Delaunay triangulation of $S$. The {\em stretch factor} (also known as {\em dilation} or {\em spanning ratio}) of $D$ is the maximum ratio, among all points $p$ and $q$…