Convexification Numerical Method for a Coefficient Inverse Problem for the Riemannian Radiative Transfer Equation

The first globally convergent numerical method for a Coefficient Inverse Problem (CIP) for the Riemannian Radiative Transfer Equation (RRTE) is constructed. This is a version of the so-called \textquotedblleft convexification" principle, which has been pursued by this research group for a number of years for some other CIPs for PDEs. Those PDEs are significantly different from RRTE. The presence of the Carleman Weight Function (CWF) in the numerical scheme is the key element of the convexification. CWF is the function, which is involved as the weight function in the Carleman estimate for the corresponding PDE operator. Convergence analysis is presented along with the results of numerical experiments, which confirm the theory. RRTE governs the propagation of photons in the diffuse medium in the case when they propagate along geodesic lines between their collisions. Geodesic lines are generated by the spatially variable dielectric constant of the medium

Superconductivity in silicon nanostructures

We present the findings of the superconductivity observed in the silicon nanostructures prepared by short time diffusion of boron on the n-type Si(100) surface. These Si-based nanostructures represent the p-type ultra-narrow self-assembled silicon quantum wells, 2nm, confined by the delta - barriers heavily doped with boron, 3nm. The EPR and the thermo-emf studies show that the delta - barriers appear to consist of the trigonal dipole centres, which are caused by the negative-U reconstruction of the shallow boron acceptors. Using the CV and thermo-emf techniques, the transport of two-dimensional holes inside SQW is demonstrated to be accompanied by single-hole tunneling through these negative-U centres that results in the superconductivity of the delta - barriers. The values of the correlation gaps obtained from these measurements are in a good agreement with the data derived from the temperature and magnetic field dependencies of the magnetic susceptibility, which reveal a strong diamagnetism and additionally identify the superconductor gap value.Comment: 4 pages, 6 figures, presented at the 4th International Conference on Vortex Matter in Superconductors, Crete, Greece, September 3-9, 200

QCD partition function in the external field in the covariant gauge

The QCD partition function in the external stationary gluomagnetic field is computed in the third order in external field invariants in arbitrary dimension and arbitrary covariant gauge. The contributions proportional to third order invariants in gluon field strength are shown to be dependent on covariant quantum gauge fixing parameter \alph

In celebration of the 60th birthday of Professor Alemdar Hasanoğlu (Hasanov)

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Polar optical phonons in wurtzite spheroidal quantum dots: Theory and application to ZnO and ZnO/MgZnO nanostructures

Polar optical-phonon modes are derived analytically for spheroidal quantum dots with wurtzite crystal structure. The developed theory is applied to a freestanding spheroidal ZnO quantum dot and to a spheroidal ZnO quantum dot embedded into a MgZnO crystal. The wurtzite (anisotropic) quantum dots are shown to have strongly different polar optical-phonon modes in comparison with zincblende (isotropic) quantum dots. The obtained results allow one to explain and accurately predict phonon peaks in the Raman spectra of wurtzite nanocrystals, nanorods (prolate spheroids), and epitaxial quantum dots (oblate spheroids).Comment: 11 page