Related papers: On characterization of integrable sesquilinear for…
In supersymmetric quantum mechanics, exact-solvability of one-dimensional quantum systems can be classified only with an additional assumption of integrability, the so-called shape invariance condition. In this paper we show that in the…
We obtain a necessary condition for the character degree graph of a solvable group G to be Eulerian.
The notion of the Haagerup approximation property, originally introduced for von Neumann algebras equipped with a faithful normal tracial state, is generalized to arbitrary von Neumann algebras. We discuss two equivalent characterisations,…
We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.
The question of complete integrability of evolution equations associated to $n\times n$ first order isospectral operators is investigated using the inverse scattering method. It is shown that for $n>2$, e.g. for the three-wave interaction,…
We give a sufficient condition for subelliptic estimates for the d-bar-Neumann operator on smoothly bounded, pseudoconvex domains in $\mathbb{C}^n$. This condition is a quantified version of McNeal's condition ($\tilde{P}$) for compactness…
We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.
In this paper we deal with semilinear problems at resonance. We present a sufficient condition for the existence of a weak solution in terms of the asymptotic properties of nonlinearity. Our condition generalizes the classical…
We formulate the necessary conditions for the integrability of a certain family of Hamiltonian systems defined in the constant curvature two-dimensional spaces. Proposed form of potential can be considered as a counterpart of a homogeneous…
A Lie superalgebrea of Riemannian type leads to a representation of a quadratic Lie algebra into a Weyl algebra. A necessary and sufficient condition that such a representation leads to a Lie superalgebra of Riemannian type is that the…
We show that any countably generated von Neumann algebra with specified normal faithful state can arise as the tail algebra of a quantum exchangeable sequence of noncommutative random variables. We also characterize the cases when the state…
In this note, we prove that an affine cellular algebra $A$ is semisimple if and only if the scheme associated to $A$ is reduced and 0-dimensional, and the bilinear forms with respect to all layers of $A$ are isomorphisms. Moreover, if the…
In order to considering the integrality of nearly holomorphic (vector-valued) Siegel modular forms, we introduce nearly Siegel modular forms and study their integrality. We show that the integrality of nearly Siegel modular forms in terms…
The purpose of this article is to develop an algebraic approach to the problem of integrable classification of differential-difference equations with one continuous and two discrete variables. As a classification criterion, we put forward…
We characterize, in a purely algebraic manner, certain linear forms, called stable, on a Lie algebra. As an application, we determine the index of a Borel subalgebra of a semi-simple Lie algebra. Finally, we give an example of a parabolic…
One of effective ways to solve the equivalence problem and describe moduli spaces for real submanifolds in complex space is the normal form approach. In this survey, we outline some normal form constructions in CR-geometry and formulate a…
Let $M$ be a strongly pseudoconvex complex $G$-manifold with compact quotient $M/G$. We provide a simple condition on forms $\alpha$ sufficient for the regular solvability of the equation $\square u=\alpha$ and other problems related to the…
We obtain a sufficient condition for boundary regularity of quasiminimizers of the p-energy integral in terms of a Wiener type sum of power type. The exponent in the sum is independent of the dimension and is explicitly expressed in terms…
For a restricted Lie algebra $L$, the conditions under which its restricted enveloping algebra $u(L)$ is semiperfect are investigated. Moreover, it is proved that $u(L)$ is left (or right) perfect if and only if $L$ is finite-dimensional.
Following Sutherland's work on one-dimensional integrable systems we formulate and study its two-dimensional version. Physically it expresses the absence of true 3-body forces among an assembly of N particles leaving exclusively effective…