Finite difference technique for solving obstacle problems

In this paper, we use the variational inequality theory coupled with finite difference technique to obtain an approximate solution for a class of obstacle problems in elasticity, like those describing the equilibrium configuration of an elastic string stretched over an elastic obstacle. The variational inequality formulation is used to discuss the problem of uniqueness and existence of the solution of the obstacle problems.     

Study on the Range of Particles Size Measured by Backscattering Method in Visual‐infrared Incident Spectrum

For the measurement of particles size with backscattering method, the suitable range of particles size measurement have been presented by independent algorithm in Visual‐infrared incident spectrum. We defined the range according to the retrieved results based on the analysis and comparison to many kinds of R‐R distribution function. The simulation computation results showed that the particles size measurement range is from 0.05 μm to 18 μm with incident spectrum from 0.4 μm to 2 μm and different refractive index. The results retrieved were satisfied even if 1 % noise was added into the backscattering intensity.     

Bifurcations and chaos control in a discrete-time predator-prey system of Leslie type

We investigate the dynamics of a discrete-time predator-prey system of Leslie type. We show algebraically that the system passes through a flip bifurcation and a Neimark-Sacker bifurcation in the interior of $\R^{2}_+$ using center manifold theorem and bifurcation theory. Numerical simulations are implimented not only to validate theoretical analysis but also exhibits chaotic behaviors, including phase portraits, period-11 orbits, invariant closed circle, and attracting chaotic sets. Furthermore, we compute Lyapunov exponents and fractal dimension numerically to justify the chaotic behaviors of the system. Finally, a state feedback control method is applied to stabilize the chaotic orbits at an unstable fixed point.     

Free convection effects on the oscillatory flow past a vertical porous plate in the presence of radiation for an optically thin fluid

The purpose of this work is to study the effect of transverse sinusoidal suction velocity on the flow and mass transfer on free convective oscillatory viscous and optically thin grey fluid over a porous vertical plate in the presence of radiation. The flow becomes three-dimensional due to the variation of suction velocity in the transverse direction. Analytical expressions for velocity and temperature fields are obtained using the perturbation technique. The governing equations has been transformed to ordinary differential equations. Numerical solutions are obtained for different values of radiation parameter, Grashof number and Schmidt number. It is found that non-dimensional velocity decreases with increase of radiation parameter, increases with increase of Grashof number, decreases with increase of Schmidt number and non-dimensional temperature decreases with the increase of radiation parameter.     

Fixed-Point Iterations for Asymptotically Nonexpansive Mappings in Banach Spaces

In this paper, we suggest and analyze a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces. The new iterative scheme includes Ishikawa-type and Mann-type interations as special cases. The results obtained in this paper represent an extension as well as refinement of previous known results.     

Three-step iterations for nonlinear accretive operator equations

In this paper, we suggest and analyze a three-step iterative scheme for solving nonlinear strongly accretive operator equation Tx=f without continuous condition in a uniformly smooth Banach space. Our results include the Ishikawa, Mann and Noor iterations as special cases. The results presented in this paper improve and extend almost all the current results in the more general setting.     

Switchable single- and dual-wavelength erbium-doped fiber laser assisted by four-wave mixing with wide and continuous tunability

A widely tunable and stable erbium-doped fiber laser based on four-wave mixing effect in a highly nonlinear fiber is proposed and experimentally demonstrated. By adjusting reflected power from a dual-selective element, the ring laser is switchable between single- and dual-wavelength operations. The tuning range of the single laser is 22.78 nm, from 1,542.07 to 1,564.85 nm, while the wavelength spacing of the dual-wavelength can be continuously tuned from 0.52 to 22.78 nm. The laser is stable with output peak power fluctuation of <1 dB in 30-min interval.     

Spectral,electron microscopic and chemical investigations of gamma-induced purple color zonings in amethyst crystals from the Dursunbey-Balıkesir region of Turkey

Amethyst crystals on matrix specimens from the Dursunbey-Bal?kesir region in Turkey have five representative purple color zonings: dark purple, light purple, lilac, orchid, and violet. The purple color zonings have been analyzed with optical absorption spectra in the visible wavelength region, chemical full trace element analyses (inductively coupled plasma-atomic emission spectroscopy and inductively coupled plasma-mass spectroscopy), and scanning electron microscopic images with high magnification. It can be proposed that the production of the purple color in amethyst crystals is due to three dominant absorption bands centered at 375, 530, and 675 nm, respectively. In addition, the purple color zonings are also due to four minor absorption bands centered at 435, 480, 620, and 760 nm. X-ray diffraction graphics of the investigated amethyst crystals indicate that these crystals are composed of a nearly pure alpha-quartz phase and do not include any moganite silica phase and/or other mineral implications. Trace element analyses of the amethyst crystals show five representative purple color zonings, suggesting that the absorption bands can be mainly attributed to extrinsic defects (chemical impurities). However, another important factor that influences all structural defects in amethyst is likely to be the gamma irradiation that exists during amethyst crystallization and its inclusion in host materials. This gamma irradiation originates from the large underlying intrusive granitoid body in the region of amethyst formation. Irradiation modifies the valence values of the impurity elements in the amethyst crystals. It is observed that the violet-colored amethyst crystals have the most stable and the least reversible coloration when exposed to strong light sources. This situation can be related to the higher impurity content of Fe (2.50 ppm), Co (3.1 ppm), Ni (38 ppm), Cu (17.9 ppm), Zn (10 ppm), Zr (3.9 ppm), and Mo (21.8 ppm).     

On General Mixed Quasivariational Inequalities

In this paper, we suggest and analyze several iterative methods for solving general mixed quasivariational inequalities by using the technique of updating the solution and the auxiliary principle. It is shown that the convergence of these methods requires either the pseudomonotonicity or the partially relaxed strong monotonicity of the operator. Proofs of convergence is very simple. Our new methods differ from the existing methods for solving various classes of variational inequalities and related optimization problems. Various special cases are also discussed.     

Parametric Quintic-Spline Approach to the Solution of a System of Fourth-Order Boundary-Value Problems

In this paper, we use parametric quintic splines to derive some consistency relations which are then used to develop a numerical method for computing the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is known that a class of variational inequalities related to contact problems in elastostatics can be characterized by a sequence of variational inequations, which are solved using some numerical method. Numerical evidence is presented to show the applicability and superiority of the new method over other collocation, finite difference, and spline methods.