Bicriteria problems to minimize maximum tardiness and due date assignment cost in various scheduling environments

We study bicriteria problems of minimizing maximum tardiness and total due date assignment cost in various scheduling environments. We assume that each job can be assigned a different due date without any restriction, and that each due date assignment cost is a non-decreasing function of the quoted due date. We settle the complexity of most of the problems studied by either proving that they are NP-hard or finding a polynomial time solution for them. We also include approximation and non-approximability results for several parallel-machine problems.     

图的直径与Betti亏数

对于任意的正数Ｍ以及正整数ｄ≥４,存在直径为ｄ的ｉ－边连通无环图Ｇ使得ζ（Ｇ）≥Ｍ,其中ζ（Ｇ）是Ｇ的Ｂｅｔｔｉ亏数,ｉ＝１,２,３。     

The nonquadratic imaginary cyclic fields of -power degrees with class numbers equal to their genus class numbers

It is known that there are only finitely many imaginary abelian number fields with class numbers equal to their genus class numbers. Here, we determine all the imaginary cyclic fields of -power degrees with class numbers equal to their genus class numbers.

     

Adaptive anisotropic noise filtering for magnitude MR data

Conventional noise filtering schemes applied to magnitude magnetic resonance (MR) images tacitly assume Gauss distributed noise. Magnitude MR data, however, are Rice distributed. Not incorporating this knowledge leads inevitably to biased results, in particular when applying such filters in regions with low signal-to-noise ratio. In this work, we show how the Rice data probability distribution can be incorporated so as to construct a noise filter that is far less biased.     

A simple version of Karzanov's blocking flow algorithm

Dinic has shown that the classic maximum flow problem on a graph of n vertices and m edges can be reduced to a sequence of at most n ? 1 so-called ‘blocking flow’ problems on acyclic graphs. For dense graphs, the best time bound known for the blocking flow problems is O(n²). Karzanov devised the first O(n²)-time blocking flow algorithm, which unfortunately is rather complicated. Later Malhotra, Kumar and Maheshwari devise another O(n²)-time algorithm, which is conceptually very simple but has some other drawbacks. In this paper we propose a simplification of Karzanov's algorithm that is easier to implement than Malhotra, Kumar and Maheshwari's method.     

A half-moment model for radiative transfer in a 3D gray medium and its reduction to a moment model for hot, opaque sources

We present in this paper a new 3D half-moment model for radiative transfer in a gray medium, called the model, which uses maximum entropy closure. This model is a generalization to 3D of the 1D version recently proposed in (J. Comp. Phys. 180 (2002) 584). The direction space Ω is divided into two pieces, Ω⁺ and Ω^-, in a dynamical way by the plane perpendicular to the total radiative flux, and the half moments are defined from these subspaces. The model closure and the integrations of the radiative transfer equation performed on the moving Ω^± spaces are detailed. 1D planar results, which have motivated the extension of the model of (J. Comp. Phys. 180 (2002) 584) to multi-dimensions, are shown. These results are very good. The model is thereafter derived for 3D spherically symmetric geometry, where the correctness of the non-trivial border terms can be checked. Two 3D spherically symmetric problems are numerically solved in order to show the accuracy of the closure and the role of the border terms. Once again, compared to the solution obtained with a ray tracing solver, results are very good. From the 3D half-moment model, a new moment model, called , is derived for the particular case of a 3D hot and opaque source radiating into a cold medium, for applications such as simulations of stellar atmospheres and fires. Two-dimensional numerical results are presented and compared to those obtained solving the RTE and with other moment models. They demonstrate the very good accuracy of the model, its good convergence properties, and better prediction compared to all other existing moment models in its domain of applicability.     

Positive Reachability for Diffusion Equations

Counterexamples are constructed for some plausible conjectures. Typical of these: as the Maximum Principle ensures that positive boundary data give a positive state at time T from 0 initial data, one might (plausibly, but falsely) conjecture that all positive terminal states should be approximately reachable in this way, i.e., subject to the requirement that the boundary data stays nonnegative.     

The dominating set problem is fixed parameter tractable for graphs of bounded genus

We describe an algorithm for the dominating set problem with time complexity O((4g+40)^kn²) for graphs of bounded genus g1, where k is the size of the set. It has previously been shown that this problem is fixed parameter tractable for planar graphs. We give a simpler proof for the previous O(8^kn²) result for planar graphs. Our method is a refinement of the earlier techniques.     

Existence of Entire Solutions of a Singular Semilinear Elliptic Problem

In this paper, we obtain some existence results for a class of singular semilinear elliptic problems where we improve some earlier results of Zhijun Zhang. We show the existence of entire positive solutions without the monotonic condition imposed in Zhang‘s paper. The main point of our technique is to choose an approximating sequence and prove its convergence. The desired compactness can be obtained by the Sobolev embedding theorems.