Related papers: Singularity exchange at the frontier of the space
The possibility is considered that turbulence is described by differential equations for which uniqueness fails maximally, at least in some limit. The inviscid Burgers equation, in the context of Onsager's suggestion that turbulence should…
Let X be a singular affine normal variety with coordinate ring R and assume that there is an R-order admitting a stability structure such that the scheme of relevant semistable representations is smooth, then we construct a partial…
A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is…
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…
We study scenarios of parallel cyclic multiverses which allow for a different evolution of the physical constants, while having the same geometry. These universes are classically disconnected, but quantum-mechanically entangled. Applying…
Optical singularities, which are positions within an electromagnetic field where certain field parameters become undefined, hold significant potential for applications in areas such as super-resolution microscopy, sensing, and…
Topological properties of photonic structures described by Hamiltonian matrices have been extensively studied in recent years. Photonic systems are often open systems, and their coupling with the environment is characterized by scattering…
The focus of this article is the study of a certain type of singularities and their transfer properties in a universally equidimensional morphism (i.e. an open morphism with constant pure-dimensional fibers). The singularities of interest…
Singularity of the potential function makes quantum tunneling problem mathematically underdetermined. To circumvent the difficulties it introduced in physics, a potential singularity cutoff is often used, followed by a reverse limit…
Colliding Einstein-Maxwell-Scalar fields need not necessarily doomed to become in a spacelike singularity. Examples are given in which null singularities emerge as intermediate stages between a spacelike singularity and a regular horizon.
Let $K_n$ denote the number of distinct values among the first $n$ terms of an infinite exchangeable sequence of random variables $(X_1,X_2,\ldots)$. We prove for $n=3$ that the extreme points of the convex set of all possible laws of $K_3$…
We study the existence of transitive exchange maps with flips defined on the unit circle. We provide a complete answer to the question of whether there exists a transitive exchange map of the unit circle defined on n subintervals and having…
It is shown that given a Lagrangian for a system with a finite number of degrees of freedom, the existence of a variational symmetry is equivalent to the existence of coordinates in the extended configuration space such that one of the…
This paper surveys some recent results on existence, uniqueness and removable singularities for fully nonlinear differential equations on manifolds. The discussion also treats restriction theorems and the strong Bellman principle.
A relation between the conformal anomaly and the logarithmic term in the entanglement entropy is known to exist for CFT's in even dimensions. In odd dimensions the local anomaly and the logarithmic term in the entropy are absent. As was…
Kinetics of collision processes with linear mixing rules are investigated analytically. The velocity distribution becomes self-similar in the long time limit and the similarity functions have algebraic or stretched exponential tails. The…
The $t$-channel singularity of a cross-section for a binary $2 \to 2$ scattering process occurs when a particle exchanged in the $t$ channel is kinematically allowed to be on its mass-shell, that is when the process can be viewed as a…
Tropical geometry is a degeneration of classical geometry which loose the property of unique factorization for polynomials. In this paper we explore a structure that is known to be a semi-degeneration between the classical algebra and the…
While intersections of convex sets are convex, their unions have rather complicated behavior. Some natural contexts where they appear include duality arguments involving boundaries of convex sets and valuations, which have an Euler…
Let $X$ be a manifold with boundary, endowed with a metric with conic singularities at the boundary components of $X$. Let $u$ be a solution to the wave equation on $\mathbb{R} \times X$. When a singularity of $u$ strikes a cone point of…