Inversion of adjunction for non-degenerate hypersurfaces

 We prove a precise inversion of adjunction formula for the log variety (ℂ ^{d +1},X), where X is a non-degenerate hypersurface. As a corollary, the minimal log discrepancies of non-degenerate normal hypersurface singularities are bounded by dimension. Received: 17 September 2002 / Revised version: 22 November 2002 Published online: 14 February 2003 Current address: DPMMS, CMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, England. e-mail: f.ambro@dpmms.cam.ac.uk Mathematics Subject Classification (2000): Primary 14B05; Secondary 14M25, 52B20     

Structural hierarchy of rock masses and the mechanisms of its formation

The formation mechanisms for the structural hierarchy in geological media are discussed. It is shown that the formation of such a hierarchy is caused by certain external and internal circumstances. The first ones consist in the fact that, because of external actions, the Earth’s poles continuously execute the translational and rotational motions responsible for a regular structure of rock fracture and for the appearance of the scale factor √2. The second ones consist in the fact that, under the action of many random factors and because of external actions, during the formation of geological media there appear dissipative structures and, hence, some self-similar fractal structures are formed.     

Loading aircraft for military operations

In this paper, we describe an aircraft loading problem submitted by the French military agency (DGA) as part of a more general military airlift planning problem. It can be viewed as a kind of bi-dimensional bin-packing problem, with heterogeneous bins and several additional constraints. We introduce two-phase methods for solving this NP-hard problem. The first phase consists in building good initial solutions, thanks to two fast algorithms: a list-based heuristic and a loading pattern generation method. Both algorithms call a constraint-based subroutine, able to determine quickly if the items already loaded can be reshuffled to accommodate a new object. The second phase improves these preliminary solutions using local search techniques. Results obtained on real data sets are presented.     

ON THE RATE OF WEIGHTED Lp CONVERGENCE BY THE GRUENWALD INTERPOLATORY OPERATORS

This paper gives the weighted Lp convergence rate estimations of the Gruenwald interpolatory polynomials based on the zeros of Chebyshev polymomials of the first kind,and proves that the order of the estimations is optimal for p≥1.     

Reply to Nathan: How to reconstruct the causal argument

Nicholas Nathan tries to resist the current version of the causal argument for sense-data in two ways. First he suggests that, on what he considers to be the correct re-construction of the argument, it equivocates on the sense of proximate cause. Second he defends a form of disjunctivism, by claiming that there might be an extra mechanism involved in producing veridical hallucination, that is not present in perception. I argue that Nathan’s reconstruction of the argument is not the appropriate one, and that, properly interpreted, the argument does not equivocate on proximate cause. Furthermore, I claim that his postulation of a modified mechanism for hallucinations is implausibly ad hoc.     

On a compromise social choice correspondence

This paper analyzes the compromise social choice correspondence derived from the τ-value of digraph games. Monotonicity of this correspondence is shown. A connection between several properties of social choice correspondences based on game theoretical solutions and game theoretical properties of the underlying solutions is given. Applications to several game theoretic solutions are provided.     

Methods for implementing the stream boundary condition in DSMC computations

In the direct simulation Monte‐Carlo (DSMC) method for simulating rarefied gas flows, the velocities of simulator particles that cross a simulation boundary and enter the simulation space are typically generated using the acceptance–rejection procedure that samples the velocities from a truncated theoretical velocity distribution that excludes low and high velocities. This paper analyses an alternative technique, where the velocities of entering particles are obtained by extending the simulation procedures to a region adjacent to the simulation space, and considering the movement of particles generated within that region during the simulation time step. The alternative method may be considered as a form of acceptance–rejection procedure, and permits the generation of all possible velocities, although the population of high velocities is depleted with respect to the theoretical distribution. Nevertheless, this is an improvement over the standard acceptance–rejection method. Previous implementations of the alternative method gave a number flux lower than the theoretical number required. Two methods for obtaining the correct number flux are presented. For upstream boundaries in high‐speed flows, the alternative method is more computationally efficient than the acceptance–rejection method. However, for downstream boundaries, the alternative method is extremely inefficient. The alternative method, with the correct theoretical number flux, should therefore be used in DSMC computations in favour of the acceptance–rejection method for upstream boundaries in high‐speed flows. Copyright © 2003 John Wiley & Sons, Ltd.