Search

This paper aims to bring together quaternions and generalized complex numbers. Generalized quaternions with generalized complex number components are expressed and their algebraic structures are examined. Several matrix representations and computational results are introduced. An alternative approach for a generalized quaternion matrix with elliptic number entries has been developed as a crucial part. [ABSTRACT FROM AUTHOR]

Split-complex (hyperbolic) numbers are ordered pairs of real numbers, written in the form x + jy with j² = 1, used to describe the geometry of the Lorentzian plane. Since a null split-complex number does not have an inverse, some methods to calculate the exponential of complex matrices are not valid for split-complex matrices. In this paper, we examined the exponential of a 2 × 2 split-complex matrix in three cases: i. Δ = 0, ii. Δ ̸= 0 and Δ is not null split-complex number, iii. Δ ̸= 0 and Δ is a null split-complex number where Δ = (trA)2 - 4 detA. [ABSTRACT FROM AUTHOR]

In this study, we consider the generalized complex number system Cp = {x + iy : x, y ∈ R, i² = p ∈ R} corresponding to elliptical complex number, parabolic complex number and hyperbolic complex number systems for the special cases of p < 0; p = 0; p > 0, respectively. This system is used to derive Bobillier Formula in the generalized complex plane. In accordance with this purpose we obtain this formula by two di¤erent methods for one-parameter planar motion in Cp ; the first method depends on using the geometrical interpretation of the generalized Euler-Savary formula and the second one uses the usual relations of the velocities and accelerations. [ABSTRACT FROM AUTHOR]

The aim of this article is to identify and analyze a new type special number system which is called bihyperbolic generalized Tribonacci numbers (BGTN for short). For this purpose, we give both classical and several new properties such as; recurrence relation, Binet formula, generating function, exponential generating function, summation formulae, matrix formula, and special determinant equations of BGTN . Also, the system of BGTN is quite a big family and includes several type special cases with respect to initial values and r, s, t values, we give the subfamilies and special cases of it. In addition to these, we construct some numerical algorithms including recurrence relation and special two types determinant equations related to calculating the terms of this new type special number system. Then, we examine several properties by taking two special cases and including some illustrative numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we give a new complex deformable derivative and integral of order λ which coincides with the classical derivative and integral for the special values of the parameters. We examine the basic properties of this derivative and integral. We also investigate the basic concepts of complex analysis for the λ-complex deformable derivative. Finally, we give some applications. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to provide a broad overview of the generalization of the various dual-complex number sequences, especially in the disciplines of mathematics and physics. By the help of dual numbers and dual-complex numbers, in this paper, we define the dual-complex generalized k-Horadam numbers. Furthermore, we investigate the Binet formula, generating function, some conjugation identities, summation formula and a theorem which is generalization of the Catalan's identity, Cassini's identity and d'Ocagne's identity. [ABSTRACT FROM AUTHOR]

In this article, we study the fractional-order SEIR mathematical model of Lumpy Skin Disease (LSD) in the sense of Caputo. The existence, uniqueness, non-negativity and boundedness of the solutions are established using fixed point theory. Using a next-generation matrix, the reproduction number R0 is determined for the disease's prognosis and durability. Using the fractional Routh-Hurwitz stability criterion, the evolving behaviour of the equilibria is investigated. Generalized Adams--Bashforth--Moulton approach is applied to arrive at the solution of the proposed model. Furthermore, to visualise the efficiency of our theoretical conclusions and to track the impact of arbitrary-order derivative, numerical simulations of the model and their graphical presentations are carried out using MATLAB(R2021a). [ABSTRACT FROM AUTHOR]

The aim of this work is to define quaternion curves and surfaces and their conjugates via operators in Euclidean projective geometric algebra (EPGA). In this space, quaternions were obtained by the geometric product of vector fields. New vector fields, which we call trajectory curves and surfaces, were obtained by using this new quaternion operator. Moreover, dual quaternion curves are determined by a similar method and then their generated motion is studied. Illustrative examples are given. [ABSTRACT FROM AUTHOR]

The aim of this article is to identify a new subfamily of spirallike functions and then to demonstrate necessary and sufficient conditions, sharp coefficients estimates for functions in this subfamily. [ABSTRACT FROM AUTHOR]

By using the definition of q-difference operator, we defined the new q-Al-Oboudi-Al-Amoudi operator, which generalize modified Al-Oboudi-Al-Amoudi operator. Using the new operator, we defined a new class of uniformly functions and obtained subordination result for functions in it. Our results not only generalize previous results but also modified some previous results. [ABSTRACT FROM AUTHOR]

Recently, Bakhet et al. [9] presented the Wright hypergeometric matrix function 2R(τ) 1 (A,B;C; z) and derived several properties. Abdalla [6] has since applied fractional operators to this function. In this paper, with the help of the generalized Pochhammer matrix symbol (A;B)n and the generalized beta matrix function B(P,Q;X), we introduce and study an extended form of the Wright hypergeometric matrix function, 2R(τ) 1 ((A;A),B;C; z;X). We establish several potentially useful results for this extended form, such as integral representations and fractional derivatives. We also derive some properties of the corresponding incomplete extendedWright hypergeometric matrix function. [ABSTRACT FROM AUTHOR]

In the present paper, the bicomplex Leonardo numbers will be introduced with the use of Leonardo numbers and some important algebraic properties including recurrence relation, generating function, Catalan's and Cassini's identities, Binet's formula, sum formulas will also be obtained. [ABSTRACT FROM AUTHOR]

In this research, the minimal and maximal operators defined by q- difference expression are given in the Hilbert space Lq² (0, ∞). The existence problem of a q−1-normal extension for the minimal operator is mentioned. In addition, the sets of the minimal operator spectrum and the maximal operator spectrum are examined. [ABSTRACT FROM AUTHOR]

The initial idea of this paper is to investigate the split complex bi-periodic Fibonacci and Lucas numbers by using SCFLN now on. We try to show some properties of SCFLN by taking into account the properties of the split complex numbers. Then, we present interesting relationships between SCFLN. [ABSTRACT FROM AUTHOR]

The inverse stereographic projection (ISP), or equivalently, bilinear transformation, is a method to produce a circular distribution based on an existing linear model. By the genesis of the ISP method, many important circular models have been provided by many researchers. In this study, we propose a new symmetric unimodal/bimodal circular distribution by the rotated ISP method considering the hyperbolic secant distribution as a baseline distribution. Rotation means that fixing the origin and rotating all other points the same amount counterclockwise. Considering the effect of rotation on the circular distribution to be obtained with the bilinear transformation, it is seen that it actually induces a location parameter in the obtained circular probability distribution. We analyze some of the stochastic properties of the proposed distribution. The methods for the parameter estimation of the new circular model and the simulation-based compare results of these estimators are extensively provided by the paper. Furthermore, we compare the fitting performance of the new model according to its well-known symmetric alternatives, such as Von-Misses, and wrapped Cauchy distributions, on a real data set. From the information obtained by the analysis on the real data, we say that the fitting performance of the new distribution is better than its alternatives according to the criteria frequently used in the literature. [ABSTRACT FROM AUTHOR]