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21.
Luxing Yang Moez Draief Xiaofan Yang 《Mathematical Methods in the Applied Sciences》2017,40(5):1396-1413
The node‐based epidemic modeling is an effective approach to the understanding of the impact of the structure of the propagation network on the epidemics of electronic virus. In view of the heterogeneity of the propagation network, a heterogeneous node‐based SIRS model is proposed. Theoretical analysis shows that the maximum eigenvalue of a matrix related to the model determines whether viruses tend to extinction or persist. When viruses persist, the connectedness of the propagation network implies the existence and uniqueness of a viral equilibrium, and a set of sufficient conditions for the global stability of the viral equilibrium are given. Numerical examples verify the correctness of our results. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
22.
Based on the theory of exact boundary controllability of nodal profile for hyperbolic systems, the authors propose the concept of exact boundary controllability of partial nodal profile to expand the scope of applications. With the new concept, we can shorten the controllability time, save the number of controls, and increase the number of charged nodes with given nodal profiles. Furthermore, we introduce the concept of in-situ controlled node to deal with a new situation that one node can be charged and controlled simultaneously. The minimum number of boundary controls on the entire tree-like network is determined by using the concept of ‘degree of freedom of charged nodes’ introduced. And the concept of ‘control path’ is introduced to appropriately divide the network, so that we can determine the infimum of controllability time. General frameworks of constructive proof are given on a single interval, a star-like network, a chain-like network and a planar tree-like network for linear wave equation(s) with Dirichlet, Neumann, Robin and dissipative boundary conditions to establish a complete theory on the exact boundary controllability of partial nodal profile. 相似文献
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As a truly boundary-type meshless method, the hybrid boundary node method (HdBNM) does not require ‘boundary element mesh’, either for the purpose of interpolation of the solution variables or for the integration of ‘energy’. In this paper, the HdBNM is coupled with the finite element method (FEM) for predicting the mechanical behaviors of reinforced concrete. The steel bars are considered as body forces in the concrete. A bond model is presented to simulate the bond-slip between the concrete and steels using fictitious spring elements. The computational scale and cost for meshing can be further reduced. Numerical examples, in 2D and 3D cases, demonstrate the efficiency of the proposed approach. 相似文献
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In this survey we attempt to give a unified presentation of a variety of results on the lifting of valid inequalities, as
well as a standard procedure combining mixed integer rounding with lifting for the development of strong valid inequalities
for knapsack and single node flow sets. Our hope is that the latter can be used in practice to generate cutting planes for
mixed integer programs.
The survey contains essentially two parts. In the first we present lifting in a very general way, emphasizing superadditive
lifting which allows one to lift simultaneously different sets of variables. In the second, our procedure for generating strong
valid inequalities consists of reduction to a knapsack set with a single continuous variable, construction of a mixed integer
rounding inequality, and superadditive lifting. It is applied to several generalizations of the 0–1 single node flow set.
This paper appeared in 4OR, 1, 173–208 (2003).
The first author is supported by the FNRS as a chercheur qualifié. This paper presents research results of the Belgian Program on Interuniversity Poles of Attraction
initiated by the Belgian State, Prime Minister’s Office, Science Policy Programming. The scientific responsibility is assumed
by the authors. 相似文献
27.
The concept of super value nodes was established to allow dynamic programming to be performed within the theory of influence diagrams and to reduce the computational complexity in solving problems by means of influence diagrams. This paper is focused on how influence diagrams with super value nodes are affected by the presence of imprecise information. We analyze how to reduce the complexity when evaluating an influence diagram in this framework by modelling these kinds of nodes and random magnitudes in terms of fuzzy random variables. Finally, an applied example of the theoretical results is developed. 相似文献
28.
Simply generated families of trees are described by the equation T(z) = ϕ(T(z)) for their generating function. If a tree has n nodes, we say that it is increasing if each node has a label ∈ { 1,…,n}, no label occurs twice, and whenever we proceed from the root to a leaf, the labels are increasing. This leads to the concept of simple families of increasing trees. Three such families are especially important: recursive trees, heap ordered trees, and binary increasing trees. They belong to the subclass of very simple families of increasing trees, which can be characterized in 3 different ways. This paper contains results about these families as well as about polynomial families (the function ϕ(u) is just a polynomial). The random variable of interest is the level of the node (labelled) j, in random trees of size n ≥ j. For very simple families, this is independent of n, and the limiting distribution is Gaussian. For polynomial families, we can prove this as well for j,n → ∞ such that n − j is fixed. Additional results are also given. These results follow from the study of certain trivariate generating functions and Hwang's quasi power theorem. They unify and extend earlier results by Devroye, Mahmoud, and others. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007 相似文献
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