602 research outputs found
Docking positrophilic electrons into molecular attractive potential of fluorinated methanes
The present study shows that the positrophilic electrons of a molecule dock
into the positron attractive potential region in the annihilation process under
the plane-wave approximation. The positron-electron annihilation processes of
both polar and non-polar fluorinated methanes (CH4-nFn, n=0, 1,..., 4) are
studied under this role. The predicted gamma-ray spectra of these fluorinated
methanes agree well with the experiments. It further indicates that the
positrophilic electrons of a molecule docking at the negative end of a bond
dipole are independent from the molecular dipole moment in the annihilation
process.Comment: 11 pages, 5 figure
Density of Eigenvalues of Random Normal Matrices with an Arbitrary Potential, and of Generalized Normal Matrices
Following the works by Wiegmann-Zabrodin, Elbau-Felder, Hedenmalm-Makarov,
and others, we consider the normal matrix model with an arbitrary potential
function, and explain how the problem of finding the support domain for the
asymptotic eigenvalue density of such matrices (when the size of the matrices
goes to infinity) is related to the problem of Hele-Shaw flows on curved
surfaces, considered by Entov and the first author in 1990-s. In the case when
the potential function is the sum of a rotationally invariant function and the
real part of a polynomial of the complex coordinate, we use this relation and
the conformal mapping method developed by Entov and the first author to find
the shape of the support domain explicitly (up to finitely many undetermined
parameters, which are to be found from a finite system of equations). In the
case when the rotationally invariant function is , this is done by
Wiegmann-Zabrodin and Elbau-Felder. We apply our results to the generalized
normal matrix model, which deals with random block matrices that give rise to
*-representations of the deformed preprojective algebra of the affine quiver of
type . We show that this model is equivalent to the usual normal
matrix model in the large limit. Thus the conformal mapping method can be
applied to find explicitly the support domain for the generalized normal matrix
model.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on
Integrable Systems and Related Topics, published in SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
On universal Lie nilpotent associative algebras
We study the quotient Q_i(A) of a free algebra A by the ideal M_i(A)
generated by relation that the i-th commutator of any elements is zero. In
particular, we completely describe such quotient for i=4 (for i<=3 this was
done previously by Feigin and Shoikhet). We also study properties of the ideals
M_i(A), e.g. when M_i(A)M_j(A) is contained in M_{i+j-1}(A) (by a result of
Gupta and Levin, it is always contained in M_{i+j-2}(A)).Comment: 7 page
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