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Filters and Ultrafilters as Approximate Solutions in the Attainability Problems with Constraints of Asymptotic Character  [PDF]
Alexander Chentsov
Intelligent Information Management (IIM) , 2010, DOI: 10.4236/iim.2010.29062
Abstract: Abstract problems about attainability in topological spaces are considered. Some nonsequential version of the Warga approximate solutions is investigated: we use filters and ultrafilters of measurable spaces. Attrac- tion sets are constructed. AMS (MOS) subject classification. 46A, 49 K 40.
Filters and Ultrafilters as Approximate Solutions in the Attainability Problems with Constrains of Asymptotic Character
Alexander G. Chentsov
Mathematics , 2010,
Abstract: Problems about attainability in topological spaces are considered. Some nonsequential version of the Warga approximate solutions is investigated: we use filters and ultrafilters of measurable spaces. Attraction sets are constructed.
Constraints of Asymptotic Character and Attainability Problems  [PDF]
Alexander G. Chentsov
Intelligent Information Management (IIM) , 2017, DOI: 10.4236/iim.2017.95011
Abstract: The attainability problem with “asymptotic constraints” is considered. Concrete variants of this problem arise in control theory. Namely, we can consider the problem about construction and investigation of attainability domain under perturbation of traditional constraints (boundary and immediate conditions; phase constraints). The natural asymptotic analog of the usual attainability domain is attraction set, for representation of which, the Warga generalized controls can be applied. More exactly, for this, attainability domain in the class of generalized controls is constructed. This approach is similar to methods for optimal control theory (we keep in mind approximate and generalized controls of J. Warga). But, in the case of attainability problem, essential difficulties arise. Namely, here it should be constructed whole set of limits corresponding to different variants of all more precise realization of usual solutions in the sense of constraints validity. Moreover, typically, the above-mentioned control problems are infinite-dimensional. Real possibility for investigation of the arising limit sets is connected with extension of control space. For control problems with geometric constraints on the choice of programmed controls, procedure of this extensions was realized (for extremal problems) by J. Warga. More complicated situation arises in theory of impulse control. It is useful to note that, for investigation of the problem about constraints validity, it is natural to apply asymptotic approach realized in part of perturbation of standard constraints. And what is more, we can essentially generalize self notion of constraints: namely, we can consider arbitrary systems of conditions defined in terms of nonempty families of sets in the space of usual controls. Thus, constraints of asymptotic character arise.
Spectral variability of the peculiar A-type supergiant 3Pup
Eugenij Chentsov,Valentina Klochkova,Anatoly Miroshnichenko
Physics , 2010, DOI: 10.1134/S1990341310020057
Abstract: Optical spectra of the peculiar supergiant 3Pup taken in 1997-2008 are used to analyze the spectral peculiarities and velocity field in its atmosphere. The profiles of strong FeII lines and of the lines of other iron-group ions have a specific shape: the wings are raised by emissions, whereas the core is sharpened by a depression. The latter feature becomes more pronounced with the increasing line strength, and the increasing wavelength. Line profiles are variable: the magnitude and sign of the absorption asymmetry, and the blue-to-red emission intensity ratios vary from one spectrum to another. The temporal Vr variations are minimal for the forbidden emissions and sharp shell cores of the absorption features of FeII(42), and other strong lines of iron-group ions. The average velocity for the above lines can be adopted as the systemic velocity: Vsys=28.5+/-0.5km/s. The weakest photospheric absorptions and photospheric MgII, SiII absorptions exhibit well-defined day-to-day velocity variations of up to 7km/s. Quantitative spectral classification yields the spectral type of A2.7+/-0.3 Ib. The equivalent widths and profiles of Hdelta and Hgamma, and the equivalent width of the OI7774A triplet yield an absolute magnitude estimate of Mv=-5.5+/-0.3mag, implying the heliocentric distance of 0.7kpc.
The Inhomogeneous Wind of the LBV Candidate CygOB2-No.12
Valentina Klochkova,Eugene Chentsov,Anatoly Miroshnichenko
Physics , 2010, DOI: 10.1017/S174392131101091X
Abstract: We present the results of high-resolution spectroscopy of the extremely luminous star CygOB2-No.12. We identified about 200 spectral features in the range 4552-7939 AA, including the interstellar NaI, KI lines and numerous very strong DIBs, along with the HeI, CII, and SiII lines. An MK spectral type we derived for the object is B4.5Ia+. Our analysis of the radial velocity data shows the presence of a gradient in the stellar atmosphere, caused by both atmospheric expansion and matter infall onto the star. The Halpha emission displays broad Thompson wings, a slightly blue-shifted PCyg type absorption component and a time-variable core absorption. We conclude that the wind is variable in time.
Detailed optical spectroscopy of the B[e] star MWC 17
V. G. Klochkova,E. L. Chentsov
Physics , 2015,
Abstract: Based on the data of multiple high-resolution R=60 000 observations obtained at the 6-meter telescope BTA in combination with the NES spectrograph, we studied the features of the optical spectrum of the star MWC 17 with the B[e] phenomenon. In the wavelength interval 4050-6750 A we identified numerous permitted and forbidden emissions, interstellar NaI lines, and diffuse interstellar bands (DIBs). Radial velocities were estimated from lines of various origin. As the systemic velocity, Vsys, the velocity from the forbidden emissions can be accepted: Vr=-47 km/s (relative to the local standard Vlsr=-42 km/s). Comparison of the obtained data with the ealier measurements allows us to conclude on the absence of considerable variability of spectral details.
Optical spectrum of the IR-source IRC+10420 in 1992-1996
V. G. Klochkova,E. L. Chentsov,V. E. Panchuk
Physics , 1997, DOI: 10.1093/mnras/292.1.19
Abstract: To understand the evolutionary stage of the peculiar supergiant IRC+10420, we have been taking spectra for several years at the 6m telescope. The optical spectrum of IRC+10420 of the years from 1992 through 1996 points to the increase in the temperature: spectral class A5 instead of the former F8, as was pointed out by Humpreys et al., (1973). Now it resembles the spectra of late-type B[e] stars. The spectrum contains absorptions (mainly of ions) formed in the photosphere, apparently stationary with respect to the star center of mass, and emissions too, which can be formed in the fossil expanding envelope as well as partly in its compressing region. Using our spectra and spectral data obtained by Oudmaijer (1995) we estimated the atmospheric parameters Teff=8500 K, logg=1.0, Vt=12km/s and concluded that metallicity of IRC+10420 is solar: the average value [(V,Cr,Fe)/H]=-0.03. Combination of results allows us to consider IRC+10420 as a massive supergiant evolving to the WR-stage.
Modeling of atmospheres of the brightest stars belonging to the Cyg OB2 association
Olga Maryeva,V. G. Klochkova,E. L Chentsov
Physics , 2013,
Abstract: We present the results of modeling of the spectrum of the brightest stars belonging to the Cyg OB2 association - #7 (O3If*) and #11 (O5Ifc). #7 is one of the hottest stars in our Galaxy, while #11 belongs to the spectral class Ofc, which was recently introduced and yet small in numbers (Walborn et al., 2010). We determine the physical properties and chemical composition of their atmosphere using CMFGEN code. The atmosphere of #7 reveals an excess of nitrogen X(N*)/X(Nsun) = 3.2 and the carbon and oxygen deficiency X(C*)/X(Csun) = 0.08, X(O*)/X(Osun) = 0.09, while the atmosphere of #11 is enriched with carbon X(C*)/X(Csun)=1 and silicon X(Si *)/X(Si sun)=2.
Is UU Herculis a post-AGB star?
V. G. Klochkova,V. E. Panchuk,E. L. Chentsov
Physics , 1997,
Abstract: In order to understand the evolutionary status of the anomalous supergiant UUHer, the prototype of the class of variable supergiants located at high galactic latitudes, we obtained several high-resolution spectra of this star, with the 6m telescope, over 5 years. This material was used for a search of possible temporal variations of the radial velocity at the different depths in the photosphere and for studying the chemical composition. The average radial velocity Vr approximately 130 km/sec suggests that UUHer belongs to the old population of the Galaxy. No systematic dependence of the velocity on depth of the line formation layer or on ionization and excitation potential is observed. The radial velocity of the H_alpha absorption differs strongly from the average photospheric velocity. The iron abundance in the photosphere of UUHer is significantly lower than that of the Sun: [Fe/H]=-1.32. The enhancement of nitrogen relatively to iron content [N/Fe]=+0.40 in combination with the carbon underabundance [C/Fe]=-0.30 suggests that only a first dredge-up episode occurred. The Na content is normal relatively to iron, therefore there is no evidence for dredging-up of Ne-Na cycle products. The heavy s-process metals Y, Ba are depleted relative to H and Fe, which again implies that the third dredge-up did not occur.
Spectral atlas of A-type supergiants
V. G. Klochkova,E. G. Sendzikas,E. L. Chentsov
Physics , 2015, DOI: 10.1134/S1990341315010113
Abstract: Based on high-spectral-resolution observations (R=60000) performed with the 6-m BTA telescope in combination with the echelle spectrograph NES, we have studied the optical spectra of three A-type supergiants: a peculiar supergiant 3 Pup, a post-AGB star BD+48 1220, and a massive $\alpha$ Cyg, which belong to essentially different stages of evolution. A spectral atlas for these stars is prepared in the wavelength interval of 3920 to 6720 \AA.
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