Related papers: A note on the ultrahyperbolic wave equation in 3+3…
The notion of the wave spectrum of a semi-bounded symmetric operator was introduced by one of the authors in 2013. The wave spectrum is a topological space determined by the operator in a canonical way. The definition uses a dynamical…
By analogy with complex numbers, a system of hyperbolic numbers can be introduced in the same way: z=x+h*y with h*h=1 and x,y real numbers. As complex numbers are linked to the Euclidean geometry, so this system of numbers is linked to the…
We introduce a new superintegrable Kepler-Coulomb system with non-central terms in $N$-dimensional Euclidean space. We show this system is multiseparable and allows separation of variables in hyperspherical and hyperparabolic coordinates.…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
We show that any immersion, which is not a covering of an embedded 2-orbifold, of a totally geodesic hyperbolic turnover in a complete orientable hyperbolic 3-orbifold is contained in a hyperbolic 3-suborbifold with totally geodesic…
Using recently developed Seifert fibering operators for 3D $\mathcal{N} = 2$ gauge theories, we formulate the necessary ingredients for a state-integral model of the topological quantum field theory dual to a given Seifert manifold under…
The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel…
Pseudodifferential parabolic equations with an operator square root arise in wave propagation problems as a one-way counterpart of the Helmholtz equation. The expression under the square root usually involves a differential operator and a…
The choice of approximate posterior distributions plays a central role in stochastic variational inference (SVI). One effective solution is the use of normalizing flows \cut{defined on Euclidean spaces} to construct flexible posterior…
For matrix model and QFT, we discuss how dual gravitational geometry emerges from matrix degrees of freedom (specifically, adjoint scalars in super Yang-Mills theory) and how operator algebra that describes an arbitrary region of the bulk…
Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a…
This paper argues that curvelets provide a powerful tool for representing very general linear symmetric systems of hyperbolic differential equations. Curvelets are a recently developed multiscale system in which the elements are highly…
The transmutation (transformation) operator associated with the perturbed Bessel equation is considered. It is shown that its integral kernel can be uniformly approximated by linear combinations of constructed here generalized wave…
In this work we study the essential spectra of composition operators on weighted Bergman spaces of analytic functions which might be termed as "quasi-parabolic." This is the class of composition operators on $A_{\alpha}^{2}$ with symbols…
We show that each connected component of the moduli space of smooth real binary quintics is isomorphic to an open subset of an arithmetic quotient of the real hyperbolic plane. Moreover, our main result says that the induced metric on this…
Given a pair of normally hyperbolic operators over (possibily different) globally hyperbolic spacetimes on a given smooth manifold, the existence of a geometric isomorphism, called {\em M{\o}ller operator}, between the space of solutions is…
Properties and applications of a plasmonic cross-shaped nano-antenna is presented and compared to those of array of holes. A simple analytical model based on the superposition of waves are proposed and compared to the numerical results. A…
We investigate the effect of counter-rotating-wave terms on nonlocality and entanglement for three qubits coupled with a common bath for strong and ultrastrong coupling regimes beyond the traditional treatment of Born-Markovian,…
We study higher-order elliptic operators on one-dimensional ramified structures (networks). We introduce a general variational framework for fourth-order operators that allows us to study features of both hyperbolic and parabolic equations…
We introduce here explicit integral formulas for linking, twisting, writhing and helicity on the 3-sphere and in hyperbolic 3-space. These formulas, like their prototypes in Euclidean 3-space, are geometric rather than just topological, in…