We report on the simultaneous g′,r′,i′,z′ multiband, high time sampling (18-24s) ground-based photometric observations, which we use to measure the planetary radius and orbital inclination of the extrasolar transiting hot Jupiter WASP-4b. We recorded 987 images during three complete transits with the GROND instrument, mounted on the MPG/ESO-2.2m telescope at La Silla Observatory. Assuming a quadratic law for the stellar limb darkening we derive system parameters by fitting a composite transit light curve over all bandpasses simultaneously. To compute uncertainties of the fitted parameters we employ the Bootstrap Monte Carlo Method. The three central transit times are measured with precision down to 6 s. We find a planetary radius Rp = 1.413 ± 0.020RJup, an orbital inclination i = 88.°57 ± 0.45° and calculate new ephemeris, a period P = 1.33823144 ± 0.00000032 days and reference transit epoch T0 = 2454697.798311 ± 0.000046 (BJD). The analysis of the new transit mid-times in combination with previous measurements imply a constant orbital period and no compelling evidence for TTVs due to additional bodies in the system.

We investigate nonlinear resonances and the averaged potential in a bounded non-isothermal plasma, placed in a constant magnetic field and a parallel external a.c. electric field. The treatment assumes one component MHD. It is assumed that a standing Alfvén wave exists before the electric field is switched on.

Resonance frequencies of a plane plasma condenser in crossed electric and magnetic fields are determined, using the two-component magnetic hydrodynamical equations. The perturbed plasma parameters (ion and electron densities and velocities and the electric field in the plasma), due to an external a.c. electric field are found. The calculated resonance is not exact since dissipative processes are neglected.

A nonlinear relaxation is observed when an electron beam interacts with plasma in an external magnetic field. An acceleration of electrons to energies which are more than twice that of the initial beam energy is observed. The acceleration mechanism is connected with the modulation instability of the plasma waves which is excited when the beam relaxes.

In this paper we present a novel method of nonlinear macro model of a cantilever for mixed domain simulation only with SPICE. Based on lumped elements of equivalent circuits a model is developed, which realizes a coupled electro-thermal-mechanical simulation including crosstalk effects. The model is verified with measurement and helps to class and solve crosstalk. With SPICE as electrical circuit simulator the cantilever array could be simulate in conjunction with the excitations and analysis electronics more detailed like the system level models and faster like FEM-simulation.

About twenty years ago van den Bergh (1964) recognized 188 OB associations in the Andromeda Nebula. He used plates taken by the 52-inches Tautenburgh Schmidt telescope in GDR. Later on Richter (1971) added 7 new associations in the south-western periphery of M31. Now we have the opportunity to continue the search of stellar associations in M31 with the 2m Ritchey-Chrétien (RC) telescope of the Bulgarian National Astronomical Observatory. The limiting magnitude of this telescope is approximately the same as that of the Tautenburg 2m Schmidt telescope but it possesses somewhat smaller field (1°x1°) with plate-scale 12.8 mm−1. That is why a new search of stellar associations in M31 by means of the 2m RC telescope is very efficient. Indeed, some previous inspections of the RC plates (Efremov, 1982) indicated some new associations in M31.

Using rich photometric material on the Cepheids in the Galaxy and the Large and Small Magellanic Clouds, the structure of the instability strip in the HR diagram is investigated. The method of the δ-δ diagrams is used, δ being the difference of certain Cepheid characteristics from the means for a given period. The Cepheids in the three galaxies, studied separately, show the same relationship: the light amplitude increases toward the low temperature limit of the instability strip and is also related with the temperature at maximum in the sense that Cepheids with a given period and fixed mean temperature have a greater light amplitude for a higher temperature at maximum. Our results do not coincide with those by Sandage and Tammann, probably because they have studied the Cepheids in the different star systems as one single complex.