Abstract. We consider the mixed reduction condition for the Kaup-Newell equation based on the Darboux transformation. By direct calculations, both the first-order rogue wave and the second-order rogue wave on a periodic background are obtained. By taking a certain perturbation coefficient to eigenfunction, we show that the second-order rogue wave can display either a fundamental pattern or a triangle pattern on the periodic background.

Abstract. This paper describes the problem of finding potential functions admitted by Klein-Gordon equations, via a method based on a geometric selection rule. We exemplify the method by applying it to geometries that admit simply-transitive group of motions, in particular, Petrov type II, III, N and D. We derive the functional forms of the potentials under certain restrictions involving subgroups and linear combinations of the homothety group. Due to the volume of results and for utilizing space economically, the results are presented in the form of tables.

Abstract. This paper obtains traveling wave solutions to four distinct, non-integrable, Boussinesq-like equations with the effect of spatial dispersion for two variants of the Boussinesq equation, and with the effect of spatial-temporal dispersion for other two variants. The sine-cosine method is used to study these equations and to derive the traveling wave solutions.

Abstract. This paper is devoted to investigate, from the numerical point of view, fractional-order Gegenbauer functions to solve fractional variational problems and fractional optimal control problems. We first introduce an orthonormal system of fractional-order Gegenbauer functions. Then, a formulation for the fractional-order Gegenbauer operational matrix of fractional integration is constructed. An error upper bound for the operational matrix of the fractional integration is also given. The properties of the fractional-order Gegenbauer functions are utilized to reduce the given optimization problems to systems of algebraic equations. Some numerical examples are included to demonstrate the efficiency and the accuracy of the proposed approach.

Abstract. In the present paper, an effective approach is introduced to overcome the difficulties of imposing boundary conditions at infinity, which are used to modelling the boundary layer flow of a nanofluid past a stretching sheet. The proposed scheme is mainly based on the Adomian decomposition method with an effective procedure to imposing the boundary conditions at infinity. On applying the present approach to approximate the solution of a boundary value problem in the literature, it is found that only two components of Adomian's series are sufficient to achieve the same accuracy of the homotopy analysis method using forty iterations.

Abstract. The main feature of the boundary layer flow problems, such as Blasius and Falkner-Skan problems, is the inclusion of the boundary conditions at infinity. As a well known fact, such boundary conditions cause difficulties for any of the series methods. This is because the boundary conditions at infinity can not be imposed directly into the series solution, where Pade approximant should be first constructed before applying such conditions. To overcome this difficulty, an approach has been suggested recently by Ebaid and Al-Armani [Abstr. Appl. Anal., 753049 (2013)], which is based on changing the boundary conditions at infinity to classical ones by using a proper transformation. This approach is applied in the present paper to solve a class of Falkner-Skan equation analytically and numerically. Moreover, an exact solution is deduced at a certain value of the velocity ratio parameter. In addition, the current numerical results are compared with the other existing solutions, and good agreement has been achieved. Indeed, the main advantage of the present approach is the complete avoidance of Pade approximant to deal with the boundary condition at infinity.

Abstract. The hyperbolic Kepler equation is of practical interest in astronomy. It is often used to describe the eccentric anomaly of a comet of extrasolar origin in its hyperbolic trajectory past the Sun. Efficient determination of the radial distance and/or the Cartesian coordinates of the comet requires accurate calculation of the eccentric anomaly, hence the need for a convenient, robust method to solve Kepler's equation of hyperbolic type. In this paper, the Adomian's asymptotic decomposition method is proposed to solve this equation. Our calculations have demonstrated a rapid rate of convergence of the sequence of the obtained approximate solutions, which are displayed in several graphs. Also, we have shown in this paper that only a few terms of the Adomian decomposition series are sufficient to achieve extremely accurate numerical results even for much higher values than those in the literature for the mean anomaly and the eccentricity of the orbit. The main characteristic of the obtained approximate solutions is that they are all odd functions in the mean anomaly, which we have illustrated through graphs. In addition, it is found that the absolute remainder error using only three components of Adomian's solution decreases across a specified domain and approaches zero as the eccentric anomaly tends to infinity. Moreover, the absolute remainder error decreases by increasing the number of components of the Adomian decomposition series. Finally, the current analysis may be the first to make an effective application of the Adomian's asymptotic decomposition method in astronomical physics.

Abstract. We study, both analytically and numerically, families of periodic solutions of the nonlinear Schrodinger equation with periodically-modulated third-order dispersion (TOD) and complex-valued potential. The TOD and the complex potential are built as solutions of an inverse problem, which predicts the explicit expressions of the complex-valued potential and the TOD supporting a required phase-gradient structure of the periodic solutions. We investigate in detail the band structure of the stability problem of the periodic solutions in the corresponding periodic complex potential by means of plane-wave-expansion method and direct numerical simulations of the evolution of the perturbed inputs. The results show that the band stability domains of the periodic solutions may be narrowed when increasing the nonlinear effects and the amplitudes of periodic solutions.

Abstract. We theoretically investigate the effects of Gallium Arsenide (GaAs) as an absorbing material in a complex waveguide structure model. Finite Difference Time Domain (FDTD) method is used to discretize the Maxwell's curl equations for the proposed structure. A comparison between Amorphous Silicon (a-Si) and GaAs as absorbing materials is presented through the computation of the absorption spectra. It has been realized that GaAs is still a promising candidate to be used in the waveguide structure models through maximizing the absorption and minimizing the reflectance in the proposed waveguide structure.

Abstract. We report the results of numerical simulations on the dynamical behavior of quantum dots laser subject to T-type optical feedback. We find that under certain conditions, due to the influence of the external feedback, the system displays strong chaotic behaviour appropriate for chaos-based communications. We demonstrate the influence of the relevant device parameters, such as feedback phases and strengths on the laser dynamics. The synchronization features of two quantum dots lasers coupled unidirectionally are studied numerically. Finally, we find the appropriate conditions for high bit rate message encoding by chaos modulation technique using compact quantum dots lasers under the influence of T-type feedback loops.

Abstract. We perform spin-polarized two-dimensional angular correlation of annihilation radiation (2D-ACAR) calculations for the recently predicted ZrCo₂Sn-Weyl Heusler compound within the density functional theory using the generalized gradient approximation (GGA) and its extension GGA+U. We confirm that within the GGA+U method, a pair of Weyl-points are revealed, and that by doping with Niobium, for the composition Nb_0.3Zr_0.7Co₂Sn, the Weyl points are reaching the Fermi level. Our 2D-ACAR results indicate the existence of the Weyl points, however, within the present calculation, it is uncertain if the smearing at the Fermi level can be attributed to the positron wave function.

Abstract. CT-imaging based planning in intracavitary brachytherapy allows optimization of the dose distribution by patient basis. In addition to classical used point dose, the dose-volume histogram (DVH) analysis enables further possibilities for prescribing and reporting the correct dose. A group of 18 patients were treated with 38 fractions using different applicators and CT-based treatment planning. Each application was analyzed in detail. The clinical target volumes were contoured and also the organs at risk. The dose administered to bladder and rectum was analyzed according to ICRU Reports 38 and dose-volume parameters (e.g. D2cc represents the minimal dose for the most irradiated 2 cm³). The values of the doses were analyzed including the external beam radiotherapy. Total doses were biologically normalized to conventional 2 Gy fractions (α/β = 10 Gy for target and 3 Gy for organs at risk). Individual changes for active dwell positions and dwell weights are guided by a concept of DVH constraints for target and organs at risk. This helps to detect and avoid the severe overdoses.

Abstract. The content of seven major and 26 trace elements were investigated by Epithermal Neuron Activation Analysis in a set of 17 samples of soil collected at a depth of 20 to 40 cm from Romanesti and Cricova vineyards. All data were interpreted within the Upper Continental Crust and Average Soil models as well as in accordance with sanitary norms concerning soil contamination. It was evidenced that the mineral material is very close to the Upper Continental Crust with a certain degree of chemical weathering and a prolonged process of sorting and recycling, which sustains the hypothesis of a mature, well developed soil. The content of Cr, Mn, Co, Zn and As, proved that, with excepting As, the soil have no traces of anthropogenic contamination. The As content, according to existing data, can be regarded as a characteristic of Moldavian soils, not related to any industrial polluting process.

Abstract. Using Excel spreadsheets, we developed a simple simulation software that simulate the vibration of a string and designed to be used in the physics teaching process. Using a special devised animation, the tool will help students to understand and, especially, to visualize the solutions of the equation of the oscillating string. We devised two spreadsheets, one for the plucked and one for the strucked string. We used this tool to analyze the vibration modes of the string and to investigate the way that it may be used in increasing the effectiveness of teaching.