abstract

Two new luminosity functions of galaxies can be built starting from three and four parameter generalized gamma distributions. In the astrophysical conversion, the number of parameters increases by one, due to the addition of the overall density of galaxies. A third new galaxy luminosity function is built starting from a three parameter generalized gamma distribution for the mass of galaxies once a simple nonlinear relationship between mass and luminosity is assumed; in this case the number of parameters is five because the overall density of galaxies and a parameter that regulates mass and luminosity are added. The three new galaxy luminosity functions were tested on the Sloan Digital Sky Survey (SDSS) in five different bands; the results always produce a “better fit” than the Schechter function. The formalism that has been developed allows to analyze the Schechter function with a transformation of location. A test between theoretical and observed number of galaxies as a function of redshift was done on data extracted from a two-degree field galaxy redshift survey.

abstract

The goal of the recently approved space-based LARES mission is to measure the general relativistic Lense–Thirring effect in the gravitational field of the spinning Earth at a repeatedly claimed \(1\%\) accuracy by combining its node \({\mit \Omega }\) with those of the existing LAGEOS and LAGEOS II laser-ranged satellites. In this paper we show that, in view of the lower altitude of LARES (\(h=1450\) km) with respect to LAGEOS and LAGEOS II (\(h\simeq 6000\) km), the cross-coupling between the effect of the atmospheric drag, both neutral and charged, on the inclination of LARES and its classical node precession due to the Earth’s oblateness may induce a 3–9% year\(^{-1}\) systematic bias on the total relativistic precession. Since its extraction from the data will take about 5–10 years, such a perturbing effect may degrade the total accuracy of the test, especially in view of the large uncertainties in modeling the drag force.

abstract

This paper analyzes the pitchfork and Hopf bifurcations of a new 3-D four-wing quadratic autonomous system proposed by Qi et al. The center manifold technique is used to reduce the dimensions of this system. The pitchfork and Hopf bifurcations of the system are theoretically analyzed. The influence of system parameters on other bifurcations are also investigated. The theoretical analysis and simulations demonstrate the rich dynamics of the system.

abstract

In the general theory of relativity, matter energy can be expressed geometrically, and Weyl put forward the hypothesis that a curved-space formulation of the Dirac equation \([i{\gamma }^{\,k}(\partial _k-i eA_k)-m]\psi =0\) for a relativistic spin-1/2 field \(\psi \) would lead to a possible reinterpretation of the mass parameter \(m\) in purely geometrical terms. Here, we show how this idea can be realized in the general-relativistically covariant Dirac equation \([i{\gamma }^{\,k}(\partial _k-{\mit \Gamma }_k-ieA_k)-m]\psi =0\) due to Fock, where \({\mit \Gamma }_i\) is the spinorial connection, after rewriting \(m^2\) as \(m^2({\gamma }^0)^2\) in comoving coordinates. Thus, \(m\) is replaced by the matrix mass \(m{\gamma }^0\), which can then be set equal to \(i{\gamma }^{\,k}{\mit \Gamma }_k\) in an anti-de Sitter space-time background that can be attributed to fermionic zero-point vacuum fluctuations. This result is analogous to the reidentification of the gauge field \(eA_i\) with Im\({\mit \Gamma }_i\) in a Majorana representation of the \({\gamma }_i\).

abstract

We present in details a numerical approach for solving supersymmetric quantum mechanical systems with a gauge symmetry valid in all fermionic sectors. The method uses a recursive algorithm to calculate matrix elements of any gauge invariant operator in the Fock basis, in particular of the Hamiltonian operator, and can be used for any gauge group. We describe its application to a supersymmetric anharmonic oscillator model with discrete spectrum.

abstract

In the the framework of Regge phenomenology and meson–meson mass mixing, we estimated the masses of pseudoscalar meson nonet. The results suggest that the \(X(1835)\) should be assigned as the second radial excitation of the \(\eta '\) rather than the ground pseudoscalar glueball. As a byproduct, we obtain the mass of ground pseudoscalar glueball in the glueball dominance picture, which is well agreement with predictions of other different theoretical models.

abstract

The scenario of a collective expansion of matter created in proton–proton (\(p\)–\(p\)) collisions at the CERN Large Hadron Collider (LHC) is discussed. Assuming a small transverse size and a formation time of 0.1 fm/\(c\) of the source we observe the build up of a substantial transverse flow in relativistic hydrodynamic simulations. In order to demonstrate the collectivity in \(p\)–\(p\) collisions we propose to look at the multiplicity dependence of the elliptic flow coefficient. If high multiplicity events originate from azimuthally asymmetric events containing two flux tubes, an observable signal above the statistical fluctuations in the measured elliptic flow could appear.

abstract

Angular distributions of \(^{7}\)Li(\(^{7}\)Li,t), (\(^{7}\)Li,\(\alpha \)) and (\(^{7}\)Li,\(^{6}\)He) reactions were measured for laboratory energies from 2–16 MeV. Exact finite range DWBA analyses were performed with the aim to identify contributions of direct processes and to investigate the applicability of DWBA to such few nucleon systems. It turned out that DWBA can be successfully applied to estimate differential and total cross-sections of direct transfer processes in \(^{7}\)Li+\(^{7}\)Li interaction. The direct mechanism was found to play a dominant role in most of these reactions but significant contributions of other, strongly energy dependent processes were also established. It is suggested that these processes might be due to isolated resonances superimposed on the background of statistical fluctuations arising from interference of compound nucleus and direct transfer contributions.

abstract

We demonstrate behaviour of the momentum space screened Coulomb t-matrix, obtained by a numerical solution of the three-dimensional Lippmann–Schwinger equation. Examples are given for different types of screening. They prove that it is possible to obtain numerically a reliable three-dimensional screened Coulomb t-matrix, what is important in view of its application in few-body calculations.

abstract

We construct a quintom dark energy model with two non-minimally coupled scalar fields, one quintessence and the other phantom field, confined on the warped DGP brane. We study some important issues such as phantom divide line crossing, existence of the bouncing solutions and the stability of the solutions in this framework. We show that this model accounts for crossing the phantom divide line and realization of the bouncing solutions. This model allows for stability of the solutions in separate regions of the \(\omega \)–\(\omega '\) phase-plane.

abstract

If we want to explain the recently discovered accelerated stage of the universe, one of the option we have is to modify the Einstein tensor. The simplest such modification, in agreement with all observations, is the positive cosmological constant \({\mit \Lambda }\). Such a modification will also have its impact on local observables and on the propagation of weak gravitational waves. We show here that the inclusion of a cosmological constant impedes the detection of a gravitational wave if the latter is produced at a distance larger than \({\cal L}_{\rm crit}=(6\sqrt {2}\pi f \hat {h}/\sqrt {5})r_{{\mit \Lambda }}^2\), where \(r_{{\mit \Lambda }}=1/\sqrt {{\mit \Lambda }}\) and \(f\) and \(\hat {h}\) are the frequency and the strain of the wave, respectively. \({\cal L}_{\rm crit}\) is of astrophysical order of magnitude. We interpret the result in the sense that the gravitational wave interpretation is only possible if the characteristic wave properties are smaller than the non-oscillatory solution due to \({\mit \Lambda }\).

abstract

Some remarks to paper of M. Kafatos et al. are given.