148 research outputs found

    Magnetohydrodynamic wave spectra in large tokamaks with non-circular cross section of magnetic surfaces

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    There is considered the problem on the spectra of magnetohydrodynamic (MHD) waves with the frequencies of the order of the ion cyclotron frequency propagating almost along the toroidal magnetic field in the large-size tokamaks with a non-circular cross section of magnetic surfaces. In this case the waves can propagate in the small vicinity of the extremum point for the square of the refractive index of the MHD wave travelling along the torus. Developing the dielectric permittivity tensor of the “cold” plasma in a Taylor series around this point enables one to separate the variables and to express the natural functions of the boundary problem for Maxwell’s equations through Hermite functions and to determine the natural frequencies of MHD waves. The solution obtained is a generalization of the previous result for arbitrary radial and azimuth numbers. On the ground of the perturbation theory the corrections to the natural functions and natural values are found which take into account the rotational transform

    Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC

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    An extremal property of Jacobi polynomials in two-sided chernoff-type inequalities for higher order derivatives

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    For a weight function generating the classical Jacobi polynomials, the sharp double estimate of the distance from the subspace of all polynomials of an arbitrary fixed order is established. © 2008 American Mathematical Society

    On optimal Banach spaces containing a weight cone of monotone or quasiconcave functions

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    Optimal (minimal) Banach spaces containing given cones of monotone or quasiconcave functions on the semiaxis from weighted Lebesgue spaces are described. Exact formulas for the norm of the optimal space are presented. All cases of the summation parameter are studied. © 2015, Pleiades Publishing, Ltd

    On optimal Banach spaces containing a weighted cone of monotone or quasi-concave functions

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    A precise description of optimal Banach spaces containing a weighted cone of monotone or quasi-concave functions is given. © 2015, Pleiades Publishing, Ltd

    On a supremum operator

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    For a supremum operator on the semi-axis with a measurable non-negative function φ(x, y) the weighted Lp -Lq boundedness on the cone of non-increasing functions is characterized. © 2012 Springer Basel AG. All rights reserved

    On optimal Banach spaces containing a weight cone of monotone or quasiconcave functions

    No full text
    Optimal (minimal) Banach spaces containing given cones of monotone or quasiconcave functions on the semiaxis from weighted Lebesgue spaces are described. Exact formulas for the norm of the optimal space are presented. All cases of the summation parameter are studied. © 2015, Pleiades Publishing, Ltd

    On a supremum operator

    No full text
    For a supremum operator on the semi-axis with a measurable non-negative function φ(x, y) the weighted Lp -Lq boundedness on the cone of non-increasing functions is characterized. © 2012 Springer Basel AG. All rights reserved

    On optimal Banach spaces containing a weighted cone of monotone or quasi-concave functions

    No full text
    A precise description of optimal Banach spaces containing a weighted cone of monotone or quasi-concave functions is given. © 2015, Pleiades Publishing, Ltd
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