Related papers: Singular Solutions in Soft Limits
In the pure scattering theory, the universality of the soft limit has been studied for a long time. In this talk we review the property of soft limit to relate an $n$-point amplitude to an $(n-1)$-point amplitude. We show how this property…
It is conjectured that for any fixed relatively prime positive integers $a,b$ and $c$ all greater than 1 there is at most one solution to the equation $a^x+b^y=c^z$ in positive integers $x,y$ and $z$, except for specific cases. In this…
In this paper, we study the potential singular points of interior and boundary suitable weak solutions to the 3D Navier--Stokes equations. It is shown that upper box dimension of interior singular points and boundary singular points are…
In three dimensional scattering, the energy continuum wavefunction is obtained by utilizing two independent solutions of the reference wave equation. One of them is typically singular (usually, near the origin of configuration space). Both…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
We extend the investigation of nonextremal enhancons, finding the most general solutions with the correct symmetry and charges. There are two families of solutions. One of these contains a solution with a regular horizon found previously;…
As a crucial technique for integrated circuits (IC) test response compaction, $X$-compact employs a special kind of codes called $X$-codes for reliable compressions of the test response in the presence of unknown logic values ($X$s). From a…
In a previous work the authors described a fast high-fidelity computer model for acoustic scattering from multi-layered elastic spheres. This work is now extended with a scaling strategy significantly mitigating the problem of overflow and…
The soft limits of scattering amplitudes have been extensively studied due to their essential role in the computation of physical observables in collider physics. The universal factorisation that occurs in these kinematic limits has been…
Soft theorems describe the behavior of scattering amplitudes when one or several external particles are taken to be energetically soft. In tree-level gravity there are universal soft theorems for the three leading orders in the soft…
We study the asymptotics of solutions to a particular class of systems of linear wave equations, namely, of silent equations. We obtain asymptotic estimates of all orders for the solutions, and show that solutions are uniquely determined by…
It is known that, for each real number x such that 1,x,x^2 are linearly independent over Q, the uniform exponent of simultaneous approximation to (1,x,x^2) by rational numbers is at most (sqrt{5}-1)/2 (approximately 0.618) and that this…
We construct solutions of the Friedmann equations near a sudden singularity using generalized series expansions for the scale factor, the density, and the pressure of the fluid content. In this way, we are able to arrive at a solution with…
We show, in this second part, that the maximal number of singular points of a quartic surface $X \subset \mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic 2 is at most 14, and that, if we have 14…
In this paper we study microlocal singularities of solutions to Schrodinger equations on scattering manifolds, i.e., noncompact Riemannian manifolds with asymptotically conic ends. We characterize the wave front set of the solutions in…
We construct solutions of the fast diffusion equation, which exist for all $t\in\mathbb{R}$ and are singular on the set $\Gamma(t):= \{ \xi(s) ; -\infty <s \leq ct \}$, $c>0$, where $\xi\in C^3(\mathbb{R};\mathbb{R}^n)$, $n\geq 2$. We also…
Static spherically symmetric solutions in SU(N)-EYM and EYMD theories are classified by the node numbers of their non-trivial gauge field functions. With increasing node numbers, the solutions form sequences, tending to limiting solutions.…
We consider random systems of linear equations over GF(2) in which every equation binds k variables. We obtain a precise description of the clustering of solutions in such systems. In particular, we prove that with probability that tends to…
The necessity and benefit of singular solutions in the study of physical systems is shown. By singular solutions we mean solutions that are not contained in the general solution of the system of equations that describes the dynamic system…
In this paper we are concerned with existence of positive solutions for a Schr\"odinger-Maxwell system with singular or strongly-singular terms. We overcome the difficulty given by the singular terms through an approximation scheme and…