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91.
92.
93.
Anders Björner Andreas Paffenholz Jonas Sjöstrand Günter M. Ziegler 《Discrete and Computational Geometry》2005,34(1):71-86
In 1992 Thomas Bier presented a strikingly simple method to produce a
huge number of simplicial (n – 2)-spheres on 2n vertices, as deleted
joins of a simplicial complex on n vertices with its combinatorial
Alexander dual.
Here we interpret his construction as giving the poset of all the
intervals in a boolean algebra that “cut across an ideal.” Thus we
arrive at a substantial generalization of Bier’s construction: the
Bier posets Bier(P, I) of an arbitrary bounded poset P of
finite length. In the case of face posets of PL spheres this yields
cellular “generalized Bier spheres.” In the case of Eulerian or
Cohen–Macaulay posets P we show that the Bier posets Bier(P, I)
inherit these properties.
In the boolean case originally considered by Bier, we show that all the
spheres produced by his construction are shellable, which yields “many
shellable spheres,” most of which lack convex realization.
Finally, we present simple explicit formulas for the g-vectors of
these simplicial spheres and verify that they satisfy a strong form of
the g-conjecture for spheres. 相似文献
94.
Clemens Nothegger Alfred Mayer Andreas Chwatal Günther R. Raidl 《Annals of Operations Research》2012,194(1):325-339
In this work we present a new approach to tackle the problem of Post Enrolment Course Timetabling as specified for the International Timetabling Competition 2007 (ITC2007), competition track 2. The heuristic procedure is
based on Ant Colony Optimization (ACO) where artificial ants successively construct solutions based on pheromones (stigmergy) and local information. The key feature of our algorithm is the use of two distinct but simplified pheromone matrices
in order to improve convergence but still provide enough flexibility for effectively guiding the solution construction process.
We show that by parallelizing the algorithm we can improve the solution quality significantly. We applied our algorithm to
the instances used for the ITC2007. The results document that our approach is among the leading algorithms for this problem;
in all cases the optimal solution could be found. Furthermore we discuss the characteristics of the instances where the algorithm
performs especially well. 相似文献
95.
The paper deals with the numerical treatment of stochastic differential-algebraic equations of index one with a scalar driving
Wiener process. Therefore, a particularly customized stochastic Runge-Kutta method is introduced. Order conditions for convergence
with order 1.0 in the mean-square sense are calculated and coefficients for some schemes are presented. The proposed schemes
are stiffly accurate and applicable to nonlinear stochastic differential-algebraic equations. As an advantage they do not
require the calculation of any pseudo-inverses or projectors. Further, the mean-square stability of the proposed schemes is
analyzed and simulation results are presented bringing out their good performance. 相似文献
96.
Jochen Kripfganz Andreas Laser Michael G. Schmidt 《Zeitschrift fur Physik C Particles and Fields》1997,73(2):353-362
The main perturbative contribution to the free energy of an electroweak interface is due to the effective potential and the tree level kinetic term. The derivative corrections are investigated with one-loop perturbation theory. The action is treated in derivative, in heat kernel, and in a multi local expansion. The massive contributions turn out to be well described by the Z-factor. The massless mode, plagued by infrared problems, is numerically less important. Its perturbatively reliable part can by calculated in derivative expansion as well. A self consistent way to include the Z-factor in the formula for the interface tension is presented. 相似文献
97.
The more-dimensional bin packing problem (BPP) considered here requires packing a set of rectangular-shaped items into a minimum
number of identical rectangular-shaped bins. All items may be rotated and the guillotine cut constraint has to be respected.
A straightforward heuristic is presented that is based on a method for the container loading problem following a wall-building
approach and on a method for the one-dimensional BPP. 1,800 new benchmark instances are introduced for the two-dimensional
and three-dimensional BPP. The instances include more than 1,500 items on average. Applied to these very large instances,
the heuristic generates solutions of acceptable quality in short computation times. Moreover, the influence of different instance
parameters on the solution quality is investigated by an extended computational study. 相似文献
98.
Dennis?JankaEmail author Christian?Kirches Sebastian?Sager Andreas?W?chter 《Mathematical Programming Computation》2016,8(4):435-459
We present a quasi-Newton sequential quadratic programming (SQP) algorithm for nonlinear programs in which the Hessian of the Lagrangian function is block-diagonal. Problems with this characteristic frequently arise in the context of optimal control; for example, when a direct multiple shooting parametrization is used. In this article, we describe an implementation of a filter line-search SQP method that computes search directions using an active-set quadratic programming (QP) solver. To take advantage of the block-diagonal structure of the Hessian matrix, each block is approximated separately by quasi-Newton updates. For nonconvex instances, that arise, for example, in optimum experimental design control problems, these blocks are often found to be indefinite. In that case, the block-BFGS quasi-Newton update can lead to poor convergence. The novel aspect in this work is the use of SR1 updates in place of BFGS approximations whenever possible. The resulting indefinite QPs necessitate an inertia control mechanism within the sparse Schur-complement factorization that is carried out by the active-set QP solver. This permits an adaptive selection of the Hessian approximation that guarantees sufficient progress towards a stationary point of the problem. Numerical results demonstrate that the proposed approach reduces the number of SQP iterations and CPU time required for the solution of a set of optimal control problems. 相似文献
99.
Andreas E. Schroth 《Journal of Geometry》1999,65(1-2):169-189
A new and rather general definition of circle geometries is given. This definition is such that circle planes and chain spaces are circle geometries. Also the geometry of points and traces of an antiregular quadrangle is a partial circle geometry. Orthogonal quadrangles can then be characterised as those antiregular generalised quadrangles where in the associated partial circle geometry the Miquel condition is satisfied. 相似文献
100.