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We give a semiclassical analysis of a nonlinear eigenvalue problem arising from the study of the failure of analytic hypoellipticity and obtain a general family of hypoelliptic, but not analytic hypoelliptic operators.
Since its discovery in follicular lymphoma cells at the breakpoint t(14;18), Bcl-2 has been studied extensively in many basic and clinical science settings. Bcl-2 can locate as an integral mitochondrial membrane component, where its primary role is to block apoptosis by maintaining membrane integrity. Here we show that Bcl-2 also can position on the outer… (More)
In this article, we prove the finiteness of the number of eigenvalues for a class of Schrödinger operators H = −∆ + V (x) with a complex-valued potential V (x) on R n , n ≥ 2. If ℑV is sufficiently small, ℑV ≤ 0 and ℑV = 0, we show that N (V) = N (ℜV) + k, where k is the multiplicity of the zero resonance of the selfadjoint operator −∆+ℜV and N (W) the… (More)
For a class of dissipative Schrödinger operators H = −∆ + V (x) with a complex-valued potential V = V 1 −iV 2 with V 2 ≥ 0 and |V (x)| = O(|x| −2) as |x| tends to infinity, we prove that the complex eigenvalues of H can not accumulate to zero. In the perturbation regime where V 2 is sufficiently small, we show under some conditions that N (V) = N (V 1) + k,… (More)
In this paper, we study the inverse scattering related to channel scattering operator S in many-body problems. If the incoming and outgoing channels are associated with a same, but arbitary cluster decomposition, a, of the N-particle system, we prove that all eeective interactions between the mass-centers of the clusters in a can be recovered from the high… (More)
Traditional nanostructured metals are inherently comprised of a high density of high-energy interfaces that make this class of materials not stable in extreme conditions. Therefore, high performance bulk nanostructured metals containing stable interfaces are highly desirable for extreme environments applications. Here, we reported an attractive bulk Cu/V… (More)