Partial measures

We study sigma-additive set functions defined on a hereditary subclass of a sigma-algebra and taken values in the extended real line. Analogs of the Jordan decomposition theorem and the Radon-Nikodym theorem are obtained.Comment: 4 pages. Submitted to Lobachevskii Journal of Mathematics ( http://ljm.ksu.ru

“Financial bubbles” and monetary policy

The relevance of this research is caused by the need of strengthening a role of monetary regulators to prevent financial bubbles in the financial markets. The aim of the article is the analysis of a problem of crisis phenomena in the markets of financial assets owing to an inadequate growth of their cost, owing to subjective reasons. The leading approach to mechanism research of crisis phenomena in the market of financial assets is the approach based on a balance effect. Results: authors developed offers to prevent the crisis phenomena in the financial markets due to credit expansion. There is proved the necessity to develop a risk assessment system on existing and new financial instruments, with their obligatory application by commercial banks and rating agencies. The materials of the article can be useful at further studying the reasons for financial bubbles, development of actions for their prevention, and also in an educational process when studying certain subjects. © 2016 Tikhonov, Pudovkina and Permjakova

The Stellar Structures around Disk Galaxies

We present a brief summary of our current results on the stellar distribution and population gradients of the resolved stars in the surroundings of ~50 nearby disk galaxies, observed with space- (Hubble & Spitzer) and ground-based telescopes (Subaru, VLT, BTA, Palomar, CFHT & INT). We examine the radial (in-plane) and vertical (extraplanar) distributions of resolved stars as a function of stellar age and metallicity by tracking changes in the color-magnitude diagram of face-on and edge-on galaxies. Our data show, that the scale length and height of a stellar population increases with age, with the oldest detected stellar populations identified at a large galactocentric radius or extraplanar height, out to typically a few kpc. In the most massive of the studied galaxies there is evidence for a break in number density and color gradients of evolved stars, which plausibly correspond to the thick disk and halo components of the galaxies. The ratio of intermediate-age to old stars in the outermost fields correlate with the gas fraction, while relative sizes of the thick-to-thin disks anticorrelate with galactic circular velocity.Comment: To appear in the proceedings for the IAUS 241 'Stellar Populations as Building Blocks of Galaxies' held in La Palma, Spain, December 10-16 200

Condensation of Silica Nanoparticles on a Phospholipid Membrane

The structure of the transient layer at the interface between air and the aqueous solution of silica nanoparticles with the size distribution of particles that has been determined from small-angle scattering has been studied by the X-ray reflectometry method. The reconstructed depth profile of the polarizability of the substance indicates the presence of a structure consisting of several layers of nanoparticles with the thickness that is more than twice as large as the thickness of the previously described structure. The adsorption of 1,2-distearoyl-sn-glycero-3-phosphocholine molecules at the hydrosol/air interface is accompanied by the condensation of anion silica nanoparticles at the interface. This phenomenon can be qualitatively explained by the formation of the positive surface potential due to the penetration and accumulation of Na+ cations in the phospholipid membrane.Comment: 7 pages, 5 figure

Ion-Size Effect at the Surface of a Silica Hydrosol

The author used synchrotron x-ray reflectivity to study the ion-size effect for alkali ions (Na$^+$, K$^+$, Rb$^+$, and Cs$^+$), with densities as high as $4 \times 10^{18}- 7 \times 10^{18}$ m$^{-2}$, suspended above the surface of a colloidal solution of silica nanoparticles in the field generated by the surface electric-double layer. According to the data, large alkali ions preferentially accumulate at the sol's surface replacing smaller ions, a finding that qualitatively agrees with the dependence of the Kharkats-Ulstrup single-ion electrostatic free energy on the ion's radius.Comment: 17 pages, 4 figure

Difficulties with Recovering The Masses of Supermassive Black Holes from Stellar Kinematical Data

We investigate the ability of three-integral, axisymmetric, orbit-based modeling algorithms to recover the parameters defining the gravitational potential (M/L ratio and black hole mass Mh) in spheroidal stellar systems using stellar kinematical data. We show that the potential estimation problem is generically under-determined when applied to long-slit kinematical data of the kind used in most black hole mass determinations to date. A range of parameters (M/L, Mh) can provide equally good fits to the data, making it impossible to assign best-fit values. We illustrate the indeterminacy using a variety of data sets derived from realistic models as well as published observations of the galaxy M32. In the case of M32, our reanalysis demonstrates that data published prior to 2000 are equally consistent with Mh in the range 1.5x10^6-5x10^6 solar masses, with no preferred value in that range. While the HST/STIS data for this galaxy may overcome the degeneracy in Mh, HST data for most galaxies do not resolve the black hole's sphere of influence and in these galaxies the degree of degeneracy allowed by the data may be substantial. We investigate the effect on the degeneracy of enforcing smoothness (regularization) constraints. However we find no indication that the true potential can be recovered simply by enforcing smoothness. For a given smoothing level, all solutions in the minimum-chisquare valley exhibit similar levels of noise. These experiments affirm that the indeterminacy is real and not an artifact associated with non-smooth solutions. (Abridged)Comment: Accepted for publication in The Astrophysical Journal. Changes include discussion of regularizatio