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21.
Maria Chudnovsky Jim Geelen Bert Gerards Luis Goddyn Michael Lohman Paul Seymour 《Combinatorica》2006,26(5):521-532
Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A⊂V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If Γ is not abelian, we sum the labels in their order along the path.) We are interested in the maximum number of vertex-disjoint
A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem. The general case also includes Mader's S-paths problem. We prove that for any positive integer k, either there are k vertex-disjoint A-paths each of non-zero weight, or there is a set of at most 2k −2 vertices that meets each of the non-zero A-paths. This result is obtained as a consequence of an exact min-max theorem.
These results were obtained at a workshop on Structural Graph Theory at the PIMS Institute in Vancouver, Canada. This research
was partially conducted during the period the first author served as a Clay Mathematics Institute Long-Term Prize Fellow. 相似文献
22.
In the present Note, we study the asymptotic behavior of the distribution density of the stock price process in the Hull–White model. The leading terms in the asymptotic expansions at zero and infinity are found for such a density and the corresponding error estimates are given. Similar problems are solved for time averages of the volatility process, which are also of interest in the study of Asian options. To cite this article: A. Gulisashvili, E.M. Stein, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
23.
CV Tomy D Pal SS Banerjee S Ramakrishnan AK Grover S Bhattacharya MJ Higgins G Balakrishnan McK Paul 《Pramana》2002,58(5-6):925-935
The weakly pinned single crystals of the hexagonal 2H-NbSe2 compound have emerged as prototypes for determining and characterizing the phase boundaries of the possible order-disorder
transformations in the vortex matter. We present here a status report based on the ac and dc magnetization measurements of
the peak effect phenomenon in three crystals of 2H-NbSe2, in which the critical current densities vary over two orders of magnitude. We sketch the generic vortex phase diagram of
a weakly pinned superconductor, which also utilizes theoretical proposals. We also establish the connection between the metastability
effects and pinning. 相似文献
24.
We provide an approximate analysis of the transient sojourn time for a processor sharing queue with time varying arrival and
service rates, where the load can vary over time, including periods of overload. Using the same asymptotic technique as uniform
acceleration as demonstrated in [12] and [13], we obtain fluid and diffusion limits for the sojourn time of the Mt/Mt/1 processor-sharing queue. Our analysis is enabled by the introduction of a “virtual customer” which differs from the notion
of a “tagged customer” in that the former has no effect on the processing time of the other customers in the system. Our analysis
generalizes to non-exponential service and interarrival times, when the fluid and diffusion limits for the queueing process
are known. 相似文献
25.
This paper is devoted to the proof of almost global existence results for Klein‐Gordon equations on Zoll manifolds (e.g., spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof relies on Birkhoff normal form methods and on the specific distribution of eigenvalues of the Laplacian perturbed by a potential on Zoll manifolds. © 2007 Wiley Periodicals, Inc. 相似文献
26.
We study quantum antiferromagnetism on the highly frustrated planar pyrochlore lattice, also known as the square lattice with crossings. The quantum Heisenberg antiferromagnet on this lattice is of interest as a two-dimensional analogue of the pyrochlore lattice magnet. By combining several approaches we conclude that this system is most likely ordered for all values of spin, S, with a two-fold degenerate valence-bond solid being the ground state for small S. We show next that the Ising antiferromagnet with a weak four-spin exchange, equivalent to square ice with the leading quantum dynamics, exhibits analogous plaquette order. As a byproduct of this analysis we obtain, in the system of weakly coupled ice planes, a sliding phase with XY symmetry; at intermediate couplings, long range “anti-ferroelectric” order is stabilized. 相似文献
27.
We study the stationary measure for the two-dimensional Boussinesq equation with random forcing. We prove the ergodicity for the two-dimensional stochastically forced Boussinesq equation. We also study the Galerkin truncations of the three-dimensional Boussinesq equations under degenerate stochastic forcing. We follow closely the previous results on the stochastically forced Navier–Stokes equations. 相似文献
28.
We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space. 相似文献
29.
This paper examines the effect of infinitesimal functional variations in a rigid rotor He-HF potential surface on several different types of observables: inelastic cross sections, rate constants, and rotational energy level populations. The dynamics and kinetic observables studied were found to be sensitive to a large number of Legendre components of the potential with the region of highest sensitivity dependent upon the energy or temperature as well as the states related by the individual observable. Sensitivity to the entire surface tends to show a large degree of structure due to competition among sensitivities to the individual potential components. Significant information loss has been observed in the transition from microscopic to macroscopic observables. 相似文献
30.
In previous work the authors consider the dynamic assignment problem, which involves solving sequences of assignment problems over time in the presence of uncertain information about the future. The algorithm proposed by the authors provides generally high-quality but non-optimal solutions. In this work, though, the authors prove that if the optimal solution to a dynamic assignment problem in one of two problem classes is unique, then the optimal solution is a fixed point under the algorithm. 相似文献