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  • 47B50  (1)
  • 60G10  (1)
  • Gravitation cosmology  (1)
  • 1995-1999  (3)
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Keywords
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  • 1995-1999  (3)
Year
  • 1
    Electronic Resource
    Electronic Resource
    On the mode-change problem for random measures (1996)
    Springer
    Georgian mathematical journal 3 (1996), S. 343-362 
    Details
    ISSN: 1572-9176
    Keywords: 62G05 ; 62G10 ; 60G10 ; Lévy random measure ; Lévy bridge ; Lévy broken bridge ; compound Poisson random measure ; change-set
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The classical change-point problem in modern terms, i.e., the mode-change problem, is stated for sufficiently general set-indexed random processes, namely for random measures. A method is shown for solving this problem both in the general form and for the intensity of compound Poisson random measures. The results obtained are novel for the change-point problem, too.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02256724
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  • 2
    Electronic Resource
    Electronic Resource
    On strongly stable normal operators in Krein spaces (1998)
    Springer
    Integral equations and operator theory 31 (1998), S. 255-258 
    Details
    ISSN: 1420-8989
    Keywords: 47B50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For bounded normal operators in Krein spaces we give a necessary and sufficient condition for strong stability. The same result for unitary operators was obtained by M.G.Krein [1] (see also [2]). For selfadjoint operators we refer to the papers of P.Jonas, H.Langer [3] and H.Langer [4].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01214253
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  • 3
    Electronic Resource
    Electronic Resource
    The Quantum Evolution of the Closed Friedman Universe with “Bouncing Off” (1999)
    Springer
    General relativity and gravitation 31 (1999), S. 21-30 
    Details
    ISSN: 1572-9532
    Keywords: Gravitation cosmology ; “bouncing off” ; instaton
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The homogeneous and isotropic closed Friedmanuniverse evolution in higher-order gravity theories isconsidered. The model takes into account vacuumpolarisation of conformal and nonconformal fields. That leads to the following addition in the Einsteinlagrangian: R2 ln |R/R0|. Near theregular minimum of the scale factor the model has ananalytical solution depending on an integration constantC. If |R/R0| 〉 1, the solution passes through the regularminimum, experiences inflation with a decreasing valueof R and approaches to the critical value R =R0. In the interval |R/R0| 〈 1,the solutions have non-linear oscillations (i.e. the scalaronstage). On this stage of the evolution the universe isfilled with relativistic plasma. The continuoustransition through the critical point R = R0is possible in only one type of solution, the separatrix.Though other solutions have no features in this point,they experience the discontinuity in derivatives of R.It is unsuitable since higher-order gravity theories are considered. Thus the measure of continuoussolutions giving a hot universe is negligible. Howeversolutions of the model can be continued in the imaginarytime. In such a case the Euclidean action will have a non-zero value because of the spaceclosed boundedness of the universe and the finiteness ofthe imaginary time interval (instanton). The last allowsus to calculate the probability of the quantum tunnelling of the Friedman universe from theinflation region into the scalaron region.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018859203315
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