“Pandora box” — Matrix in the calculus of observations

Summary If the condition R(A)=k(n), whereA is the design matrix of the type n × k and k the number of parameters to be determined, is not satisfied, or if the covariance matrixH is singular, it is possible to determine the adjusted value of the unbiased estimable function of the parameters f(), its dispersion D( (x)) and ² as the unbiased estimate of the value of ² by means of an arbitrary g-inversion of the matrix . The matrix , because of its remarkable properties, is called the Pandora Box matrix. The paper gives the proofs of these properties and the manner in which they can be employed in the calculus of observations.     

Identity of the characteristics of electrodynamic seismographs with non-standard periods of seismometers and galvanometers

Summary The maximum changes of magnification were determined for electrodynamic seismographs with standard characteristics and for some experimental long-period seismographs, the constants of which are given in Tab. 1, when the period of the seismometer or galvanometer has a deviation of not more than 5% from the standard value. Under the assumption of control of the other constants of the seismograph, identical amplitude and phase responses with a small change of the absolute magnification of the seismograph may be achieved with characteristicsAII ( ² >0.2), AIV ( ² 0.4), B ( ² >0.3) Nos28, 32 and33. This deviation can also be compensated by adjusting the optical distance. The procedure of adjusting the identical characteristics is suitable for systems with which an accurate setting of the period is difficult and for systems with an uncontrollable period, provided their values are within the limits of allowed deviations from the standard constants.     

Studies on the thermoluminescence depth profile produced by 600-MeV protons in artificial lunar soil

The thermoluminescence (TL) of various plagioclase feldspars embedded in a thick target of 150 kg of artificial lunar soil was measured after a 600-MeV proton irradiation. No correlation was observed between the parameters of the characteristic feldspar glow peak and the anorthite contents. The relative TL sensitivities of the individual plagioclase variants were measured and found to be practically the same for⁶⁰Co-γ- and 600-MeV proton-irradiated samples.The TL intensity distribution within the target arrangement, converted to a 2π isotropic p-influx, resulted in an approximate TL depth profile of a thermally undisturbed lunar soil bomarded by galactic cosmic protons. The undisturbed TL intensity at a depth of 28 g/cm² (? 17 cm) decreased to 39% at a depth of 106 g/cm² (? 60 cm). For the evaluation of the temperature gradients by TL in lunar samples the experimental data at the sites of Taurus-Littrow and of Hadley-Rille yielded minimum depth intervals for sampling of ～ 20 cm and ～ 40 cm respectively, presuming an error of ± 15% in the TL determination. Certain aspects are seen by using the relation TL intensity/²²Na-activity ratio versus depth (thus representing the total ionization profile) to establish²²Na depth profiles.     

A special-relativistic approach to gravitation and its astrophysical consequences

In the framework of Rastall's conservative program for the construction of gravitation theory we present a variant of modified classical gravitation theory based on Einstein's energy-mass equivalence principle. We pursue further the special-relativistic arguments and obtain a theory for the static spherically-symmetric gravitation field that is based only on the well-established physical principles and accounts for all experimental tests known in gravitation. Some astrophysical consequences of the modified classical gravitation theory (e.g., the non-existence of black holes, the creation of real particles in a strong gravitation field) are also discussed.     

Constraining the mass and moment of inertia of neutron stars from quasi-periodic oscillations in X-ray binaries

Neutron stars are the densest objects known in the Universe. Being the final product of stellar evolution, their internal composition and structure is rather poorly constrained by measurements.     

Relationship of ground level enhancements with solar,interplanetary and geophysical parameters

Cosmic rays registered by Neutron Monitor on the surface of the Earth are believed to originate from outer space, and sometimes also from the exotic objects of the Sun. Whilst the intensities of the cosmic rays are observed to be enhanced with sudden, sharp and short-lived increases, they are termed as ground level enhancements (GLEs). They are the occurrences in solar cosmic ray intensity variations on short-term basis, so different solar factors erupted from the Sun can be responsible for causing them. In this context, an attempt has been made to determine quantitative relationships of the GLEs having peak increase >5% with simultaneous solar, interplanetary and geophysical factors from 1997 through 2006, thereby searching the responsible factors which seem to cause the enhancements. Results suggest that GLE peaks might be caused by solar energetic particle fluxes and solar flares. The proton fluxes which seemed to cause GLE peaks were also supported by their corresponding fluences. For most of the flares, the time integrated rising portion of the flare emission refers to the strong portion of X-ray fluxes which might be the concern to GLE peak. On an average, GLE peak associated X-ray flux (0.71×10⁻⁴ w/m²) is much stronger than GLE background associated X-ray flux (0.11×10⁻⁶ w/m²). It gives a general consent that the GLE peak is presumably caused by the solar flare. Coronal mass ejection alone does not seem to cause GLE. Coronal mass ejection presumably causes geomagnetic disturbances characterized by geomagnetic indices and polarities of interplanetary magnetic fields.     

Homologous Flares and Magnetic Field Topology in Active Region NOAA 10501 on 20 November 2003

We present and interpret observations of two morphologically homologous flares that occurred in active region (AR) NOAA 10501 on 20 November 2003. Both flares displayed four homologous Hα ribbons and were both accompanied by coronal mass ejections (CMEs). The central flare ribbons were located at the site of an emerging bipole in the centre of the active region. The negative polarity of this bipole fragmented in two main pieces, one rotating around the positive polarity by ≈ 110° within 32 hours. We model the coronal magnetic field and compute its topology, using as boundary condition the magnetogram closest in time to each flare. In particular, we calculate the location of quasi-separatrix layers (QSLs) in order to understand the connectivity between the flare ribbons. Though several polarities were present in AR 10501, the global magnetic field topology corresponds to a quadrupolar magnetic field distribution without magnetic null points. For both flares, the photospheric traces of QSLs are similar and match well the locations of the four Hα ribbons. This globally unchanged topology and the continuous shearing by the rotating bipole are two key factors responsible for the flare homology. However, our analyses also indicate that different magnetic connectivity domains of the quadrupolar configuration become unstable during each flare, so that magnetic reconnection proceeds differently in both events.     

The model of a flat (Euclidean) expansive homogeneous and isotropic relativistic universe in the light of the general relativity,quantum mechanics,and observations

Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial solutions: Einstein special theory of relativity and Newton gravitation theory), quantum mechanics, and observations, too.