The bilinear assignment problem: complexity and polynomially solvable special cases

Mathematical Programming - In this paper we study the bilinear assignment problem (BAP) with size parameters m and n, $$m\le n$$ . BAP is a generalization of the well known quadratic assignment...     

Sympathetic cooling in an optically trapped mixture of alkali and spin-singlet atoms

We report on the realization of a stable mixture of ultracold lithium and ytterbium atoms confined in a far-off-resonance optical dipole trap. We observe sympathetic cooling of 6Li by 174Yb and extract the s-wave scattering length magnitude |a(6Li-174Yb)|=(13±3)a0 from the rate of interspecies thermalization. Using forced evaporative cooling of 174Yb, we achieve reduction of the 6Li temperature to below the Fermi temperature, purely through interspecies sympathetic cooling.     

Non-central sections of convex bodies

Let K be a convex body in ? ⁿ . Is K uniquely determined by the areas of its sections? There are classical results that explain what happens in the case of sections passing through the origin. However, much less is known about sections that do not contain the origin. We discuss several problems of this type and establish the corresponding uniqueness results.     

Collapse in coupled nonlinear Schrödinger equations: Sufficient conditions and applications

In this paper we study blow-up phenomena in general coupled nonlinear Schrödinger equations with different dispersion coefficients. We find sufficient conditions for blow-up and for the existence of global solutions. We discuss several applications of our results to heteronuclear multispecies Bose-Einstein condensates and to degenerate boson-fermion mixtures.     

Fractionation of Lycopodiaceae Alkaloids and Evaluation of Their Anticholinesterase and Cytotoxic Activities

In view of the abundant evidence that Lycopodiaceae alkaloids, including the well-known huperzine A (HupA), are among the potent acetylcholinesterase (AChE) inhibitors, an attempt was made to search for new compounds responsible for this property. For this purpose, three plant species belonging to the Lycopodiaceae family, commonly found in the Euro-Asia region, were subjected to the isolation of bioactive compounds, their identification and subsequent evaluation of their anticholinesterase and cytotoxic activities. Methanolic extracts of two Lycopodium and one Hupezia species were obtained via optimized pressurized liquid extraction (PLE) and then pre-purified using innovative gradient vacuum liquid chromatography (gVLC). For the first time, three sorbents of different porosity packed in polypropylene cartridges and mobile phase systems of different polarity were used to elute the target compounds. This technique proved to be a rapid tool for the obtainment of alkaloid fractions and allowed one to select the appropriate process conditions to yield potent AChE inhibitors in each of the species studied. More than 100 collected fractions were analyzed via HPLC/ESI-QTOF-MS, which enabled one to detect more than 50 compounds, including several new ones previously unreported. Some of them were present in high purity fractions (60–90% of the established purity). TLC bioautography assays proved that the analyzed species are rich sources of AChE inhibitors, but H. selago showed the highest anti-AChE activity. Additionally, the modified silanized silica gel sorbent used allowed one to isolate L. clavatum alkaloids more efficiently using an aqueous reversed-phase solvent system. Furthermore, the tested extracts from the three plant extracts were found to be safe, as they did not exhibit cytotoxicity to skin fibroblasts.     

Numerical study of formation of solitary strain waves in a nonlinear elastic layered composite material

Propagation of nonlinear strain waves through a layered composite material is considered. The governing macroscopic wave equation for the long-wave case was obtained earlier by the higher-order asymptotic homogenization method (Andrianov et al., 2013). Non-stationary dynamic processes are investigated by a pseudo-spectral numerical procedure. The time integration is performed by the Runge–Kutta method; the approximation with respect to the spatial co-ordinate is provided by the Fourier series expansion. The convergence of the Fourier series is substantially improved and the Gibbs–Wilbraham phenomenon is reduced with the help of Padé approximants. As result, we explore how fast and under what conditions the solitary strain waves can be generated from an initial excitation. The numerical and analytical solutions (when the latter can be obtained) are in good agreement.     

Simple estimation on effective transport properties of a random composite material with cylindrical fibres

Improved bounds for effective transport properties of a random non-percolated composite with cylindrical fibres are developed by means of the security-spheres approach. The key point of the method is to obtain a solution for a regular composite that can be valid for all values of the volume fractions and properties of the components. For this aim we use the asymptotic homogenization method; a cell problem is solved by a modified version of the boundary shape perturbation technique.     

Modified Busemann-Petty problem on sections of convex bodies

The Busemann-Petty problem asks whether convex origin-symmetric bodies in ℝ ⁿ with smaller central hyperplane sections necessarily have smallern-dimensional volume. It is known that the answer is affirmative ifn≤4 and negative ifn≥5. In this article we replace the assumptions of the original Busemann-Petty problem by certain conditions on the volumes of central hyperplane sections so that the answer becomes affirmative in all dimensions. The first-named author was supported in part by the NSF grant DMS-0136022 and by a grant from the University of Missouri Research Board.     

Quantum Cryptography with Correlated Twin Laser Beams

The data transmission protocol using strongly correlated twin laser beams is proposed. The properties of the laser beam states are described in detail. The protocol is based on the strong correlation of photon numbers in both beams in each measurement. The protocol stability against eavesdropping attacks is analyzed.