11,396 research outputs found
Properties of Catlin's reduced graphs and supereulerian graphs
A graph is called collapsible if for every even subset ,
there is a spanning connected subgraph of such that is the set of
vertices of odd degree in . A graph is the reduction of if it is
obtained from by contracting all the nontrivial collapsible subgraphs. A
graph is reduced if it has no nontrivial collapsible subgraphs. In this paper,
we first prove a few results on the properties of reduced graphs. As an
application, for 3-edge-connected graphs of order with for any where are given, we show how such graphs
change if they have no spanning Eulerian subgraphs when is increased from
to 10 then to
An Energy Sharing Game with Generalized Demand Bidding: Model and Properties
This paper proposes a novel energy sharing mechanism for prosumers who can
produce and consume. Different from most existing works, the role of individual
prosumer as a seller or buyer in our model is endogenously determined. Several
desirable properties of the proposed mechanism are proved based on a
generalized game-theoretic model. We show that the Nash equilibrium exists and
is the unique solution of an equivalent convex optimization problem. The
sharing price at the Nash equilibrium equals to the average marginal disutility
of all prosumers. We also prove that every prosumer has the incentive to
participate in the sharing market, and prosumers' total cost decreases with
increasing absolute value of price sensitivity. Furthermore, the Nash
equilibrium approaches the social optimal as the number of prosumers grows, and
competition can improve social welfare.Comment: 16 pages, 7 figure
Common wave behavior for mergers and acquisitions in OECD countries? a unique analysis using new Markov switching panel model approach
This paper investigates whether or not there is co-waved merger and acquisition (M&A) activity in 26 OECD countries. We apply the Markov Switching model to panel data (MSP hereafter), an approach which has not previously been attempted. Two distinct regimes are recognized in emerge from M&A data: the wave merger regime and normal merger regime. Our MSP captures the co-wave pattern of the sample countries and has a much better fit than either the univariate Markov Switching model or the conventional linear panel model.
Gapped spin liquid with -topological order for kagome Heisenberg model
We apply symmetric tensor network state (TNS) to study the nearest neighbor
spin-1/2 antiferromagnetic Heisenberg model on Kagome lattice. Our method keeps
track of the global and gauge symmetries in TNS update procedure and in tensor
renormalization group (TRG) calculation. We also introduce a very sensitive
probe for the gap of the ground state -- the modular matrices, which can also
determine the topological order if the ground state is gapped. We find that the
ground state of Heisenberg model on Kagome lattice is a gapped spin liquid with
the -topological order (or toric code type), which has a long
correlation length unit cell length. We justify that the TRG
method can handle very large systems with over thousands of spins. Such a long
explains the gapless behaviors observed in simulations on smaller systems
with less than 300 spins or shorter than 10 unit cell length. We also discuss
experimental implications of the topological excitations encoded in our
symmetric tensors.Comment: 10 pages, 7 figure
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