We provide sufficient normal curvature conditions on the boundary of a domain D ⊂ R to guarantee unboundedness of the bilinear Fourier multiplier operator TD with symbol χD outside the local L 2 setting, i.e. from L1 (R) × L2 (R) → L ′ 3 (R) with P 1 pj = 1 and pj < 2 for some j. In particular, these curvature conditions are satisfied by any domain D that is locally strictly convex at a single ...

Each relation induces a new closure operator, which is (in the sense of data mining) stronger than or equal to the Galois one. The goal is to give some evidence that the new closure operator is often properly stronger than the Galois one. An easy characterization of the new closure operator as a largest fixed point of an appropriate contraction map leads to a (modest) computer program. Finally,...

In this paper, the concepts of L-concave structures, concave Linterior operators and concave L-neighborhood systems are introduced. It is shown that the category of L-concave spaces and the category of concave Linterior spaces are isomorphic, and they are both isomorphic to the category of concave L-neighborhood systems whenever L is a completely distributive lattice. Also, it is proved that th...

A pair (X, ) of a finite set X and a closure operator : 2X → 2X is called a closure space. The class of closure spaces includes matroids as well as antimatroids. Associated with a closure space (X, ), the extreme point operator ex: 2X → 2X is defined as ex(A) = {p|p ∈ A,p / ∈ (A − {p})}. We give characterizations of extreme point operators of closure spaces, matroids and antimatroids, respectiv...

In this paper, sharp upper bounds for ∣∣ap+2 − ηa2p+1∣∣ and |ap+3| are derived for a class of Mocanu α-convex p-valent functions defined by an extended linear multiplier differential operator (LMDO) J δ p (λ, μ, l). Mathematics Subject Classification (2010): Primary 30C45, 30C50, Secondary 30C80.

We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.

Previous results on Hessian measures by Trudinger and Wang are extended to the subelliptic case. Specifically we prove the weak continuity of the 2-Hessian operator, with respect to local L 1 convergence, for a system of m vector fields of step 2 and derive gradient estimates for the corresponding k-convex functions, 1 ≤ k ≤ m.

This paper focuses on the basic operations of Chomsky’s languages. The validity and the effectiveness of some closure operations, such as union operator, product operator and Kleene Closure operator, are discussed in detail. The crosstalk problems in Context-Sensitive Languages (CSL) and Phrase Structure Languages (PSL) are analyzed, and a valuable method to solve this problem is presented by s...

Previous results on Hessian measures by Trudinger and Wang are extended to the subelliptic case. Specifically we prove the weak continuity of the 2-Hessian operator, with respect to local L 1 convergence, for a system of m vector fields of step 2 and derive gradient estimates for the corresponding k-convex functions, 1 ≤ k ≤ m.