Charge-exchange resonances and restoration of the Wigner SU(4)-symmetry in heavy and superheavy nuclei

Energies of the giant Gamow-Teller and analog resonances - $E_{\rm G}$ and $E_{\rm A}$, are presented, calculated using the microscopic theory of finite Fermi system. The calculated differences $\Delta E_{\rm G-A}=E_{\rm G}-E_{\rm A}$ go to zero in heavier nuclei indicating the restoration of Wigner SU(4)-symmetry. The calculated $\Delta E_{\rm G-A}$ values are in good agreement with the experimental data. The average deviation is 0.30 MeV for the 33 considered nuclei for which experimental data is available. The $\Delta E_{\rm G-A}$ values were calculated for heavy and superheavy nuclei up to the mass number $A$= 290. Using the experimental data for the analog resonances energies, the isotopic dependence of the difference of the Coulomb energies of neighboring nuclei isobars analyzed within the SU(4)-approach for more than 400 nuclei in the mass number range of $A$ = 3 - 244. The Wigner SU(4)-symmetry restoration for heavy and superheavy nuclei is confirmed. It is shown that the restoration of SU(4)-symmetry does not contradict the possibility of the existence of the "island of stability" in the region of superheavy nuclei.Comment: 5 pages, 2 figure

On prescribed change of profile for solutions of parabolic equations

Parabolic equations with homogeneous Dirichlet conditions on the boundary are studied in a setting where the solutions are required to have a prescribed change of the profile in fixed time, instead of a Cauchy condition. It is shown that this problem is well-posed in L_2-setting. Existence and regularity results are established, as well as an analog of the maximum principle

Quasi-Optimal Filtering in Inverse Problems

A way of constructing a nonlinear filter close to the optimal Kolmogorov - Wiener filter is proposed within the framework of the statistical approach to inverse problems. Quasi-optimal filtering, which has no Bayesian assumptions, produces stable and efficient solutions by relying solely on the internal resources of the inverse theory. The exact representation is given of the Feasible Region for inverse solutions that follows from the statistical consideration.Comment: 9 pages, 240 K