We show that if a Banach space X contains uniformly complemented l₂ⁿ 's then there exists a universal constant b = b(X) > 0 such that for each Banach space Y, and any sequence dn ↓ 0 there is a bounded linear operator T : ...

We present a direct construction of retroreflecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class C¹, except for a hyper-finite set of values, such that the probability ...

Two-dimensional ruled surfaces in the spaces of constant curvature Rⁿ, Sⁿ, Hn and in the Riemannian products Sⁿ x R¹, Hⁿ x R¹ are considered. A ruled surface is proved to represent a pseudospherical congruence if and only ...

We study the spectral structure of Schrodinger operators H = Δ+V for random potentials supported on sparse sets. In the past years examples of such operators whose spectra almost surely satisfy the following properties ...

We develop direct and inverse scattering theory for Jacobi operators with step-like coeffcients which are asymptotically close to different finite-gap quasiperiodic coeffcients on di erent sides. We give a complete ...

The small oscillations of a magnetizable ideal fluid in partially filled vessel are considered. Solvability of the initial-boundary problem is proved and the generic properties of the frequencies spectrum of normal free ...

In the paper a hyperbolic version of the Smarandache pedal polygon theorem is considered.

In the paper solutions to the homogeneous boundary value problems of free vibrations of a nite string are obtained in the d'Alembert form. The initial boundary value problems to vibrations of a string with free ends as ...

It is proved that a differentiable with respect to each variable function f : R2 → R is a solution of the equation ∂u/∂x + ∂u/∂y = 0 if and only if there exists a function φ : R → R such that f(x, y) = φ(x - y). This gives ...