Results 1 to 10 of about 41 (36)
Journal of Mathematics, 2021 In this paper, we give an extended quaternion as a matrix form involving complex components. We introduce a semicommutative subalgebra ℂℂ2 of the complex matrix algebra M4,ℂ. We exhibit regular functions defined on a domain in ℂ4 but taking values in ℂℂ2.
Ji Eun Kim
doaj +3 more sources
Hyperholomorphic functions and hyper-conjugate harmonic functions of octonion variables
Journal of Inequalities and Applications, 2013 We represent hyperholomorphic functions on octonionic function theory and octonionic differential operators. We research the properties of hyperholomorphic functions, hyper-conjugate harmonic functions and the integral calculus of hyperholomorphic ...
Su Jin Lim, K. Shon
semanticscholar +2 more sources
Entire solutions for several complex partial differential-difference equations of Fermat type in ℂ2
Open Mathematics, 2021 By utilizing the Nevanlinna theory of meromorphic functions in several complex variables, we mainly investigate the existence and the forms of entire solutions for the partial differential-difference equation of Fermat type α∂f(z1,z2)∂z1+β∂f(z1,z2)∂z2m+f(
Gui Xian Min +3 more
doaj +1 more source
On the well-posedness of global fully nonlinear first order elliptic systems
Advances in Nonlinear Analysis, 2018 In the very recent paper [15], the second author proved that for any f∈L2(ℝn,ℝN){f\in L^{2}(\mathbb{R}^{n},\mathbb{R}^{N})}, the fully nonlinear first order system F(⋅,Du)=f{F(\,\cdot\,,\mathrm{D}u)=f} is well posed in the so-called J. L.
Abugirda Hussien, Katzourakis Nikos
doaj +1 more source
Solutions of several general quadratic partial differential-difference equations in ℂ2
Demonstratio MathematicaIn this article, we have introduced general transformation to solving the general quadratic equations. It is of interest to know about the existence and form of the solutions of general quadratic functional equations.
Ahamed Molla Basir, Mandal Sanju
doaj +1 more source
Split quaternion Fourier transforms for two-dimensional real invariant field
Demonstratio MathematicaThe article gives the corresponding split quaternions in Clifford analysis and the split Fourier transform (FT). Also, we investigate some properties of the split FT and apply to generalizations of the quaternion FT.
Kim Ji Eun
doaj +1 more source
Structural properties of s-regular functions in the split quaternionic setting
Open MathematicsIn this paper we study a slice-based notion of regularity for the split quaternionic algebra S $\mathbb{S}$ , whose natural quadratic form has signature (2,2). For each hyperbolic unit J∈T $J\in \mathcal{T}$ (with J 2 = 1) we consider the slice LJ={x+Jy:
Kim Ji Eun
doaj +1 more source
Complex ManifoldsWe revisit the second order estimate for solutions to the quaternionic Calabi–Yau problem on hyperkähler manifolds, originally established by Dinew and Sroka in [S. Dinew and M.
Gentili Giovanni, Vezzoni Luigi
doaj +1 more source
Demonstratio MathematicaThis study is devoted to exploring the existence and the precise form of finite-order transcendental entire solutions of second-order trinomial partial differential-difference equations L(f)2+2hL(f)f(z1+c1,z2+c2)+f(z1+c1,z2+c2)2=eg(z1,z2)L{(f)}^{2}+2hL(f)
Xu Hong Yan, Haldar Goutam
doaj +1 more source
The description of entire solutions of complex PDEs and PDDEs
Demonstratio MathematicaBy utilizing the Hadamard factorization theory and Nevanlinna theory of meromorphic functions in Cn ${\mathbb{C}}^{n}$ , we mainly give some description of the solutions of complex partial differential equation (PDE) (auz1+buz2)(cuz1+duz2)=eg, $\left(a{u}
Wu Zhao Jun, Xu Hong Yan, Xuan Zu Xing
doaj +1 more source