abstract

Symmetry groups of Friedman equations both without and with dissipation, and of Bianchi type I equations with dissipation are discussed. It is shown that the symmetry groups of these equations correctly single out corresponding equations of state.

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It is proven that the linear Schrödinger (Klein–Gordon) field coupled to Yang–Mills fields has no non-zero static, finite energy, solutions. The case of nonlinear scalar fields is discussed, and necessary criteria for existence of nonzero solutions are given.

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A search for scalar leptons, charged Higgs and excited leptons has been done with the five experiments installed at PETRA (CELLO-JADE-MARK J-PLUTO-TASSO). No scalar lepton or Higgs particles with conventional decay are created in e e annihilation. The highest value of the mass for such particles is close to the beam energy (17 GeV/\(c\)). Direct production of excited lepton gives also a negative result up to a mass value equal to 30 6eV/\(c^2\). Comparison with QED for reaction e\(^+\)e\(^- \to \gamma \gamma \) gives a limit of 59 GeV/\(c^2\) for the e mass.

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The influence of the bag shape on the lowest lying gluonium states is investigated. The MIT and the surface tension version of the bag model are considered.

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A simple method of generating the relative motion continuum wave functions in the region of isolated resonances by using an energy-dependent effective one-body potential is proposed. The method accounts for the effects of the configuration mixing and predicts splitting of the single-particle resonances in quantitative agreement with the shell model diagonalization approach.

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The \(^{28}\)Si(\(\rho ,\gamma \))\(^{29}\)P reaction data have been analysed in terms of a modified direct-semidirect capture model which accounts for the presence of broad shape (single-particle) resonances in the entrance channel. Values of the spectroscopic factors for the ground state and 1.65 MeV and 2.88 MeV resonances in \(^{29}\)P nuclei were extracted and found to be consistent with those obtained in other experiments. The modified theoretical analysis scheme was found to provide a convenient tool for analysing the radiative capture reaction data.

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It is shown that for locally Hermit–Einstein, self-dual gravitational instanton, Einstein’s equations can be reduced to a single, second-order, non-linear equation.

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It is shown that the quarkonium–gluonium mixture model of \(\theta \) (1670) state fails in many points. On the other hand, the mixing of the s\(\overline {\rm s}\) state with the u\(\overline {\rm u}\)s\(\overline {\rm s}\) member of 36-plet is shown to yield the decay properties of f’ (1515) and \(\theta \) (1670) consistent with the experimental observations.