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- Satellite-to-Satellite Tracking and Satellite Gravity Gradiometry (2001)
- The purpose of satellite-to-satellite tracking (SST) and/or satellite gravity gradiometry (SGG) is to determine the gravitational field on and outside the Earth's surface from given gradients of the gravitational potential and/or the gravitational field at satellite altitude. In this paper both satellite techniques are analysed and characterized from mathematical point of view. Uniqueness results are formulated. The justification is given for approximating the external gravitational field by finite linear combination of certain gradient fields (for example, gradient fields of single-poles or multi-poles) consistent to a given set of SGG and/or SST data. A strategy of modelling the gravitational field from satellite data within a multiscale concept is described; illustrations based on the EGM96 model are given.

- Anchored hyperplane location problems (2001)
- The anchored hyperplane location problem is to locate a hyperplane passing through some given points P IR^n and minimizing either the sum of weighted distances (median problem), or the maximum weighted distance (center problem) to some other points Q IR^n . If the distances are measured by a norm, it will be shown that in the median case there exists an optimal hyperplane that passes through at least n - k affinely independent points of Q, if k is the maximum number of affinely independent points of P. In the center case, there exists an optimal hyperplane which isatmaximum distance to at least n - k + 1 affinely independent points of Q. Furthermore, if the norm is a smooth norm, all optimal hyperplanes satisfy these criteria. These new results generalize known results about unrestricted hyperplane location problems.

- Part1: Spectral and Multiscale Signal-to-Noise Thresholding of Spherical Scalar Fields; Part2: Spectral and Multiscale Signal-to-Noise Thresholding of Spherical Vector Fields (2001)
- Abstract: The basic concepts of selective multiscale reconstruction of functions on the sphere from error-affected data is outlined for scalar functions. The selective reconstruction mechanism is based on the premise that multiscale approximation can be well-represented in terms of only a relatively small number of expansion coefficients at various resolution levels. A new pyramid scheme is presented to efficiently remove the noise at different scales using a priori statistical information.

- Earliest Arrival Flow with Time Dependent Capacity Approach to the Evacuation Problems (2001)
- Abstract: Evacuation problems can be modeled as flow problems in dynamic networks. A dynamic network is defined by a directed graph G = (N,A) with sources, sinks and non-negative integral travel times and capacities for every arc (i,j) e A. The earliest arrival flow problem is to send a maximum amount of dynamic flow reaching the sink not only for the given time horizon T, but also for any time T' < T . This problem mimics the evacuation problem of public buildings where occupancies may not known. For the buildings where the number of occupancies is known and concentrated only in one source, the quickest flow model is used to find the minimum egress time. We propose in this paper a solution procedure for evacuation problems with a single source of the building where the occupancy number is either known or unknown. The possibility that the flow capacity may change due to the increasing of smoke density or fire obstructions can be mirrored in our model. The solution procedure looks iteratively for the shortest conditional augmenting path (SCAP) from source to sink and compute the time intervals in which flow reaches the sink via this path.

- Wannier-Stark resonances in semiconductor superlattices (2001)
- Wannier-Stark states for semiconductor superlattices in strong static fields, where the interband Landau-Zener tunneling cannot be neglected, are rigorously calculated. The lifetime of these metastable states was found to show multiscale oscillations as a function of the static field, which is explained by an interaction with above-barrier resonances. An equation, expressing the absorption spectrum of semiconductor superlattices in terms of the resonance Wannier-Stark states is obtained and used to calculate the absorption spectrum in the region of high static fields.

- Gross-Ooguri Phase Transition at Zero and Finite Temperature: Two Circular Wilson Loop Case (2001)
- Abstract: In the context of AdS/CFT correspondence the two Wilson loop correlator is examined at both zero and finite temperatures. On the basis of an entirely analytical approach we have found for Nambu-Goto strings the functional relation dSc(Reg) /dL = 2*pi*k between Euclidean action Sc and loop separation L with integration constant k, which corresponds to the analogous formula for point-particles. The physical implications of this relation are explored in particular for the Gross-Ooguri phase transition at finite temperature.

- Holographic Trace Anomaly and Cocycle of Weyl Group (2001)
- Abstract: The behavior of the divergent part of the bulk AdS/CFT effective action is considered with respect to the special finite diffeomorphism transformations acting on the boundary as a Weyl transformation of the boundary metric. The resulting 1-cocycle of the Weyl group is in full agreement with the 1-cocycle of the Weyl group obtained from the cohomological consideration of the effective action of the corresponding CFT.

- Conformal partial wave analysis of AdS amplitudes for dilaton-axion four-point functions (2001)
- Abstract: Operator product expansions are applied to dilaton-axion four-point functions. In the expansions of the bilocal fields "doubble Phi", CC and "Phi"C, the conformal fields which are symmetric traceless tensors of rank l and have dimensions "delta" = 2+l or 8+l+ "eta"(l) and "eta"(l) = O(N ^ -2) are identified. The unidentified field have dimension "delta" = "lambda"+l+eta(l) with "lambda" >= 10. The anomalous dimensions eta(l) are calculated at order O(N ^ -2) for both 2 ^ -1/2(-"doubble Phi" + CC) and 2 ^ -1/2(-"Phi"C + C"Phi") and are found to be the same, proving U(1)_Y symmetry. The relevant coupling constants are given at order O(1).

- Locating New Stops in a Railway Network (2001)
- Given a railway network together with information on the population and their use of the railway infrastructure, we are considering the e ffects of introducing new train stops in the existing railway network. One e ffect concerns the accessibility of the railway infrastructure to the population, measured in how far people live from their nearest train stop. The second effect we study is the change in travel time for the railway customers that is induced by new train stops. Based on these two models, we introduce two combinatorial optimization problems and give NP-hardness results for them. We suggest an algorithmic approach for the model based on travel time and give first experimental results.

- Point-to-Point and Multi-Goal Path Planning for Industrial Robots (2001)
- This article presents contributions in the field of path planning for industrial robots with 6 degrees of freedom. This work presents the results of our research in the last 4 years at the Institute for Process Control and Robotics at the University of Karlsruhe. The path planning approach we present works in an implicit and discretized C-space. Collisions are detected in the Cartesian workspace by a hierarchical distance computation. The method is based on the A* search algorithm and needs no essential off-line computation. A new optimal discretization method leads to smaller search spaces, thus speeding up the planning. For a further acceleration, the search was parallelized. With a static load distribution good speedups can be achieved. By extending the algorithm to a bidirectional search, the planner is able to automatically select the easier search direction. The new dynamic switching of start and goal leads finally to the multi-goal path planning, which is able to compute a collision-free path between a set of goal poses (e.g., spot welding points) while minimizing the total path length.