Related papers: On the Majorana solution to the Thomas-Fermi equat…
This paper is concerned with properties of maximal solutions of the Ricci and cross curvature flows on locally homogeneous three-manifolds of type SL(2,R). We prove that, generically, a maximal solution originates at a sub-Riemannian…
We prove a topological criterion for the existence of zero-energy Majorana bound-state on a disclination, a rotation symmetry breaking point defect, in 4-fold symmetric topological crystalline superconductors (TCS). We first establish a…
A family of solutions to the Ernst equation is presented, which, in a certain limit, recovers the Yamazaki-Hori solution - an extension of the Tomimatsu-Sato solutions for all integer values of the deformation parameter $\delta$. Our…
We introduce Majorana Propagation, an algorithmic framework for the classical simulation of Fermionic circuits. Inspired by Pauli Propagation, Majorana Propagation operates by applying successive truncations throughout the Heisenberg…
In this paper we study the Newton's method for finding a singularity of a differentiable vector field defined on a Riemannian manifold. Under the assumption of invertibility of covariant derivative of the vector field at its singularity, we…
A theoretical model describing neutron-proton scattering developed by Majorana as early as in 1932, is discussed in detail with the experiments that motivated it. Majorana using collisions' theory, obtained the explicit expression of…
Sampling edges from a graph in sublinear time is a fundamental problem and a powerful subroutine for designing sublinear-time algorithms. Suppose we have access to the vertices of the graph and know a constant-factor approximation to the…
The Schwinger-Dyson equation of fermion self-energy in the linearization approximation is solved exactly in a theory with gauge and effective four-fermion interactions. Different expressions for the indepedent solutions which respectively…
This paper is devoted to finding solutions of polynomial equations in roots of unity. It was conjectured by S. Lang and proved by M. Laurent that all such solutions can be described in terms of a finite number of parametric families called…
The aim of this paper is to find the exact solutions of the Schrodinger equation. As is known, the Schrodinger equation can be reduced to the continuum equation. In this paper, using the non-linear Legendre transform the equation of…
Explicit Robinson--Trautman solutions with electromagnetic field satisfying nonlinear field equations are derived and analyzed. The solutions are generated from the spherically symmetric ones. In all cases the electromagnetic field…
In the present paper we study, in a mathematically non-formal way, the validity of the Fermat's Last Theorem (FLT) by generalizing the usual procedure of extracting the square root of non convenient objects initially introduced by P. A. M.…
Results on the rational approximation of functions containing singularities are presented. We build further on the ''lightning method'', recently proposed by Trefethen and collaborators, based on exponentially clustering poles close to the…
The thin obstacle problem or $n$-dimensional Signorini problem is a classical variational problem arising in several applications, starting with its first introduction in elasticity theory. The vast literature concerns mostly quadratic…
We examine theoretically the visualization of Majorana fermions in a two-dimensional trapped ultracold atomic Fermi gas with spin-orbit coupling. By increasing an external Zeeman field, the trapped gas transits from non-topological to…
In this paper, we introduce an algorithm that provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions, which, after an appropriate change of variables, can be rewritten as…
The accuracy of the numerical solution of a fractional differential equation depends on the differentiability class of the solution. The derivatives of the solutions of fractional differential equations often have a singularity at the…
A recursive computation of scattering amplitudes including Majorana fermions requires a consistent definition of the fermion flow, which is introduced by Denner et al. in a diagrammatic setting. A systematic treatment in the off-shell…
Given a Jordan domain $\Omega\subset\mathbb{C}$ and two disjoint arcs $A, B$ on $\partial\Omega$, the modulus $m$ of the curve family connecting $A$ and $B$ in $\Omega$ is equal to the modulus of the curve family connecting the vertical…
We verify functional a posteriori error estimate proposed by S. Repin for a class of obstacle problems. The obstacle problem is formulated as a quadratic minimization problem with constrains equivalently formulated as a variational…