Articles you may be interested inThe generalized eigenvalue problem, warping matrices, and the transformation of an isovelocity environment to a variable velocity environment Simple eigenvalue tests are given to ascertain that a given real 4X 4 matrix transforms the four-vector of Stokes parameters of a beam of light into the four-vector of Stokes parameters of another beam of light, and to determine whether a given 4X4 matrix is a weighted sum of pure Mueller matrices. The latter result is derived for matrices satisfying a certain symmetry condition. To derive these results indefinite inner products are applied. 5072
The velocity distribution of a spatially uniform diluted guest population of charged particles moving within a host medium under the influence of a D. C. electric field is studied. A simplified one-dimensional Boltzmann model of the Kač type is adopted. Necessary conditions and sufficient conditions are established for the existence, uniqueness, and attractivity of a stationary non-negative distribution corresponding to a specified concentration level. Conditions for the onset of the runaway process are established.
We consider a class of abstract evolution problems characterized by the sum of two unbounded linear operators $A$ and $B$, where $A$ is assumed to generate a positive semigroup of contractions on an $L^1$-space and $B$ is positive. We study the relations between the semigroup generator $G$ and the operator $A + B$. $A$ characterization theorem for $G =A+B$ is stated. The results are based on the spectral analysis of $B(\lambda-A)^{-1}$. The main point is to study the conditions under which the value 1 belongs to the resolvent set, the continuous spectrum, or the residual spectrum of \ud
$B(\lambda - A)^{-1}$
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