The simplest equation method to study perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity

The simplest equation method is a powerful solution method for obtaining exact solutions of nonlinear evolution equations.In this paper, the simplest equation method is used to construct exact solutions of nonlinear Schrödinger’s equation and perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity. It is shown that the proposed method is effective and general.     

The first integral method to some complex nonlinear partial differential equations

In this paper, the first integral method is used to construct exact solutions of the Hamiltonian amplitude equation and coupled Higgs field equation. The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones.     

Synthesis of nanocrystalline γ-Al_2O_3 by sol-gel and precipitation methods for methanol dehydration to dimethyl ether

The capability of sol-gel and conventional precipitation techniques for the synthesis of nanocrystalline γ-alumina was investigated. These catalysts were used for vapor-phase dehydration of methanol to dimethyl ether in a fixed-bed reactor under the same operating conditions (T = 300 ?C, P = 1 bar, LHSV = 2.8, 11.7, 26.1 h?1) and characterized by means of N2 adsorption-desorption, NH3-TPD, XRD, TGA and SEM techniques. According to the experimental results, the catalysts prepared using sol-gel method in non-aqueous medium showed better performance compared with those prepared by other methods.     

Optimized quantization for diffractive phase elements by use of uneven phase levels

Many applications of diffractive phase elements involve the calculation of a continuous phase profile, which is subsequently quantized for fabrication. The quantization process maps the continuous range of phase values to a limited number of discrete steps. We present a new scheme with unevenly spaced levels for the design of diffractive elements and apply it to the design of intracavity mode-selecting elements. We show that this modified quantization can produce significantly better results than are possible with a regular or even the bias-phase-optimized quantization scheme that we reported here earlier. In principle this process can be employed to a greater or lesser extent in any quantization process, allowing the fabrication of diffractive elements with much improved performance.     

Iterative algorithm for the design of diffractive phase elements for laser beam shaping

An improved iterative algorithm for designing diffractive phase elements for laser beam shaping in free space is presented. The algorithm begins with the Gerchberg-Saxton approach to obtain a stable solution. This is followed by several new iterations, in which modified constraining functions are imposed in the Fourier domain while the phase distribution of each iteration remains unchanged. For super-Gaussian beam shaping suitable for inertial confinement fusion applications the mean-square errors of the amplitude and the intensity profile of the entire beam fitted to the corresponding parameters of the 12th-power super-Gaussian beam are approximately 0.035 and 9.75x10(-3), respectively. Approximately 97.4% of the incident energy is converged into the desired region.     

Almost local stability in discrete delayed chaotic systems

This work studies dynamic of delayed discrete chaotic systems with bounded and unbounded delays. The time lags appear in additive which is coupled with a smooth function and nonadditive forms. It has been shown that, in both additive and nonadditive cases, the primal (non-delayed) system is neutral to the bounded delay to possess an attractive fixed point. Nevertheless, if a nonadditive and unbounded delay is supposed to affect a chaotic and measure preserving system locally, then the delay function might be sensitive to initial states. A local stabilization to the dynamics of Logistic and Gaussian maps are made and creation of attractive fixed points is illustrated.     

Proanthocyanidins Modulate Rumen Enzyme Activities and Protein Utilization In Vitro

This study investigated the principal leaf protein (rubisco) solubilization and in vitro ruminal enzyme activity in relation to the molecular structure of proanthocyanidins extracted from leaves of Anogeissus pendula and Eugenia jambolana. Six proanthocyanidin fractions were extracted by 50% (v/v) methanol–water followed by 70% (v/v) acetone–water and then distilled water from leaves of A. pendula (AP) and E. jambolana (EJ) to yield EJ–70, EJ–50, EJ–DW, AP–70, AP–50 and AP–DW. Fractions were examined for their molecular structure and their effects on sheep ruminal enzymes and solubilization of rubisco in vitro. All fractions significantly (p < 0.05) inhibited the activity of ruminal glutamic oxaloacetic transaminase and glutamic pyruvic transaminase. The fractions AP–50 and EJ–50 significantly inhibited the activity of the R-cellulase enzyme. Most of the fractions inhibited R-glutamate dehydrogenase activity (p < 0.05) by increasing its concentration, while protease activity decreased by up to 58% with increasing incubation time and concentration. The solubilization of rubisco was observed to be comparatively higher in A. pendula (16.60 ± 1.97%) and E. jambolana (15.03 ± 1.06%) than that of wheat straw (8.95 ± 0.95%) and berseem hay (3.04 ± 0.08%). A significant (p < 0.05) increase in protein solubilization was observed when wheat straw and berseem hay were supplemented with A. pendula and E. jambolana leaves at different proportions. The efficiency of microbial protein was significantly (p < 0.05) greater with the supplementation of leaves of A. pendula in comparison to E. jambolana. The overall conclusion is that the proanthocyanidins obtained from E. jambolana exhibited greater inhibitory activities on rumen enzymes, whereas A. pendula recorded higher protein solubilization. Thus, PAs from A. pendula and E. jambolana appear to have the potential to manipulate rumen enzyme activities for efficient utilization of protein and fiber in ruminants.     

A novel magnetic metal organic framework nanocomposite for extraction and preconcentration of heavy metal ions, and its optimization via experimental design methodology

We describe a novel magnetic metal-organic framework (MOF) prepared from dithizone-modified Fe₃O₄ nanoparticles and a copper-(benzene-1,3,5-tricarboxylate) MOF and its use in the preconcentration of Cd(II), Pb(II), Ni(II), and Zn(II) ions. The parameters affecting preconcentration were optimized by a Box-Behnken design through response surface methodology. Three variables (extraction time, amount of the magnetic sorbent, and pH value) were selected as the main factors affecting adsorption, while four variables (type, volume and concentration of the eluent; desorption time) were selected for desorption in the optimization study. Following preconcentration and elution, the ions were quantified by FAAS. The limits of detection are 0.12, 0.39, 0.98, and 1.2 ng mL^?1 for Cd(II), Zn(II), Ni(II), and Pb(II) ions, respectively. The relative standard deviations were <4.5 % for five separate batch determinations of 50 ng mL^?1 of Cd(II), Zn(II), Ni(II), and Pb(II) ions. The adsorption capacities (in mg g^?1) of this new MOF are 188 for Cd(II), 104 for Pb(II), 98 Ni(II), and 206 for Zn(II). The magnetic MOF nanocomposite has a higher capacity than the Fe₃O₄/dithizone conjugate. This magnetic MOF nanocomposite was successfully applied to the rapid extraction of trace quantities of heavy metal ions in fish, sediment, soil, and water samples.