scholarly journals A rank formula for HNN-extension with finite edge group

2021 ◽  
Vol 1850 (1) ◽  
pp. 012062
Author(s):  
Kamonthep Mecam ◽  
Monalisa Bergmoser
Keyword(s):  
Edge Group ◽  
Hnn Extension

New π -Donor Molecules with a Pyrazino Group and their Conducting Salts

2001 ◽  
Vol 56 (3) ◽  
pp. 297-300 ◽  
Author(s):  
G. C. Papavassiliou ◽  
Yohji Misaki ◽  
Kazuko Takahashi ◽  
Jun-ichi Yamada ◽  
G. A. Mousdis ◽  
...  
Keyword(s):  
Charge Transfer ◽  
Cation Radical ◽  
Charge Transfer Complexes ◽  
Edge Group

Abstract The preparation and characterization of some π-donors with a pyrazine-edge-group as well as with tetrathiapentalene-, thiophene-, and dihydrobenzoselenophene-spacer-groups are de­ scribed. Some of these donors give conducting charge transfer complexes with TCNQ and/or cation radical salts with I3-, BF4-and PF6-as counter anions.

scholarly journals A correspondence between a class of monoids and self-similar group actions II

2015 ◽  
Vol 25 (04) ◽  
pp. 633-668
Author(s):  
Mark V. Lawson ◽  
Alistair R. Wallis
Keyword(s):  
Group Actions ◽  
Similar Group ◽  
Universal Group ◽  
Length Functions ◽  
Group Of Units ◽  
Hnn Extensions ◽  
Hnn Extension ◽  
Self Similar ◽  
Cancellative Monoids

The first author showed in a previous paper that there is a correspondence between self-similar group actions and a class of left cancellative monoids called left Rees monoids. These monoids can be constructed either directly from the action using Zappa–Szép products, a construction that ultimately goes back to Perrot, or as left cancellative tensor monoids from the covering bimodule, utilizing a construction due to Nekrashevych. In this paper, we generalize the tensor monoid construction to arbitrary bimodules. We call the monoids that arise in this way Levi monoids and show that they are precisely the equidivisible monoids equipped with length functions. Left Rees monoids are then just the left cancellative Levi monoids. We single out the class of irreducible Levi monoids and prove that they are determined by an isomorphism between two divisors of its group of units. The irreducible Rees monoids are thereby shown to be determined by a partial automorphism of their group of units; this result turns out to be significant since it connects irreducible Rees monoids directly with HNN extensions. In fact, the universal group of an irreducible Rees monoid is an HNN extension of the group of units by a single stable letter and every such HNN extension arises in this way.

scholarly journals EUS-directed transgastric endoscopic retrograde cholangiopancreatography versus laparoscopic-assisted ERCP versus deep enteroscopy-assisted ERCP for patients with RYGB

2020 ◽  
Vol 08 (07) ◽  
pp. E877-E882 ◽  
Author(s):  
Gursimran S. Kochhar ◽  
Nabeeha Mohy-ud-din ◽  
Abhinav Grover ◽  
Neil Carleton ◽  
Abhijit Kulkarni ◽  
...  
Keyword(s):  
Endoscopic Retrograde Cholangiopancreatography ◽  
Retrospective Chart Review ◽  
Complication Rates ◽  
Success Rates ◽  
Technical Success ◽  
Endoscopic Retrograde ◽  
Technical Success Rate ◽  
Edge Group ◽  
History Of ◽  
Laparoscopic Assisted

Abstract Background and study aims Endoscopic ultrasound-directed transgastric endoscopic retrograde cholangiopancreatography (ERCP) (EDGE) is a novel technique for managing pancreaticobiliary diseases in patients with a history of Roux-en-Y Gastric Bypass (RYGB). It has shown to have high technical success rates and fewer adverse events as compared to laparoscopic-assisted ERCP (LA-ERCP). We compared the technical success and clinical outcomes of EDGE vs. LA-ERCP vs. E-ERCP. Patients and methods A retrospective chart review was performed for 56 patients, of whom 18 underwent LA-ERCP, 12 underwent E-ERCP, and 26 had EDGE, and a comparison of technical success and complication rates was done. Results Baseline demographic characteristics of patients undergoing these procedures, including age and gender, were comparable. The technical success rate for patients in the EDGE group were 100 % (n = 26), compared with 94 % (n = 17) and 75 % (n = 9) in the LA-ERCP and E-ERCP groups (P = 0.02). In the EDGE group, 8 % of patients (n = 2) had bleeding, and 4 % of patients (n = 1) had lumen-apposing metal stent migration occur during the procedure. In the LA-ERCP group 6 % (n = 1) of patient had bleeding, 6 % (n = 1) post-ERCP pancreatitis and 6 % (n = 1) were diagnosed with an intra-abdominal infection post-procedure. Time to complete the EDGE procedure was significantly shorter at 79 ± 31 mins, compared with 158 ± 50 mins for LA-ERCP and 102 ± 43 mins for E-ERCP (P < 0.001). Conclusion EDGE is a novel procedure with short procedure times and an effective alternative to LA-ERCP and E-ERCP in management of pancreaticobiliary diseases in patients with a history of RYGB.

scholarly journals Combinatorics of Edge Symmetry: Chiral and Achiral Edge Colorings of Icosahedral Giant Fullerenes: C80, C180, and C240

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1308
Author(s):  
Krishnan Balasubramanian
Keyword(s):  
Equivalence Classes ◽  
Group Symmetry ◽  
Irreducible Representations ◽  
Inversion Method ◽  
High Symmetry ◽  
Edge Colorings ◽  
Edge Group ◽  
Resonance Energies ◽  
Conjugated Circuits ◽  
Cycle Indices

We develop the combinatorics of edge symmetry and edge colorings under the action of the edge group for icosahedral giant fullerenes from C80 to C240. We use computational symmetry techniques that employ Sheehan’s modification of Pόlya’s theorem and the Möbius inversion method together with generalized character cycle indices. These techniques are applied to generate edge group symmetry comprised of induced edge permutations and thus colorings of giant fullerenes under the edge symmetry action for all irreducible representations. We primarily consider high-symmetry icosahedral fullerenes such as C80 with a chamfered dodecahedron structure, icosahedral C180, and C240 with a chamfered truncated icosahedron geometry. These symmetry-based combinatorial techniques enumerate both achiral and chiral edge colorings of such giant fullerenes with or without constraints. Our computed results show that there are several equivalence classes of edge colorings for giant fullerenes, most of which are chiral. The techniques can be applied to superaromaticity, sextet polynomials, the rapid computation of conjugated circuits and resonance energies, chirality measures, etc., through the enumeration of equivalence classes of edge colorings.

On the profinite topology on solvable groups

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Khadijeh Alibabaei
Keyword(s):  
Abelian Group ◽  
Wreath Product ◽  
Solvable Group ◽  
Solvable Groups ◽  
Polycyclic Group ◽  
Finitely Generated ◽  
Metabelian Groups ◽  
Finitely Generated Group ◽  
Hnn Extension ◽  
Profinite Topology

AbstractWe show that the wreath product of a finitely generated abelian group with a polycyclic group is a LERF group. This theorem yields as a corollary that finitely generated free metabelian groups are LERF, a result due to Coulbois. We also show that a free solvable group of class 3 and rank at least 2 does not contain a strictly ascending HNN-extension of a finitely generated group. Since such groups are known not to be LERF, this settles, in the negative, a question of J. O. Button.

scholarly journals Fracture toughness of zirconia ceramic crowns made by feather-edge tooth preparation design

2012 ◽  
Vol 69 (7) ◽  
pp. 562-568 ◽  
Author(s):  
Nemanja Mirkovic ◽  
Aleksandra Spadijer-Gostovic ◽  
Zoran Lazic ◽  
Branka Trifkovic
Keyword(s):  
Fracture Toughness ◽  
Testing Machine ◽  
High Fracture Toughness ◽  
Zirconia Ceramic ◽  
Ceramic Samples ◽  
Edge Group ◽  
Group I ◽  
Ceramic Crowns ◽  
Tooth Preparation ◽  
Edge Preparation

Background/Aim. Fracture toughness determines functional crown strenght and prevents damages on ceramics during mastication. There is a lack of relevant literature data about fracture toughness of crowns made by feather-edge preparation. Mechanical testing of ceramic samples is supposed to show if feather-edge tooth preparation is a successful method for making ceramic crowns without any risk of reduction of their mechanical properties. This research was done to establish effects of feather-edge tooth preparation on fracture toughness of single zirconia ceramic crowns. Methods. The research was performed as an experimental study. Sixty (60) ceramic crowns were made on non-carious extracted human premolars. Thirty (30) crowns were made on the basis of feather-edge preparation (experimental group I). The group II included 30 crowns made on 1 mm rounded shoulder. Crowns fabrication was executed on a copy mill production system ?Zirkonzahn? (Zirkonzahn GMBH, Gais, Germany). The spherical compression test was used to determine fracture toughness, using 6 mm diameter ceramic ball. Fracture load for damaging ceramic crown was recorded on a universal testing machine - Zwick, type 1464, with the speed of 0.05 mm/min. Results. The results of this research introduced significant differences between fracture toughness of ceramic samples in every examined group. However, fracture toughness of crowns from both group was above 2 000 N, what was double beyond a recommended value. The mean value of fracture toughness in the feather-edge group was 2 090 N, and in shoulder group it was 2 214 N. Conclusion. This research showed a high fracture toughness of zirconia crowns made on feather-edge preparation. The examined crowns showed a fracture resistance at a sufficient distance in relation to the minimum values of functional loads. Further research of functional loads of these crown is necessary, as well as research of marginal adaptation of cemented crowns and gingival inflammatory response.

scholarly journals Relationship between anterior occlusion and frontal sinus size

2017 ◽  
Vol 87 (5) ◽  
pp. 752-758 ◽  
Author(s):  
Omar T. Said ◽  
P. Emile Rossouw ◽  
Leonard S. Fishman ◽  
Changyong Feng
Keyword(s):  
Frontal Sinus ◽  
Pairwise Comparison ◽  
Cranial Base ◽  
Class I ◽  
Maxillary Incisor ◽  
Skeletal Malocclusion ◽  
Edge Group ◽  
Anterior Cranial Base ◽  
Significant Difference ◽  
Incisor Inclination

ABSTRACT Objective: To determine the relationship between anterior occlusion and frontal sinus size. Methods: The patient database at the Eastman Institute for Oral Health, University of Rochester, was searched for male patients older than 15 years and females older than 13 years of age. After applying inclusion and exclusion criteria, participants' photos and lateral cephalometric and posteroanterior radiographs were examined then classified into a control class I group (n = 20, 15.7 ± 2.7 years) and eight malocclusion groups (n = 136, 16.1 ± 2.1 years). The frontal sinus area on the lateral cephalometric radiograph and on the posteroanterior radiograph were measured and compared between groups. Results: One-way analysis of variance demonstrated a significant difference among all nine groups (P = .0001). Pairwise comparison showed a significant difference between the class I group and all other malocclusion groups (P &lt; .05) except the edge-to-edge group for both radiographs and except the bimaxillary protrusion group for the lateral cephalometric radiographs. Tukey's method was not able to demonstrate a significant difference among the subgroups of skeletal malocclusions (P &gt; .05). Linear regression analyses with stepwise model selection demonstrated that anterior cranial base, mandibular plane angle, and upper incisor inclination commonly have a significant effect on frontal sinus size. Conclusion: The frontal sinus size could be used as an indicator of harmonious anterior occlusion. There were no differences among the subgroups of each skeletal malocclusion. The anterior cranial base, facial height, and maxillary incisor inclination appear to have a significant effect on frontal sinus size.

ON RESIDUAL FINITENESS OF GRAPHS OF NILPOTENT GROUPS

2004 ◽  
Vol 14 (04) ◽  
pp. 403-408
Author(s):  
E. RAPTIS ◽  
O. TALELLI ◽  
D. VARSOS
Keyword(s):  
Finite Groups ◽  
Finite Graph ◽  
Nilpotent Groups ◽  
Fundamental Groups ◽  
Residual Finiteness ◽  
Graph Of Groups ◽  
Residually Finite ◽  
Edge Group ◽  
Residually Finite Groups ◽  
Torsion Free

Here we characterize the residually finite groups G which are the fundamental groups of a finite graph of finitely generated torsion-free nilpotent groups. Namely we show that G is residually finite if and only if for each edge group of the graph of groups the two edge monomorphisms differ essentially by an isomorphism of certain subgroups of the Mal'cev completion of the corresponding vertex groups.

scholarly journals Deficiency and abelianized deficiency of some virtually free groups

2007 ◽  
Vol 143 (2) ◽  
pp. 257-264 ◽  
Author(s):  
MARTIN R. BRIDSON ◽  
MICHAEL TWEEDALE
Keyword(s):  
Free Groups ◽  
Defining Relations ◽  
Hnn Extension

AbstractLet Qm be the HNN extension of Z/m × Z/m where the stable letter conjugates the first factor to the second. We explore small presentations of the groups Γm,n = Qm* Qn. We show that for certain choices of (m,n), for example (2,3), the group Γm,n has a relation gap unless it admits a presentation with at most 3 defining relations, and we establish restrictions on the possible form of such a presentation. We then associate to each (m,n) a 3-complex with 16 cells. This 3-complex is a counterexample to the D(2) conjecture if Γm,n has a relation gap.

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