scholarly journals Properties of Suborbits of the Dihedral Group D<sub>n</sub> Acting on Ordered Subsets

2017 ◽  
Vol 07 (08) ◽  
pp. 375-382
Author(s):  
Rose W. Gachogu ◽  
Ireri N. Kamuti ◽  
Moses N. Gichuki
Keyword(s):  
Dihedral Group ◽  
Group D

scholarly journals Some characterizatsion of coprime graph of dihedral group D 2n

2021 ◽  
Vol 1722 ◽  
pp. 012051
Author(s):  
A G Syarifudin ◽  
Nurhabibah ◽  
D P Malik ◽  
I G A W Wardhana
Keyword(s):  
Dihedral Group ◽  
Group D

scholarly journals Strong duality for metacyclic groups

2002 ◽  
Vol 73 (3) ◽  
pp. 377-392 ◽  
Author(s):  
R. Quackenbush ◽  
C. S. Szabó
Keyword(s):  
Finite Group ◽  
Dihedral Group ◽  
Strong Duality ◽  
Sylow Subgroups ◽  
Metacyclic Groups ◽  
Group D

AbstractDavey and Quackenbush proved a strong duality for each dihedral group Dm with m odd. In this paper we extend this to a strong duality for each finite group with cyclic Sylow subgroups (such groups are known to be metacyclic).

Units in Group Rings of the Infinite Dihedral Group

1991 ◽  
Vol 34 (1) ◽  
pp. 83-89 ◽  
Author(s):  
Maciej Mirowicz
Keyword(s):  
Group Ring ◽  
Integral Domain ◽  
Dihedral Group ◽  
Group Rings ◽  
Finitely Generated ◽  
Group Of Units ◽  
Group D

AbstractThis paper studies the group of units U(RD∞) of the group ring of the infinite dihedral group D∞ over a commutative integral domain R. The structures of U(Z2D∞) and U(Z3D∞) are determined, and it is shown that U(ZD∞) is not finitely generated.

SYMMETRIC BIFURCATIONS IN A RING OF COUPLED DIFFERENTIAL EQUATION WITH PIECEWISE CONTINUOUS ARGUMENTS

2011 ◽  
Vol 21 (02) ◽  
pp. 431-436 ◽  
Author(s):  
BAODONG ZHENG ◽  
JIAN MA ◽  
HUIFENG ZHENG ◽  
CHUNRUI ZHANG
Keyword(s):  
Differential Equation ◽  
Dihedral Group ◽  
Equilibrium Points ◽  
Piecewise Continuous ◽  
Piecewise Continuous Arguments ◽  
Group D

Symmetry bifurcations of equilibrium points of three coupled differential equation with piecewise continuous arguments (EPCA) oscillators are studied. The system is equivariant under dihedral group D3 with order 6. This causes several types of symmetrical bifurcations.

scholarly journals COMMENTS ON DIHEDRAL AND SUPERSYMMETRIC EXTENSIONS OF A FAMILY OF HAMILTONIANS ON A PLANE

2010 ◽  
Vol 25 (27) ◽  
pp. 2373-2380 ◽  
Author(s):  
C. QUESNE
Keyword(s):  
Dihedral Group ◽  
Creation And Annihilation Operators ◽  
Group D ◽  
Trigonometric Identities

For any odd k, a connection is established between the dihedral and supersymmetric extensions of the Tremblay–Turbiner–Winternitz Hamiltonians Hk on a plane. For this purpose, the elements of the dihedral group D2k are realized in terms of two independent pairs of fermionic creation and annihilation operators and some interesting trigonometric identities are demonstrated.

Coordinating Visual and Analytic Strategies: A Study of Students' Understanding of the Group D4

1996 ◽  
Vol 27 (4) ◽  
pp. 435-457
Author(s):  
Rina Zazkis ◽  
Ed Dubinsky ◽  
Jennie Dautermann
Keyword(s):  
Alternative Model ◽  
Dihedral Group ◽  
Classification Scheme ◽  
Mathematical Thinking ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
Analytic Thinking ◽  
Clinical Interviews ◽  
Visual Approach ◽  
Group D

This study contributes to the ongoing discussion of visualization and analysis in mathematical thinking. On the basis of data gathered from clinical interviews with 32 students in their first abstract algebra course, we consider the tasks of listing the elements of the dihedral group D4 and finding the product of two such elements. These problems can be solved either using a “visual” approach of transforming a square or an “analytic” approach of multiplying permutations. Rather than clearly preferring either a visual or analytic strategy, most students in our study used some combination of these approaches. Our results suggest that the conventional analyzer/visualizer dichotomy may not be an appropriate classification scheme for describing learning processes or for designing instruction. We propose an alternative model, the Visualizer/Analyzer or VA model, that assumes visualization and analysis to be mutually dependent in mathematical problem solving, rather than unrelated opposites. Our model provides one description of how this mutual dependence might function. We end by considering how pedagogical approaches might be designed in consonance with this model to help students coordinate visual and analytic thinking.

scholarly journals Dihedral Group D4—A New Feature Extraction Algorithm

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 548
Author(s):  
Puneet Sharma
Keyword(s):  
Dihedral Group ◽  
Feature Vector ◽  
Feature Descriptor ◽  
Image Region ◽  
Histograms Of Oriented Gradients ◽  
Wide Range ◽  
Extraction Algorithm ◽  
Complete Set ◽  
New Feature ◽  
Group D

In this paper, we propose a new feature descriptor for images that is based on the dihedral group D 4 , the symmetry group of the square. The group action of the D 4 elements on a square image region is used to create a vector space that forms the basis for the feature vector. For the evaluation, we employed the Error-Correcting Output Coding (ECOC) algorithm and tested our model with four diverse datasets. The results from the four databases used in this paper indicate that the feature vectors obtained from our proposed D 4 algorithm are comparable in performance to that of Histograms of Oriented Gradients (HOG) model. Furthermore, as the D 4 model encapsulates a complete set of orientations pertaining to the D 4 group, it enables its generalization to a wide range of image classification applications.

scholarly journals EXCHANGE OPERATOR FORMALISM FOR AN INFINITE FAMILY OF SOLVABLE AND INTEGRABLE QUANTUM SYSTEMS ON A PLANE

2010 ◽  
Vol 25 (01) ◽  
pp. 15-24 ◽  
Author(s):  
C. QUESNE
Keyword(s):  
Dihedral Group ◽  
Infinite Family ◽  
Quantum Systems ◽  
Polar Coordinates ◽  
Difference Operators ◽  
Operator Formalism ◽  
Exactly Solvable ◽  
Exchange Operator ◽  
Identity Representation ◽  
Group D

The exchange operator formalism in polar coordinates, previously considered for the Calogero–Marchioro–Wolfes problem, is generalized to a recently introduced, infinite family of exactly solvable and integrable Hamiltonians Hk, k = 1, 2, 3,…, on a plane. The elements of the dihedral group D2k are realized as operators on this plane and used to define some differential-difference operators Dr and Dφ. The latter serve to construct D2k-extended and invariant Hamiltonians [Formula: see text], from which the starting Hamiltonians Hk can be retrieved by projection in the D2k identity representation space.

An Orbit-Based Search Algorithm to Solve N-Queens Problem

2012 ◽  
Vol 195-196 ◽  
pp. 1049-1054
Author(s):  
Jun Zhang ◽  
Zi Li Zhang
Keyword(s):  
Dihedral Group ◽  
Search Algorithm ◽  
Orbit Space ◽  
Group D

To analyze N-Queens problem in permutation space, this paper defines isomorphic operations of permutation to dihedral group D4. With these operations to find elements within an orbit, two operations on orbits are also defined to generate new orbit from existing ones. Orbit signature is proposed to uniquely identify different orbits on orbit space. A search algorithm based on orbit signature is presented, and finally the effectiveness of the algorithm is illustrated by an example.

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