Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators

We investigate the eigenvalues of perturbed spherical Schr\"odinger operators under the assumption that the perturbation $q(x)$ satisfies $x q(x) \in L^1(0,1)$. We show that the square roots of eigenvalues are given by the square roots of the unperturbed eigenvalues up to an decaying error depending on the behavior of $q(x)$ near $x=0$. Furthermore, we provide sets of spectral data which uniquely determine $q(x)$.Comment: 14 page

Current Ultrasonography Potential in the Diagnosis of Juvenile Recurrent Parotitis

Objective: To determine the diagnostic significance of sonographic signs indicating the parotid glands’ condition in children with juvenile recurrent parotitis (JRP).   Materials and methods: We examined 42 patients with JRP and 30 children aged 3-17 years from the control group. Both groups underwent B-mode and color Doppler ultrasonography of parotid glands to assess linear dimensions, contours, structures, echogenicity, pronouncement of the stromal component, parenchymal vascularization, and condition of intraglandular lymph nodes. The diagnostic significance of the sonographic signs was assessed by ROC analysis.   Results and discussion: We found significant differences between the study and control groups in terms of such sonographic signs as gland enlargement, decreased parenchymal echogenicity, change in the echotexture, increased stromal component, increased parenchymal vascularization, and reactive parotid lymph nodes (P < .05). With the high-frequency probe we were able to study the structure of JRP-associated hypoechoic foci in the parenchyma and prove that they are not cystic dilatation of the ducts but foci of infiltration around the peripheral ducts with structurally altered walls.   Conclusions: Ultrasonography plays a pivotal role in the JRP diagnosis and can identify its most significant sonographic signs, such as increased size, distinctive changes in the parenchymal echotexture, decreased echogenicity, and increased parenchymal vascularization

Holographic Recording Media based on Electron Donor Oligomers

For optical holographic recording by photothermoplastic technique reversible holographic media based on oligomers with hole type of conductivity are used. New carbazole containing radial tetrasubstituted silanes and germanes are described in the present work

Review of scientific topics for Millimetron space observatory

This paper describes outstanding issues in astrophysics and cosmology that can be solved by astronomical observations in a broad spectral range from far infrared to millimeter wavelengths. The discussed problems related to the formation of stars and planets, galaxies and the interstellar medium, studies of black holes and the development of the cosmological model can be addressed by the planned space observatory Millimetron (the "Spectr-M" project) equipped with a cooled 10-m mirror. Millimetron can operate both as a single-dish telescope and as a part of a space-ground interferometer with very long baseline.Comment: The translation of the original article in Physics Uspekhi http://ufn.ru/ru/articles/2014/12/c

X-ray variation statistics and wind clumping in Vela X-1

We investigate the structure of the wind in the neutron star X-ray binary system Vela X-1 by analyzing its flaring behavior. Vela X-1 shows constant flaring, with some flares reaching fluxes of more than 3.0 Crab between 20-60 keV for several 100 seconds, while the average flux is around 250 mCrab. We analyzed all archival INTEGRAL data, calculating the brightness distribution in the 20-60 keV band, which, as we show, closely follows a log-normal distribution. Orbital resolved analysis shows that the structure is strongly variable, explainable by shocks and a fluctuating accretion wake. Analysis of RXTE ASM data suggests a strong orbital change of N_H. Accreted clump masses derived from the INTEGRAL data are on the order of 5 x 10^19 -10^21 g. We show that the lightcurve can be described with a model of multiplicative random numbers. In the course of the simulation we calculate the power spectral density of the system in the 20-100 keV energy band and show that it follows a red-noise power law. We suggest that a mixture of a clumpy wind, shocks, and turbulence can explain the measured mass distribution. As the recently discovered class of supergiant fast X-ray transients (SFXT) seems to show the same parameters for the wind, the link between persistent HMXB like Vela X-1 and SFXT is further strengthened.Comment: 8 pages, 6 figures, accepted for publication in A&

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page

The diterpenoid alkaloid noroxoaconitine is a Mapkap kinase 5 (MK5/PRAK) inhibitor

The mitogen-activated protein kinase-activated protein kinase MK5 is ubiquitously expressed in vertebrates and is implicated in cell proliferation, cytoskeletal remodeling, and anxiety behavior. This makes MK5 an attractive drug target. We tested several diterpenoid alkaloids for their ability to suppress MK5 kinase activity. We identified noroxoaconitine as an ATP competitor that inhibited the catalytic activity of MK5 in vitro (IC50 = 37.5 μM; Ki = 0.675 μM) and prevented PKA-induced nuclear export of MK5, a process that depends on kinase active MK5. MK5 is closely related to MK2 and MK3, and noroxoaconitine inhibited MK3- and MK5- but not MK2-mediated phosphorylation of the common substrate Hsp27. Molecular docking of noroxoaconitine into the ATP binding sites indicated that noroxoaconitine binds more strongly to MK5 than to MK3. Noroxoaconitine and derivatives may help in elucidating the precise biological functions of MK5 and may prove to have therapeutic values

Transmutations and spectral parameter power series in eigenvalue problems

We give an overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS). The possibility to write down the dispersion (characteristic) equations corresponding to a variety of spectral problems related to Sturm-Liouville equations in an analytic form is an attractive feature of the SPPS method. It is based on a computation of certain systems of recursive integrals. Considered as families of functions these systems are complete in the $L_{2}$-space and result to be the images of the nonnegative integer powers of the independent variable under the action of a corresponding transmutation operator. This recently revealed property of the Delsarte transmutations opens the way to apply the transmutation operator even when its integral kernel is unknown and gives the possibility to obtain further interesting properties concerning the Darboux transformed Schr\"{o}dinger operators. We introduce the systems of recursive integrals and the SPPS approach, explain some of its applications to spectral problems with numerical illustrations, give the definition and basic properties of transmutation operators, introduce a parametrized family of transmutation operators, study their mapping properties and construct the transmutation operators for Darboux transformed Schr\"{o}dinger operators.Comment: 30 pages, 4 figures. arXiv admin note: text overlap with arXiv:1111.444