Evaluation of steerable filter for detection of fibers in flowing suspensions

Steerable filters are concluded to be useful in order to determine the orientation of fibers captured in digital images. The fiber orientation is a key variable in the study of flowing fiber suspensions. Here, digital image analysis based on a filter within the class of steerable filters is evaluated for suitability of finding the position and orientation of fibers suspended in flowing suspensions. In sharp images with small noise levels, the steerable filter succeeds in determining the orientation of artificially generated fibers with well-defined angles. The influence of reduced image quality on the orientation has been quantified. The effect of unsharpness and noise is studied and the results show that the error in orientation is less than 1° for moderate levels. Images from two flow cases, one laminar shear flow and one turbulent, are also analyzed. The fiber orientation distribution is determined in the flow-vorticity plane. For the laminar case a comparison is made to a robust, but computationally more expensive, method involving convolutions with an oriented elliptic filter. A good agreement is found when comparing the resulting fiber orientation distributions obtained with the two methods. For the turbulent case, it is demonstrated that correct results are obtained and that the method can handle overlapping fibers.     

The free loop space and the algebraic k-theory of spaces

Let A(X) be the space defined by Waldhausen whose homotopy groups define the algebraic K-groups of the space X and let . Here (X) denotes the free loop space of X and Q denotes the functor . For X = Y, the suspension of a connected space Y, we shall prove that the homotopy fibers Ã(X), B(X) of the maps A(X) A (point), B(X) B (point) are equivalent as infinite loop spaces.     

On the Cowen-Douglas Class for Banach Space Operators

In [3], M. J. Cowen and R. G. Douglas prove that the adjoint of a Hilbert space operator T is in the class if and only if T is unitarily equivalent with the operator M _z on a Hilbert space -valued analytic functions, where M _z denotes the operator of multiplication by the independent variable. The proof involves holomorphic vector bundles and Grauert’s theorem. In this paper we use a theorem by I. Gohberg and L. Rodman [4] to give a more elementary proof of this fact, which also works for Banach space operators.      

Covering homology

We introduce the notion of covering homology of a commutative S-algebra with respect to certain families of coverings of topological spaces. The construction of covering homology is extracted from Bökstedt, Hsiang and Madsen's topological cyclic homology. In fact covering homology with respect to the family of orientation preserving isogenies of the circle is equal to topological cyclic homology. Our basic tool for the analysis of covering homology is a cofibration sequence involving homotopy orbits and a restriction map similar to the restriction map used in Bökstedt, Hsiang and Madsen's construction of topological cyclic homology.Covering homology with respect to families of isogenies of a torus is constructed from iterated topological Hochschild homology. It receives a trace map from iterated algebraic K-theory and there is a hope that the rich structure, and the calculability of covering homology will make it useful in the exploration of J. Rognes' “red shift conjecture”.     

Integrated Production and Distribution Planning for Södra Cell AB

In this paper we consider integrated planning of transportation of raw material, production and distribution of products of the supply chain at Södra Cell AB, a major European pulp mill company. The strategic planning period is one year. Decisions included in the planning are transportation of raw materials from harvest areas to pulp mills, production mix and contents at pulp mills, distribution of pulp products from mills to customer via terminals or directly and selection of potential orders and their levels at customers. Distribution is carried out by three different transportation modes; vessels, trains and trucks. We propose a mathematical model for the entire supply chain which includes a large number of continuous variables and a set of binary variables to reflect decisions about product mix and order selection at customers. Five different alternatives regarding production mix in a case study carried out at Södra Cell are analyzed and evaluated. Each alternative describes which products will be produced at which pulp mills.