Stabilizing heteroatom‐centered 16‐vertex group 11 tetrahedral architectures: Bonding and structural considerations toward versatile endohedral species

2019 ◽  
Vol 119 (24) ◽  
Author(s):  
Franck Gam ◽  
Ramiro Arratia‐Pérez ◽  
Samia Kahlal ◽  
Jean‐Yves Saillard ◽  
Alvaro Muñoz‐Castro
Keyword(s):  
Vertex Group

On the Residual Finiteness of Polygonal Products of Nilpotent Groups

1992 ◽  
Vol 35 (3) ◽  
pp. 390-399 ◽  
Author(s):  
Goansu Kim ◽  
C. Y. Tang
Keyword(s):  
Nilpotent Groups ◽  
Vertex Group ◽  
Residual Finiteness ◽  
Finitely Generated ◽  
Residually Finite ◽  
Cyclic Subgroups ◽  
Isolated Subgroup ◽  
Torsion Free

AbstractIn general polygonal products of finitely generated torsion-free nilpotent groups amalgamating cyclic subgroups need not be residually finite. In this paper we prove that polygonal products of finitely generated torsion-free nilpotent groups amalgamating maximal cyclic subgroups such that the amalgamated cycles generate an isolated subgroup in the vertex group containing them, are residually finite. We also prove that, for finitely generated torsion-free nilpotent groups, if the subgroups generated by the amalgamated cycles have the same nilpotency classes as their respective vertex groups, then their polygonal product is residually finite.

scholarly journals Rigid cohomology of topological groupoids

1978 ◽  
Vol 26 (3) ◽  
pp. 277-301 ◽  
Author(s):  
K. A. MacKenzie
Keyword(s):  
Vector Bundles ◽  
Cohomology Theory ◽  
Unexpected Result ◽  
Vertex Group ◽  
Topological Groups ◽  
Locally Compact ◽  
Cohomology Space ◽  
Rigid Cohomology ◽  
Topological Groupoids

AbstractA cohomology theory for locally trivial, locally compact topological groupoids with coefficients in vector bundles is constructed, generalizing constructions of Hochschild and Mostow (1962) for topological groups and Higgins (1971) for discrete groupoids. It is calculated to be naturally isomorphic to the cohomology of the vertex groups, and is thus independent of the twistedness of the groupoid. The second cohomology space is accordingly realized as those “rigid” extensions which essentially arise from extensions of the vertex group; the cohomological machinery now yields the unexpected result that in fact all extensions, satisfying some natural weak conditions, are rigid.

Effects of POSS vertex group on structure, thermal and mechanical properties of PMMA/POSS hybrid materials

2016 ◽  
Vol 54 ◽  
pp. 214-222 ◽  
Author(s):  
Cesar H. Wanke ◽  
Denise Pozzo ◽  
Caroline Luvison ◽  
Israel Krindges ◽  
Cesar Aguzzoli ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Hybrid Materials ◽  
Vertex Group ◽  
Thermal And Mechanical Properties

THE COMBINATION THEOREM AND QUASICONVEXITY

2001 ◽  
Vol 11 (02) ◽  
pp. 185-216 ◽  
Author(s):  
ILYA KAPOVICH
Keyword(s):  
Fundamental Group ◽  
Isometric Embedding ◽  
Normal Forms ◽  
Vertex Group ◽  
Graph Of Groups

We show that if G is a fundamental group of a finite k-acylindrical graph of groups where every vertex group is word-hyperbolic and where every edge-monomorphism is a quasi-isometric embedding, then all the vertex groups are quasiconvex in G (the group G is word-hyperbolic by the Combination Theorem of M. Bestvina and M. Feighn). This allows one, in particular, to approximate the word metric on G by normal forms for this graph of groups.

On the vertex group of n-manifolds

1996 ◽  
Vol 62 (1) ◽  
Author(s):  
S�stenes Lins ◽  
Michele Mulazzani
Keyword(s):  
Vertex Group

Finding group Steiner trees in graphs with both vertex and edge weights

2021 ◽  
Vol 14 (7) ◽  
pp. 1137-1149
Author(s):  
Yahui Sun ◽  
Xiaokui Xiao ◽  
Bin Cui ◽  
Saman Halgamuge ◽  
Theodoros Lappas ◽  
...  
Keyword(s):  
Approximation Algorithm ◽  
Undirected Graph ◽  
State Of The Art ◽  
Steiner Trees ◽  
Programming Approach ◽  
Weighted Graphs ◽  
Vertex Group ◽  
Dynamic Programming Approach ◽  
Knowledge Graphs ◽  
Approximation Guarantee

Given an undirected graph and a number of vertex groups, the group Steiner trees problem is to find a tree such that (i) this tree contains at least one vertex in each vertex group; and (ii) the sum of vertex and edge weights in this tree is minimized. Solving this problem is useful in various scenarios, ranging from social networks to knowledge graphs. Most existing work focuses on solving this problem in vertex-unweighted graphs, and not enough work has been done to solve this problem in graphs with both vertex and edge weights. Here, we develop several algorithms to address this issue. Initially, we extend two algorithms from vertex-unweighted graphs to vertex- and edge-weighted graphs. The first one has no approximation guarantee, but often produces good solutions in practice. The second one has an approximation guarantee of |Γ| - 1, where |Γ| is the number of vertex groups. Since the extended (|Γ| - 1)-approximation algorithm is too slow when all vertex groups are large, we develop two new (|Γ| - 1)-approximation algorithms that overcome this weakness. Furthermore, by employing a dynamic programming approach, we develop another (|Γ| - h + 1)-approximation algorithm, where h is a parameter between 2 and |Γ|. Experiments show that, while no algorithm is the best in all cases, our algorithms considerably outperform the state of the art in many scenarios.

scholarly journals The A-T-menability of some graphs of groups with cyclic edge groups

2016 ◽  
Vol 163 (1) ◽  
pp. 145-159 ◽  
Author(s):  
MATHIEU CARETTE ◽  
DANIEL T. WISE ◽  
DANIEL J. WOODHOUSE
Keyword(s):  
Vertex Group ◽  
Graphs Of Groups

AbstractWe show that certain graphs of groups with cyclic edge groups are aTmenable. In particular, this holds when each vertex group is either virtually special or acts properly and semisimply on ℍn.

scholarly journals Decomposition of the vertex group of 3-manifolds

1992 ◽  
Vol 103 (1) ◽  
pp. 49-55
Author(s):  
Louis Kauffman ◽  
Sóstenes Lins
Keyword(s):  
Vertex Group

The Influence of Birth Order and Presentation on Intrauterine Growth of Twins

1993 ◽  
Vol 42 (2) ◽  
pp. 151-158 ◽  
Author(s):  
I. Blickstein ◽  
R. Namir ◽  
A. Weissman ◽  
Y. Diamant
Keyword(s):  
Birth Order ◽  
Growth Curves ◽  
Abdominal Circumference ◽  
Adaptive Mechanism ◽  
Vertex Group ◽  
Femur Length ◽  
Intrauterine Growth ◽  
Biparietal Diameter ◽  
Biometric Indices ◽  
Estimated Fetal Weight

AbstractIn order to evaluate the influence of birth order and fetal presentation on antenatal growth of twins we conducted a comparison of prospective measurements of five fetal biometric indices in 50 vertex-vertex and 47 vertex-breech twins. We compared (a) twin A to twin B in both groups; (b) the second and (c) the first twins of both groups. Both groups had similar maternal and neonatal characteristics. The growth curves of the twins were also very similar except for three significant (p<0.05) deviations: (a) Twin A of the vertex-vertex group, had larger femur length (FL) at 18-19 weeks, abdominal circumference (AC) and estimated fetal weight (EFW) at 29 weeks, and EFW measurements at 36 weeks, (b) Second breech twins, compared to their second vertex cohorts, had significantly smaller biparietal diameter (BPD), head circumference (HC) and FL at 18-19 weeks, BPD and HC at 29 weeks, and EFW at 37 weeks, (c) First twins of the vertex-breech group, as compared to first twins of the vertex-vertex group, had significantly smaller BPD and AC at 18-19 weeks, FL and AC at 21-22 and 29 weeks, FL at 31 weeks, and EFW at 27-28 and 36 weeks' gestation. We concluded that significantly different sonographic fetal indices may be measured at about 20 and 30 weeks' gestation, but not later. An adaptive mechanism attributed to fetal presentation is suggested to explain similar birthweights in spite of these antepartum differences.

scholarly journals RIGIDITY OF GRAPH PRODUCTS OF ABELIAN GROUPS

2008 ◽  
Vol 77 (2) ◽  
pp. 187-196 ◽  
Author(s):  
MAURICIO GUTIERREZ ◽  
ADAM PIGGOTT
Keyword(s):  
Abelian Group ◽  
Cyclic Group ◽  
Abelian Groups ◽  
Graph Products ◽  
Vertex Group ◽  
Graph Product ◽  
Finitely Generated ◽  
Product Decomposition ◽  
Unique Decomposition ◽  
Product Of Groups

AbstractWe show that if G is a group and G has a graph-product decomposition with finitely generated abelian vertex groups, then G has two canonical decompositions as a graph product of groups: a unique decomposition in which each vertex group is a directly indecomposable cyclic group, and a unique decomposition in which each vertex group is a finitely generated abelian group and the graph satisfies the T0 property. Our results build on results by Droms, Laurence and Radcliffe.

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