abstract

A numerical solution of the Fredholm linear integral equation of the 2-nd kind by the Monte-Carlo method, which is directly applicable to obtaining various functionals in the theory of incoherent radiation and neutron transfer, is suggested. The method resembles a well-known statistics quota sample realized in a generalized space of variable dimension. The necessary distribution of states according to a set of subspaces is achieved by means of the Markov Chain Technique. The numerical calculation, made for the particular case of breaking up into subspaces of photon scattering of various multiplicities, reveals the high efficiency of the method in comparison with the known estimate by collisions for not very large mean values of photon scattering, \(\overline N\), in the medium.

abstract

It is shown that in the post-newtonian approximation the gravitational momentum of a system of point particles is equal to the sum of field momentum and inertial momentum only in two classes of coordinate systems. This equality may be treated as a natural condition on a coordinate system in which the generally covariant Einstein equations are to be solved.

abstract

Post-newtonian equations of motion for two bodies are obtained by means of the Lagrange function of many body system in the potential coordinates. Dependence of first integrals on the coordinate system is examined. It is shown that corrections to Newtonian first integrals do not depend on the choice of coordinates.

abstract

General discussions on the non-leptonic decays of D\(^+\) and D\(^0\) are presented from the isospin point of view. We point out that the two recent data on \(\tau ^{{{\rm D}^+}}/\tau ^{{{\rm D}^0}}\) and D\(^0 \to \overline {\rm K}^0\pi ^0\) are strongly correlated. We show that the annihilation mechanism for D\(^0 \to {\rm K}\pi \) is not at all suppressed as is usually believed. A mechanism is suggested in which the light quark in the D meson plays a more selective role than its usual spectator one. This mechanism and the annihilation one provide a natural explanation for the recent data without requiring any revision of our usual understanding of weak and strong interactions.

abstract

Results on momentum distributions of pions emitted from the recoiling system X\(^{--}\) in the reaction \(\pi ^-\)n\(\to \)pX\(^{--}\) are presented and interpreted in the framework of the one pion exchange model. The Feynman \(x\) distributions of pions from inclusive reactions \(\pi ^-\)n\(^- \to \pi ^-+\)X\(^-\) and \(\pi ^-\pi ^- \to \pi ^++\)X\(^{---}\) are similar to those observed in \(\pi \)p on-mass-shell experiments and their energy dependence is consistent with predictions based on Regge–Mueller phenomenology applied to \(\pi ^-\pi ^-\) reactions.

abstract

The solution of the leading log QCD evolution equation for the non-singlet evolution function is given in the form of a convergent series. The convergence is rapid for small values of \(x\). An asymptotic expansion in powers of (\(1-x\)) is also obtained. Its first few terms reproduce within about one per cent all the moments of the evolution function in the kinematical range of present and near future interest. Using simultaneously the two expansions it is easy to calculate structure functions in all the region \(0 \lt x \leq 1\) with an accuracy of the order of one per cent.

abstract

Lepton and quark families \(\{v_N\}\), \(\{e_N\}\) and \(\{u_N\}\), \(\{d_N\}\) are conjectured to be quantum-dynamical systems in the space of generations \(N = 0\), 1, 2 … . Such a conjecture, called the “zeroth quantization”, implies the form of lepton and quark mass spectra, if lepton and quark families are supposed to be almost in thermal equilibrium with the rest of the Universe. Toponium is predicted at about 38 GeV, while the next charged lepton at 28.5 GeV (in accord with the author’s previous predictions made on a more phenomenological ground).