The production process of a certain item exhibits some quality characteristics governed by a probability measure
μ(
A). The consumption (or usage) of all items of this production is described by ...another probability measure
ν(
B), where
A and
B are elements in the product space of all quality characteristics of the totality of produced items. When a product with characteristics
x
ϵ
A is being used instead of a product with characteristics
y
ϵ
B, then a loss ϕ(x,y) is incurred. Any ditribution plan
θ(
A,
B) of the product for consumption produces a total expected loss
τφ(
θ) =
E
φ
(
x,
y). Using some general results in the theory of probability metrics, under given marginals, we develop models for finding the optimal distribution plan θ and the corresponding minimal total losses
τ
φ
and establish some particular forms and inequalities. A brief discussion of the results follows.
The RPC muon detector of the CMS experiment at the LHC (CERN, Geneva, Switzerland) is equipped with a Gas Gain Monitoring (GGM) system. A report on the stability of the system during the 2011-2012 ...data taking run is given, as well as the observation of an effect which suggests a novel method for the monitoring of gas mixture composition.
The set of equations for magnetohydrodynamic (MHD) waves in a shear flow is
consecutively derived. The proposed scenario involves the presence of a
self-sustained turbulence and magnetic field. In ...the framework of
Langevin--Burgers approach the influence of the turbulence is described by an
additional external random force in the MHD system. Kinetic equation for the
spectral density of the slow magnetosonic (Alfvenic) mode is derived in the
short wavelength (WKB) approximation. The results show a pressing need for
conduction of numerical Monte Carlo (MC) simulations with a random driver to
take into account the influence of the long wavelength modes and to give a more
precise analytical assessment of the short ones. Realistic MC calculations for
the heating rate and shear stress tensor should give an answer to the
perplexing problem for the missing viscosity in accretion disks and reveal why
the quasars are the most powerful sources of light in the universe. The planned
MC calculations can be incorporated in global models for accretion disks and
also in all other physical conditions where there is a shear flow in a
magnetized turbulent plasma. It is supposed that the heating mechanism by
Alfven waves absorption is common for many kinds of space plasmas from solar
corona to active galactic nuclei and the solution of these longstanding puzzles
deserves active interdisciplinary research. The work is illustrated by
numerical calculations and by exact solutions for the time dependence of the
magnetic field given by the Heun function.
The set of equations for magnetohydrodynamic (MHD) waves in a shear flow is consecutively derived. The proposed scenario involves the presence of a self-sustained turbulence and magnetic field. In ...the framework of Langevin--Burgers approach the influence of the turbulence is described by an additional external random force in the MHD system. Kinetic equation for the spectral density of the slow magnetosonic (Alfvenic) mode is derived in the short wavelength (WKB) approximation. The results show a pressing need for conduction of numerical Monte Carlo (MC) simulations with a random driver to take into account the influence of the long wavelength modes and to give a more precise analytical assessment of the short ones. Realistic MC calculations for the heating rate and shear stress tensor should give an answer to the perplexing problem for the missing viscosity in accretion disks and reveal why the quasars are the most powerful sources of light in the universe. The planned MC calculations can be incorporated in global models for accretion disks and also in all other physical conditions where there is a shear flow in a magnetized turbulent plasma. It is supposed that the heating mechanism by Alfven waves absorption is common for many kinds of space plasmas from solar corona to active galactic nuclei and the solution of these longstanding puzzles deserves active interdisciplinary research. The work is illustrated by numerical calculations and by exact solutions for the time dependence of the magnetic field given by the Heun function.
PDF
