Mathematical constructions in optimal linear filtering theory

The linear optimal ltering problems in innite dimensional Hilbert spaces and their extensions are investigated. The quality functional is allowed to be a general quadratic functional dened by a possibly degenerate operator. We describe the solution of the stable and the causal ltering problems. In case of the causal ltering we establish the relation with a relaxed causal ltering problem in the extended space. We solve the last problem in continuous and discrete cases and give the necessary and sucient conditions for the solvability of the original causal problem and conditions for the analogue of Bode{Shannon formula to dene an optimal lter

Surface-induced magnetic anisotropy for impurity spins in granular AuFe films

The theory of the surface-induced anisotropy is extended to the case of granular films of dilute magnetic alloys. Since the surface-induced blocking of a magnetic-impurity spin appears to be very sensitive to the specific polycrystalline structure, we speculate that the apparent discrepancy between the experimental results of different groups for the size dependence of the Kondo resistivity can be linked to different microstructure of the samples. We apply our model to calculate the magnetization of impurity spins in small AuFe grains and to interpret the experimental data on the anomalous Hall effect in thin Fe doped Au films.Comment: 4 pages, 5 figures, E-mail addresses: [email protected], [email protected], [email protected]

Shape of nanosize superconducting grains: Does it influence pairing characteristics?

The Richardson exact solution for the reduced BCS Hamiltonian is applied to examine how sensitive are the pairing characteristics (condensation energy, spectroscopic gap, parity gap) to a specific configuration of single-electron energy levels in nanosize metallic grains. Using single-electron energy spectra in parallelepiped-shaped potential boxes with various volumes and aspect ratios as a model of energy levels in grains, we show that this sensitivity is extremely high. Just due to such an extreme sensitivity, the detailed shape of grains cannot be detected through the pairing characteristics, averaged over an ensemble of grains, even in the case of relatively small size dispersion within this ensemble. We analyse the effect of the pairing interaction on the excited-level spacings in superconducting grains and comment on the influence of shape-dependent fluctuations in single-electron energy spectra on the possibility to reveal this effect through tunnelling measurements.Comment: 13 pages, 5 figures, to be published in Solid State Communications, E-mail addresses: [email protected], [email protected], [email protected]

Influence of the Characteristics of the STM-tip on the Electroluminescence Spectra

We analyze the influence of the characteristics of the STM-tip (applied voltage, tip radius) on the electroluminescence spectra from an STM-tip-induced quantum dot taking into account the many-body effects. We find that positions of electroluminescence peaks, attributed to the electron-hole recombination in the quantum dot, are very sensitive to the shape and size of the confinement potential as determined by the tip radius and the applied voltage. A critical value of the tip radius is found, at which the luminescence peak positions as a function of the tip radius manifest a transition from decreasing behavior for smaller radii to increasing behavior for larger radii. We find that this critical value of the tip radius is related to the confinement in the lateral and normal direction.Comment: 15 pages, 5 figure

Method for Qualitative and Quantitative Analysis of Ancient Lead Enamel Using Laser Inducted Breakdown Spectroscopy

The method of laser induced breakdown spectroscopy (LIBS) was used in analysis of the archaeological enamel samples from the ancient settlement of Jochi Khan (XIV century). During the qualitative analysis, it was found that the elements of the enamel matrix are Si, Pb, K, Na, Mg, Ca, Al. The glaze color is due to the presence of copper and iron. Clustering by the k-means method revealed two groups of samples similar in composition of enamel, but differing in place of origin within the settlement. For the studied samples the semi-quantitative composition of glazes was established from the spectra of LIBS using a method based on the hypothesis of local thermodynamic equilibrium (LTE) and a chemometric approach (Projection to Latent Structures, PLS). Probabilistic deterministic design of experiment was used to search for pairs of element lines that are not subject to changes when the conditions for spectra registration vary, and to determine the coefficients in the equations based on LTR. Calculations using the PLC method were carried out in the “R” programming environment. The following content of the matrix elements was obtained in terms of the most stable oxides, %: SiO2 — 49–61, PbO — 23–31, MgO — 1.7–2.3, CaO — 4.6–6.9, Na2O — 4.1–5.3, K2O — 5.1–6.4, Al2O3 — 0.8–1.7, CuO — 0.32–0.4, Fe2O3 — 0.09–0.16. The results of both methods are generally consistent with each other. The inaccuracy between 4 parallel determinations were 15-24 % for LTE, and 9–14 % for PLS. Taking into account the data of semi-quantitative analysis, it was concluded that the division into two groups is based on a different ratio of copper and iron in enamel

Single-mode cavities at frequencies of 172 and 178 MHz

In the report presented here the projects of two accelerating cavities with strong damping of higher modes (HOM) with special vacuum loads are presented. The designs of the cavities and loads are described. The design parameters of cavities, their spectra of higher modes and calculation results of the beam phase motion stability are given for the VEPP-2000 and NANOHANA Projects

Development of a Momentum Determined Electron Beam in the 1 -45 GeV Range

A beam line for electrons with energies in the range of 1 to 45 GeV, low contamination of hadrons and muons and high intensity up to 10^6 per accelerator spill at 27 GeV was setup at U70 accelerator in Protvino, Russia. A beam tagging system based on drift chambers with 160 micron resolution was able to measure relative electron beam momentum precisely. The resolution sigma_p p was 0.13% at 45 GeV where multiple scattering is negligible. This test beam setup provided the possibility to study properties of lead tungstate crystals (PbWO_4) for the BTeV experiment at Fermilab.Comment: 12 pages, 8 figures; work done by the BTeV Electromagnetic Calorimeter grou

Study of Radiation Damage in Lead Tungstate Crystals Using Intense High Energy Beams

We report on the effects of radiation on the light output of lead tungstate crystals. The crystals were irradiated by pure, intense high energy electron and hadron beams as well as by a mixture of hadrons, neutrons and gammas. The crystals were manufactured in Bogoroditsk, Apatity (both Russia), and Shanghai (China). These studies were carried out at the 70-GeV proton accelerator in Protvino

RF system of the race-track microtron – recuperator for high power free electron laser

A brief description of the RF system of 100 MeV race-track microtron-recuperator being built in Novosibirsk for the Free Electron Laser project at Siberian center of Photochemistry research is presented. The frequency of RF system is 180.4 MHz. The RF system consists of 2 parts: the RF system of 2 MeV injector and the RF system of microtron. The injector RF system includes 3 RF cavities - one buncher cavity and two accelerating cavities. RF cavities are driven by a 2.5 kW amplifier and two high power single-tube 130 kW RF amplifiers respectively. The RF system of microtron includes 16 RF cavities operating at a gap voltage of 850kV each. Two 4-tubes power amplifiers supply the RF power of 600 kW each to the cavities via distribution feeders. In the high power amplifier stages the tetrodes GU-101A are used. The control system controls the amplitude and phase of RF voltage in the cavities and provides signals for synchronization of the electron gun. The results of the operation of the injector RF system and status of large RF system for the microtron are discussed