Related papers: Harmonic projection and hypercentral extensions
The generalized H\'enon-Heiles Hamiltonian $H=1/2(P_X^2+P_Y^2+c_1X^2+c_2Y^2)+aXY^2-bX^3/3$ with an additional nonpolynomial term $\mu Y^{-2}$ is known to be Liouville integrable for three sets of values of $(b/a,c_1,c_2)$. It has been…
Add to each level of binary tree edges to make the induced graph on the level a uniform expander. It is shown that such a graph admits no non-constant bounded harmonic functions.
It is shown that the method of nonlinear realization of local supersymmetry being applied to the n=(1,1) superconformal symmetry allows one reduce the new version of the super-Liouville equation to the ordinary one owing to the relaxation…
We discuss extensions of an inner product from a vector space to its full antidual. None of these extensions is weakly continuous, but partial extensions recapture some familiar structure including the Hilbert space completion and the…
In this paper fractional generalization of Liouville equation is considered. We derive fractional analog of normalization condition for distribution function. Fractional generalization of the Liouvile equation for dissipative and…
The possibility of extending operations of topological and semitopological algebras to their Stone-\v{C}ech compactification and factorization of continuous functions through homomorphisms to metrizable algebras are investigated. Most…
We study properties related to nice enumerability of countably categorical structures and properties related to extreme amenability of automorphism groups of these structures. The text substantially differs from the previous version. In…
In this paper we classify the solutions to the geometric Neumann problem for the Liouville equation in the upper half-plane or an upper half-disk, with the energy condition given by finite area. As a result, we classify the conformal…
It is shown that a linear separation relations are fundamental objects for integration by quadratures of St\"{a}ckel separable Liouville integrable systems (the so-called St\"{a}ckel systems). These relations are further employed for the…
Similarly to the bosonic Liouville theory, the $\mathcal{N}=2$ supersymmetric Liouville theory was conjectured to be equipped with the duality that exchanges the superpotential and the K\"ahler potential. The conjectured duality, however,…
In this paper we showed that every connected extremal K\"ahler submanifold of a complex projetive space has a natural extension which is a complete K\"ahler manifold and admits a holomorphic isometric immersion into the same ambient space.…
We investigate preservation of the Lindel\"of property of topological spaces under forcing extensions. We give sufficient conditions for a forcing notion to preserve several strengthenings of the Lindel\"of property, such as indestructible…
The homogeneous cosmological models with a Liouville scalar field are investigated in classical and quantum context of Wheeler-DeWitt geometrodynamics. In the quantum case of quintessence field with potential unbounded from below and…
In this paper a new supersymmetric extension of conformal mechanics is put forward. The beauty of this extension is that all variables have a clear geometrical meaning and the super-Hamiltonian turns out to be the Lie-derivative of the…
Let $UC(K)$ denote the Banach space of all bounded uniformly continuous functions on a hypergroup $K$. The main results of this article concern on the $\alpha$-amenability of $UC(K)$ and quotients and products of hypergroups. It is also…
For a partial lattice L the so-called two-point extension is defined in order to extend L to a lattice. We are motivated by the fact that the one-point extension broadly used for partial algebras does not work in this case, i.e. the…
It is a long-standing problem in Hodge theory to generalize the Satake--Baily--Borel (SBB) compactification of a locally Hermitian symmetric space to arbitrary period maps. A proper topological SBB-type completion has been constructed, and…
The paper describes relations between Liouville type theorems for solutions of a periodic elliptic equation (or a system) on an abelian cover of a compact Riemannian manifold and the structure of the dispersion relation for this equation at…
We demonstrate that companionships and conjunctions in double $\infty$-categories -- and more generally, in double Segal spaces -- extend to functors out of the free-living companionship and conjunction respectively. Specifically, we prove…
The purpose of this paper is to further exemplify an approach to evolutionary problems originally developed in earlier works for a special case and later extended to more general evolutionary problems. We are here concerned with the $(1+1)$…