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151.
Balinski uses his signature method for the proof of the Hirsch-conjecture for dual transportation polyhedra to obtain an efficient
algorithm for the assignment problem. We will show how to extend this method to other primal transportation problems, including
transportation problems with unit demands. We then prove that Balinski's assignment algorithm is equivalent, cycle by cycle,
to that of Hung and Rom. We demonstrate that, under some assumptions for our probability model, a modification of the latter
algorithm has an average complexity of O(n
2logn) and present some computational results confirming this. We also present results that indicate that this modification compares
favorably with Balinski's algorithm and other codes.
Research of both authors supported, in part, by grants of the Alexander von Humboldt-Stiftung.
Supported, in part, by NSF grant DMS-8504050. 相似文献
152.
We give a new algorithm for solving the Fermat-Weber location problem involving mixed gauges. This algorithm, which is derived
from the partial inverse method developed by J.E. Spingarn, simultaneously generates two sequences globally converging to
a primal and a dual solution respectively. In addition, the updating formulae are very simple; a stopping rule can be defined
though the method is not dual feasible and the entire set of optimal locations can be obtained from the dual solution by making
use of optimality conditions.
When polyhedral gauges are used, we show that the algorithm terminates in a finite number of steps, provided that the set
of optimal locations has nonepty interior and a counterexample to finite termination is given in a case where this property
is violated. Finally, numerical results are reported and we discuss possible extensions of these results. 相似文献
153.
In this paper the main focus is on a stability concept for solutions of a linear complementarity problem. A solution of such
a problem is robust if it is stable against slight perturbations of the data of the problem. Relations are investigated between
the robustness, the nondegenerateness and the isolatedness of solutions. It turns out that an isolated nondegenerate solution
is robust and also that a robust nondegenerate solution is isolated. Since the class of linear complementarity problems with
only robust solutions or only nondegenerate solutions is not an open set, attention is paid to Garcia's classG
n
of linear complementarity problems. The nondegenerate problems inG
n
form an open set. 相似文献
154.
An asymptotic equivalence theorem is proven between the solutions of the initial value problem in all space for the Boltzmann and Enskog equations for initial data which assure global existence for the solutions to the initial value problem for one of the two equations. The proof is given starting from the solution of the Boltzmann equation, then the proof line is simply indicated when one starts from the Enskog equation. The proof holds for Knudsen numbers of the order of unity and equivalence is proven when the scale of the dimensions of the gas particles characterizing the Enskog equation tends to zero.On leave from Department of Mathematics, University of Warsaw, Poland. 相似文献
155.
156.
It is well known that each solution of the modified Korteveg–de Vries (mKdV) equation gives rise, via the Miura transformation, to a solution of the Korteveg–de Vries (KdV) equation. In this work, we show that a similar Miura-type transformation exists also for the “good” Boussinesq equation. This transformation maps solutions of a second-order equation to solutions of the fourth-order Boussinesq equation. Just like in the case of mKdV and KdV, the correspondence exists also at the level of the underlying Riemann–Hilbert problems and this is in fact how we construct the new transformation. 相似文献
157.
158.
孙厚钧 《应用数学和力学(英文版)》1985,6(7):631-642
It is shown in this paper that in geometrical space two polarization planes of thelinearly polarized light waves scattered by particles in measuring ellipsoid constitute anangle of π/2. while in sequence of time the signals sent out by two symmetricphotodetectors in PLDA ard separated by a phase angle π.This property of PLDAenables the improvement of SNR.The similarity between power spectrum of photoelectrical current of PLDA andprobability density function P_d(u_c)of investigated flow velocity has been provedtheoretically and checked by agreement of obtained results with classical theory andgenerally accepted experiments. 相似文献
159.
The bending of a cantilever rectangular plate is a very complicated problem in thetheory of plates.For a long time,there have been only approximate solutions for thisproblem by energy methods and numerical methods.since 1979,Prof.F.V.Chang of Tsing Hua University obtained,by the method ofsuperposition,a series of analytic solutions for cantilever rectangular plates under uniformload and concentrated load.In this paper,the two-direction trigonometric series is used to obtain the solution forthe bending of cantilever rectangular plates under uniform load.The obtained results arecompared with the results by the method of superposition.The comparison shows that theresults of these two methods are in good agreement,hence they are mutually confirmed to becorrect. 相似文献
160.
在实的局部凸的Hausdorff拓扑线性空间中,考虑带约束的向量均衡问题,利用凸集分离定理,给出了带约束的类凸向量均衡问题的弱有效解,Henig有效解,全局有效解和超有效解的充分必要条件,并通过举例说明了锥类凸映射是比锥凸映射更弱的映射。 相似文献