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- Mathematik (75) (remove)

- Measure and Integration on Lipschitz-Manifolds (2007)
- The first part of this paper is concerned with various definitions of a k-dimensional Lipschitz-manifold and a discussion of the equivalence of these definitions. The second part is then devoted to the geometrically intrinsic construction of a sigma-algebra L of subsets of the manifold and a measure on L.

- On the benefits of using NP-hard problems in Branch & Bound (2008)
- We present a Brand-and-Bound (B&B) method using combinatorial bounds for solving makespan minimization problems with sequence dependent setup costs. As an application we present a laser source sharing problem arising in car manufacturing.

- Double and bordered alpha-circulant self-dual codes over finite commutative chain rings (2008)
- In this paper we investigate codes over finite commutative rings R, whose generator matrices are built from alpha-circulant matrices. For a non-trivial ideal I < R we give a method to lift such codes over R/I to codes over R, such that some isomorphic copies are avoided. For the case where I is the minimal ideal of a finite chain ring we refine this lifting method: We impose the additional restriction that lifting preserves self-duality. It will be shown that this can be achieved by solving a linear system of equations over a finite field. Finally we apply this technique to Z_4-linear double nega-circulant and bordered circulant self-dual codes. We determine the best minimum Lee distance of these codes up to length 64.

- Existence and stability of stellardynamic models (2008)
- We examine existence and stability of stationary solutions to the Vlasov-Poisson system. This system is used in stellardynmaics to describe the evolution of galaxies where collissions are neglected and the evolution is determined by the self-consistent gravitational field which is created by the particles, e.g. the stars . In the first part we examine steady states which decsribe static shells under the influence of a fixed point mass. These solutions can be used as a model for a galaxy with a massive black hole in its center. For the Vlasov--Poisson system under the influence of such a point mass, we prove a global existence result. In the second part, we construct axially symmetric solutions depending on Jacobis integral. The presented results are in accordance with the numerical examinations of the P.O. Vandervoort.

- Stability of flat galaxies (2008)
- In this thesis we investigate the existence and properties of stationary solutions of the flat Vlasov-Poisson system. This system of partial differential equations can be used as a model of extremely flat astronomical objects and is a combination between the two-dimensional motion of particles and the three-dimensional interaction through their gravitational potential.

- Bounds for the minimum oriented diameter (2008)
- We consider the problem of finding an orientation with minimum diameter of a connected bridgeless graph. Fomin et. al. discovered a relation between the minimum oriented diameter an the size of a minimal dominating set. We improve their upper bound.

- Integral point sets over Z_n^m (2007)
- There are many papers studying properties of point sets in the Euclidean space or on integer grids, with pairwise integral or rational distances. In this article we consider the distances or coordinates of the point sets which instead of being integers are elements of Z_n, and study the properties of the resulting combinatorial structures.

- There are integral heptagons, no three points on a line, no four on a circle (2007)
- We give two configurations of seven points in the plane, no three points in a line, no four points on a circle with pairwise integral distances. This answers a famous question of Paul Erdös.

- On the minimum diameter of plane integral point sets (2007)
- Since ancient times mathematicians consider geometrical objects with integral side lengths. We consider plane integral point sets P, which are sets of n points in the plane with pairwise integral distances where not all the points are collinear. The largest occurring distance is called its diameter. Naturally the question about the minimum possible diameter d(2,n) of a plane integral point set consisting of n points arises. We give some new exact values and describe state-of-the-art algorithms to obtain them. It turns out that plane integral point sets with minimum diameter consist very likely of subsets with many collinear points. For this special kind of point sets we prove a lower bound for d(2,n) achieving the known upper bound n^{c_2loglog n} up to a constant in the exponent.

- The Top-Dog Index: A New Measurement for the Demand Consistency of the Size Distribution in Pre-Pack Orders for a Fashion Discounter with Many Small Branches (2008)
- We propose the new Top-Dog-Index, a measure for the branch-dependent historic deviation of the supply data of apparel sizes from the sales data of a fashion discounter. A common approach is to estimate demand for sizes directly from the sales data. This approach may yield information for the demand for sizes if aggregated over all branches and products. However, as we will show in a real-world business case, this direct approach is in general not capable to provide information about each branchs individual demand for sizes: the supply per branch is so small that either the number of sales is statistically too small for a good estimate (early measurement) or there will be too much unsatisfied demand neglected in the sales data (late measurement). Moreover, in our real-world data we could not verify any of the demand distribution assumptions suggested in the literature. Our approach cannot estimate the demand for sizes directly. It can, however, individually measure for each branch the scarcest and the amplest sizes, aggregated over all products. This measurement can iteratively be used to adapt the size distributions in the pre-pack orders for the future. A real-world blind study shows the potential of this distribution free heuristic optimization approach: The gross yield measured in percent of gross value was almost one percentage point higher in the test-group branches than in the control-group branches.