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Item The hausdorff metric and its extensions.(De Gruyter, 2002-01-01) Moshokoa, Seithuti P.We consider a complete metric space (X, p) such that closed balls are compact. The paper is devoted to the Hausdorff distance d defined on 5?, the space of all nonempty compact subsets of X. We construct an embedding (5R, d) (Sr, distf), where S is the family of all closed subsets of X. We show that (Sr, distf) is compact.Item On completeness of Quasi-pseudometric spaces.(Hindawi publishing corporation, 2005-04-21) Moshokoa, Seithuti P.We discuss completeness in terms of a notion of absolute closure. This will be done in the context of separated quasi-pseudometric spaces and bitopological spaces. The notion isequivalent to the classical notion of completeness when restricted to the class of metric spaces.Item On (δ, p)-continuous functions and (δ, p)-closed graphs.(2000-01-01) Caldas, M.; Ekici, E.; Jafari, S.; Moshokoa, S. P.It is the object of this paper to introduce the notions of (δ, p) - continuity and (δ, p)-closed graphs by utilizing the notion of (δ, p)-open sets and investigate the fundamental properties of (δ, p)-continuous functions and also present some properties of functions with (δ, p)-closed graphs.Item On some new maximal and minimal sets via θ-open sets.(The Korean Mathematical Society, 2006-04-06) Caldas, Miguel; Jafari, Saeid; Moshokoa, Seithuti P.Nakaoka and Oda ([1] and [2]) introduced the notion of maximal open sets and minimal closed sets in topological spaces. In this paper, we introduce new classes of sets called maximal θ-open sets, minimal θ-closed sets, θ-semi maximal open and θ-semi minimal closed and investigate some of their fundamental properties.Item Primitive shifts on ψ-spaces.(Elsevier, 2011-01-01) Gutek, A.; Moshokoa, S.P.; Rajagopalan, M.; Sundaresan, K.Let D be a countable discrete space and let p ∈ D. For any primitive shift σ : D → D \ {p} there are 2c σ-invariant maximal almost disjoint families on D. This implies that there are 2c pairwise non-homeomorphic Ψ∗ spaces admitting primitive shifts. Under a = c there exists a maximal almost disjoint family F on a countable discrete space D such that the spaces Ψ (F) and Ψ∗(F) admit no primitive shift.Item Shifts on zero-dimensional compact metric spaces.(Elsevier, 2013-09-13) Gutek, A.; Moshokoa, S.P.; Rajagopalan, M.It is shown that every compact zero-dimensional metric space X with either no isolated points or infinitely many isolated points has a complex shift. If X is a disjoint union of a compact infinite scattered metric space and the Cantor set then X has a real shift also. If X is a disjoint union of a nonempty finite scattered metric space and the Cantor set then X has no shift.Item Soliton solutions to resonant nonlinear schrodinger’s equation with time-dependent coefficients by modified simple equation method.(Elsevier, 2016-09-13) Arnous, Ahmed H.; Mirzazadeh, Mohammad; Zhou, Qin; Moshokoa, Seithuti P.; Biswas, Anjan; Belic, MilivojThis paper studies resonant nonlinear Schrodinger’s equation with time-dependent coefficients and four forms of nonlinear media. They are Kerr law, power law, parabolic law and dual-power law. Soliton solutions are recovered by the aid of modified simple equation method.Item Singular optical solitons in birefringent nano-fibers.(Elsevier, 2016-06-27) Savescu, Michelle; Zhou, Qin; Moraru, Luminita; Biswas, Anjan; Moshokoa, Seithuti P.; Belic, Milivoj B.This paper serves as a sequel to previously published results on bright, dark and singular solitons in birefringent fibers with spatio-temporal dispersion, during 2014. The second form of singular soliton solutions is retrieved in this paper for birefringent nano-fibers with Kerr and parabolic laws of nonlinearity. There are constraint conditions that evolve with the solution structure.Item Small inductive dimension and Alexandroff topological spaces.(Elsevier, 2014-01-01) Georgiou, Dimitris N.; Megaritis, Athanasios C.; Moshokoa, Seithuti P.Alexandroff spaces include finite spaces and have a wide range of applications in many areas such as computer graphics and image analysis. We give results on small inductive dimension of Alexandroff T0-spaces. Particularly, we characterize the small inductive dimension through connected tuples and study standard properties of Dimension Theory using this characterization. Also, we investigate the relations between the small inductive dimension, the large inductive dimension, and the covering dimension in the class of all Alexandroff T0-spaces. We finally put questions on dimension of Alexandroff T0-spaces.Item Local fractional Laplace variational iteration method for solving diffusion and wave equations on cantor sets within local fractional operators.(Hindawi Publishing Corporation, 2015-01-26) Jassim, Hassan Kamil; Ünlü, Canan; Moshokoa, Seithuti Philemon; Khalique, Chaudry MasoodThe local fractional Laplace variational iteration method (LFLVIM) is employed to handle the diffusion and wave equations on Cantor set. The operators are taken in the local sense. The nondifferentiable approximate solutions are obtained by using the local fractional Laplace variational iteration method, which is the coupling method of local fractional variational iteration method and Laplace transform. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.Item Reduced differential transform method for partial differential equations within local fractional derivative operators.(SAGE, 2016-01-21) Jafari, Hossein; Jassim, Hassan K; Moshokoa, Seithuti P.; Ariyan, Vernon M.; Tchier, FairouzThe non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.Item Laplace homotopy perturbation method for burgers equation with space- and time-fractional order.(De Gruyter, 2015-12-20) Johnston, S. J.; Jafari, H.; Moshokoa, S. P.; Ariyan, V. M.; Baleanu, D.The fractional Burgers equation describes the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. The Laplace homotopy perturbation method is discussed to obtain the approximate analytical solution of space-fractional and time-fractional Burgers equations. The method used combines the Laplace transform and the homotopy perturbation method. Numerical results show that the approach is easy to implement and accurate when applied to partial differential equations of fractional orders.Item Solitons in magneto-optic waveguides by extended trial function scheme.(Elsevier, 2017-04-12) Ekici, Mehmet; Zhou, Qin; Sonmezoglu, Abdullah; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Biswas, Anjan; Belic, MilivojThis paper obtains soliton solutions to magneto-optic waveguides that appear with Kerr, power and log-law nonlinearities. The extended trial function method is employed to obtain these solutions. Thus, bright, dark and singular soliton solutions are retrieved. In addition, Gaussons are obtained for log-law nonlinear waveguides. All of these solutions appear with constraints that guarantees the existence of solitons and Gaussons.Item Dispersive optical solitons with Schrödinger–Hirota equation by extended trial equation method.(Elsevier, 2017-02-12) Ekici, Mehmet; Mirzazadeh, Mohammad; Sonmezoglu, Abdullah; Ullah, Malik Zaka; Asma, Mir; Zhou, Qin; Moshokoa, Seithuti P.; Biswas, Anjan; Belic, MilivojThis paper obtains bright, dark and singular soliton solutions from perturbed Schrödinger–Hirota equation that governs the propagation of dispersive pulses through optical fibers. The trial equation method is adopted to achieve this goal. Both Kerr and power laws of nonlinearity are covered.Item Optical solitons for Lakshmanan–Porsezian–Daniel model with spatio-temporal dispersion using the method of undetermined coefficients.(Elsevier, 2017-06-23) Vega-Guzman, Jose; Alqahtani, Rubayyi T.; Zhou, Qin; Mahmood, Mohammad F.; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Biswas, Anjan; Belic, MilivojThis paper obtains optical soliton solutions to the Lakshmanan–Porsezian–Daniel model. The method of undetermined coefficients is applied to extract these solutions. Bright, dark and singular soliton solutions are obtained and the constraint conditions for the existence of these solitons are presented.Item Embedded solitons and conservation law with χ (2) and χ (3) nonlinear susceptibilities.(Jagiellonian University, 2016-10-27) Savescu, M.; Kara, A.H.; Kumar, S.; Krishnan, E.V.; Ullah, M. Zaka; Moshokoa, S.P.; Zhou, Qin; Biswas, A.This paper studies embedded solitons that are confined to continuous spectrum, with χ(2) and χ(3) nonlinear susceptibilities. Bright and singular soliton solutions are obtained by the method of undetermined coefficients. Subsequently, the Lie symmetry analysis and mapping method retrieves additional solutions to the model such as shock waves, singular solitons, cnoidal waves, and several others. Finally, a conservation law for this model is secured through the Lie symmetry analysis.Item Solitons in nonlinear directional couplers with optical metamaterials by trial function scheme.(Jagiellonian University, 2017-03-23) Arnous, A.H.; Ekici, M.; Moshokoa, S.P.; Ullah, M. Zaka; Biswa, A.; Belic., M.This paper obtains soliton solutions to nonlinear directional couplers in optical metamaterials by the aid of trial function method. Three types of couplers are studied. Four forms of nonlinearity are considered. Bright, dark, and singular soliton solutions are retrieved. These soliton solutions appear with certain constraint conditions that guarantee their existence.Item Optical solitons with higher order dispersions in parabolic law medium by trial solution approach.(Elsevier, 2016-09-13) Arnous, Ahmed H.; Mirzazadeh, Mohammad; Zhou, Qin; Moshokoa, Seithuti P.; Biswas, Anjan; Belic, MilivojThis paper obtains bright, dark and singular soliton solutions in optical fibers with parabolic law nonlinearity in the presence of third and fourth order dispersions. The trial solutions approach is employed to carry out this integration. Besides solitons, periodic singular solutions are also obtained as a byproduct. The corresponding constraint conditions are also listed.Item Optical solitons with DWDM technology and four-wave mixing.(Elsevier, 2017-04-17) Ekici, Mehmet; Zhou, Qin; Sonmezoglu, Abdullah; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Biswas, Anjan; Belic, MilivojThis paper obtains bright and singular optical soliton solutions to DWDM system in presence of four-wave mixing. The extended trial function scheme is adopted. The two types of nonlinear media studied are Kerr law and parabolic law. There are other types of waves that appears as a byproduct to this scheme.Item Dark and singular dispersive optical solitons of Schrödinger–Hirota equation by modified simple equation method.(Elsevier, 2017-02-14) Arnous, Ahmed H.; Ullah, Malik Zaka; Asma, Mir; Moshokoa, Seithuti P.; Zhou, Qin; Mirzazadeh, Mohammad; Biswas, Anjan; Belic, MilivojThis paper obtains dispersive dark and singular optical solitons, governed by Schrödinger–Hirota equation, in optical fibers. The integration algorithm is the modified simple equation method. Both Kerr law and power laws of nonlinearity are considered.
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