scholarly journals Symmetry classes of tensors associated with the semi-dihedral groups SD8n

2013 ◽  
Vol 131 (1) ◽  
pp. 59-67 ◽  
Author(s):  
Mahdi Hormozi ◽  
Kijti Rodtes
Keyword(s):  
Dihedral Groups ◽  
Symmetry Classes

scholarly journals Orthogonal bases of Brauer symmetry classes of tensors for groups having cyclic support on non-linear Brauer characters

2016 ◽  
Vol 31 ◽  
pp. 263-285 ◽  
Author(s):  
Mahdi Hormozi ◽  
Kijti Rodtes
Keyword(s):  
Cyclic Group ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Dihedral Groups ◽  
Symmetry Classes ◽  
Dimension Formula ◽  
Non Linear ◽  
Brauer Characters ◽  
Vanishing Elements ◽  
Necessary And Sufficient

This paper provides some properties of Brauer symmetry classes of tensors. A dimension formula is derived for the orbital subspaces in the Brauer symmetry classes of tensors corresponding to the irreducible Brauer characters of the groups whose non-linear Brauer characters have support being a cyclic group. Using the derived formula, necessary and sufficient condition are investigated for the existence of an o-basis of dicyclic groups, semi-dihedral groups, and also those things are reinvestigated on dihedral groups. Some criteria for the non-vanishing elements in the Brauer symmetry classes of tensors associated to those groups are also included.

scholarly journals Power graphs and exchange property for resolving sets

2019 ◽  
Vol 17 (1) ◽  
pp. 1303-1309 ◽  
Author(s):  
Ghulam Abbas ◽  
Usman Ali ◽  
Mobeen Munir ◽  
Syed Ahtsham Ul Haq Bokhary ◽  
Shin Min Kang
Keyword(s):  
Present Article ◽  
Linear Algebra ◽  
Finite Groups ◽  
Robot Navigation ◽  
Simple Graph ◽  
Exchange Property ◽  
Metric Dimension ◽  
Sufficient Condition ◽  
Resolving Set ◽  
Dihedral Groups

Abstract Classical applications of resolving sets and metric dimension can be observed in robot navigation, networking and pharmacy. In the present article, a formula for computing the metric dimension of a simple graph wihtout singleton twins is given. A sufficient condition for the graph to have the exchange property for resolving sets is found. Consequently, every minimal resolving set in the graph forms a basis for a matriod in the context of independence defined by Boutin [Determining sets, resolving set and the exchange property, Graphs Combin., 2009, 25, 789-806]. Also, a new way to define a matroid on finite ground is deduced. It is proved that the matroid is strongly base orderable and hence satisfies the conjecture of White [An unique exchange property for bases, Linear Algebra Appl., 1980, 31, 81-91]. As an application, it is shown that the power graphs of some finite groups can define a matroid. Moreover, we also compute the metric dimension of the power graphs of dihedral groups.

scholarly journals A study of curvature theory for different symmetry classes of Hamiltonian

Pramana ◽  
2021 ◽  
Vol 95 (3) ◽  
Author(s):  
Y R Kartik ◽  
Ranjith R Kumar ◽  
S Rahul ◽  
Sujit Sarkar
Keyword(s):  
Symmetry Classes ◽  
Curvature Theory

Regular Cayley maps for dihedral groups

2021 ◽  
Vol 148 ◽  
pp. 84-124
Author(s):  
István Kovács ◽  
Young Soo Kwon
Keyword(s):  
Dihedral Groups ◽  
Cayley Maps

scholarly journals Structure–function relationships of the plant cuticle and cuticular waxes — a smart material?

2006 ◽  
Vol 33 (10) ◽  
pp. 893 ◽  
Author(s):  
Hendrik Bargel ◽  
Kerstin Koch ◽  
Zdenek Cerman ◽  
Christoph Neinhuis
Keyword(s):  
Structure Function ◽  
Smart Materials ◽  
Self Assembly ◽  
Water Repellency ◽  
Cuticular Waxes ◽  
Form Complex ◽  
Symmetry Classes ◽  
Research Activities ◽  
Terrestrial Habitats ◽  
Surface Waxes

The cuticle is the main interface between plants and their environment. It covers the epidermis of all aerial primary parts of plant organs as a continuous extracellular matrix. This hydrophobic natural composite consists mainly of the biopolymer, cutin, and cuticular lipids collectively called waxes, with a high degree of variability in composition and structure. The cuticle and cuticular waxes exhibit a multitude of functions that enable plant life in many different terrestrial habitats and play important roles in interfacial interactions. This review highlights structure–function relationships that are the subjects of current research activities. The surface waxes often form complex crystalline microstructures that originate from self-assembly processes. The concepts and results of the analysis of model structures and the influence of template effects are critically discussed. Recent investigations of surface waxes by electron and X-ray diffraction revealed that these could be assigned to three crystal symmetry classes, while the background layer is not amorphous, but has an orthorhombic order. In addition, advantages of the characterisation of formation of model wax types on a molecular scale are presented. Epicuticular wax crystals may cause extreme water repellency and, in addition, a striking self-cleaning property. The principles of wetting and up-to-date concepts of the transfer of plant surface properties to biomimetic technical applications are reviewed. Finally, biomechanical studies have demonstrated that the cuticle is a mechanically important structure, whose properties are dynamically modified by the plant in response to internal and external stimuli. Thus, the cuticle combines many aspects attributed to smart materials.

On *-clean non-commutative group rings

2016 ◽  
Vol 15 (08) ◽  
pp. 1650150 ◽  
Author(s):  
Hongdi Huang ◽  
Yuanlin Li ◽  
Gaohua Tang
Keyword(s):  
Finite Field ◽  
Local Ring ◽  
Group Algebra ◽  
Rational Numbers ◽  
Semisimple Group ◽  
Group Algebras ◽  
Group Rings ◽  
Dihedral Groups ◽  
Commutative Local Ring ◽  
Generalized Quaternion

A ring with involution ∗ is called ∗-clean if each of its elements is the sum of a unit and a projection (∗-invariant idempotent). In this paper, we consider the group algebras of the dihedral groups [Formula: see text], and the generalized quaternion groups [Formula: see text] with standard involution ∗. For the non-semisimple group algebra case, we characterize the ∗-cleanness of [Formula: see text] with a prime [Formula: see text], and [Formula: see text] with [Formula: see text], where [Formula: see text] is a commutative local ring. For the semisimple group algebra case, we investigate when [Formula: see text] is ∗-clean, where [Formula: see text] is the field of rational numbers [Formula: see text] or a finite field [Formula: see text] and [Formula: see text] or [Formula: see text].

A Number-Theoretic Approach to Counting Subgroups of Dihedral Groups

1992 ◽  
Vol 23 (2) ◽  
pp. 150
Author(s):  
David W. Jensen ◽  
Eric R. Bussian
Keyword(s):  
Theoretic Approach ◽  
Dihedral Groups
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