5,045 research outputs found
Inverse Additive Problems for Minkowski Sumsets II
The Brunn-Minkowski Theorem asserts that for convex bodies , where
denotes the -dimensional Lebesgue measure. It is well-known that
equality holds if and only if and are homothetic, but few
characterizations of equality in other related bounds are known. Let be a
hyperplane. Bonnesen later strengthened this bound by showing where
and
. Standard
compression arguments show that the above bound also holds when
and , where denotes a
projection of onto , which gives an alternative generalization
of the Brunn-Minkowski bound. In this paper, we characterize the cases of
equality in this later bound, showing that equality holds if and only if
and are obtained from a pair of homothetic convex bodies by `stretching'
along the direction of the projection, which is made formal in the paper. When
, we characterize the case of equality in the former bound as well
On the critical pair theory in abelian groups : Beyond Chowla's Theorem
We obtain critical pair theorems for subsets S and T of an abelian group such
that |S+T| < |S|+|T|+1. We generalize some results of Chowla, Vosper, Kemperman
and a more recent result due to Rodseth and one of the authors.Comment: Submitted to Combinatorica, 23 pages, revised versio
Density of States for a Specified Correlation Function and the Energy Landscape
The degeneracy of two-phase disordered microstructures consistent with a
specified correlation function is analyzed by mapping it to a ground-state
degeneracy. We determine for the first time the associated density of states
via a Monte Carlo algorithm. Our results are described in terms of the
roughness of the energy landscape, defined on a hypercubic configuration space.
The use of a Hamming distance in this space enables us to define a roughness
metric, which is calculated from the correlation function alone and related
quantitatively to the structural degeneracy. This relation is validated for a
wide variety of disordered systems.Comment: Accepted for publication in Physical Review Letter
Effective Mass Dirac-Morse Problem with any kappa-value
The Dirac-Morse problem are investigated within the framework of an
approximation to the term proportional to in the view of the
position-dependent mass formalism. The energy eigenvalues and corresponding
wave functions are obtained by using the parametric generalization of the
Nikiforov-Uvarov method for any -value. It is also studied the
approximate energy eigenvalues, and corresponding wave functions in the case of
the constant-mass for pseudospin, and spin cases, respectively.Comment: 12 page
Symmetry breaking and the random-phase approximation in small quantum dots
The random-phase approximation has been used to compute the properties of
parabolic two-dimensional quantum dots beyond the mean-field approximation.
Special emphasis is put on the ground state correlation energy, the symmetry
restoration and the role of the spurious modes within the random-phase
approximation. A systematics with the Coulombic interaction strength is
presented for the 2-electron dot, while for the 6- and 12-electron dots
selected cases are discussed. The validity of the random-phase approximation is
assessed by comparison with available exact results.Comment: 9 pages, 4 embedded + 6 gif Figs. Published versio
LRRK2 affects vesicle trafficking, neurotransmitter extracellular level and membrane receptor localization
The leucine-rich repeat kinase 2 (LRRK2) gene was found to play a role in the pathogenesis of both familial and sporadic Parkinson's disease (PD). LRRK2 encodes a large multi-domain protein that is expressed in different tissues. To date, the physiological and pathological functions of LRRK2 are not clearly defined. In this study we have explored the role of LRRK2 in controlling vesicle trafficking in different cellular or animal models and using various readouts. In neuronal cells, the presence of LRRK2(G2019S) pathological mutant determines increased extracellular dopamine levels either under basal conditions or upon nicotine stimulation. Moreover, mutant LRRK2 affects the levels of dopamine receptor D1 on the membrane surface in neuronal cells or animal models. Ultrastructural analysis of PC12-derived cells expressing mutant LRRK2(G2019S) shows an altered intracellular vesicle distribution. Taken together, our results point to the key role of LRRK2 to control vesicle trafficking in neuronal cells
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