40,212 research outputs found
Joint Mixability of Elliptical Distributions and Related Families
In this paper, we further develop the theory of complete mixability and joint
mixability for some distribution families. We generalize a result of
R\"uschendorf and Uckelmann (2002) related to complete mixability of continuous
distribution function having a symmetric and unimodal density. Two different
proofs to a result of Wang and Wang (2016) which related to the joint
mixability of elliptical distributions with the same characteristic generator
are present. We solve the Open Problem 7 in Wang (2015) by constructing a
bimodal-symmetric distribution. The joint mixability of slash-elliptical
distributions and skew-elliptical distributions is studied and the extension to
multivariate distributions is also investigated.Comment: 15page
Sharp convex bounds on the aggregate sums--An alternative proof
It is well known that a random vector with given marginal distributions is
comonotonic if and only if it has the largest sum with respect to the convex
order [ Kaas, Dhaene, Vyncke, Goovaerts, Denuit (2002), A simple geometric
proof that comonotonic risks have the convex-largest sum, ASTIN Bulletin 32,
71-80. Cheung (2010), Characterizing a comonotonic random vector by the
distribution of the sum of its components, Insurance: Mathematics and Economics
47(2), 130-136] and that a random vector with given marginal distributions is
mutually exclusive if and only if it has the minimal convex sum [Cheung and Lo
(2014), Characterizing mutual exclusivity as the strongest negative
multivariate dependence structure, Insurance: Mathematics and Economics 55,
180-190]. In this note, we give a new proof of this two results using the
theories of distortion risk measure and expected utility.Comment: 11page
Convergence to diffusion waves for solutions of Euler equations with time-depending damping on quadrant
This paper is concerned with the asymptotic behavior of the solution to the
Euler equations with time-depending damping on quadrant , \begin{equation}\notag \partial_t v
-
\partial_x u=0, \qquad \partial_t u
+
\partial_x p(v)
=\displaystyle
-\frac{\alpha}{(1+t)^\lambda} u, \end{equation} with null-Dirichlet boundary
condition or null-Neumann boundary condition on . We show that the
corresponding initial-boundary value problem admits a unique global smooth
solution which tends time-asymptotically to the nonlinear diffusion wave.
Compared with the previous work about Euler equations with constant coefficient
damping, studied by Nishihara and Yang (1999, J. Differential Equations, 156,
439-458), and Jiang and Zhu (2009, Discrete Contin. Dyn. Syst., 23, 887-918),
we obtain a general result when the initial perturbation belongs to the same
space. In addition, our main novelty lies in the facts that the cut-off points
of the convergence rates are different from our previous result about the
Cauchy problem. Our proof is based on the classical energy method and the
analyses of the nonlinear diffusion wave
Skyrmion dynamics in a chiral magnet driven by periodically varying spin currents
In this work, we investigated the spin dynamics in a slab of chiral magnets
induced by an alternating (ac) spin current. Periodic trajectories of the
skyrmion in real space are discovered under the ac current as a result of the
Magnus and viscous forces, which originate from the Gilbert damping, the spin
transfer torque, and the -nonadiabatic torque effects. The results are
obtained by numerically solving the Landau-Lifshitz-Gilbert equation and can be
explained by the Thiele equation characterizing the skyrmion core motion
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