Related papers: Integrability of the n-centre problem at high ener…
The problem of center-of-mass (CM) contaminations in ab initio nuclear structure calculations using configuration interaction (CI) and coupled-cluster (CC) approaches is analyzed. A rigorous and quantitative scheme for diagnosing the CM…
For a system of ordinary differential equations (ODEs) or, more generally, an involutive distribution of vector fields, the problem of its integration is considered. Among the many approaches to this problem, solvable structures provide a…
This paper presents high-order integral equation methods for evaluation of electromagnetic wave scattering by dielectric bumps and dielectric cavities on perfectly conducting or dielectric half-planes. In detail, the algorithms introduced…
Extending earlier work on a vibronic theory of the FA centers in alkali halides, the reorientation is now considered of an off-center Li+ impurity, either isolated or near an F center. We derive analytically periodic potential energy…
The present paper is concerned with the existence of positive high energy solution of the Choquard equation. Under certain assumptions, the ground state of Choquard equation can not be achieved. However, by global compactness analysis, we…
We consider particle collision inside the inner horizon of the Reissner-Nordstrom metric in the so-called R region. We show that there exist scenario in which the enrgy in the center of mass frame grows unbounded. In contrast to the…
In this article we are making an attempt to connect the theory of functions integrable in the unit disk to the problems of steady-state heat transfer in cases when the heat source is inside the disk.
In this article, we analyse an integral equation of the second kind that represents the solution of $N$ interacting dielectric spherical particles undergoing mutual polarisation. A traditional analysis can not quantify the scaling of the…
The existence of vacancy--impurity clusters due to quantum properties of vacancies in phase separated solid solutions of 4He in 3He is analyzed and discussed. Additional mechanism called vacancy assisted nucleation is proposed. According to…
We propose an integrability setup for the computation of correlation functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at higher orders in the large $N_{\text{c}}$ genus expansion and at any order in…
It is a long-standing open problem raised by Starostin to describe all finite groups with soluble centralizers of involutions. One can observe that if the centralizer fusion system of an involution is nilpotent, then the centralizer of that…
Integrable models are often constructed with real systems in mind. The exact solvability of the models leads to results which are unambiguous and provide the correct physical picture. In this review, we discuss the physical basis of some…
A large class of physical systems involves the vanishing of a 1-form on a manifold as a constraint on the acceptable states. This means that one is always dealing with the Pfaff problem in those cases. In particular, knowing the degree of…
We prove that completely integrable systems are normalisable in the C infinity category near focus-focus singularities.
Liouville (super)integrability of a Hamiltonian system of differential equations is based on the existence of globally well-defined constants of the motion, while Lie point symmetries provide a local approach to conserved integrals.…
The fundamental structure of the full set of solutions of the BCS $^3 P_2$ pairing problem in neutron matter is established. The relations between different spin-angle components in these solutions are shown to be practically independent of…
We consider generic nonextremal stationary dirty black holes. It is shown that in the vicinity of any bifurcation surface the energy of collision of two particles in the centre of mass frame can grow unbound. This is a generic property…
The Equation Problem in finitely presented groups asks if there exists an algorithm which determines in finite amount of time whether any given equation system has a solution or not. We show that the Equation Problem in central extensions…
Consider analytical three-dimensional differential systems having a singular point at the origin such that its linear part is $y\partial_x-\lambda z\partial_z$ for some $\lambda\neq 0$. The restriction of such systems to a Center Manifold…
This paper presents an analysis of the motion of an impurity ion in a nanometer scale $^4$He cluster. Due to induction forces, ions are strongly localized near the center of the cluster, with a root mean squared thermal displacements of…