Related papers: A new solvable many-body problem of goldfish type
We present a different combinatorial interpretations of Lucas and Gibonacci numbers. Using these interpretations we prove several new identities, and simplify the proofs of several known identities. Some open problems are discussed towards…
Inhomogeneous Kirchhoff type equations with indefinite data are considered. Some necessary and sufficient conditions for the existence of positive solutions of the problem under consideration are presented.
We construct a class of finitely presented groups where the isomorphism problem is solvable but the commensurability problem is unsolvable. Conversely, we construct a class of finitely presented groups within which the commensurability…
It is shown that the irreversible behavior of classical systems of interacting particles is a common property for both few-body and many-body systems. It is due to the delay in the interactions between the particles. PACS: 45.50.Jf Few- and…
By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.
General reduction of the elliptic hypergeometric equation to the level of complex hypergeometric functions is described. The derived equation is generalized to the Hamiltonian eigenvalue problem for new rational integrable $N$-body systems…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
We discuss a many-body Hamiltonian with two- and three-body interactions in two dimensions introduced recently by Murthy, Bhaduri and Sen. Apart from an analysis of some exact solutions in the many-body system, we analyze in detail the…
The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified…
This is an update of my problem list.
Closed quantum many-body systems out of equilibrium pose several long-standing problems in physics. Recent years have seen a tremendous progress in approaching these questions, not least due to experiments with cold atoms and trapped ions…
The paper concerns singular solutions of nonlinear elliptic equations.
We examine a Gelfand type system and show the extremal solutions are bounded provided we are close enough to the scalar case.
A new proof is given of the existence of the solution to electromagnetic (EM) wave scattering problem for an impedance body of an arbitrary shape. The proof is based on the elliptic systems theory and elliptic estimates for the solutions of…
We review the recently proposed unreduced, complex-dynamical solution to the many-body problem with arbitrary interaction and its application to the unified solution of fundamental problems, including dynamic foundations of causally…
An English summary is given of Jean Delsarte's article "Nombre de solutions des equations polynomiales sur un corps fini."
Because of the relevance of the results, this paper is merged into the paper titled "On the Number of Solutions to Asymptotic Plateau Problem" (arXiv:math.DG/0505593) as a new section.
New cases of the multiplicity conjecture are considered.
The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here…
Optimization problems with more than one objective consist in a very attractive topic for researchers due to its applicability in real-world situations. Over the years, the research effort in the Computational Intelligence field resulted in…