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Abstract: We study the characteristic properties of scattering data for the differential system with a singularity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y'-x^{-1}Ay-q(x)y=\rho By$$\end{document}in the case of an integrable potential \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q(\,\cdot\,)$$\end{document}. Structural and analytical properties are established for the conjugation matrix – a part of the scattering data related to the continuous spectrum.

Abstract: In this paper, we study the Weyl-type solutions of the differential system with a singularity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ y'-x^{-1}Ay-q(x)y=\rho By$$\end{document}in the case of an integrable potential \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q(\cdot)$$\end{document}.

We study the phenomenology of light scalar quarks and the properties of a new family of hadrons containing such quarks in the framework of QCD taking into account non-perturbative effects caused by a possible existence of the condensate of the colored scalar fields. We suggest that 1-- bound state of scalar quark and antiquark may lie in the already accessible region and be observable as resonance in PETRAe+e- collisions.

The production rate of light photinos in radiative pion decay is calculated. Experimental constraints on masses and mass splittings of scalar quarks imply the following upper bound on the decay rate .

We consider a class of supersymmetric models lepton number nonconservation due to mixing of scalar leptons. It is shown that a range of parameters exists such that the processes µ?e?, µ?e??, µ?3e, µ+e-?µ-e+ are strongly suppressed, whereas the decay can proceed with a rate . The signatures of such decay can be the production of right-handed electrons with the energy aroundmµ/3 and modification of the energy spectrum of the electrons in that region as compared with the standard model prediction.