scholarly journals The Dual and Mirror Images of the Dunwoody 3-Manifolds

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Soo Hwan Kim ◽  
Yangkok Kim
Keyword(s):  
Lens Space ◽  
Group Presentation ◽  
Heegaard Diagram

Recently, in 2013, we proved that certain presentations present the Dunwoody3-manifold groups. Since the Dunwoody3-manifolds do not have a unique Heegaard diagram, we cannot determine a unique group presentation for the Dunwoody3-manifolds. It is well known that every(1,1)-knots in a lens space can be represented by the set𝒟of the 4-tuples(a,b,c,r)(Cattabriga and Mulazzani (2004); S. H. Kim and Y. Kim (2012, 2013)). In particular, to determine a unique Heegaard diagram of the Dunwoody3-manifolds, we proved the fact that the certain subset of𝒟representing all2-bridge knots of(1,1)-knots is determined completely by using the dual and mirror(1,1)-decompositions (S. H. Kim and Y. Kim (2011)). In this paper, we show how to obtain the dual and mirror images of all elements in𝒟as the generalization of some results by Grasselli and Mulazzani (2001); S. H. Kim and Y. Kim (2011).

An equivalent description of the lens space L(p,q) with p prime

2020 ◽  
Vol 29 (10) ◽  
pp. 2042005
Author(s):  
Fengling Li ◽  
Dongxu Wang ◽  
Liang Liang ◽  
Fengchun Lei
Keyword(s):  
Complete System ◽  
Lens Space ◽  
Heegaard Splitting ◽  
Prime Integer ◽  
Heegaard Diagrams ◽  
Heegaard Diagram ◽  
Genus Formula ◽  
Equivalent Description

In the paper, we give an equivalent description of the lens space [Formula: see text] with [Formula: see text] prime in terms of any corresponding Heegaard diagrams as follows: Let [Formula: see text] be a closed orientable 3-manifold with [Formula: see text] and [Formula: see text] a Heegaard splitting of genus [Formula: see text] for [Formula: see text] with an associated Heegaard diagram [Formula: see text]. Assume [Formula: see text] is a prime integer. Then [Formula: see text] is homeomorphic to the lens space [Formula: see text] if and only if there exists an embedding [Formula: see text] such that [Formula: see text] bounds a complete system of surfaces for [Formula: see text].

IMPLEMENTING SIM-OVG MODEL IN LEARNING ECONOMICS AT SMA NEGERI 10 SAMARINDA

2019 ◽  
Vol 1 (2) ◽  
pp. 151-164
Author(s):  
Watini Watini
Keyword(s):  
Learning Outcomes ◽  
Classroom Observation ◽  
Second Grade ◽  
Learning Models ◽  
Group Presentation ◽  
Second Grade Students ◽  
High Level ◽  
Work Method ◽  
High Level Thinking ◽  
Passing Grade

The reason underlying the implementation of the present study was because there was a finding revealing that there were still several students from cross-economics class of XI MIPA having difficulties in understanding the lessons. In addition, the students also had a kind of thought that economics was just about memorizing things which was not interesting and challenging that resulted in their unsatisfied learning outcomes. Therefore, the SIM-OVG model needed to be implemented in the learning process. The instruments of the present study were observation and, students’ learning reports and work method. The population of the study was the second grade students (4 classes) who enrolled economics subject at SMA Negeri 10 Samarinda, whereas the samples of the study were the students of XI MIPA-1 class (cross-economics class) at SMA Negeri 10 Samarinda. The number of the population and samples was 101 and 23 students respectively. The study lasted for one semester. The description of the classroom observation, the students’ scores and the group presentation were obtained for the data analysis. After implementing the SIM-OVG model, the results showed that; 1) in the affective aspect, the students showed a better attitude, 2) in the cognitive aspect, there was an improvement on the students’ learning outcomes (before the implementation of SIM-OVG model in XI MIPA-1 class, 52,17% of the students did not reach the passing-grade, but after the implementation, 100% of the students reached the passing-grade, and they also looked enthusiastic in doing their assignments, and 3) in the psychomotor aspect, the students became more skillful, creative, and be able to perform high level thinking. The researcher suggested that the dissemination should be done through MGMP forum and SIM-OVG model workshop. In addition, the researcher also suggested the integration of SIM-OVG model with other learning models and hoped that every school provided adequate facilities to support the implementation of SIM-OVG model.

scholarly journals Fermentation revival in the classroom: investigating ancient human practices as CUREs for modern diseases

2020 ◽  
Vol 367 (21) ◽  
Author(s):  
Jennifer K Lyles ◽  
Monika Oli
Keyword(s):  
Undergraduate Research ◽  
Bioinformatic Analysis ◽  
Research Experience ◽  
Group Presentation ◽  
Student Knowledge ◽  
Laboratory Equipment ◽  
Lecture Material ◽  
Hands On ◽  
Human Practices ◽  
Survey Responses

ABSTRACT A course-based undergraduate research experience (CURE) was designed to integrate key microbiological principles and techniques into an authentic research experience in a classroom setting and was implemented in an undergraduate microbiology laboratory course. Students conducted a 6-week study in order to determine the identity and quantity of unique probiotic species from various types of kefir. This course module followed an inquiry-based pedagogical approach in which students use the scientific process to investigate an unknown question with no predetermined outcome. During each lab, relevant microbiological topics and laboratory concepts were presented. Students then performed various laboratory techniques, reinforcing the lecture material with hands-on experience. In addition, students participated in reflection through group presentation of their results, bioinformatic analysis and literature review. Based on data collected from pre- and post-study survey responses, both student knowledge and attitudes towards the topics covered improved due to participation in this CURE. Importantly, this CURE can be implemented at many levels of education, requiring only minimal resources and common laboratory equipment.

Knots with the Lens Space Surgery

2011 ◽  
Vol 10 (1) ◽  
pp. 561-570
Author(s):  
Alberto Cavicchioli ◽  
Ilaria Telloni
Keyword(s):  
Lens Space

scholarly journals COMBINATORIAL KNOT FLOER HOMOLOGY AND DOUBLE BRANCHED COVERS

2013 ◽  
Vol 22 (06) ◽  
pp. 1350014
Author(s):  
FATEMEH DOUROUDIAN
Keyword(s):  
Floer Homology ◽  
Combinatorial Proof ◽  
Branched Covers ◽  
Knot Floer Homology ◽  
Branched Cover ◽  
Heegaard Diagram

Using a Heegaard diagram for the pullback of a knot K ⊂ S3 in its double branched cover Σ2(K), we give a combinatorial proof for the invariance of the associated knot Floer homology over ℤ.

Topology of ambient manifolds of non-singular Morse – Smale flows with three periodic orbits

2021 ◽  
Vol 29 (6) ◽  
pp. 863-868
Author(s):  
Danila Shubin ◽  
◽  
Keyword(s):  
Periodic Orbits ◽  
Three Dimensional ◽  
Solid Torus ◽  
Lens Space ◽  
Tubular Neighborhood ◽  
Lens Spaces ◽  
Ambient Manifold ◽  
Orientable Manifold ◽  
Smale Flows ◽  
Published Result

The purpose of this study is to establish the topological properties of three-dimensional manifolds which admit Morse – Smale flows without fixed points (non-singular or NMS-flows) and give examples of such manifolds that are not lens spaces. Despite the fact that it is known that any such manifold is a union of circular handles, their topology can be investigated additionally and refined in the case of a small number of orbits. For example, in the case of a flow with two non-twisted (having a tubular neighborhood homeomorphic to a solid torus) orbits, the topology of such manifolds is established exactly: any ambient manifold of an NMS-flow with two orbits is a lens space. Previously, it was believed that all prime manifolds admitting NMS-flows with at most three non-twisted orbits have the same topology. Methods. In this paper, we consider suspensions over Morse – Smale diffeomorphisms with three periodic orbits. These suspensions, in turn, are NMS-flows with three periodic trajectories. Universal coverings of the ambient manifolds of these flows and lens spaces are considered. Results. In this paper, we present a countable set of pairwise distinct simple 3-manifolds admitting NMS-flows with exactly three non-twisted orbits. Conclusion. From the results of this paper it follows that there is a countable set of pairwise distinct three-dimensional manifolds other than lens spaces, which refutes the previously published result that any simple orientable manifold admitting an NMS-flow with at most three orbits is lens space.

scholarly journals The Breast Cancer Working Group Presentation was Divided into Three Sections: The Epidemiology, Pathology and Treatment of Breast Cancer

2010 ◽  
Vol 40 (Supplement 1) ◽  
pp. i13-i18 ◽  
Author(s):  
M. Toi ◽  
Y. Ohashi ◽  
A. Seow ◽  
T. Moriya ◽  
G. Tse ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Working Group ◽  
Group Presentation

Lens Space

2004 ◽  
pp. 226-226
Author(s):  
Steven Duplij ◽  
Steven Duplij ◽  
Steven Duplij
Keyword(s):  
Lens Space
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