Neutrino Mass Matrix and Hierarchy

We build a model to describe neutrinos based on strict hierarchy, incorporating as much as possible, the latest known data, for $\Delta_{sol}$ and $\Delta_{atm}$, and for the mixing angles determined from neutrino oscillation experiments, including that from KamLAND. Since the hierarchy assumption is a statement about mass ratios, it lets us obtain all three neutrino masses. We obtain a mass matrix, $M_\nu$ and a mixing matrix, $U$, where both $M_\nu$ and $U$ are given in terms of powers of $\Lambda$, the analog of the Cabibbo angle $\lambda$ in the Wolfenstein representation, and two parameters, $\rho$ and $\kappa$, each of order one. The expansion parameter, $\Lambda$, is defined by $\Lambda^2 = m_2/m_3 = \surd (\Delta_{sol}/\Delta_{atm}) \approx$ 0.16, and $\rho$ expresses our ignorance of the lightest neutrino mass $m_1, (m_1 = \rho \Lambda^4 m_3$), while $\kappa$ scales $s_{13}$ to the experimental upper limit, $s_{13} = \kappa \Lambda^2 \approx 0.16 \kappa$. These matrices are similar in structure to those for the quark and lepton families, but with $\Lambda$ about 1.6 times larger than the $\lambda$ for the quarks and charged leptons. The upper limit for the effective neutrino mass in double $\beta$-decay experiments is $4 \times 10^{-3} eV$ if $s_{13} = 0$ and $6 \times 10^{-3} eV$ if $s_{13}$ is maximal. The model, which is fairly unique, given the hierarchy assumption and the data, is compared to supersymmetric extension and texture zero models of mass generation.Comment: 8 pages, LaTex, This paper updates an earlier version by incorporating KamLAND dat

Integrable Anisotropic Evolution Equations on a Sphere

V.V. Sokolov's modifying symmetry approach is applied to anisotropic evolution equations of the third order on the n-dimensional sphere. The main result is a complete classification of such equations. Auto-B\"acklund transformations are also found for all equations.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

European Cyber Security System

Nowadays computer networks are widely spread in all spheres of human life. That is why the problem of cyber security of mankind is of great importance. Today, the European Union makes efforts to guarantee network safety in Europe by means of increase its member states in power and international cooperation in cyber security, including non-member countries, to prevent cyber crimes. Striving to join the European Union, Ukraine is involved in the process of providing cyber security. This paper examines the main strategies of EU standards in cyber security to be followed by Ukraine as one of European countries