Sharp spectral stability estimates via the Lebesgue measure of domains for higher order elliptic operators

We prove sharp stability estimates for the variation of the eigenvalues of non-negative self-adjoint elliptic operators of arbitrary even order upon variation of the open sets on which they are defined. These estimates are expressed in terms of the Lebesgue measure of the symmetric difference of the open sets. Both Dirichlet and Neumann boundary conditions are considered

Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spaces

We consider local "complementary" generalized Morrey spaces M-c({x0})p(.).omega (Omega) in which the p-means of function are controlled over Omega \ B(x(0), r) instead of B(x(0), r), where Omega subset of R-n is a bounded open set, p(x) is a variable exponent, and no monotonicity type condition is imposed onto the function omega(r) defining the "complementary" Morrey-type norm. In the case where omega is a power function, we reveal the relation of these spaces to weighted Lebesgue spaces. In the general case we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev type M-c({x0})p(.).omega (Omega) -> M-c({x0})p(.).omega (Omega)-theorem for the potential operators I-alpha(.), also of variable order. In all the cases the conditions for the boundedness are given it terms of Zygmund-type integral inequalities-on omega(r), which do not assume any assumption on monotonicity of omega(r).Science Development Foundation under the President of the Republic of Azerbaijan [EIF-2010-1(1)-40/06-1]; Scientific and Technological Research Council of Turkey (TUBITAK) [110T695]info:eu-repo/semantics/publishedVersio

Possibly interacting Vorontsov-Velyaminov galaxies. I. Observations of VV432, VV543 and VV747

Among the galaxies which were included in the Atlas and Catalogue of Interacting galaxies by Vorontsov-Velyaminov (hereafter VV) as multiple systems ("nests", "chains" and similarly looking systems), there are many objects, where the interaction is not evident. Some of them are single objects, including low-mass galaxies with active star formation (SF). In this work we present the description of observations and results of the long-slit spectrophotometry with the Russian 6-m telescope of three VV-galaxies looking like double or multiple systems, and HI-observations of one of them in order to elucidate their nature, determine their metallicity, kinematic properties and the evolution status. Galaxies VV432 and VV747 are found to be dwarf systems with low oxygen abundance (O/H = 1/22 and 1/12 of the solar value, respectively). Their velocity curves indicate quite slow rotation with respective maximum velocities of about 60 and 80 km/s, in agreement with their low luminosities. The distance to VV432 is rather uncertain. If it is a member of Virgo Cluster, this is the most metal-deficient known galaxy of this aggregate. For galaxy VV543 the measured emission-line redshift 0.047 appeared ten times larger than it was given in the original paper and is cited in databases. This "system" evidently represents an optical pair of two galaxies with large velocity difference. The fainter western component is an HII-galaxy, while the brighter one is an absorption-line early-type galaxy with the radial velocity being 1600 km/s lower.Comment: 11 pages, A&AS in press. Version of the paper with Figures 1-3 of the higher quality is available via http://precise.sao.ru/Laboratory/Publications/2000_pub.htm

Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.Comment: To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 201

Tunneling of polarized fermions in 3D double wells

We study the tunneling of a spin polarized Fermi gas in a three-dimensional double well potential, focusing on the time dynamics starting from an initial state in which there is an imbalance in the number of particles in the two wells. Although fermions in different doublets of the double well tunnel with different frequencies, we point out that (incoherent) oscillations of a large number of particles can arise, as a consequence of the presence of transverse degrees of freedom. Estimates of the doublet structure and of the occupation of transverse eigenstates for a realistic experimental setup are provided.Comment: 10 pages, Typos corrected and figures changed - published in Laser Physics, issue on the LPHYS'11 conference (Sarajevo, 2011

Discovery of a massive variable star with Z=Zo/36 in the galaxy DDO 68

The Local Volume dwarf galaxy DDO 68, from the spectroscopy of its two brightest HII regions (Knots 1 and 2) was designated as the second most metal-poor star-forming galaxy [12+log(O/H)=7.14]. In the repeated spectral observations in 2008 January with the 6-m telescope (BTA) of the HII region Knot 3 [having 12+log(O/H)=7.10+-0.06], we find a strong evidence of a transient event related to a massive star evolution. From the follow-up observation with the higher spectral resolution in 2008 February, we confirm this phenomenon, and give parameters of its emission-line spectrum comprising of Balmer HI and HeI lines. The luminosities of the strongest transient lines (Ha, Hb) are of a few 10^36 erg s^-1. We also detected an additional continuum component in the new spectrum of Knot 3, which displays the spectral energy distribution raising to ultraviolet. The estimate of the flux of this continuum leads us to its absolute V-band magnitude of ~-7.1. Based on the spectral properties of this transient component, we suggest that it is related to an evolved massive star of luminous blue variable type with Z=Zo/36. We briefly discuss observational constraints on parameters of this unique (in the aspect of the record low metallicity of the progenitor massive star) event and propose several lines of its study.Comment: 6 pages, 5 Postscript figures, to appear in MNRAS Letters in June 2008 issu

Long term variability of the Broad Emission Line profiles in AGN

Results of a long-term monitoring ($\gtrsim 10$ years) of the broad line and continuum fluxes of three Active Galactic Nuclei (AGN), 3C 390.3, NGC 4151, and NGC 5548, are presented. We analyze the H$\alpha$ and H$\beta$ profile variations during the monitoring period and study different details (as bumps, absorption bands) which can indicate structural changes in the Broad Line Region (BLR). The BLR dimensions are estimated using the time lags between the continuum and the broad lines flux variations. We find that in the case of 3C 390.3 and NGC 5548 a disk geometry can explain both the broad line profiles and their flux variations, while the BLR of NGC 4151 seems more complex and is probably composed of two or three kinematically different regions.Comment: 10 pages, 9 figures, New Astronomy Reviews (Proceeding of 7th SCSLSA), in pres