We analyze degenerate, second-order, elliptic operators H in divergence form on L2(R ×Rm). We assume the coefficients are real symmetric and a1Hδ ≥ H ≥ a2Hδ for some a1, a2 > 0 where Hδ = −∇x1 cδ1,δ′ 1(x1)∇x1 − cδ2,δ′ 2(x1)∇ 2 x2 . Here x1 ∈ R , x2 ∈ R m and cδi,δ′ i are positive measurable functions such that cδi,δ′ i(x) behaves like |x| δi as x→ 0 and |x| ′ i as x→ ∞ with δ1, δ ′ 1 ∈ [0, 1〉 a...

We obtain a vanishing theorem for the half-kernel of a Dirac operator on a Clifford module twisted by a sufficiently large power of a line bundle, whose curvature is non-degenerate at any point of the base manifold. In particular, if the base manifold is almost complex, we prove a vanishing theorem for the half-kernel of a spinc Dirac operator twisted by a line bundle with curvature of a mixed ...

We consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal Newtonian attraction and a hard height constraint. This provides a counterpoint to existing literature on repulsive-attractive nonlocal interaction models, where the repulsive effects instead arise from an interaction kernel or the addition of diffusion. We formulate our...

We investigate the initial-value problem for the relativistic Euler equations governing isothermal perfect fluid flows, and generalize an approach introduced by LeFloch and Shelukhin in the non-relativistic setting. We establish the existence of globally defined, bounded measurable, entropy solutions with arbitrary large amplitude. An earlier result by Smoller and Temple for the same system cov...

In a fuzzy classifier with ellipsoidal regions, a fuzzy rule, which is based on the Mahalanobis distance, is defined for each class. Then the fuzzy rules are tuned so that the recognition rate of the training data is maximized. In most cases, one fuzzy rule per one class is enough to obtain high generalization ability. But in some cases, we need to partition the class data to define more than o...

in this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete riemannian manifold floating in space rn+1and is tangent to the space rn at ∂h0(t); (2...