Effect of air cushion layer right before impact of a rigid body onto water surface has been investigated in this paper. The study is mainly focused on evaluation of cushioning pressure and the resulting free surface elevation. The air flow is assumed to be an irrotational flow which is governed by Laplace equation. The air problem and the resulting response of the water free surface are suppose...

It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C∗-algebra. This implies that the weakly almost periodic functionals on M(G), the measure algebra of a locally compact group G, is a C∗-subalgebra of M(G)∗ = C0(G) ∗∗. The proof builds upon a factorisation result, due to Young and Kaiser, for weakly com...

We work in set-theory without the Axiom of Choice ZF. We prove that the principle of Dependent Choices (DC) implies that the closed unit ball of a uniformly convex Banach space is weakly compact, and in particular, that the closed unit ball of a Hilbert space is weakly compact. These statements are not provable in ZF, and the latter statement does not imply DC. Furthermore, DC does not imply th...

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

Let $ (A,| cdot |) $ be a real Banach algebra, a complex algebra $ A_mathbb{C} $ be a complexification of $ A $ and $ | | cdot | | $ be an algebra norm on  $ A_mathbb{C}  $  satisfying a simple condition together with the norm $ | cdot | $ on $ A$.  In this paper we first show that $ A^* $ is a real Banach $ A^{**}$-module if and only if $ (A_mathbb{C})^* $ is a complex Banach $ (A_mathbb{C})^{...

In the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. Then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

The paper treats theWigner distribution of scalar-valued stochastic processes defined on R. We show that if the process is Gaussian and weakly harmonizable then a stochastic Wigner distribution is well defined. The special case of stationary processes is studied, in which case the Wigner distribution is weakly stationary in the time variable and the variance is equal to the deterministic Wigner...

We show that under minor technical assumptions any weakly nonlocal Hamiltonian structures compatible with a given nondegenerate weakly nonlocal symplectic operator J can be written as the Lie derivatives of J along a suitably chosen nonlocal vector field. Moreover, we present a new description for local Hamiltonian structures of arbitrary order compatible with a given nondegenerate local Hamilt...