Abstract:
The initial mass function (IMF) for the stars is usually fitted by three straight lines, which means seven parameters. The presence of brown dwarfs (BD) increases to four the straight lines and to nine the parameters. Another common fitting function is the lognormal distribution, which is characterized by two parameters. This paper is devoted to demonstrating the advantage of introducing a left truncated beta probability density function, which is characterized by four parameters. The constant of normalization, the mean, the mode and the distribution function are calculated for the left truncated beta distribution. The normal-beta (NB) distribution which results from convolving independent normally distributed and beta distributed components is also derived. The chi-square test and the K-S test are performed on a first sample of stars and BDs which belongs to the massive young cluster NGC 6611 and on a second sample which represents the star's masses of the cluster NGC 2362.

Abstract:
The luminosity function (LF) for stars is here fitted by a Schechter function and by a Gamma probability density function. The dependence of the number of stars on the distance, both in the low and high luminosity regions, requires the inclusion of a lower and upper boundary in the Schechter and Gamma LFs. Three astrophysical applications for stars are provided: deduction of the parameters at low distances, behavior of the average absolute magnitude with distance, and the location of the photometric maximum as a function of the selected flux. The use of the truncated LFs allows modeling the Malmquist bias.

Abstract:
We present the first results of a systematic analysis of radially truncated exponential discs for four galaxies of a complete sample of disc-dominated edge-on spiral galaxies. The discs of our sample galaxies are truncated at similar radii on either side of their centres. With possible the exception of the disc of ESO 416-G25, it appears that the truncations in our sample galaxies are closely symmetric, in terms of both their sharpness and the truncation length. However, the truncations occur over a larger region and not as abruptly as found in previous studies. We show that the truncated luminosity distributions of our sample galaxies, if also present in the mass distributions, comfortably meet the requirements for longevity. The formation and maintenance of disc truncations are likely closely related to stability requirements for galactic discs.

Abstract:
Using the nearly full sky Ks=11.75 2MASS Redshift Survey [2MRS]of ~45,000 galaxies we reconstruct the underlying peculiar velocity field and constrain the cosmological bulk flow within ~100. These results are obtained by maximizing the probability to estimate the absolute magnitude of a galaxy given its observed apparent magnitude and redshift. At a depth of ~60 Mpc/h we find a bulk flow Vb=(90\pm65,-230\pm65,50\pm65) km/s in agreement with the theoretical predictions of the LCDM model. The reconstructed peculiar velocity field that maximizes the likelihood is characterized by the parameter beta=0.323 +/- 0.08. Both results are in agreement with those obtained previously using the ~23,000 galaxies of the shallower Ks=11.25 2MRS survey. In our analysis we find that the luminosity function of 2MRS galaxies is poorly fitted by the Schechter form and that luminosity evolves such that objects become fainter with increasing redshift according to L(z)=L(z=0)(1+z)^(+2.7 +/-0.15).

Abstract:
We show that finite-range alternatives to the standard long-range BKS pair potential for silica might be used in molecular dynamics simulations. We study two such models that can be efficiently simulated since no Ewald summation is required. We first consider the Wolf method, where the Coulomb interactions are truncated at a cutoff distance r_c such that the requirement of charge neutrality holds. Various static and dynamic quantities are computed and compared to results from simulations using Ewald summations. We find very good agreement for r_c ~ 10 Angstroms. For lower values of r_c, the long--range structure is affected which is accompanied by a slight acceleration of dynamic properties. In a second approach, the Coulomb interaction is replaced by an effective Yukawa interaction with two new parameters determined by a force fitting procedure. The same trend as for the Wolf method is seen. However, slightly larger cutoffs have to be used in order to obtain the same accuracy with respect to static and dynamic quantities as for the Wolf method.

Abstract:
The gamma density function is usually defined in interval between zero and infinity. This paper introduces an upper and a lower boundary to this distribution. The parameters which characterize the truncated gamma distribution are evaluated. A statistical test is performed on two samples of stars. A comparison with the lognormal and the four power law distribution is made.

Abstract:
We present the broad-band 0.6-150 keV Suzaku and Swift BAT spectra of the low luminosity Seyfert galaxy, NGC 7213. The time-averaged continuum emission is well fitted by a single powerlaw of photon index Gamma = 1.75 and from consideration of the Fermi flux limit we constrain the high energy cutoff to be 350 keV < E < 25 MeV. Line emission from both near-neutral iron K_alpha at 6.39 keV and highly ionised iron, from Fe_(xxv) and Fe_(xxvi), is strongly detected in the Suzaku spectrum, further confirming the results of previous observations with Chandra and XMM-Newton. We find the centroid energies for the Fe_(xxv) and Fe_(xxvi) emission to be 6.60 keV and 6.95 keV respectively, with the latter appearing to be resolved in the Suzaku spectrum. We show that the Fe_(xxv) and Fe_(xxvi) emission can result from a highly photo-ionised plasma of column density N_(H) ~ 3 x 10^(23) cm^(-2). A Compton reflection component, e.g., originating from an optically-thick accretion disc or a Compton-thick torus, appears either very weak or absent in this AGN, subtending < 1 sr to the X-ray source, consistent with previous findings. Indeed the absence of either neutral or ionised Compton reflection coupled with the lack of any relativistic Fe K signatures in the spectrum suggests that an inner, optically-thick accretion disc is absent in this source. Instead, the accretion disc could be truncated with the inner regions perhaps replaced by a Compton-thin Radiatively Inefficient Accretion Flow. Thus, the Fe_(xxv) and Fe_(xxvi) emission could both originate in ionised material perhaps at the transition region between the hot, inner flow and the cold, truncated accretion disc on the order of 10^(3) - 10^(4) gravitational radii from the black hole. The origin for the unresolved neutral Fe K_alpha emission is then likely to be further out, perhaps originating in the optical BLR or a Compton-thin pc-scale torus.

Abstract:
For each n >1, we construct a left quantum group, i.e., a left Hopf algebra H generated by comatrix units X_{ij} and modeled after SL_q(n), which has a left antipode but no right antipode. The quantum special linear group SL_q(n) is a homomorphic image of our H.

Abstract:
After expressing the Fisher information in left truncated data in terms of the distributions of complete data, we study the relations of Fisher information between the left truncated and the complete data. The results show that under the Koziol-Green model, the left truncated data contain more Fisher information than the complete data.

Abstract:
The luminosity of the central source in ionizing radiation is an essential parameter in a photoionized environment, and one of the most fundamental physical quantities one can measure. We outline a method of determining luminosity for any emission-line region using only infrared data. In dusty environments, grains compete with hydrogen in absorbing continuum radiation. Grains produce infrared emission, and hydrogen produces recombination lines. We have computed a very large variety of photoionization models, using ranges of abundances, grain mixtures, ionizing continua, densities, and ionization parameters. The conditions were appropriate for such diverse objects as H II regions, planetary nebulae, starburst galaxies, and the narrow and broad line regions of active nuclei. The ratio of the total thermal grain emission relative to H$\beta$ (IR/H$\beta$) is the primary indicator of whether the cloud behaves as a classical Str\"{o}mgren sphere (a hydrogen-bounded nebula) or whether grains absorb most of the incident continuum (a dust-bounded nebula). We find two global limits: when $IR/H\beta<100$ infrared recombination lines determine the source luminosity in ionizing photons; when $IR/H\beta\gg100$ the grains act as a bolometer to measure the luminosity.