四维空间相交定理的几何证明

为解决研究四维空间几何元素相交时思维图象的困难，对四维空间中的相交定理用几何的方法进行了证明，并配以直观图。     

Inversion of the density gradient and the diffusion “gate” in isothermal mixing of gases

The stable quasistationary mixing of ternary gas mixtures in a system of two chambers connected by a capillary is described by a theoretical model which predicts the density distribution of the mixture along the length of the diffusion channel. It is demonstrated that inversion of the density gradient can occur due to a nonlinear concentration distribution of the heavy component in a diffusion “gate” effect. The results obtained using this model are compared with the experimental data. Zh. Tekh. Fiz. 68, 14–17 (May 1998)     

Distribution of silicon over sublattices in semiconducting A3B5 compounds

The stable site of Si substitutional impurities in GaAs and AlAs at T=0 K is determined on the basis of an analysis of the energy of solution of silicon, and of the energies of formation of intrinsic defects and the reaction energies of their interaction obtained by calculating the total energy of the disordered compounds. These calculations indicate that amphotericity and vacancies have an effect on the distribution of Si. At low Si concentrations, Si in GaAs is located on the sublattice of the group III element, and in AlAs, on the sublattice of the group V element. Fiz. Tverd. Tela (St. Petersburg) 39, 264–266 (February 1997)     

Existence and stability of periodic solutions for chains of connected oscillators

We consider a nonlinear system of difference equations. This system corresponds to chains of N symmetrically connected oscillators with sufficiently general type of connection, which includes, among others, local and global connection. We prove a theorem on the existence and stability of space-time periodic solutions of such systems for sufficiently small values of the parameter of connection ?.     

Quantum Key Distribution Using High-Dimensional Quantum Error-Avoiding Code

Using high-dimensional quantum error-avoiding code, we present two new quantum key distribution protocols over a collective noisy channel, i.e. six-photon and five-photon quantum error-avoiding codes. Compared with the previous protocols using four-photon and three-photon quantum error-avoiding code, the qubit efficiencies of the new protocols have increases of 16.67% and 5% respectively. In addition, the security of these protocols is analysed with a conclusion that the new protocols are much more secure than the four-photon and three-photon ones.     

Isobar separation at FRS-ESR – a development towards pure isomeric stored beams

One important goal of the ILIMA project at FAIR is the study of masses and decay properties of relativistic isomeric beams stored and cooled in the planned storage-ring complex. A new scheme is described, where a storage-cooler ring is used for high-resolution mass separation. Experimental results on the separation of the isobaric pair ¹⁴⁰Pr-¹⁴⁰Ce are presented. P. Beller, deceased.     

Combined X-ray-electron imaging techniques: Limitations on lateral resolution

Capabilities of the imaging techniques, in which X-rays are converted to electrons and then the emitted electrons are registered by means of an electron microscope, are analyzed, the focus being on the factors limiting lateral resolution at the stage of electron emission. Bearing in mind the tendency to use harder synchrotron X-rays for some combined X-ray-electron microscopy methods, calculations were made for two significantly different X-ray energies: E = 1.828 keV (K-edge of Si) and E = 11.923 keV (L₃-edge of Au). By using Monte Carlo simulations of the electron trajectories beneath the surface of the sample we show that the radius of the spot from which photoelectrons are emitted could be as small as 1 nm. However, when proper account is taken of an entire electron cascade associated with the re-building of electron shells after photoelectron emission, spots more than one order of magnitude larger result, limiting the best lateral resolution to 20–30 nm.