231,461 research outputs found
Small-World Network Effect in Competing Glauber- and Kawasaki-type Dynamics
In this article, we investigate the competing Glauber-type and Kawasaki-type
dynamics with small-world network (SWN) effect, in the framework of the
Gaussian model. The Glauber-type single-spin transition mechanism with
probability p simulates the contact of the system with a heat bath and the
Kawasaki-type dynamics with probability 1-p simulates an external energy flux.
Two different types of SWN effect are studied, one with the total number of
links increased and the other with it conserved. The competition of the
dynamics leads to an interesting self-organization process that can be
characterized by a phase diagram with two identifiable temperatures. By
studying the modification of the phase diagrams, the SWN effect on the two
dynamics is analyzed. For the Glauber-type dynamics, more important is the
altered average coordination number while the Kawasaki-type dynamics is
enhanced by the long range spin interaction and redistribution.Comment: 18 pages, 1 figure. Accepted for publication in "The European
Physical Journal B (EPJB)
Parametric matroid of rough set
Rough set is mainly concerned with the approximations of objects through an
equivalence relation on a universe. Matroid is a combinatorial generalization
of linear independence in vector spaces. In this paper, we define a parametric
set family, with any subset of a universe as its parameter, to connect rough
sets and matroids. On the one hand, for a universe and an equivalence relation
on the universe, a parametric set family is defined through the lower
approximation operator. This parametric set family is proved to satisfy the
independent set axiom of matroids, therefore it can generate a matroid, called
a parametric matroid of the rough set. Three equivalent representations of the
parametric set family are obtained. Moreover, the parametric matroid of the
rough set is proved to be the direct sum of a partition-circuit matroid and a
free matroid. On the other hand, since partition-circuit matroids were well
studied through the lower approximation number, we use it to investigate the
parametric matroid of the rough set. Several characteristics of the parametric
matroid of the rough set, such as independent sets, bases, circuits, the rank
function and the closure operator, are expressed by the lower approximation
number.Comment: 15 page
Asymptotic Behavior of a Viscous Liquid-Gas Model with Mass-Dependent Viscosity and Vacuum
In this paper, we consider two classes of free boundary value problems of a
viscous two-phase liquid-gas model relevant to the flow in wells and pipelines
with mass-dependent viscosity coefficient. The liquid is treated as an
incompressible fluid whereas the gas is assumed to be polytropic. We obtain the
asymptotic behavior and decay rates of the mass functions ,\
when the initial masses are assumed to be connected to vacuum both
discontinuously and continuously, which improves the corresponding result about
Navier-Stokes equations in \cite{Zhu}.Comment: 24 page
Covering matroid
In this paper, we propose a new type of matroids, namely covering matroids,
and investigate the connections with the second type of covering-based rough
sets and some existing special matroids. Firstly, as an extension of
partitions, coverings are more natural combinatorial objects and can sometimes
be more efficient to deal with problems in the real world. Through extending
partitions to coverings, we propose a new type of matroids called covering
matroids and prove them to be an extension of partition matroids. Secondly,
since some researchers have successfully applied partition matroids to
classical rough sets, we study the relationships between covering matroids and
covering-based rough sets which are an extension of classical rough sets.
Thirdly, in matroid theory, there are many special matroids, such as
transversal matroids, partition matroids, 2-circuit matroid and
partition-circuit matroids. The relationships among several special matroids
and covering matroids are studied.Comment: 15 page
- …