The study deals with the ruin problem when an insurance company having two business branches, life insurance and non-life insurance, invests its reserve into a risky asset with the price dynamics given by a geometric Brownian motion. We prove a resul
t on smoothness of the ruin probability as a function of the initial capital and obtain for it an integro-differential equation understood in the classical sense. For the case of exponentially distributed jumps we show that the survival probability is a solution of an ordinary differential equation of the 4th order. Asymptotic analysis of the latter leads to the conclusion that the ruin probability decays to zero in the same way as in the already studied cases of models with one-side jumps.
This is a historical review covering the last 30 years of the observational study of lenticular galaxies at the 6m telescope BTA of the Special Astrophysical Observatory of the Russian Academy of Sciences. The development of spectroscopic techniques
at the BTA has allowed to get comprehensive information about this class of stellar systems, starting from the study of their nuclei in the late 80th towards quite exclusive results obtained in the last years on the outermost parts of their large-scale stellar disks.
Algebras generated by strictly positive matrices are described up to similarity, including the commutative, simple, and semisimple cases. We provide sufficient conditions for some block diagonal matrix algebras to be generated by a set of nonnegative
matrices up to similarity. Also we find all realizable dimensions of algebras generated by two nonnegative semi-commuting matrices. The last result provides the solution to the problem posed by M. Kandi{c}, K. v{S}ivic (2017).
The possibility of identification of an observable CMS $mu^+ mu^-$ excess at 28 GeV in the channel $ppto mu^+ mu^- b bar b$ at $sqrt{s}$=8 TeV and 13 TeV as a manifestation of one of the minimal supersymmetric standard model (MSSM) Higgs bosons is in
vestigated. The MSSM parametric scenarios in the regime of large threshold corrections involving low-mass CP-odd scalar, a 125 GeV CP-even scalar and other Higgs bosons with suitable masses are found, where the alignment limit conditions for the Higgs couplings are respected. Perturbative unitarity bounds and constraints on the electroweak vacuum stability are discussed in the regime of substantial couplings with the top- and bottom superpartners. LHC phenomenology including top-quark decay in such a regime is analyzed.
We formulate and prove an analog of the classical Morse-Darboux lemma for the case of a surface with boundary.
We discussed quantum deformations of D=4 Lorentz and Poincare algebras. In the case of Poincare algebra it is shown that almost all classical r-matrices of S. Zakrzewski classification correspond to twisted deformations of Abelian and Jordanian types
. A part of twists corresponding to the r-matrices of Zakrzewski classification are given in explicit form.
Strongly noncircular outer stellar disks have been found in two unbarred SA0 galaxies by analyzing spectroscopic data on the rotation of stars and photometric data on the shape and orientation of the isophotes. In NGC 502, the oval distortion of the
disk is manifested as two elliptical rings, the inner and the outer ones, covering wide radial zones between the bulge and the disk and at the outer edge of the stellar disk. Such a structure may be a consequence of the so-called dry minor merger - multiple accretion of gas-free satellites. In NGC 5485, the kinematical major axis does not coincide with the orientation of isophotes in the disk-dominated region, and for this galaxy the conclusion about its global triaxial structure is unavoidable.
We suggest and verify a new photometric method enabling derivation of relative thickness of a galactic disk from two-dimensional surface-brightness distribution of the galaxy in the plane of the sky. The method is applied to images of 45 early-type (
S0-Sb) galaxies with known radial exponential or double-exponential (with a flatter outer profile) surface-brightness distributions. The data in the r-band have been retrieved from the SDSS archive. Statistics of the estimated relative thicknesses of the stellar disks of early-type disk galaxies shows the following features. The disks of lenticular and early-type spiral galaxies have similar thicknesses. The presence of a bar results in only a slight marginal increase of the thickness. However, we have found a substantial difference between the thicknesses of the disks with a single-scaled exponential brightness profile and the disks that represent the inner segments of the Type III (antitruncated) profiles. The disks are significantly thicker in the former subsample than in the latter one. This may provide evidence for a surface-brightness distribution of a single-scaled exponential disk to be formed due to viscosity effects acting over the entire period of star formation in the disk.
Members of the NGC 524 group of galaxies are studied using data obtained on the 6m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences, with the SCORPIO reducer in an imaging mode. Surface photometry has been carried
out and parameters of the large-scale galactic components - disks and bulges - have been determined for the six largest galaxies of the group. A lower than expected percentage of bars and high percentage of ring structures were found. Integrated B-V colours for a hundred of dwarf galaxies in the vicinity (within 30 kpc) of the six largest galaxies of the group have been measured. A considerable number of blue irregular galaxies with ongoing star formation is found among dwarf satellites of the lenticular galaxies of the group. The luminosity function for the dwarf galaxies of the group suggests that the total mass of the group is not very high, and that the X-ray emitting gas observed around NGC 524 relates to the central galaxy and not to the group as a whole.
By studying the stellar population properties along the radius in 15 nearby S0 galaxies, I have found that the outer stellar disks are mostly old, with the SSP-equivalent ages of 8-15 Gyr, being often older than the bulges. This fact puts into doubt
a currently accepted paradigm that S0 galaxies have formed at z=0.4 by quenching star formation in spiral galaxies.
