We derive a weighted L-estimate of the Witten spinor in a complete Riemannian spin manifold (Mn, g) of non-negative scalar curvature which is asymptotically Schwarzschild. The interior geometry of M enters this estimate only via the lowest eigenvalue of the square of the Dirac operator on a conformal compactification of M .

This paper is to characterize L-concavities and L-convexities via some derived forms of relations operators. Specifically, notions L-concave internal relation space hull are introduced. It proved that the category L-concave
 spaces isomorphic spaces. Also, L-convex enclosed

Let X be a metric space with doubling measure, L be a nonnegative selfadjoint operator in L2(X ) satisfying the Davies-Gaffney estimate, ω be a concave function on (0,∞) of strictly lower type pω ∈ (0, 1] and ρ(t) = t/ω(t) for all t ∈ (0,∞). The authors introduce the Orlicz-Hardy space Hω,L(X ) via the Lusin area function associated to the heat semigroup, and the BMO-type space BMOρ,L(X ). The ...

This paper presents an improved local ternary pattern (LTP) for automatic target recognition (ATR) in infrared imagery. Firstly, a robust LTP (RLTP) scheme is proposed to overcome the limitation of the original LTP for achieving the invariance with respect to the illumination transformation. Then, a soft concave-convex partition (SCCP) is introduced to add some flexibility to the original conca...

An antinorm is a concave nonnegative homogeneous functional on convex cone. It shown that if the cone polyhedral, then every has unique continuous extension from interior of ...

In combination with simultaneous approximation terms, summation-by-parts (SBP) operators provide a flexible and efficient methodology that leads to consistent, conservative, and provably stable high-order discretizations. Traditional diagonal-norm SBP operators with a repeating interior point operator lead to solutions that have a global order of accuracy lower than the order of the interior po...

We propose a scheme for quantizing a scalar field over the Schwarzschild manifold including the interior of the horizon. On the exterior, the timelike Killing vector and on the horizon the isometry corresponding to restricted Lorentz boosts can be used to enforce the spectral condition.. For the interior we appeal to the need for CPT invariance to construct an explicitly positive definite opera...

We present a new and interesting extension theorem for concave operators as follows. Let X be a real linear space, and let Y,K be a real order complete PL space. Let the setA ⊂ X × Y be convex. Let X0 be a real linear proper subspace of X, with θ ∈ AX −X0 , where AX {x | x, y ∈ A for some y ∈ Y}. Let g0 : X0 → Y be a concave operator such that g0 x ≤ z whenever x, z ∈ A and x ∈ X0. Then there e...

inf u 6 Ttu(x) 6 u(x) 6 Ťtu(x) 6 supu for each t > 0 and each x ∈ H. A function u : H −→ R is called k-semi-concave, k > 0, if the function x −→ u(x)−‖x‖2/k is concave. The function u is called k-semi-convex if −u is k-semiconcave. A bounded function u is t-semi-concave if and only if it belongs to the image of the operator Tt, this follows from Lemma 1 and Lemma 3 below. A function is called s...

Abstract. We consider the problem of minimizing the sum of a convex function and of p > 1 fractions subject to convex constraints. The numerators of the fractions are positive convex functions, and the denominators are positive concave functions. Thus, each fraction is quasi-convex. We give a brief discussion of the problem and prove that in spite of its special structure, the problem is NPcomp...