In this note, we find the distibution of the number of real zeros of a random polynomial. We also derive a formula for the
expected number of complex zeros lying in a given domain of the complex plane. Bibliography: 7 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 69–79. 相似文献
The main result of the paper is a theorem, using which a new proof of Roth’s theorem is obtained, a new solvability criterion
for the matrix equation AX-YB = C is proved, a formula for a particular solution of the latter is derived, and the least of
the orders of square nonsingular matrices containing a given rectangular matrix as a submatrix is determined. Bibliography:
5 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 15–23. 相似文献
The definition of the characteristic frequencies of zeroes and changes of sign for solutions is given. It is equal to the
upper medium (with respect to the time half-axis) of their number on the half-interval of length π. We also define the main frequencies for a linear homogeneous equation of order n. These main frequencies for an equation with constant coefficients coincide with the absolute values of the imaginary parts
of the roots of the corresponding characteristic polynomial. It is proved that for the second-order equation the main frequencies
are the same for all solutions and that they are stable with respect to uniformly small and infinitely small perturbations
of the coefficients. For the third-order equation they can be different, and for any of the main frequencies an example of
nonstability is given.
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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 249–294, 2005. 相似文献
Electrochemical separation of lead-silver alloys into the constituents by thin-layer electrolysis in molten electrolytes, with bismuth as metal separator, is studied. It is proposed to determine the extent of component recovery by potentiometry. 相似文献
The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begins to accelerate. 相似文献
Deformation quantization, which achieves the passage from classical mechanics to quantum mechanics by the replacement of the pointwise multiplication of functions on phase space by the star product, is a powerful tool for treating systems involving bosonic degrees of freedom, both in quantum mechanics and in quantum field theory. In the present paper we show how these methods may be naturally extended to systems involving fermions. In particular we show how supersymmetric quantum mechanics can be formulated in this approach and consider examples involving both non-relativistic and relativistic systems. 相似文献
The solar wind almost disappeared on May 11, 1999: the solar wind plasma density and dynamic pressure were less than 1cm−3 and 0.1 nPa respectively, while the interplanetary magnetic field was northward. The polar ionospheric data observed by the multi-instruments at Zhongshan Station in Antarctica on such special event day was compared with those of the control day (May 14). It was shown that geomagnetic activity was very quiet on May 11 at Zhongshan. The magnetic pulsation, which usually occurred at about magnetic noon, did not appear. The ionosphere was steady and stratified, and the F2 layer spread very little. The critical frequency of day-side F2 layer, f0F2, was larger than that of control day, and the peak of f0F2 appeared 2 hours earlier. The ionospheric drift velocity was less than usual. There were intensive auroral Es appearing at magnetic noon. All this indicates that the polar ionosphere was extremely quiet and geomagnetic field was much more dipolar on May 11. There were some signatures of auroral substorm before midnight, such as the negative deviation of the geomagnetic H component, accompanied with auroral Es and weak Pc3 pulsation.
The Wheeler–DeWitt equation of arbitrary Hartle–Hawking factor ordering for several minisuperspace universe models, such as the pure gravity Friedmann–Robertson–Walker and Taub ones, is mapped onto the dynamics of corresponding classical oscillators. The latter ones are studied by the classical Ermakov invariant method, which is a natural approach in this context. For the more realistic case of a minimally coupled massive scalar field, one can study, within the same type of approach, the corresponding squeezing features as a possible means of describing cosmological evolution. Finally, we comment on the analogy with the accelerator physics. 相似文献