abstract

The post-post-Newtonian equations of motion for the point particles using the EIH approximation method are derived. These equations are deduced from the gravitational field equations with the stress-energy tensor proposed by Infeld and Plebanski. The Infeld-coordinates and EIH-coordinates are used. Regularization of the metric tensor and its derivatives on the world lines of particles by means of the modified Dirac \(\hat \delta \)-function, which is contained in the stress-energy tensor, has been done.

abstract

Using the variable separation approach, a quite general variable separation solution of the (2+1)-dimensional Maccari systems can be derived. Special type of soliton solutions, folded solitary waves (FSWs) and foldons, are obtained by selecting some types of multi-valued functions appropriately. The FSWs and foldons may be “folded” in quite complicated waves and possess interesting interaction properties.

abstract

Für die perfekten Lie-Algebren \(\mathfrak {sl}\left ( 2,\mathbb {C}\right ) \overrightarrow {\oplus }_{R}\mathfrak {h}_{m}\) wird die Existenz eines Casimiroperators der Ordnung vier bewiesen. Weiter werden explizite Formeln für die nichtzentralen Casimiroperatoren der Algebren in Abhängigkeit der beschreibenden Darstellung \(R\) des Produktes gegeben.

abstract

Using a more accurate approximation than that applied by Lee–Oehme–Yang we show that the interpretation of the tests, measuring the difference between the \(K_{0}\) mass and the \({\bar K}_{0}\) mass as the CPT-symmetry test is wrong. We find that in fact such tests should rather be considered as tests for the existence of the hypothetical interaction allowing the first order \(|\Delta S| = 2\) transitions \(K_{0} \rightleftharpoons {\bar K}_{0}\).

abstract

The ratio of the real part to the imaginary part of the nucleon–nucleon elastic scattering amplitude is studied in terms of powers of the momentum transfer squared \(q^2\). This study includes the dependence on the phase variation of the nucleon–nucleon elastic scattering amplitudes. The Gaussian form of the effective nucleon–nucleon interaction is used to calculate the nucleon–nucleon elastic scattering amplitudes. Analytical expressions for the phase variation and for the ratios of the real to the imaginary parts are obtained. The obtained expressions are new formulae and are found to be important for the description of nucleon–nucleon elastic scattering amplitudes. Introducing of the phase variation and the ratio of the real to the imaginary parts of the elastic scattering amplitude proportional to \(q^2\) improves the theoretical calculations.

abstract

In the framework of seesaw mechanism with three neutrino flavors, we propose tentatively an efficient parametrization for the spectra of Dirac and righthanded Majorana neutrino mass matrices in terms of three free parameters. Two of them are related to (and determined by) the corresponding parameters introduced previously for the mass spectra of charged leptons and up and down quarks. The third is determined from the experimental estimate of solar \(\Delta m^2_{21}\). Then, the atmospheric \(\Delta m^2_{32}\) is predicted close to its experimental estimation. With the use of these three parameters all light active-neutrino masses \( m_1 \lt m_2 \lt m_3\) and heavy sterile-neutrino masses \( M_1 \lt M_2 \lt M_3\) are readily evaluated. The latter turn out much more hierarchical than the former. The lightest heavy mass \( M_1\) comes out to be of the order \(O(10^6\;{\rm GeV})\) so, it is too light to imply that the mechanism of baryogenesis through thermal leptogenesis might work.

abstract

Possible existence of extra SM families and/or isosinglet \(E_{6}\) quarks may sufficiently decrease \(\left \vert V_{tb}\right \vert \) of CKM matrix so that toponia can be formed. Production of pseudoscalar toponium at the LHC and VLHC has been considered. The observability of \(\ \eta _{t}\rightarrow \gamma \gamma \) signal is discussed.

abstract

A liquid-gas phase transition in the fragmentation of Pb nucleus at 158 \(A\)GeV energy has been investigated. The results of the analysis of moments of the charge distributions of fragments are consistent with the postulated occurrence of a liquid-gas phase transition in the process of fragmentation of heavy nuclei. Values of critical exponents are found and compared to those obtained at lower energies.

abstract

The Spectroscopic Monte Carlo Method is applied to the nucleus \({}^{170}\)Yb using the Monopole plus Quadrupole Pairing plus Quadrupole interaction for yrast states up to \(J^{~\pi }=12^+\). The unusually small statistical errors in the Monte Carlo calculations of the yrast energies (\(\approx 40\div 70\)Kev) despite moderately strong sign oscillations, are discussed. Energy levels, expectation values of pairing potential and the pairing strength to \(J=12\) for the neutron intruder orbit and to \(J=10\) for the proton intruder orbit are evaluated. It is shown that the Hartree–Fock–Bogoliubov wave functions obtained with variation after projection to good particle number and to good \(z\)-component of the angular momentum and reprojected to good \(J^{~2}\), \(J_z\) after variation, give excitation energies in reasonable agreement with the Monte Carlo values. The intrinsic HFB wave functions have a considerable angular momentum dependence. Wave functions which are projected to good angular momentum after variation (PAV), lead to excitation energies larger than the corresponding Monte Carlo values.

abstract

Chandra X-ray observations of the 1 E0657-56 galaxy cluster diffuse emission reveal the existence of large scale cluster merger shock. We study the observed radio and X-ray data of this cluster as a possible result of the diffusive shock acceleration. This model can explain the observations within reasonable ranges of physical parameters for the shock and the intracluster medium. The expected nonthermal soft and hard X-ray fluxes are predicted.

abstract

We demonstrate that hadron production viewed as formation of specific stochastic network can explain in natural way the power-law distributions of transverse mass spectra of pions found recently, which seem to substitute the expected Boltzmann statistical factor.