Elliptic biquaternion algebra

Özen, Kahraman Esen; Tosun, Murat

doi:10.1063/1.5020481

Cited by 9 publications

(16 citation statements)

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“…For more details, see other works. 16,[20][21][22] Binary numbers or generalized complex numbers are introduced 21 as z = x + I (x, ∈ R), I 2 = p + Iq (p, q ∈ R),…”

Section: Preliminariesmentioning

confidence: 99%

“…22 There are some of studies on elliptic numbers in literature. [16][17][18][19][20][21][22][23][24][25] The elliptic biquaternion algebra is a four-dimensional vector space over C p . It is represented as…”

Section: Preliminariesmentioning

confidence: 99%

“…When this value is nonzero, Q has a multiplicative inverse, which is expressed as Q −1 = Q∕N Q . 16 On the other hand, if there exists an invertible elliptic biquaternion X satisfying the equality X −1 QX = R, Q and R are called similar elliptic biquaternions. This case is denoted by Q ∼ R. 20…”

Section: Preliminariesmentioning

confidence: 99%

“…The readers are referred to previous studies. [16][17][18][19][20] This article is organized as follows. In Section 2, we review elliptic numbers and elliptic biquaternions and recall the fundamental concepts of elliptic matrices.…”

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On the matrix algebra of elliptic biquaternions

Özen

Tosun

2019

Math Methods in App Sciences

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In this study, we introduce the concept of elliptic biquaternion matrices. Firstly, we obtain elliptic matrix representations of elliptic biquaternion matrices and establish a universal similarity factorization equality for elliptic biquaternion matrices. Afterwards, with the aid of these representations and this equality, we obtain various results on some basic topics such as generalized inverses, eigenvalues and eigenvectors, determinants, and similarity of elliptic biquaternion matrices. These valuable results may be useful for developing a perfect theory on matrix analysis over elliptic biquaternion algebra in the future.

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“…For more details, see other works. 16,[20][21][22] Binary numbers or generalized complex numbers are introduced 21 as z = x + I (x, ∈ R), I 2 = p + Iq (p, q ∈ R),…”

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

mentioning

confidence: 99%

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On the matrix algebra of elliptic biquaternions

Özen

Tosun

2019

Math Methods in App Sciences

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“…TMK m. 700, dolaylı olarak paylaşmayı istemeye zorlamaktadır 51 . Ancak mülkiyet konusu eşyanın intifa yüklü olarak satılması bedelin düşük olmasına sebep olmaktadır 52 . Bu yüzden paylı mülkiyet konusu eşyanın satımı gerçekleştikten sonra, paylar ortadan kalktığında, intifa hakkının satım bedelinde paya isabet eden kısım üzerinde devamını sağlamak daha isabetlidir 53 .…”

Section: Paydaşlarin Eşyadan Yararlanma Haklarinin Ni̇teli̇ği̇unclassified

The joint owners’ grant exploitation rights to the third person on joint ownership goods<p>Paydaşların paylı mülkiyet konusu eşyadan üçüncü kişileri yararlandırma yetkileri

Özcan

2018

HumanSciences

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Joint ownership, which is the most prevalent type of co-ownership, is regulated between Article 688 and Article 700 of Turkish Civil Code (hereinafter referred to as “TCC”). Joint ownership is the type of co-ownership, in which more than one person, whom have the same legal status, enjoy the property rights pro rate to their shares. Joint ownership, which is widely seen in theory and practice, has important legal aspects in terms of joint owners’ rights and authorities. Each joint owner of joint ownership has the same rights and authorities as any sole property owner had. The concept of share and joint owners’ power of disposition are significant issues within the Joint ownership. Joint owners have certain rights with respect to usufruct, management and protection of that property. Exploitation rights of such property are determined pro rata to shares hold by the joint owners . Specifically, there are certain limitations for joint owners in terms of the exploitation rights of that property. The right to grant exploitation in favor of third parties by joint owners limits the exploitation rights of other joint owners. Joint owners may grant easements to any third party on the property that subjected to Joint ownership. All joint owners should cast an affirmative vote so as to grant such easement. Besides this, each joint owner may establish any easement rights in favor of any third party upon its shares.Extended English summary is in the end of Full Text PDF (TURKISH) file. Özet Birlikte mülkiyetin en yaygın türü olan paylı mülkiyet, TMK. m. 688 ve 700 arasında düzenlenmektedir. Paylı mülkiyet, aynı hukukî statüdeki birden fazla kişinin belirli bir eşyaya aynı anda payları oranında malik oldukları toplu mülkiyetin bir türüdür. Teori ve uygulamada sıklıkla karşılaşılan paylı mülkiyet birliği, sahiplerine tanıdığı hak ve yetkiler bakımından da önemlidir. Paylı mülkiyet birliğini oluşturan paydaşlardan her biri malikin sahip olduğu hak ve yükümlülüklere sahiptir. Paylı mülkiyette pay kavramı ve paydaşların pay üzerinde tasarruf yetkileri önemlidir. Paydaşların paylı mülkiyet konusu eşya üzerinde kullanma, yararlanma, yönetim yetkileri ve paylı mülkiyete konu eşyayı korumaya ilişkin yetkileri vardır. Bu yetkilerden, paydaşların yararlanma yetkileri pay oranlarına göre belirlenir. Özellikle de paydaşların paylı mülkiyet konusu eşyayı kullanma yetkilerine ilişkin kanuni ve iradi sınırlamalar bulunmaktadır. Paydaşların 3. kişileri paylı mülkiyet konusu eşyadan yararlandırma yetkisi onların eşyayı kullanma yetkisini sınırlandırmaktadır. Paydaşlar eşya üzerinde 3. kişi lehine irtifak hakkı kurabilirler. Bu durum paydaşların oybirliği ile karar almalarını gerektirir. Ayrıca her paydaş kendi payı üzerinde irtifak hakkı kurarak da 3. kişiye eşyadan yararlanma hakkı tanır.

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Elliptic Biquaternionic Sequence with Vietoris’ Numbers as Its Components

Almeida,

Catarino

2023

Springer Proceedings in Mathematics &Amp; Statistics

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Elliptic biquaternion algebra

Cited by 9 publications

References 11 publications

On the matrix algebra of elliptic biquaternions

On the matrix algebra of elliptic biquaternions

The joint owners’ grant exploitation rights to the third person on joint ownership goods<p>Paydaşların paylı mülkiyet konusu eşyadan üçüncü kişileri yararlandırma yetkileri

Elliptic Biquaternionic Sequence with Vietoris’ Numbers as Its Components

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