Power domination in planar graphs with small diameter

The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known vertex covering and dominating set problems in graph theory. In this paper, it was shown that the power domination number of an outerplanar graph with the diameter two or a 2-connected outerplanar graph with the diameter three is precisely one. Upper bounds on the power domination number for a general planar graph with the diameter two or three were determined as an immediate consequences of results proven by Dorfling, et al. Also, an infinite family of outerplanar graphs with the diameter four having arbitrarily large power domination numbers were given.

Generic Modeling and Control Framework for Power Systems Dominated by Power Converters Connected Through a Passive Transmission and Distribution Grid

In this paper,a compact mathematical model having an elegant structure,together with a generic control framework,are proposed for generic power systems dominated by power converters that are interconnected through a passive transmission and distribution(T&D)grid,by adopting the port-Hamiltonian(pH)systems theory and the fundamental circuit theory.The models of generic T&D lines are developed and then the model of a generic T&D grid is established.With the proposed control framework,the controlled converters are proven to be passive and Input-to-State Stable(ISS).The compact mathematical model is scalable and can be applied to power systems with multiple power electronic converters with generic passive controllers,passive local loads,and different types of passive T&D lines connected in a meshed configuration without self-loops,so it is very generic.Moreover,the resulting power system is proven to be ISS as well.The analysis is carried out without assumptions on constant frequency/voltage,constant loads,and/or lossless networks,except the need of passivity for all parts involved,and without using the Clarke/Park transformations or the graph theory.To simplify the presentation,three-phase balanced systems are adopted but the results can be easily adapted for single-phase or unbalanced three-phase systems.

Constructive characterizations of(γp,γ)-and(γp,γpr)-trees

Let G = （V, E） be a graph without isolated vertices. A set S lohtain in V is a domination set of G if every vertex in V - S is adjacent to a vertex in S, that is N[S] = V. The domination number of G, denoted by γ（G）, is the minimum cardinality of a domination set of G. A set S lohtain in V is a paired-domination set of G if S is a domination set of G and the induced subgraph G[S] has a perfect matching. The paired-domination number, denoted by γpr（G）, is defined to be the minimum cardinality of a paired-domination set S in G. A subset S lohtain in V is a power domination set of G if all vertices of V can be observed recursively by the following rules： （i） all vertices in N[S] are observed initially, and （ii） if an observed vertex u has all neighbors observed except one neighbor v, then v is observed （by u）. The power domination number, denoted by γp（G）, is the minimum cardinality of a power domination set of G. In this paper, the constructive characterizations for trees with γp=γ and γpr = γp are provided respectively.

Fresh-Keeping Decision and Coordination of Fresh Agricultural Product Supply Chain Considering Carbon Cap-and-Trade under Different Dominance

In the context of low carbon,this paper discussed the impact of the carbon cap-and-trade policy on the fresh-keeping decision-making of two-echelon fresh agricultural product supply chains under different dominance,and designed cost-sharing contracts to coordinate the supply chain of fresh agricultural products dominated by suppliers and retailers respectively.The results showed that:dominance has no effect on the fresh-keeping decision and total revenue of fresh agricultural product supply chain,but it affects the internal income distribution,and dominance does not always bring more benefits;the implementation of carbon cap-and-trade reduces the fresh-keeping decision-making of fresh agricultural products supply chain and reduces the free-rider income of followers;the role of higher carbon trading price is twofold,which not only brings about the speculation of leading enterprises,but also promotes the application of low-carbon technologies;consumers’high preference for freshness,low-cost and high-efficiency low-carbon technology are all conducive to improving the fresh-keeping efforts and benefits of the supply chain;cost-sharing contracts can coordinate the supply chain of fresh agricultural products.

Dynamic characteristics of bubbling fluidization through recurrence rate analysis of pressure fluctuations

Pressure fluctuations signals of a lab-scale fiuidized bed （15 cm inner diameter and 2 m height） at different superficial gas velocities were measured. Recurrence plot （RP） and recurrence rate （RR）, and the simplest variable of recurrence quantification analysis （RQA） were used to analyze the pressure signals. Different patterns observed in RP reflect different dynamic behavior of the system under study. It was also found that the variance of RR （a2R） Could reveal the peak dominant frequencies （PDF） of different dynamic systems： completely periodic, completely stochastic, Lorenz system, and fluidized bed. The results were compared with power spectral density. Additionally, the diagram of σ^2RR provides a new technique for prediction of transition velocity from bubbling to turbulent fluidization regime.