The pulse propagation in the picosecond or femtosecond regime of birefringent optical fibers is governed by the coupled mixed derivative nonlinear Schr¨odinger (CMDNLS) equations. A new type of Lax pair associated with such coupled equations is derived from the Wadati-Konno-Ichikawa spectral problem. The Darboux transformation method is applied to this integrable model, and the N-times iteration formula of the Darboux transformation is presented in terms of the compact determinant representation. Starting from the zero potential, the bright vector N-soliton solution of CMDNLS equations is expressed as a compact determinant by N complex eigenvalues and N linearly independent eigenfunctions. The collision mechanisms in two components shows that bright vector solitons can exhibit the standard elastic and inelastic collisions. Such energy-exchange collision behaviours have potential applications in the construction of logical gates, the design of fiber directional couplers, and quantum information processors.
In the present study, sulfate reducing bacteria (SRB) granular sludge was made to remove cadmium, iron and sulfate from synthetic acid rock drainage (ARD) using upflow anaerobic bioreactor in the laboratory scale. The robustness of the process was tested by increasing stepwise metal and sulfate concentrations and decreasing influent pH. The result showed the bioreactor effectively treated synthetic ARD with high concentrations of cadmium, iron and sulfate. Sulfide precipitation was found to be the main mechanism of iron and cadmium removal. The dominate sulfate reducer in the bioreactor was Desulfovibrio which resulted in effective sulfate reduction and metals removal. The result suggested the SRB granular sludge could have a good potential for ARD treatment with high concentration of metals and low pH.
In this study, for the first time, we discuss the posteriori error estimates and
adaptive algorithm for the non-self-adjoint Steklov eigenvalue problem in inverse
scattering. The differential operator corresponding to this problem is
non-self-adjoint and the associated weak formulation is not H1-elliptic. Based on the study of Armentano et al. [Appl. Numer. Math.
58 (2008), 593–601], we first introduce error indicators for
primal eigenfunction, dual eigenfunction, and eigenvalue. Second, we use
Gårding’s inequality and duality technique to give the upper and lower
bounds for energy norm of error of finite element eigenfunction, which shows that our
indicators are reliable and efficient. Finally, we present numerical results to
validate our theoretical analysis.
DNA sequences can be used for the analysis of genetic variation and gene function. The high-throughput sequencing techniques that have been developed over the past three years can read as many as one billion bases per run, and are far less expensive than the traditional Sanger sequencing method. Therefore, the high-throughput sequencing has been applied extensively to genomic analyses, such as screening for mutations, construction of genomic methylation maps, and the study of DNA-protein interactions. Although they have only been available for a short period, high-throughput sequencing techniques are profoundly affecting many of the life sciences, and are opening out new potential avenues of research. With the highly-developed commercial high-throughput sequencing platforms, each laboratory has the opportunity to explore this research field. Therefore, in this paper, we have focused on commercially-popular high-throughput sequencing techniques and the ways in which they have been applied over the past three years.