Mobius Group Generated by Two Elements of Order 2, 4, and Reduced Quadratic Irrational Numbers
The construction of circuits for the evolution of orbits and reduced quadratic irrational numbers under the action of Mobius groups have many applications like in construction of substitution box (s-box), strong-substitution box (s.s-box), image processing, data encryption, in interest for security...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/6320243 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850209897660022784 |
|---|---|
| author | Dilshad Alghazzawi M. Haris Mateen M. Aslam Malik P. Hammachukiattikul Mohammed S. Abdo |
| author_facet | Dilshad Alghazzawi M. Haris Mateen M. Aslam Malik P. Hammachukiattikul Mohammed S. Abdo |
| author_sort | Dilshad Alghazzawi |
| collection | DOAJ |
| description | The construction of circuits for the evolution of orbits and reduced quadratic irrational numbers under the action of Mobius groups have many applications like in construction of substitution box (s-box), strong-substitution box (s.s-box), image processing, data encryption, in interest for security experts, and other fields of sciences. In this paper, we investigate the behavior of reduced quadratic irrational numbers (RQINs) in the coset diagrams of the set Q′′m=η/s:η∈Q∗m,s=1,2 under the action of group H=<x′,y′:x′2=y′4=1>, where m is square free integer and Q∗m=a′+m/c′,a′,a′2−m/c′c′=1,c′≠0. We discuss the type and reduced cardinality of the orbit Q′′p. By using the notion of congruence, we give the general form of reduced numbers (RNs) in particular orbits under certain conditions on prime p. Further, we classify that for a reduced number r whether −r,r¯,−r¯ lying in orbit or not. AMS Mathematics subject classification (2010): 05C25, 20G401. |
| format | Article |
| id | doaj-art-917320a50ec74e6589be8741d2d17b3e |
| institution | OA Journals |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-917320a50ec74e6589be8741d2d17b3e2025-08-20T02:09:55ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/6320243Mobius Group Generated by Two Elements of Order 2, 4, and Reduced Quadratic Irrational NumbersDilshad Alghazzawi0M. Haris Mateen1M. Aslam Malik2P. Hammachukiattikul3Mohammed S. Abdo4Department of MathematicsDepartment of Management ScienceDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsThe construction of circuits for the evolution of orbits and reduced quadratic irrational numbers under the action of Mobius groups have many applications like in construction of substitution box (s-box), strong-substitution box (s.s-box), image processing, data encryption, in interest for security experts, and other fields of sciences. In this paper, we investigate the behavior of reduced quadratic irrational numbers (RQINs) in the coset diagrams of the set Q′′m=η/s:η∈Q∗m,s=1,2 under the action of group H=<x′,y′:x′2=y′4=1>, where m is square free integer and Q∗m=a′+m/c′,a′,a′2−m/c′c′=1,c′≠0. We discuss the type and reduced cardinality of the orbit Q′′p. By using the notion of congruence, we give the general form of reduced numbers (RNs) in particular orbits under certain conditions on prime p. Further, we classify that for a reduced number r whether −r,r¯,−r¯ lying in orbit or not. AMS Mathematics subject classification (2010): 05C25, 20G401.http://dx.doi.org/10.1155/2022/6320243 |
| spellingShingle | Dilshad Alghazzawi M. Haris Mateen M. Aslam Malik P. Hammachukiattikul Mohammed S. Abdo Mobius Group Generated by Two Elements of Order 2, 4, and Reduced Quadratic Irrational Numbers Journal of Function Spaces |
| title | Mobius Group Generated by Two Elements of Order 2, 4, and Reduced Quadratic Irrational Numbers |
| title_full | Mobius Group Generated by Two Elements of Order 2, 4, and Reduced Quadratic Irrational Numbers |
| title_fullStr | Mobius Group Generated by Two Elements of Order 2, 4, and Reduced Quadratic Irrational Numbers |
| title_full_unstemmed | Mobius Group Generated by Two Elements of Order 2, 4, and Reduced Quadratic Irrational Numbers |
| title_short | Mobius Group Generated by Two Elements of Order 2, 4, and Reduced Quadratic Irrational Numbers |
| title_sort | mobius group generated by two elements of order 2 4 and reduced quadratic irrational numbers |
| url | http://dx.doi.org/10.1155/2022/6320243 |
| work_keys_str_mv | AT dilshadalghazzawi mobiusgroupgeneratedbytwoelementsoforder24andreducedquadraticirrationalnumbers AT mharismateen mobiusgroupgeneratedbytwoelementsoforder24andreducedquadraticirrationalnumbers AT maslammalik mobiusgroupgeneratedbytwoelementsoforder24andreducedquadraticirrationalnumbers AT phammachukiattikul mobiusgroupgeneratedbytwoelementsoforder24andreducedquadraticirrationalnumbers AT mohammedsabdo mobiusgroupgeneratedbytwoelementsoforder24andreducedquadraticirrationalnumbers |