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### Planar Branch Decompositions II: The Cycle Method

Illya V. Hicks
2005 INFORMS journal on computing
This method, called the cycle method, is an improvement on the algorithm by using a "divide-and-conquer" approach.  ...  The first practical implementation of an algorithm of Seymour and Thomas for computing optimal branch decompositions of planar hypergraphs is presented.  ...  Applegate's code was used for earlier versions of the methods, while Boyer's code was used for the recent versions of the methods.  ...

### Near-Linear Time Constant-Factor Approximation Algorithm for Branch-Decomposition of Planar Graphs [article]

Qian-Ping Gu, Gengchun Xu
2016 arXiv   pre-print
We give an algorithm which for an input planar graph G of n vertices and integer k, in {O(n^3n),O(nk^2)} time either constructs a branch-decomposition of G with width at most (2+δ)k, δ>0 is a constant,  ...  For a planar graph G and k=bw(G), a branch-decomposition of width at most (2+δ)k and a g×g/2 cylinder/grid minor with g=k/β, β>2 is constant, can be computed by our algorithm in {O(n^3n k),O(nk^2 k)} time  ...  If a branch-decomposition of G|A Z is found for every A Z ∈ A, the algorithm constructs a branch-decomposition of G with width at most k + 2h from the branch-decomposition of G|A and those of G|A Z by  ...

### Treewidth computations II. Lower bounds

Hans L. Bodlaender, Arie M.C.A. Koster
2011 Information and Computation
There are preprocessing rules that apply only when a large enough lower bound on the treewidth of the graph is known.  ...  Lower bounds give indications of the quality of treewidth upper bounds and upper bound algorithms. • Better lower bounds can make preprocessing more effective.  ...  We assume that the reader is familiar with standard graph notions like degree, path, cycle, clique, planarity, cf. [19, 45] .  ...

### Character decomposition of Potts model partition functions, II: Toroidal geometry

Jean-François Richard, Jesper Lykke Jacobsen
2006 Nuclear Physics B
We develop an operational method of determining the amplitudes of the eigenvalues as well as some of their degeneracies.  ...  The elementary quantities in this decomposition are characters K_l,D labelled by a number of bridges l=0,1,...,L and an irreducible representation D of the symmetric group S_l.  ...  The authors are grateful to P. Zinn-Justin and J.-B. Zuber for some useful discussions. JLJ further thanks the members of the SPhT, where part of this work was done, for their kind hospitality.  ...

### Room-Temperature Magnetic Liquid Complexes of 2-Hexyldecanoato Ligand with Cu(II), Ni(II) and Co(II) Ions

2014 Asian Journal of Chemistry
Complexes 1-3 were paramagnetic with weak antiferromagnetic interactions between the two M(II) centres, while 4 has a significantly stronger antiferromagnetic interaction.  ...  reaction of sodium 2-hexyldecanoate (NaL) with the corresponding MCl2 (M = Cu, Ni or Co).  ...  ACKNOWLEDGEMENTS This work was funded by the Fundamental Research Grant Scheme from Malaysia Ministry of Higher Education (FP008-2011A) and the Universiti Malaya High Impact Research Grant (UM.C/625/1/  ...

### Enhancement of smectic C mesophase stability by using branched alkyl chains in the auxiliary ligands of luminescent Pt(II) and Pd(II) complexes

Monica Iliş, Marin Micutz, Florea Dumitraşcu, Iuliana Pasuk, Yann Molard, Thierry Roisnel, Viorel Cîrcu
2014 Polyhedron
We found that the introduction of branched alkoxy terminal groups lead to lower transition temperatures and stabilisation of the SmC phase in both Pd(II) and Pt(II) complexes.  ...  These new metallomesogens display either a monotropic SmC phase or both SmA and SmC phases depending on the number of alkoxy groups attached to the imine ligand, alkyl chain length or the use of branched  ...  Acknowledgments This work was supported by a grant of the Romanian Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0384.  ...

### Optimal Scheduling of Multicluster Tools With Constant Robot Moving Times, Part II: Tree-Like Topology Configurations

Wai Kin Victor Chan, Shengwei Ding, Jingang Yi, Dezhen Song
2011 IEEE Transactions on Automation Science and Engineering
The decomposition and optimality conditions for the robot pull schedule are also illustrated by Monte Carlo simulation for the industrial example.  ...  We demonstrate the application of the algorithms and analyses using a chemical-mechanical planarization polisher example. Fig. 1 . A schematic of a ten-cluster tool (a tree-like topology).  ...  We also present sufficient conditions under which the decomposition method proposed in [2] is valid and the robot pull scheduling strategy [1] - [4] , a widely used scheduling strategy in production  ...

### Separator-Based Sparsification II: Edge and Vertex Connectivity

David Eppstein, Zvi Galil, Giuseppe F. Italiano, Thomas H. Spencer
1998 SIAM journal on computing (Print)
We consider the problem of maintaining a dynamic planar graph subject to edge insertions and edge deletions that preserve planarity but that can change the embedding.  ...  All of the data structures handle insertions that keep the graph planar without regard to any particular embedding of the graph.  ...  We are deeply indebted to the anonymous referees, whose thorough reading of the paper lead to a substantial improvement in its presentation.  ...

### 1,2-polybutadiene complexes withd8 pseudo-square-planar transition-metal salts based on nickel(II), palladium(II), and platinum(II)

Laurence A. Belfiore, Pronab K. Das
2004 Journal of Polymer Science Part B: Polymer Physics
Annealing was performed below the 220 °C decomposition temperature of the undi- luted low-molecular-weight platinum(II) complex.  ...  The _ chemically crosslinked network is, most likely, hyper- branched with a high concentration of loops and entanglements: 1.  ...

### Microwave Synthesis, Spectral, Thermal and Antimicrobial Studies of Some Ni(II) and Cu(II) Schiff Base Complexes

A. P. Mishra, Neha Sharma, Rajendra K. Jain
2013 Open Journal of Synthesis Theory and Applications
The thermal behavior of metal complexes shows that the hydrated complexes loses water molecules of hydration in the first step; followed by decomposition of ligand molecules in the subsequent steps.  ...  The 1:1 or 1:2 metal complexes have been prepared by interacting these Schiff bases with metal ions viz. Ni(II), Cu(II).  ...  Thanks are also due to the Head, Department of Chemistry, Botany and Physics, Dr. Hari Singh Gour University, Sagar (M.P.) for providing Laboratory facilities.  ...

### Self-reconfiguration planning for a class of modular robots

Arancha Casal, Mark H. Yim, Gerard T. McKee, Paul S. Schenker
1999 Sensor Fusion and Decentralized Control in Robotic Systems II
Basic reconfiguration operations between the substructures in the set are precomputed, optimized and stored in a lookup table.  ...  The entire reconfiguration then consists of an ordered series of simple, precomputed sub-reconfigurations happening locally among the substructures.  ...  The topological space covered by the method is that of planar graphs (a subset of 1-dimensional combinatorial topology, see Section 3.3).  ...

### An annotated bibliography of GRASP-Part II: Applications

Paola Festa, Mauricio G. C. Resende
2009 International Transactions in Operational Research
Since 1989, numerous papers on the basic aspects of GRASP, as well as enhancements to the basic metaheuristic have appeared in the literature.  ...  This is the second of two papers with an annotated bibliography of the GRASP literature from 1989 to 2008. In the companion paper, algorithmic aspects of GRASP are surveyed.  ...  Both methods are based on swapping parts of sequence of flight legs assigned to an aircraft (rotation cycle) between two randomly chosen aircrafts.  ...

### A support theorem for Hilbert schemes of planar curves, II [article]

Luca Migliorini, Vivek Shende, Filippo Viviani
2018 arXiv   pre-print
We study the cohomology of Jacobians and Hilbert schemes of points on reduced and locally planar curves, which are however allowed to be singular and reducible.  ...  We show that the cohomologies of all Hilbert schemes of all subcurves are encoded in the cohomologies of the fine compactified Jacobians of connected subcurves, via the perverse Leray filtration.  ...  The set Λ is the set of branches of R, i.e. minimal prime ideals of R, and we set λ :" 7Λ. The normalizationR of R is isomorphic toR » ś aPΛ krrT a ss, where T a is a parameter on the a-th branch.  ...

### A Process Decomposition Technique for Distributed Workflow Management [chapter]

Giacomo Piccinelli
1999 Distributed Applications and Interoperable Systems II
In this paper, we propose a process decomposition technique for workflow processes. Starting from a generic workflow definition, we derive role-specific projections of the processes involved.  ...  Projections can be distributed for execution on distinct process engines, and the network of projections reproduces the semantics of the original workflow process.  ...  From the blackboard model we take the planar distribution of the items in that space.  ...

### Tropical curves in abelian surfaces II: enumeration of curves in linear systems [article]

Thomas Blomme
2022 arXiv   pre-print
To do this, we relate the linear system defined by a complex curve to certain integrals of 1-forms over cycles in the curve.  ...  We then give an expression for the tropical multiplicity provided by the correspondence theorem, and prove the invariance for the associated refined multiplicity, thus introducing refined invariants of  ...  A planar tropical curve is irreducible if it cannot be written as the union of two planar tropical curves.  ...
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