Let λ be an infinite cardinal number and let `∞(λ) denote the subspace of `∞(λ) consisting of all functions which assume at most countably many non zero values. We classify all infinite dimensional complemented subspaces of `∞(λ), proving that they are isomorphic to `∞(κ) for some cardinal number κ. Then we show that the Banach algebra of all bounded linear operators on `∞(λ) or `∞(λ) has the u...

Let I be an ideal of the polynomial ring A[x] = A[x1, . . . , xn] over the commutative, noetherian ring A. Geometrically I defines a family of affine schemes over Spec(A): For p ∈ Spec(A), the fibre over p is the closed subscheme of affine space over the residue field k(p), which is determined by the extension of I under the canonical map σp : A[x] → k(p)[x]. If I is homogeneous there is an ana...

This paper is a continuation of the work done in [9]. We are interested in the following question within the context of σ-ideals of σ-porous type. Let X be a metric space and let be a σ-ideal of subsets of X . Let S⊂ X be a Suslin set with S / ∈ . Does there exist a closed set F ⊂ S which is not in ? The answer is positive provided that X is locally compact and is a σ-ideal of σP-porous sets, w...

0-efficient triangulations of 3-manifolds are defined and studied. It is shown that any triangulation of a closed, orientable, irreducible 3-manifold M can be modified to a 0-efficient triangulation orM can be shown to be one of the manifolds S3,RP3 or L(3, 1). Similarly, any triangulation of a compact, orientable, irreducible, ∂-irreducible 3-manifold can be modified to a 0-efficient triangula...

In this paper, we investigate some topics around the closed image S of a rational map λ given by some homogeneous elements f1, . . . , fn of the same degree in a graded algebra A. We first compute the degree of this closed image in case λ is generically finite and f1, . . . , fn define isolated base points in Proj(A). We then relate the definition ideal of S to the symmetric and the Rees algebr...

D. Rees and J. Sally defined the core of an R-ideal I as the intersection of all (minimal) reductions of I. However, it is not easy to give an explicit characterization of it in terms of data attached to the ideal. Until recently, the only case in which a closed formula was known is the one of integrally closed ideals in a two-dimensional regular local ring, due to C. Huneke and I. Swanson. The...

A new method for PID controller tuning based on process models for cascaded control systems is proposed in this paper. The method consists of first finding the ideal controller that gives the desired closed loop response and then finding the PID approximation of the ideal controller by Maclaurin series. This method can be applied to any open loop stable processes. Furthermore, it enables us to ...

An investigation into the total blockage effects on aerodynamic drag in closed-wall wind tunnel testing has been carried out by computational fluid dynamics (CFD). The simulation of flow past two different realistic, full-scale, heavy-duty truck models was conducted. The models were placed at different yawing angles in the virtual wind tunnels with blockage ratio of about 10%; which is exactly ...