Results 1 to 8 of about 8 (8)

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, Xu Hong Yan, Tang Wen Ju, Wang Hua   +3 more
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Characteristics of Regular Functions Defined on a Semicommutative Subalgebra of 4-Dimensional Complex Matrix Algebra

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
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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⁢(⋅,D⁢u)=f{F(\,\cdot\,,\mathrm{D}u)=f} is well posed in the so-called J. L.
Abugirda Hussien, Katzourakis Nikos
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Solutions of several general quadratic partial differential-difference equations in ℂ2

Demonstratio Mathematica
In 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
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Split quaternion Fourier transforms for two-dimensional real invariant field

Demonstratio Mathematica
The 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
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Characterizations of transcendental entire solutions of trinomial partial differential-difference equations in ℂ2#

Demonstratio Mathematica
This 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
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The description of entire solutions of complex PDEs and PDDEs

Demonstratio Mathematica
By 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
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Erythropoietin prevents necrotizing enterocolitis in very preterm infants: a randomized controlled trial. [PDF]

J Transl Med, 2020
Wang Y, Song J, Sun H, Xu F, Li K, Nie C, Zhang X, Peng X, Xia L, Shen Z, Yuan X, Zhang S, Ding X, Zhang Y, Kang W, Qian L, Zhou W, Wang X, Cheng X, Zhu C.   +19 more
europepmc   +1 more source