On a problem of Zygmund

It is proved that there exists an integrable function on [0, 1]² whose integral is nondifferentiable in each direction belonging to a set everywhere dense in [0, 2π] but is strongly differentiable. Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 749–762, November, 1998.     

Calculation of the noise factor of a traveling-wave gyrotron

The problem of calculating the noise factor of a traveling-wave gyrotron is solved for a model of a thin annular multistart-helical electron flux taking into account the effect of the quasistatic space-charge field. Plots of the gain and the noise factor of the traveling-wave gyrotron versus the electrical parameters of the amplifier are obtained. Zh. Tekh. Fiz. 68, 130–132 (February 1998)     

Experiments on two-step heating of a dense plasma in the GOL-3 facility

This paper presents the results of experiments on two-stage heating of a dense plasma by a relativistic electron beam in the GOL-3 facility. A dense plasma with a length of about a meter and a hydrogen density up to 10¹⁷ cm⁻³ was created in the main plasma, whose density was 10¹⁵ cm⁻³. In the process of interacting with the plasma, the electron beam (1 MeV, 40 kA, 4 μs) imparts its energy to the electrons of the main plasma through collective effects. The heated electrons, as they disperse along the magnetic field lines, in turn reach the region of dense plasma and impart their energy to it by pairwise collisions. Estimates based on experimental data are given for the parameters of the flux of hot plasma electrons, the energy released in the dense plasma, and the energy balance of the beam-plasma system. The paper discusses the dynamics of the plasma, which is inhomogeneous in density and temperature, including the appearance of pressure waves. Zh. éksp. Teor. Fiz. 113, 897–917 (March 1998)     

Orientational ordering of liquid crystals containing a difluoro-substituted phenyl ring

The orientational ordering of several liquid crystals containing a difluorosubstituted phenyl ring has been studied through the use of C-13 NMR. The fluorinated phenyl ring of these liquid crystals have C_s symmetry, so three order parameters are required to completely describe the ordering of this ring. All three of these order parameters have been calculated from carbon-fluorine dipolar coupling constants obtained from the carbon-fluorine splittings in the C-13 NMR spectra. Because of the complexity of the fluorine-coupled spectra, variable angle spinning (VAS) was used to resolve the carbon-fluorine splittings. In order to study the orientational ordering over wide ranges of temperature, we have developed an empirical correlation between the order parameter and the value of a carbon-fluorine dipolar coupling constant. This enabled us to study the change in the order parameter with temperature. The results of applying this method to several structurally similar liquid crystals containing the same type of difluorinated phenyl ring are presented. A comparison is made to a similar mono-fluorinated liquid crystal.     

Influence of humic substances on sorption and methylation processes of inorganic- and organo-tin species

The influence of humic substances on sorption and methylation processes for inorganic- and organotin species is presented. Four sediment samples from different locations of the Rivers Elbe, Mulde and Spittelwasser, Germany, with different organotin and humic contents were selected to extract the humic and fulvic acids. The various fractions—the original sediment, the humic acid, the fulvic acid and the residual sediment—were analysed for their organotin content. The individual buyltin species show quite different distribution patterns. Monobutyltin is found mostly associated with humic acids. Dibutyltin shows a nonunique behaviour. At low total organotin content, dibutyltin is found bonded to humic and fulvic acids, whereas at high organotin content dibutyltin is distributed more with the residual sediment. Most of the tributyltin remains in the sediment unextracted; only small quantities of it are in the fulvic acid fraction. Tetrabutyltin is only in the humic acid fraction when it binds to humic matter; it mostly remains in the sediment. General observations indicate that ionic butyltin species bind to fulvic acids whereas the non-polar tetrabutyltin is not found in the fulvic acid fractions in any of the samples. The appearance of monomethyl- and dimethyl-tin species in the humic and fulvic acid fractions after the alkaline extraction was surprising. There is a correlation between the humic content of the sample and the formation of methyltin species. Evidence is provided by experiments that humic substances act as methylation agents.     

Determination of the Tolman cone angle from crystallographic parameters and a statistical analysis using the crystallographic data base

Summary A new method of evaluating the Tolman cone angle from X-ray structural data available from the Cambridge Crystallographic Data Base has been developed and a statistical analysis of the cone angles of the phosphines PPh₃, PMe₂Ph, PMePh₂, PMe₃, PEt₃ and PCy₃ (Cy = cyclohexyl) in transition metal complexes has been completed.     

IRISTER - magneto-optical disk for magnetically inducedSuperResolution

IRISTER (IRIS Thermal Eclipse Reading) is a remarkable technique for achieving superresolution in optical disks. Two applications of IRISTER are Magnetically induced SuperResolution (MSR) and Premastered optical disk by SuperResolution (PSR). Magnetically induced SuperResolution (MSR) has been realized in magneto-optical disks using exchange-coupled magnetic multilayer films. Two new detection methods have been developed. In the front aperture detection (FAD) method, the heated area in the light spot works as an optical mask so that the signal is read out only from the remaining crescent-shaped area in the spot. In the rear aperture detection (RAD) method, the signal is read out only from the heated area. The cutoff spatial frequency for both types of detection is more than two times higher than that in conventional detection. A high C/N of 42 dB is obtained in the MSR disks by both methods for a mark length of 0.3 μm, which is much shorter than the optical limit. Premastered optical disk by SuperResolution (PSR) has been realized in read-only optical disks using phase-change materials. In the front aperture detection (FAD) method for PSR, the prerecorded signal is read out only from the high reflective crescent-shaped area in the light spot, because the reflectance of the heated area is too low. A C/N of 51 dB for a mark length of 0.3 μm has been obtained for the PSR disk     

Design parameters and measured performance of the IRAM 30-mMillimeter Radio Telescope

The “Millimeter Radio Telescope” (MRT) is operated by the Institute for Radio Astronomy in the millimeter range (IRAM) and is located at 2850-m altitude in the Sierra Nevada, near Granada, Spain. It is a reflector antenna of 30-m diameter with a surface accuracy of 0.08 mm and a pointing accuracy of better than 2 arcsec. The telescope is equipped with sensitive receivers for the atmospheric windows between 0.8- and 7-mm wavelength. The authors describe the optics layout of the receiver and calibration system, which allows simultaneous observations at a number of frequencies. The special design aspects of the antenna, in particular the control of thermal deformations and the achievement of a high reflector and pointing accuracy are described. The authors compare the design computations with the characteristics of the telescope, derived from several years of operation and optimization. The success of the design is demonstrated by observational experience. The authors conclude the paper with a short review of some of the astronomical results obtained with the telescope