ON THE MINIMUM WEIGHT OF A 3-CONNECTED 1-PLANAR GRAPH

Zai Ping Lu; Ning Song

doi:10.4134/bkms.b160296

A note on the 2-rainbow bondage numbers in graphs

Asian-European Journal of Mathematics ◽

10.1142/s1793557116500133 ◽

2016 ◽

Vol 09 (01) ◽

pp. 1650013

Author(s):

L. Asgharsharghi ◽

S. M. Sheikholeslami ◽

L. Volkmann

Keyword(s):

Planar Graph ◽

Maximum Degree ◽

Minimum Weight ◽

Domination Number ◽

Minimum Cardinality ◽

Bondage Number ◽

Rainbow Domination ◽

Vertex Set ◽

Number Formula ◽

Appl Math

A 2-rainbow dominating function (2RDF) of a graph [Formula: see text] is a function [Formula: see text] from the vertex set [Formula: see text] to the set of all subsets of the set [Formula: see text] such that for any vertex [Formula: see text] with [Formula: see text], the condition [Formula: see text] is fulfilled. The weight of a 2RDF [Formula: see text] is the value [Formula: see text]. The [Formula: see text]-rainbow domination number of a graph [Formula: see text], denoted by [Formula: see text], is the minimum weight of a 2RDF of [Formula: see text]. The rainbow bondage number [Formula: see text] of a graph [Formula: see text] with maximum degree at least two is the minimum cardinality of all sets [Formula: see text] for which [Formula: see text]. Dehgardi, Sheikholeslami and Volkmann, [The [Formula: see text]-rainbow bondage number of a graph, Discrete Appl. Math. 174 (2014) 133–139] proved that the rainbow bondage number of a planar graph does not exceed 15. In this paper, we generalize their result for graphs which admit a [Formula: see text]-cell embedding on a surface with non-negative Euler characteristic.

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Computational Micrograph Registration with Sieve Processes

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100164660 ◽

1996 ◽

Vol 54 ◽

pp. 440-441

Author(s):

P.J. Phillips ◽

J. Huang ◽

S. M. Dunn

Keyword(s):

Planar Graph ◽

Efficient Algorithm ◽

Spatial Organization ◽

Spatial Arrangement ◽

Stereo Image ◽

Image Model ◽

Geometric Invariants ◽

Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

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Further Studies on the Mechanisms for the Antithrombotic Effects of Sulfated Polysaccharides in Rabbits

Thrombosis and Haemostasis ◽

10.1055/s-0038-1647027 ◽

1988 ◽

Vol 60 (02) ◽

pp. 188-192 ◽

Cited By ~ 15

Author(s):

F A Ofosu ◽

F Fernandez ◽

N Anvari ◽

C Caranobe ◽

F Dol ◽

...

Keyword(s):

Antithrombin Iii ◽

Ex Vivo ◽

Thrombus Formation ◽

Minimum Weight ◽

Sulfated Polysaccharides ◽

Pentosan Polysulfate ◽

Heparin Cofactor Ii ◽

Thrombin Inhibition ◽

The Relationship ◽

Prothrombin Activation

SummaryA recent study (Fernandez et al., Thromb. Haemostas. 1987; 57: 286-93) demonstrated that when rabbits were injected with the minimum weight of a variety of glycosaminoglycans required to inhibit tissue factor-induced thrombus formation by —80%, exogenous thrombin was inactivated —twice as fast in the post-treatment plasmas as the pre-treatment plasmas. In this study, we investigated the relationship between inhibition of thrombus formation and the extent of thrombin inhibition ex vivo. We also investigated the relationship between inhibition of thrombus formation and inhibition of prothrombin activation ex vivo. Four sulfated polysaccharides (SPS) which influence coagulation in a variety of ways were used in this study. Unfractionated heparin and the fraction of heparin with high affinity to antithrombin III potentiate the antiproteinase activity of antithrombin III. Pentosan polysulfate potentiates the activity of heparin cofactor II. At less than 10 pg/ml of plasma, all three SPS also inhibit intrinsic prothrombin activation. The fourth agent, dermatan sulfate, potentiates the activity of heparin cofactor II but fails to inhibit intrinsic prothrombin activation even at concentrations which exceed 60 pg/ml of plasma. Inhibition of thrombus formation by each sulfated polysaccharides was linearly related to the extent of thrombin inhibition achieved ex vivo. These observations confirm the utility of catalysis of thrombin inhibition as an index for assessing antithrombotic potential of glycosaminoglycans and other sulfated polysaccharides in rabbits. With the exception of pentosan polysulfate, there was no clear relationship between inhibition of thrombus formation and inhibition of prothrombin activation ex vivo.

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CARTECH Ti-3Al-8V-6Cr-4Mo-4Zr (BETA C)

Alloy Digest ◽

10.31399/asm.ad.ti0172 ◽

2020 ◽

Vol 69 (11) ◽

Keyword(s):

Corrosion Resistance ◽

Minimum Weight ◽

High Strength ◽

Heat Treating ◽

Beta Alloy ◽

Heat Treated ◽

Technology Corporation ◽

Carpenter Technology Corporation ◽

Metastable Beta ◽

Good Workability

Abstract CarTech Ti-3Al-8V-6Cr-4Mo-4Zr, also known as Ti-3-8-6-4-4 and Beta C, is a metastable beta alloy used in the solution heat treated or solution heat treated and aged condition. It is appropriate for applications where very high strength, minimum weight, and corrosion resistance are important. Ti-3Al-8V-6Cr-4Mo-4Zr has gained in popularity among beta alloys because it is easier to melt and process, exhibiting low segregation, good workability, and good heat-treating properties. This datasheet provides information on composition, physical properties, elasticity, and tensile properties. It also includes information on corrosion resistance as well as forming, heat treating, machining, and joining. Filing Code: Ti-172. Producer or source: Carpenter Technology Corporation.

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The identification of minimum-weight sound packages

Noise Control Engineering Journal ◽

10.3397/1/376644 ◽

2018 ◽

Vol 66 (6) ◽

pp. 523-540 ◽

Cited By ~ 1

Author(s):

Hyunjun Shin ◽

J. Stuart Bolton

Keyword(s):

Minimum Weight

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Quadruple Roman Domination in Trees

Symmetry ◽

10.3390/sym13081318 ◽

2021 ◽

Vol 13 (8) ◽

pp. 1318

Author(s):

Zheng Kou ◽

Saeed Kosari ◽

Guoliang Hao ◽

Jafar Amjadi ◽

Nesa Khalili

Keyword(s):

Open Neighborhood ◽

Minimum Weight ◽

Domination Number ◽

Theoretical Computer Science ◽

Upper And Lower Bounds ◽

Discrete Mathematics ◽

Roman Domination ◽

Roman Domination Number ◽

Vertex Set ◽

Roman Dominating Function

This paper is devoted to the study of the quadruple Roman domination in trees, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. For any positive integer k, a [k]-Roman dominating function ([k]-RDF) of a simple graph G is a function from the vertex set V of G to the set {0,1,2,…,k+1} if for any vertex u∈V with f(u)<k, ∑x∈N(u)∪{u}f(x)≥|{x∈N(u):f(x)≥1}|+k, where N(u) is the open neighborhood of u. The weight of a [k]-RDF is the value Σv∈Vf(v). The minimum weight of a [k]-RDF is called the [k]-Roman domination number γ[kR](G) of G. In this paper, we establish sharp upper and lower bounds on γ[4R](T) for nontrivial trees T and characterize extremal trees.

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