Well-posedness for a modified nonlinear Schrödinger equation modeling the formation of rogue waves
OMA-Vol. 5 (2021), Issue 1, pp. 105 – 117 Open Access Full-Text PDF
Curtis Holliman, Logan Hyslop
Abstract: The Cauchy problem for a higher order modification of the nonlinear Schrödinger equation (MNLS) on the line is shown to be well-posed in Sobolev spaces with exponent \(s > \frac{1}{4}\). This result is achieved by demonstrating that the associated integral operator is a contraction on a Bourgain space that has been adapted to the particular linear symbol present in the equation. The contraction is proved by using microlocal analysis and a trilinear estimate that is shown via the \([k; Z]\)-multiplier norm method developed by Terence Tao.
Characterization of orthogonality conditions in certain classes of normed spaces
OMA-Vol. 5 (2021), Issue 1, pp. 98 – 104 Open Access Full-Text PDF
W.L. Otae, N.B. Okelo, O. Ongati
Abstract: In this paper, we give characterizations of orthogonality conditions in certain classes of normed spaces. We first consider Range-Kernel orthogonality in norm-attainable classes then we characterize orthogonality conditions for Jordan elementary operators.
A study of the power-cosine copula
OMA-Vol. 5 (2021), Issue 1, pp. 85 – 97 Open Access Full-Text PDF
Christophe Chesneau
Abstract: Copulas played a key role in numerous areas of statistics over the last few decades. In this paper, we offer a new kind of trigonometric bivariate copula based on power and cosine functions. We present it via analytical and graphical approaches. We show that it may be used to create a new bivariate normal distribution with interesting shapes. Subsequently, the simplest version of the suggested copula is highlighted. We discuss some of its relationships with the Farlie-Gumbel-Morgensten and simple polynomial-sine copulas, establish that it is a member of a well-known semi-parametric family of copulas, investigate its dependence domains, and show that it has no tail dependence.
On generalization of extended Gegenbauer polynomials of two variables
OMA-Vol. 5 (2021), Issue 1, pp. 76 – 84 Open Access Full-Text PDF
Ahmed Ali Al-Gonah, Ahmed Ali Atash
Abstract: Recently, many extensions of some special functions are defined by using the extended Beta function. In this paper, we introduce a new generalization of extended Gegenbauer polynomials of two variables by using the extended Gamma function. Some properties of these generalized polynomials such as integral representation, recurrence relation and generating functions are obtained.
A hybrid method for solution of linear Volterra integro-differential equations (LVIDES) via finite difference and Simpson’s numerical methods (FDSM)
OMA-Vol. 5 (2021), Issue 1, pp. 69 – 75 Open Access Full-Text PDF
Bashir Danladi Garba, Sirajo Lawan Bichi
Abstract: In this paper, a hybrid of Finite difference-Simpson’s approach was applied to solve linear Volterra integro-differential equations. The method works efficiently great by reducing the problem into a system of linear algebraic equations. The numerical results shows the simplicity and effectiveness of the method, error estimation of the method is provided which shows that the method is of second order convergence.
Starlikeness of meromorphic functions involving certain differential inequalities
OMA-Vol. 5 (2021), Issue 1, pp. 64 – 68 Open Access Full-Text PDF
Kuldeep Kaur Shergill, Sukhwinder Singh Billing
Abstract: In the present paper, we define a class of non-Bazilevic functions in punctured unit disk and study a differential inequality to obtain certain new criteria for starlikeness of meromorphic functions.
A fuzzy solution of nonlinear partial differential equations
OMA-Vol. 5 (2021), Issue 1, pp. 51 – 63 Open Access Full-Text PDF
Mawia Osman, Zengtai Gong, Altyeb Mohammed Mustafa
Abstract: In this paper, the reduced differential transform method (RDTM) is applied to solve fuzzy nonlinear partial differential equations (PDEs). The solutions are considered as infinite series expansions which converge rapidly to the solutions. Some examples are solved to illustrate the proposed method.
Certain new subclasses of \(m\)-fold symmetric bi-pseudo-starlike functions using \(Q\)-derivative operator
OMA-Vol. 5 (2021), Issue 1, pp. 42 – 50 Open Access Full-Text PDF
Timilehin Gideon Shaba
Abstract: In this current study, we introduced and investigated two new subclasses of the bi-univalent functions associated with \(q\)-derivative operator; both \(f\) and \(f^{-1}\) are \(m\)-fold symmetric holomorphic functions in the open unit disk. Among other results, upper bounds for the coefficients \(|\rho_{m+1}|\) and \(|\rho_{2m+1}|\) are found in this study. Also certain special cases are indicated.
Fixed point theorems for generalized \(\left( \psi ,\varphi ,F\right)\)-contraction type mappings in \(b\)-metric spaces with Applications
OMA-Vol. 5 (2021), Issue 1, pp. 35 – 41 Open Access Full-Text PDF
Taieb Hamaizia
Abstract: The purpose of this paper is to prove a fixed point theorem for \(C\)-class functions in complete \(b\)-metric spaces. Moreover, the solution of the integral equation is obtained using our main result.
A variety of uncertainty principles for the Hankel-Stockwell transform
OMA-Vol. 5 (2021), Issue 1, pp. 22 – 34 Open Access Full-Text PDF
Khaled Hleili
Abstract: In this work, we establish \(L^p\) local uncertainty principle for the Hankel-Stockwell transform and we deduce \(L^p\) version of Heisenberg-Pauli-Weyl uncertainty principle. Next, By combining these principles and the techniques of Donoho-Stark we present uncertainty principles of concentration type in the \(L^p\) theory, when \(1\)<\(p\leqslant2\). Finally, Pitt's inequality and Beckner's uncertainty principle are proved for this transform.