M. H. Al-Abbadi and M. Darus 2009 recently introduced a new generalized derivative operator μ λ1 ,λ2 , which generalizedmany well-known operators studied earlier by many different authors. In this present paper, we shall investigate a new subclass of analytic functions in the open unit disk U {z ∈ C : |z| < 1} which is defined by new generalized derivative operator. Some results on coefficient ...

In this paper, we investigate moment methods from a general point of view using an operator notation. This theoretical approach lets us explore the moment closure problem in more detail. This gives rise to a new idea, proposed in [14, 15], of how to improve the well-known PN approximations. We systematically develop a diffusive correction to the PN equations from the operator formulation — the ...

Suppose L is a differential operator of order k. Moreover, let u be a function defined and k times continuously differentiable in the closure of a domain Ω of R. Provided the adjoint differential operator possesses a fundamental solution, we shall see that u can be recovered from Lu and the boundary values of u. Strictly speaking, we shall get an integral representation of u in form of the sum ...

The notion of dependencies between ”attributes” arises in many areas such as relational databases, data analysis, data-mining, formal concept analysis, knowledge structures . . .. Formalization of dependencies leads to the notion of so-called full implicational systems (or full family of functional dependencies) which is in oneto-one correspondence with the other significant notions of closure ...

This paper deals with maximization of set f'unctions delined as minimum values of monotone linkage functions. In previous research, it has been shown that such a set function can be maximized by a greedy type algorithm over a family of all subsets of a finite set. ln this paper, we extend this finding to meet-semilattices. We show that the class of functions defined as minimum values of monoton...

This report studies an abstract approach to modeling the motion of large eddies in a turbulent flow. If the Navier-Stokes equations (NSE) are averaged with a local, spatial convolution type filter, φ = gδ ∗ φ, the resulting system is not closed due to the filtered nonlinear term uu. An approximate deconvolution operator D is a bounded linear operator which is an approximate filter inverse D(u) ...

Given a Banach space operator with interior points in the localizable spectrum and without non-trivial divisible subspaces, this article centers around the construction of an infinite-dimensional linear subspace of vectors at which the local resolvent function of the operator is bounded and even admits a continuous extension to the closure of its natural domain. As a consequence, it is shown th...

Let K be an absolutely convex infinite-dimensional compact in a Banach space X . The set of all bounded linear operators T on X satisfying TK ⊃ K is denoted by G(K). Our starting point is the study of the closure WG(K) of G(K) in the weak operator topology. We prove that WG(K) contains the algebra of all operators leaving lin(K) invariant. More precise results are obtained in terms of the Kolmo...

This talk will aim to provide an account of the apoha theory of delineation by analogy with the construction of propositions in some non-classical logics. In such logics, not all sets of possible worlds are taken to be propositions. In quantum logic, for example, an arbitrary set of states may not exactly represent the semantical counterpart of a legitimate proposition. Moreover, the negation o...

Of concern are the minimal and maximal operators on L2(R") associated with the differential expression Te = J2{id/dxJ + qJ{x))2 + W{x) j=i where (q.#„) = gradQ for some real function W on R" and W satisfies ¿M-2 < W(Jf) < C|x|~2 . In particular, for Q = 0, Xq reduces to the singular Schrödinger operator -A+ W{x). Among other results, it is shown that the maximal operator (associated with the xq...