Related papers: On Sylvester Waves and restricted partitions
We prove and apply two theorems: First, a quantitative, scale-free unique continuation estimate for functions in a spectral subspace of a Schr\"odinger operator on a bounded or unbounded domain, second, a perturbation and lifting estimate…
The $S$-functional calculus is based on the theory of slice hyperholomorphic functions and it defines functions of $n$-tuples of not necessarily commuting operators or of quaternionic operators. This calculus relays on the notion of…
An initial-boundary value problem for a viscoelastic wave equation subject to a strong time-localized delay in a Kelvin & Voigt-type material law is considered. Transforming the equation to an abstract Cauchy problem on the extended phase…
We consider damped wave (resp. Schr{\"o}dinger and plate) equations driven by a hypoelliptic "sum of squares" operator L on a compact manifold and a damping function b(x). We assume the Chow-Rashevski-H{\"o}rmander condition at rank k (at…
Stokes wave is a finite amplitude periodic gravity wave propagating with constant velocity in inviscid fluid. Complex analytical structure of Stokes wave is analyzed using a conformal mapping of a free fluid surface of Stokes wave into the…
We use an old elementary arithmetic argument to find new upper and lower bounds for Sylvester's denumerant function. These bounds are tight enough to get the asymptotic behavior of the denumerant.
We prove new Skoda-type division, or ideal membership, theorems. We work in a geometric setting of line bundles over Kahler manifolds that are Stein away from an analytic subvariety. (This includes complex projective manifolds.) Our…
Acoustic and elastic wave equations are routinely used in geophysical and engineering studies to simulate the propagation of waves, with a broad range of applications, including seismology, near surface characterization, non-destructive…
We study a class of stochastic semilinear damped wave equations driven by additive Wiener noise. Owing to the damping term, under appropriate conditions on the nonlinearity, the solution admits a unique invariant distribution. We apply…
The Doppler shift of de Broglie wave is obtained for fermions and massive bosons using the conventional form of Lorentz transformations for momentum and energy of the particles. A formalism is developed to obtain the variation of wave…
Building on results of Haagerup and Schultz, we decompose an arbitrary operator in a diffuse, finite von Neumann algebra into the sum of a normal operator and an s.o.t.-quasinilpotent operator. We also prove an analogue of Weyl's inequality…
Given a frequency $\lambda=(\lambda_n)$, we study when almost all vertical limits of a $\mathcal{H}_1$-Dirichlet series $\sum a_n e^{-\lambda_ns}$ are Riesz-summable almost everywhere on the imaginary axis. Equivalently, this means to…
A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the…
Partitions of the set of primes are introduced based on the Chebyshev polynomials at rationals. The prime densities of all such partitions are established. Euler's Criterion for $SL(2,\mathbb Q)$ is formulated, which is the bridge between…
We consider a Klein-Gordon-Wave system, describing the evolution of a massive field and a massless one interacting through a Yukawa-like coupling, and we explicitly derive its Hamiltonian normal form to first and second order. To the…
Let $T$ be a bounded quaternionic normal operator on a right quaternionic Hilbert space $\mathcal{H}$. We show that $T$ can be factorized in a strongly irreducible sense, that is, for any $\delta >0$ there exist a compact operator $K$ with…
Acoustic wave propagation in a one-dimensional waveguide connected with Helmholtz resonators is studied numerically. Finite amplitude waves and viscous boundary layers are considered. The model consists of two coupled evolution equations: a…
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
Picard-Lefschetz theory is applied to solutions of the Helmholtz equation, formulated in terms of sums of integrals of a proper-time, or `einbein', wave function $\Psi(\Lambda) = \exp(i\mathbb S(\Lambda))$ along complex contours bounded by…
In this paper, we present a semiclassical description of surface waves or modes in an elastic medium near a boundary, in spatial dimension three. The medium is assumed to be essentially stratified near the boundary at some scale comparable…