Related papers: Safe domain and elementary geometry
The origin of cosmic structure is widely regarded as quantum, yet the Universe today appears classical. Standard lore attributes this to a "quantum-to-classical" transition on super-horizon scales during inflation. Gravity plays a central…
The presence of a cosmological constant, Lambda, in an action with higher powers of the curvature can produce rapidly oscillating metrics. We develop a perturbative approach for generating periodic solutions to the non-linear field…
The sum of elliptic integrals simultaneously determines orbits in thr Kepler problem and the addition of divisors on elliptic curves. Periodic motion of a body in physical space is defined by symmetries, whereas periodic motion of divisors…
In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio $\rho$ between the area of a domain and its perimeter, measured in units of the wavelength…
In this paper we investigate the Erd\"os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We prove a good upper bound for spherical means that have been…
We consider the curves whose all normal planes are at the same distance from a fixed point and obtain some characterizations of them in the 3-dimensional Euclidean space.
We consider a rigid body freely moving in a compressible inviscid fluid within a bounded domain $\Omega\subset\mathbb{R}^3$. The fluid is thereby governed by the non necessarily isentropic compressible Euler equations, while the rigid body…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…
We establish a rigidity theorem for annular sector-like domains in the setting of overdetermined elliptic problems on model Riemannian manifolds. Specifically, if such a domain admits a solution to the inhomogeneous Helmholtz equation…
We consider a motion of a weakly relativistic charged particle with an arbitrary spin in central potential $e/r$ in terms of classical mechanics. We show that the spin-orbital interaction causes the precession of the plane of orbit around…
In the operational approach to general probabilistic theories one distinguishes two spaces, the state space of the "elementary systems" and the physical space in which "laboratory devices" are embedded. Each of those spaces has its own…
We introduce a notion of distance between supervised learning problems, which we call the Risk distance. This distance, inspired by optimal transport, facilitates stability results; one can quantify how seriously issues like sampling bias,…
Discrete symmetries are widely imposed in particle theories. It is well-known that the spontaneous breaking of discrete symmetries leads to domain walls. Current studies of domain walls have focused on those from the spontaneous breaking of…
Positive solutions of homogeneous Dirichlet boundary value problems or initial-value problems for certain elliptic or parabolic equations must be radially symmetric and monotone in the radial direction if just one of their level surfaces is…
Using a recent description of the geometric stability manifold, we show the geometric stability manifold associated to any smooth projective complex surface is contractible. We then use this result to demonstrate infinitely many new…
Discrete R symmetries are interesting from a variety of points of view. They raise the specter, however, of domain walls, which may be cosmologically problematic. In this note, we describe some of the issues. In many schemes for…
In a recent paper (arXiv:1412.6000) a general mechanism for emergence of cosmological space-time geometry from a quantum gravity setting was devised and departure from standard dispersion relations for elementary particle were predicted. We…
In ZM theory the direction of time has a non-zero projection onto space and this projection corresponds to the local velocity relative to the observer. Classical trajectories can be obtained by following the local direction of time. The…
In this paper we consider the plane elliptic motion which occurs if the moving centrode is a circle of radius $r$ and the fixed centrode a circle of radius $2r$. Every point of the moving plane generates an ellipse in the fixed plane. Let a…
We consider positive solutions to a singular semilinear elliptic equation in bounded smooth domains, with zero Dirichlet boundary conditions. We provide some weak and strong maximum principles for the H^1_0 part of the solution that allow…