abstract

We analyze numerically the equation giving the number of missing label operators for reduction chains \(\mathfrak {k}\hookrightarrow \mathfrak {g}\) of Lie algebras to obtain information about the maximal possible dimension of certain types of subalgebras, mainly Abelian. Applications to the minimal dimension of faithful representations are given, and the number of invariants of codimension one and two subalgebras is analyzed.

abstract

The entropy S of the horizon \(\theta = \pi \)/\(2\) of the Hawking wormhole written in spherical Rindler coordinates is computed in this letter. Using Padmanabhan’s prescription, we found that the surface gravity of the horizon is constant and equals the proper acceleration of the Rindler observer. S is a monotonic function of the radial coordinate \(\xi \) and vanishes when \(\xi \) equals the Planck length. In addition, its expression is similar with the Kaul-Majumdar one for the black hole entropy, including logarithmic corrections in quantum gravity scenarios.

abstract

The standard way of evaluating residues and some real integrals through the residue theorem (Cauchy’s theorem) is well-known and widely applied in many branches of Physics. Herein we present an alternative technique based on the negative dimensional integration method (NDIM) originally developed to handle Feynman integrals. The advantage of this new technique is that we need only to apply Gaussian integration and solve systems of linear algebraic equations, with no need to determine the poles themselves or their residues, as well as obtaining a whole class of results for differing orders of poles simultaneously.

abstract

In this study, in context of general relativity we consider Einstein, Bergmann–Thomson, Møller and Landau–Lifshitz energy-momentum definitions and we compute the total energy distribution (due to matter and fields including gravitation) of the universe based on Szekeres class I and class II space-times. We show that Einstein and Bergmann–Thomson definitions of the energy-momentum complexes give the same results, while Møller’s and Landau–Lifshitz’s energy-momentum definition does not provide same results for Szekeres class II space. The definitions of Einstein, Bergmann–Thomson and Møller definitions of the energy-momentum complexes give similar results in Szekeres class I space-time.

abstract

This study is purposed to elaborate the problem of energy and momentum distribution of the Rigidly Rotating Wormhole space-time in general theory of relativity. In this connection, we use the energy-momentum definitions of Einstein, Bergmann–Thomson and Tolman. We obtained that the energy and momentum distributions of Einstein, Bergmann–Thomson and Tolman definitions give the same results in Rigidly Rotating Wormhole space-time.

abstract

The off-diagonal part of the active-neutrino mass matrix is constructed from two \(3\times 3\) matrices playing the role of annihilation and creation matrices acting in the neutrino-generation space of \(\nu _1 , \nu _2 , \nu _3\). The construction leads to a new relation, \(M_{\mu \,\tau } = 4\sqrt {3} M_{e\,\mu }\,\), which predicts in the case of tribimaximal neutrino mixing that \(m_3 - m_1 = \eta \,(m_2 - m_1)\) with \(\eta = 5.28547\). Then, the maximal possible value of \({\Delta m^2_{32}}/{\Delta m^2_{21}}\) is equal to \(\eta ^2 -1 = 26.9362\) and gives \(m_1 = 0\). With the experimental estimate \({\Delta m^2_{21}}\sim 8.0\times 10^{-5}\;{\rm eV}^2\), this maximal value, if realized, predicts \(\Delta m^2_{32} \sim 2.2\times 10^{-3}\;{\rm eV}^2\), near to the popular experimental estimation \(\Delta m^2_{32} \sim 2.4\times 10^{-3}\;{\rm eV}^2\).

abstract

The spectrum of Supersymmetric Yang–Mills Quantum Mechanics (SYMQM) in \(D=4\) dimensions for SU\((2)\) gauge group is computed for a maximal number of bosonic quanta \(B \leq 60\) in the two-fermion sector with the angular momentum \(j=0\). We analyse the eigenfunctions of discrete and continuous spectra, test the scaling relation for the continuous spectrum and confirm the dispersion relation to high accuracy.

abstract

The observability of the Higgs boson via the \(WW^{~*}\) decay channel at the Tevatron is discussed taking into account the enhancements due to the possible existence of the extra standard model (SM) families. It seems that the existence of new SM families can give the Tevatron experiments (D0 and CDF) the opportunity to observe the intermediate mass Higgs boson before the LHC.

abstract

Large-scale shell model calculations were performed for neutron-rich even–even \(^{132-136}\)Te using a realistic effective interaction derived from CD-Bonn nucleon–nucleon potential for the positive and negative parity states. The calculated results are compared with the recently available experimental data and with the recent theoretical work. The transition rates \(B\)(\(E\)2; 0\(^+\rightarrow \)2\(^+\)) are also calculated by taking into consideration core polarization effect by choosing best effective charges for proton and neutron. The result of our theoretical calculations are compared with experimental data and with the previous theoretical work. A very good agreement were obtained for all nuclei.

abstract

The importance of the nuclear potential shape in the entrance channel heavy ion collision as well as in the process of cluster formation is discussed. For more central collisions it is specially important for multiplicity distributions of intermediate mass fragments and for the parallel velocity distribution of reaction products. For peripheral collisions the entrance channel nuclear interaction is mainly responsible for the deflection angle.

abstract

A mean field calculation for obtaining the equation of state (EOS) for symmetric nuclear matter from a density dependent M3Y interaction supplemented by a zero-range potential is described. The energy per nucleon is minimized to obtain the ground state of symmetric nuclear matter. The saturation energy per nucleon used for nuclear matter calculations is determined from the co-efficient of the volume term of Bethe–Weizsäcker mass formula which is evaluated by fitting the recent experimental and estimated atomic mass excesses from Audi–Wapstra–Thibault atomic mass table by minimizing the mean square deviation. The constants of density dependence of the effective interaction are obtained by reproducing the saturation energy per nucleon and the saturation density of spin and isospin symmetric cold infinite nuclear matter. The EOS of symmetric nuclear matter, thus obtained, provide reasonably good estimate of nuclear incompressibility. Once the constants of density dependence are determined, EOS for asymmetric nuclear matter is calculated by adding to the isoscalar part, the isovector component of the M3Y interaction that do not contribute to the EOS of symmetric nuclear matter. These EOS are then used to calculate the pressure, the energy density and the velocity of sound in symmetric as well as isospin asymmetric nuclear matter.

abstract

We estimate four-nucleon force effects between different \(^4\)He wave functions by calculating the expectation values of four-nucleon potentials which were recently derived within the framework of chiral effective field theory. We find that the four-nucleon force is attractive for the wave functions with a totally symmetric momentum part. The additional binding energy provided by the long-ranged part of the four-nucleon force is of the order of a few hundred keV.

abstract

Present day chiral nucleon–nucleon potentials up to next-to-next-to-next-to leading order and three nucleon forces at next-to-next-to leading order are used to analyze nucleon–deuteron radiative capture at deuteron laboratory energies below \(E_{\rm d}\approx 100\) MeV. The differential cross section and the deuteron analyzing powers \(A_y(d)\) and \(A_{yy}\) are presented and compared to data. The theoretical predictions are obtained in the momentum-space Faddeev approach using the nuclear electromagnetic current operator with exchange currents introduced via the Siegert theorem. The chiral forces provide the same quality of data description as a combination of the two-nucleon AV18 and the three-nucleon Urbana IX interactions. However, the different parametrizations of the chiral potentials lead to broad bands of predictions.

abstract

When an ultrasonic wave passes through a liquid medium, containing microscopic gas inclusion, it can produce cavitation. At the boundary of a cavitating zone, a voltage appears as a effect of the collapse/rebound cycle of the cavitation bubbles. In this paper we establish a mathematical model of the voltage induced at the boundary of an acoustic cavitation zone, when the liquid was the crude oil. It is compared to that obtained for diesel, in order to prove that the ARIMA process can appropriately describe the fluctuations of generated voltage in different liquids. We also discuss the hypothesis of the relation between the ARIMA parameters and the liquid nature.

abstract

A new simple nonlocal generalization of the Frenkel–Kontorova model of dislocation in solid body as a type of the nonlocal sine-Gordon equation with the generalized interaction term is suggested. Its limit cases, symmetries and exact analytical solutions are obtained. This type of the nonlocal sine-Gordon equation is shown to possess one-solitonic solutions which are a nonlocal deformation of the corresponding classical solutions of the sine-Gordon equation. Exact analytical solutions of this equation and its Lagrangian integrability and geometrical approach are considered.