With the help of the Lenard recursion equations, we derive a new hierarchy of soliton equations associated with a 3×3 matrix spectral problem and establish Dubrovin type equations in terms of the introduced trigonal curve ...

We study holomorphic almost periodic functions on a tube domain with the spectrum in a cone. We extend to this case Levin's theorem on a connection between the Jessen function, secular constant, and the Phragmen-Lindeloof ...

A known analogue of the Pitt compactness theorem for function spaces asserts that if 1 ≤ p < 2 and p < r < ∞, then every operator T : Lp → Lr is narrow. Using a technique developed by M.I. Kadets and A. Pełczyński, we prove ...

Motivated by the Jaynes–Cummings (JC) model, we consider here a quantum dot coupled simultaneously to a reservoir of photons and two electric leads (free-fermion reservoirs). This new Jaynes–Cummings-leads (JCL)-type model ...

We describe a particular class of pseudo-spherical surfaces in E⁴ which admit Bianchi transformations

In the paper, the inverse problem with respect to (w.r.t.) domain for two-dimensional Schrodinger operator and operator L = Δ² is considered. The definition of s-functions is introduced. The method of determination of the ...

We study operator equations generalizing the chain rule and the substitution rule for the integral and the derivative of the type f ○ g + c = I (Tf ○ g ∙ Tg), f, g є C¹(R), (1) where T : C¹ (R) → C(R) and where I is ...

We study the groups of transformations which transform antipodal polygons into antipodal ones as well as their order and the number of equivalence classes of n-gons inscribed into the regular (2n - 1)-gon.

In the paper, the method of approximate solution of boundary integral equations of the original problem is proposed. The systems of boundary integral equations of the problem are obtained by the method of parametric ...

Let v(z) be a subharmonic function of order ρ > 0, and Fr(v) be the limit set in the sense of Azarin. Let z be fixed and I(z) = {u(z) : u is in Fr(v)}. We prove that I(z) is either a closed interval or a semiclosed interval ...