Projective varieties with projectively equivalent singular 0-dimensional sections

Fix integers m, n such that 1 ≤ m ≤ n ? 3. Let X ? Pⁿ be an integral non-degenerate m-dimensional variety. Assume either char(K) = 0 or char(K) > deg(X). Here we prove that all general 0-dimensional sections of X containing a tangent vector to a smooth point of X are protectively equivalent if and only if n ? m + 1 ≤ deg(X) ≤ n ? m + 2.     

Real-time active suppression of scattered acoustic radiation

Active noise control usually aims at reducing the total acoustic pressure due to a noise source; it may also be used in principle to reduce the scattered acoustic radiation from a reflecting body in order to render it invisible to incident acoustic waves. In this paper, a real-time control strategy is introduced to achieve, with ordinary noise sources and sensors, the effective suppression of the noise scattered by a 3-D surface. Numerical simulations of 2-D and 3-D control are used to illustrate the potential of this control strategy. Preliminary experimental results are also given for the 1-D case of a rigid body inserted into a duct.     

The Flux-Across-Surfaces Theorem and Zero-Energy Resonances

In this contribution we shall first introduce the Flux Across Surfaces (FAS) theorem, placing it in the general context of the Quantum Scattering Theory. Then we shall review briefly the theory of resonances in non-relativistic Quantum Mechanics and outline a proof of the FAS theorem for non-relativistic potential scattering, which covers also the case in which there is a zero energy resonance.     

Decrease in the group velocity of a light pulse in the Bose-Einstein condensate of a dilute gas

A semiclassical theory of electromagnetically induced transparency in a Bose-Einstein condensate is considered. A nonlinear Schrödinger equation that describes the interaction of the Bose-Einstein condensate with an electromagnetic field is derived. An analysis of the obtained solutions to this equation demonstrates a decrease in the group velocity of the light pulse.     

Commuting Rank 2 Differential Operators Corresponding to a Curve of Genus 2

We construct commuting rank 2 formally self-adjoint ordinary differential operators corresponding to a curve of genus 2.     

Cycloaddition of Thiourea to Tri(1-propenyl)amine

Russian Journal of General Chemistry -     

Martensite Transformation in Nanoparticles and Nanomaterials

Journal of Nanoparticle Research - It was shown that the thermoelastic martensite transformation B2 ? B19 inside nanoparticles surrounded by amorphous matrix in Ni–Ti–Cu alloys as...