S. K. Al-Omari

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Over the past 20 years we have encountered 13 cases of lower genital tract atresia or obstruction. There were eight cases due to a high transverse vaginal septum. These were dealt with by standard surgical reconstruction. One later recurred and required hysterectomy. Five patients presented with cervical atresia. These were successfully treated by a new(More)
and Applied Analysis 3 Proof. Let ξ be fixed. If φ t is in S, then its diffraction Fresnel transform certainly exists. Moreover, differentiating the right-hand side of 2.3 with respect to ξ, under the integral sign, ktimes, yields a sum of polynomials, pk t ξ , say of combinations of t and ξ. That is, ∣ ∣ ∣ ∣ ∣ d dtk Fd ( φ ) ξ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ pk t ξ φ(More)
and Applied Analysis 3 Proof. It is clear that K V f and K p V g are continuous and bounded on R+. Moreover, the Fubini’s theorem allows us to interchange the order of integration: ∫ R + f (x) (K V g) (x) dx = ∫ R + (∫ R + f (x) Z p (xy) dx)g (y) dy. (15) Equation (15) follows since the Krätzel kernel Z p (xy) applies for the functions f and g, when the(More)
During the course of time researchers have defined ultradistributions as the duals of various types of ultradifferentiable functions of Roumieu type and of Buerling type, Roumieu type ultradifferentiable functions have been considered in the present paper. Three types of spaces of rapidly decreasing ultradifferentiable functions of Roumieu type have been(More)
and Applied Analysis 3 Theorem 3. The distributional Hartley-Hilbert transform ̂ Bf is linear. Proof. Let f, g ∈ C󸀠 then their components Af,Af,Ag, Aog ∈ C. Hence, ̂ B A (f + g) (y) = ⟨A o (f + g) (x) , cos (xy)⟩ + ⟨A e (f + g) (x) , sin (xy)⟩ . (24) By factoring and rearranging components we get that ̂ B A (f + g) (y) = ̂ B A f (y) + ̂ B A g (y) . (25)(More)
Lie symmetries and their Lie group transformations for a class of Timoshenko systems are presented. The class considered is the class of nonlinear Timoshenko systems of partial differential equations (PDEs). An optimal system of one-dimensional sub-algebras of the corresponding Lie algebra is derived. All possible invariant variables of the optimal system(More)
In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences.(More)
The Mellin integral transform is an important tool in mathematics and is closely related to Fourier and bi-lateral Laplace transforms. In this article we aim to investigate the Mellin transform in a class of quaternions which are coordinates for rotations and orientations. We consider a set of quaternions as a set of generalized functions. Then we provide a(More)
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