Let X be a compact Kähler manifold and let L be a pseudoeffective line bundle on X with singular metric φ. We first define a notion of numerical dimension of the pseudo-effective pair (L,φ) and then discuss the properties of it. We prove also a very general KawamataViehweg-Nadel type vanishing theorem on an arbitrary compact Kähler manifold.

Let G be a locally compact non-compact group. We show that under a very mild assumption on the weight function w, the weighted group algebra L1(G, w) is strongly Arens irregular in the sense of [Dal–Lam–Lau 01]. To this end, we first derive a general factorization theorem for bounded families in the L∞ ( G, w ) ∗ -module L∞ ( G, w ) .

The existence of admissible vectors for a locally compact group is closely related to the group's profile. In the compact groups, according to Peter-weyl theorem, every irreducible representation has admissible vector. In this paper, the conditions under which the inverse of this case is being investigated has been investigated. Conditions such as views that are admissible and stable will get c...

The least element 0 of a finite meet semi-distributive lattice is a meet of meet-prime elements. We investigate conditions under which the least element of an algebraic, meet semi-distributive lattice is a (complete) meet of meet-prime elements. For example, this is true if the lattice has only countably many compact elements, or if |L| < 2א0 , or if L is in the variety generated by a finite me...

Suppose L is a semisimple Levi subgroup of a connected Lie group G, X is a Borel G-space with finite invariant measure, and α : X × G → GLn(R) is a Borel cocycle. Assume L has finite center, and that the real rank of every simple factor of L is at least two. We show that if L is ergodic on X, and the restriction of α to X × L is cohomologous to a homomorphism (modulo a compact group), then, aft...

We show that a strong form of the so called Lindström’s Theorem [4] fails to generalize to extensions of Lκω and Lκκ : For weakly compact κ there is no strongest extension of Lκω with the (κ, κ)-compactness property and the Löwenheim-Skolem theorem down to κ . With an additional set-theoretic assumption, there is no strongest extension of Lκκ with the (κ, κ)-compactness property and the Löwenhe...

the compact finite difference schemes have been found to give simple ways of reaching the objectives of high accuracy and low computational cost. during the past two decades, the compact schemes have been used extensively for numerical simulation of various fluid dynamics problems. these methods have also been applied for numerical solution of some prototype geophysical fluid dynamics problems ...

In this article, we study the sampling recovery problem for certain relevant multivariate function classes on cube [0, 1] d , which are not compactly embedded into L∞(<mml...

Assuming Jensen's diamond principle (⋄) we construct for every natural number n>0 a compact Hausdorff space K such that whenever the Banach spaces C(K) and C(L) are isomorphic some L, then covering dimension of L is equal to n. The constructed separable connected, has few operators i.e. bounded linear operator T:C(K)→C(K) form T(f)=fg+S(f), where g∈C(K) S weakly compact.