Hierarchy of interactions and mass relations in asymptotically free E6 model of unified interactions

The hierarchy of gauge interactions within the E₆ model is proved, and the vector and spinor field masses are obtained. The mass spectrum of the charged W-bosons is found, and the mass scale is fixed so that the mass of the lightest of them is about 70 GeV. The lepton spectroscopy is studied and a new charged lepton, with mass of order 4–8 GeV is predicted. For the low-energy phenomenology, the model may be considered as a theory of 6 flavoured quarks and 4 charged leptons, each with its neutrino. Being 4-component the neutrinos are massive except for the ν_e (m_νe = 0, exactly) and ν_μ (m_νμ ≈ 0, approximately) particles. The problem of the “superfluous” particles which as a rule accompanies the asymptotic freedom in such theories is also briefly discussed.     

Low-energy pion-nucleus potential in the extended tree-level model for the pion-nucleon interaction

Starting from the extended tree-level model for the πN interaction [1] (hereafter ETLM) we demonstrated that the observed local pion-nucleus repulsion arises from the reduction of baryon masses in nucleus due to strong scalar nuclear field [2]. This is rather convincing argument in favour of nuclear relativism because such repulsion has no explanation within the traditional nonrelativistic approach to nucleus.     

Motion of a helium atom in a quartz crystal with dislocations

The motion of a helium atom through the quartz crystal structure disturbed by dislocations has been considered. Two cases of their action on the motion of the helium atom have been discussed. (1) Dislocations, in particular, screw dislocations, can be represented as contracted or extended helical (six-, four-, three-membered) channels consisting of SiO₄ tetrahedra. In this case, the helium atom moves inside the dislocation as in the crystallographic channel with changed parameters. (2) Dislocations can cross the crystallographic channel. This leads to an excess or a deficit of oxygen atoms of SiO₄ tetrahedra in the immediate environment of the helium atom located in the channel. In both cases, the displacement of the helium atom appears as a Frenkel-Kontorova soliton. However, in the latter case, the dependence of the activation energy of this soliton on the number of defects is discontinuous and exhibits a “mobility gap” of the helium atom.     

Extended Antipodal Theorems

In infinite-dimensional Hilbert spaces, we prove that the iterative sequence generated by the extragradient method for solving pseudo-monotone variational inequalities converges weakly to a solution. A class of pseudo-monotone variational inequalities is considered to illustrate the convergent behavior. The result obtained in this note extends some recent results in the literature; especially, it gives a positive answer to a question raised in Khanh (Acta Math Vietnam 41:251–263, 2016).     

Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection

Light scattered from biological tissues can exhibit an inverse power law spectral component. We develop a model based on the Born approximation and von Karman (self-affine) spatial correlation of submicron tissue refractive index to account for this. The model is applied to light scattering spectra obtained from excised esophagi of normal and carcinogen-treated rats. Power law exponents used to fit dysplastic tissue site spectra are significantly smaller than those from normal sites, indicating that changes in tissue self-affinity can serve as a potential biomarker for precancer.     

Change in the Structure and Corrosion Resistance of a Nickel-Chrome Coating on Stainless Steel During Implantation of High Energy Al+ and B+ Ions

Russian Physics Journal - Magnetron sputtering, vacuum arc deposition, and ion implantation have been used to create a three-layer anti-corrosive coating structure on stainless steel samples. The...