Geodesic ideal triangulations exist virtually

It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability of peripheral subgroups.

     

Scheduling coordination problems in supply chain planning

Scheduling algorithms and their role in supply chain planning are topics that have been discussed in scheduling literature for many years. Based on examples and experience with commercial supply chain planning software, this paper presents background information about production planning and scheduling functionality in commercial supply chain planning software and interesting scheduling coordination problems in supply chain planning for researchers. We first provide an overview of different planning activities in supply chain planning, while taking into consideration existing functionalities that are available in commercial supply chain planning software. As a second step, we show three scheduling coordination problems in supply chain planning, namely the integration of production planning and production scheduling, the integration of sales order confirmation and production scheduling and the integration of VMI planning and production scheduling. We conclude this paper with a detailed discussion of an implementation of a supply chain planning solution at the tissue producer SCA Hygiene in Sweden. This paper expresses the authors opinion and does not represent an official statement from SAP.     

Colourings of graphs with two consecutive odd cycle lengths

In 1992 Gyárfás showed that a graph G having only k odd cycle lengths is (2k+1)-colourable, if it does not contain a K_2k+2. In this paper, we will present the results for graphs containing only odd cycles of length 2m−1 and 2m+1 as done in [S. Matos Camacho, Colourings of graph with prescribed cycle lengths, diploma thesis, TU Bergakademie Freiberg, 2006. [3]]. We will show that these graphs are 4-colourable.     

Universally prestarlike functions as convolution multipliers

Universally prestarlike functions (of order α ≤ 1) in the slit domain L:=\mathbbC\[1,￥]{\Lambda:=\mathbb{C}{\setminus}[1,\infty]} have recently been introduced in Ruscheweyh et al. (Israel J Math, to appear). This notation generalizes the corresponding one for functions in the unit disk \mathbbD{\mathbb{D}} (and other circular domains in \mathbbC{\mathbb{C}}). In this paper we study the behaviour of universally prestarlike functions under the Hadamard product. In particular it is shown that these function classes (with α fixed), are closed under convolution, and that their members, as Hadamard multipliers, also preserve the prestarlikeness (of the same order) of functions in arbitrary circular domains containing the origin.     

Positivity and time behavior of a linear reaction–diffusion system,non-local in space and time

We consider a general linear reaction–diffusion system in three dimensions and time, containing diffusion (local interaction), jumps (nonlocal interaction) and memory effects. We prove a maximum principle and positivity of the solution and investigate its asymptotic behavior. Moreover, we give an explicit expression of the limit of the solution for large times. In order to obtain these results, we use the following method: We construct a Riemannian manifold with complicated microstructure depending on a small parameter. We study the asymptotic behavior of the solution to a simple diffusion equation on this manifold as the small parameter tends to zero. It turns out that the homogenized system coincides with the original reaction–diffusion system. Using this and the facts that the diffusion equation on manifolds satisfies the maximum principle and its solution converges to a easily calculated constant, we can obtain analogous properties for the original system. Copyright © 2008 John Wiley & Sons, Ltd.     

Simulated annealing in the presence of noise

In many practical optimization problems, evaluation of a solution is subject to noise, e.g., due to stochastic simulations or measuring errors. Therefore, heuristics are needed that are capable of handling such noise. This paper first reviews the state-of-the-art in applying simulated annealing to noisy optimization problems. Then, two new algorithmic variants are proposed: an improved version of stochastic annealing that allows for arbitrary annealing schedules, and a new approach called simulated annealing in noisy environments (SANE). The latter integrates ideas from statistical sequential selection in order to reduce the number of samples required for making an acceptance decision with sufficient statistical confidence. Finally, SANE is shown to significantly outperform other state-of-the-art simulated annealing techniques on a stochastic travelling salesperson problem.     

Boundary Integral Equations for Mixed Boundary Value Problems in R3

Both exterior and interior mixed Dirichlet-Neumann problems in R³ for the scalar Helmholtz equation are solved via boundary integral equations. The integral equations are equivalent to the original problem in the sense that the traces of the weak seolution satisfy the integral equations, and, conversely, the solution of the integral equations inserted into Green's formula yields the solution of the mixed boundary value problem. The calculus of pseudodifferential operators is used to prove existence and regularity of the solution of the integral equations. The regularity results — obtained via Wiener-Hopf technique — show the explicit “edge” behavior of the solution near the submanifold which separates the Dirichlet boundary from the Neumann boundary.     

Vandermonde matrices on the circle: Spectral properties and conditioning

Summary We study Vandermonde matrices whose nodes are given by a Van der Corput sequence on the unit circle. Our primary interest is in the singular values of these matrices and the respective (spectral) condition numbers. Detailed information about multiplicities and eigenvectors, however, is also obtained. Two applications are given to the theory of polynomials.Dedicated to R. S. Varga on the occasion of his sixtieth birthdayResearch of A. C. supported by the Fundación Andes, Chile, and by the German Academic Exchange Service (DAAD), Federal Republic of GermanyResearch of W. G. supported, in part, by the National Science Foundation, USA, (Grant CCR-8704404)Research of S. R. supported by the Fondo Nacional de Desarollo Cientßfico y Tecnológico (FONDECYT), Chile, (Grant 237/89), by the Universidad Técnica F. Santa Marßa, Valparaßso, Chile, (Grant 89.12.06), and by the German Academic Exchange Service (DAAD), Federal Republic of Germany     

Preparation,catalytical activity and crystal structure of a heptanuclear zinc acetate cluster

Reaction of [Zn₄(µ₄-O)(O₂CCH₃)₆] with one equivalent of 4-tertiary-butylpyridine leads to a nearly quantitative formation of the heptanuclear cluster [Zn₇O₂(O₂CCH₃)₁₀(^tbupy)₂] (1). Here, we present the crystal structure of 1 and first results of the examination of its catalytic activity in transesterification reactions and polymerization of lactide compared to the activity of [Zn₄(µ₄-O)(O₂CCH₃)₆] in the presence of 4-tertiary-butylpyridine.     

Immobilization and Characterization of <Emphasis Type="Italic">E. gracilis</Emphasis> Extract with Enriched Laminaribiose Phosphorylase Activity for Bienzymatic Production of Laminaribiose

Immobilization methods and carriers were screened for immobilization of Euglena gracilis extract with laminaribiose phosphorylase activity. The extract was successfully immobilized on three different carriers via covalent linkage. Suitable immobilization carriers were Sepabeads EC-EP/S and ECR 8209M with epoxy groups and ECR 8309M with amino groups as functional units. Immobilization on Sepabeads EC-EP/S resulted in highest retained activity (65%). The immobilizates were characterized for pH, temperature, and buffer molarity preferences. The immobilized enzyme lost 48% of its activity when used seven times. Together with sucrose phosphorylase, laminaribiose phosphorylase was successfully applied for bienzymatic production of laminaribiose from sucrose and glucose with a final laminaribiose concentration of 14.3 ± 2.1 g/L (20% yield).