Geanina Zaharia’s research while affiliated with Ovidius University and other places

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Publications (5)


A Method for Solving quadratic Equations in Real Quaternion Algebra by using Scilab software
  • Article
  • Full-text available

August 2024

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10 Reads

Italian Journal of Pure and Applied Mathematics

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Geanina Zaharia

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In this paper, we present some numerical applications for the equation x 2 + ax + b = 0, where a, b are two quaternionic elements in H(α, β). H(α, β) represents the algebra of real quaternions with parameterized coefficients by α and β. The algebra of real quaternions is an extension of complex numbers and is represented by algebraic objects called quaternions. These quaternions are composed of four components: a real part and three imaginary components. In general, H(α, β) indicates a family of parameterized quaternion algebras, in which the specific values of α and β determine the specific properties and structure of the quaternion algebra. Based on well-known solving methods, we have developed a new numerical algorithm that solves the equation for any quaternions a and b in any algebra H(α, β).

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Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their Applications

April 2022

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46 Reads

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1 Citation

Mathematics

Due to the computational aspects which appear in the study of algebras obtained by the Cayley–Dickson process, it is difficult to obtain nice properties for these algebras. For this reason, finding some identities in such algebras plays an important role in obtaining new properties of these algebras and facilitates computations. In this regard, in the first part of this paper, we present some new identities and properties in algebras obtained by the Cayley–Dickson process. As another remark regarding the computational aspects in these algebras, in the last part of this paper, we solve some quadratic equations in the real division quaternion algebra when their coefficients are some special elements. These special coefficients allowed us to solve interesting quadratic equations, providing solutions directly, without using specialized softs.


Properties and applications of some special integer number sequences

February 2020

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157 Reads

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5 Citations

Mathematical Methods in the Applied Sciences

In this paper, we provide properties and applications of some special integer sequences. We generalize and give some properties of Pisano period. Moreover, we provide a new application in cryptography and applications of some quaternion elements.


Citations (2)


... In a publication from 2022, [7] exploring algebras derived from the Cayley-Dickson process presents challenges in achieving desirable properties due to computational complexities. Hence, the discovery of identities within these algebras it gains meaning, helping to acquire new properties and making calculations easier. ...

Reference:

A Method for Solving quadratic Equations in Real Quaternion Algebra by using Scilab software
Remarks Regarding Computational Aspects in Algebras Obtained by Cayley–Dickson Process and Some of Their Applications

Mathematics

... In [12,13], the used methods are based on the blocked message matrices. In [14], the authors present an application in cryptography and applications of some quaternion elements. In [15], the authors presented a public key cryptosystem using an Affine-Hill chipher with a generalized Fibonacci (multinacci) matrix with large power k, denoted by Q k λ , as a key. ...

Properties and applications of some special integer number sequences

Mathematical Methods in the Applied Sciences