Suppose that a policyholder faces $n$ risks X1, ..., Xn which are insured under the policy limit with the total limit of l. Usually, the policyholder is asked to protect each Xi with an arbitrary limit of li such that ∑ni=1li=l. If the risks are independent and identically distributed with log-concave cumulative distribution function, using the notions of majorization and stochastic orderings, ...

Abstract We give topological criteria for the convexity and the concavity of a current or a voltage in a resistive circuit, as a function of a source voltage or current, when the nonlinear resistor characteristics are all either convex or concave. When the criteria are satisfied, all circuits with the same structure will have a convex, or all will have a concave transfer characteristic. The app...

We study the properties of certain affine invariant measures of symmetry associated to a compact convex body L in a Euclidean vector space. As functions of the interior of L, these measures of symmetry are proved or disproved to be concave in specific situations, notably for the reduced moduli of spherical minimal immersions. MSC 2000: 53C42

We establish quantitative stability results for the entropy power inequality (EPI). Specifically, we show that if uniformly log-concave densities nearly saturate the EPI, then they must be close to Gaussian densities in the quadratic Wasserstein distance. Further, if one of the densities is log-concave and the other is Gaussian, then the deficit in the EPI can be controlled in terms of the L-Wa...

in this paper, under the condition that $k$ is concave, we characterize lacunary series in $q_{k}$ spaces. we improve a result due to h. wulan and k. zhu.

We treat the exterior Dirichlet problem for a class of fully nonlinear elliptic equations form [Formula: see text] with prescribed asymptotic behavior at infinity. The this type had been studied extensively by Caffarelli et al. [The second-order equations. III. Functions eigenvalues Hessian, Acta Math. 155 (1985) 261–301], Trudinger [On Hessian equations, 175 (1995) 151–164] and many others, th...

The mammalian respiratory chain complexes assemble into supercomplexes (SCs) and reside in the inner mitochondrial membrane to transfer electrons and establish the proton gradient for complex V to synthesize ATP. The precise arrangement of SCs is largely unknown. Here, we report a 4.0-Å cryo-electron microscopy (cryo-EM) structure of the major SC in porcine heart, the 1.7-MDa SCI1III2IV1. The c...