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31.
We use a Dyck path model for unit-interval graphs to study the chromatic quasisymmetric functions introduced by Shareshian and Wachs, as well as unicellular LLT polynomials, revealing some parallel structure and phenomena regarding their -positivity.The Dyck path model is also extended to circular arc digraphs to obtain larger families of polynomials, giving a new extension of LLT polynomials. Carrying over a lot of the non-circular combinatorics, we prove several statements regarding the -coefficients of chromatic quasisymmetric functions and LLT polynomials, including a natural combinatorial interpretation for the -coefficients for the line graph and the cycle graph for both families. We believe that certain -positivity conjectures hold in all these families above.Furthermore, beyond the chromatic analogy, we study vertical-strip LLT polynomials, which are modified Hall–Littlewood polynomials. 相似文献
32.
An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles 总被引:2,自引:0,他引:2
Nabila Azi Michel Gendreau Jean-Yves Potvin 《European Journal of Operational Research》2010,202(3):756-763
The vehicle routing problem with multiple use of vehicles is a variant of the classical vehicle routing problem. It arises when each vehicle performs several routes during the workday due to strict time limits on route duration (e.g., when perishable goods are transported). The routes are defined over customers with a revenue, a demand and a time window. Given a fixed-size fleet of vehicles, it might not be possible to serve all customers. Thus, the customers must be chosen based on their associated revenue minus the traveling cost to reach them. We introduce a branch-and-price approach to address this problem where lower bounds are computed by solving the linear programming relaxation of a set packing formulation, using column generation. The pricing subproblems are elementary shortest path problems with resource constraints. Computational results are reported on euclidean problems derived from well-known benchmark instances for the vehicle routing problem with time windows. 相似文献
33.
This paper reports on the forms of reasoning elicited as fourth grade students in a suburban district and sixth grade students in an urban district worked on similar tasks involving reasoning with the use of Cuisenaire rods. Analysis of the two data sets shows similarities in the reasoning used by both groups of students on specific tasks, and the tendency of a particular task to elicit numerous forms of reasoning in both groups of students. Attributes of that task and ways that those attributes can be replicated in other domains may have implications in the teaching of early reasoning. 相似文献
34.
For a space X, X2 denotes the collection of all non-empty closed sets of X with the Vietoris topology, and K(X) denotes the collection of all non-empty compact sets of X with the subspace topology of X2. The following are known:
- •
- ω2 is not normal, where ω denotes the discrete space of countably infinite cardinality.
- •
- For every non-zero ordinal γ with the usual order topology, K(γ) is normal iff whenever cf γ is uncountable.
- (1)
- ω2 is strongly zero-dimensional.
- (2)
- K(γ) is strongly zero-dimensional, for every non-zero ordinal γ.
35.
Nobuyuki Kemoto 《Topology and its Applications》2010,157(15):2446-2447
We correct the proof of Theorem 8 in “Normality and countable paracompactness of hyperspaces of ordinals” [Topology Appl. 154 (2007) 358-362]. 相似文献
36.
We study a filtered generalization of the operation of elementary modification of vector bundles. The generalization is motivated by applications to the degeneration theory of linear systems. 相似文献
37.
Benjamin Fine Olga G. Kharlampovich Alexei G. Myasnikov Vladimir N. Remeslennikov G. Rosenberger 《代数通讯》2013,41(8):3386-3394
We prove that the automorphism group of a finitely generated fully residually free group is tame. 相似文献
38.
The family of separating circles of two finite sets in the plane consists of all the circles that enclose the first set but exclude the second set. We prove some theoretical results on distances between families of circles, and properties about enclosure and intersection. Most of these results state that a property that involves one or more infinite families of circles can be verified by examining a finite subcollection of circles. As a result enclosure and intersection can be decided, and distances can be computed with simple geometric algorithms. Furthermore, the circles of the finite subcollections correspond to the vertices of a polytope in the parameter space of separating circles. A polytope of separating circle parameters is well-known computational geometry, but we prove some new properties and we introduce the concept of an elementary circular separation as a concise way to define such a polytope. 相似文献
39.
40.
E. Floriani R. Lima R. Vilela Mendes 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,46(2):295-302
In this paper, we examine the effects of the
gravitational field on the dynamical evolution of the cavity-field
entropy and the creation of the Schr?dinger-cat state in the
Jaynes-Cummings model. We consider a moving two-level atom
interacting with a single mode quantized cavity-field in the
presence of a classical homogeneous gravitational field. Based on
an
su(2) algebra, as the dynamical symmetry group of the model, we derive the reduced density operator of the cavity-field
which includes the effects of the atomic motion and the gravitational field. Also, we obtain the exact solution and the approximate
solution for the system-state vector, and examine the atomic dynamics. By considering the temporal evolution of the
cavity-field entropy as well as the dynamics of the Q-function of the cavity-field we study the effects of the gravitational
field on the generation of the Schr?dinger-cat states of the cavity-field by using the Q-function,
field entropy and approximate solution for the system-state vector. The results show that the
gravitational field destroys the generation of the Schr?dinger-cat state of the cavity-field. 相似文献