L^2-ERROR OF EXTRAPOLATION CASCADIC MULTIGRID （EXCMG）

Based on an asymptotic expansion of finite element, an extrapolation cascadic multigrid method （EXCMG） is proposed, in which the new extrapolation and quadratic interpolation are used to provide a better initial value on refined grid. In the case of multiple grids, both superconvergence error in H^1-norm and the optimal error in l2-norm are analyzed. The numerical experiment shows the advantage of EXCMG in comparison with CMG.     

Symmetry Reductions,Group‐Invariant Solutions,and Conservation Laws of a (2+1)‐Dimensional Nonlinear Schrödinger Equation in a Heisenberg Ferromagnetic Spin Chain

Nonlinear spin excitations in ferromagnetic spin chains are studied for spintronic and magnetic devices including magnetic‐field sensors and for high‐density data storage. Here, (2+1)‐dimensional nonlinear Schrödinger equation is investigated, which describes the nonlinear spin dynamics for a Heisenberg ferromagnetic spin chain. Lie point symmetry generators and Lie symmetry groups of that equation are derived. Lie symmetry groups are related to the time, space, scale, rotation transformations, and Galilean boosts of that equation. Certain solutions, which are associated with the known solutions, are constructed. Based on the Lie symmetry generators, the reduced systems of such an equation are obtained. Based on the polynomial expansion and through one of the reduced systems, group‐invariant solutions are constructed. Soliton‐type group‐invariant solutions are graphically investigated and effects of the magnetic coupling coefficients, that is, α₁, α₂, α₃, and α₄, on the soliton's amplitude, width, and velocity are discussed. It is seen that α₁, α₂, α₃, and α₄ have no influence on the soliton's amplitude, but can affect the soliton's velocity and width. Lax pair and conservation laws of such an equation are derived.     

XRF法测定铁矿石中TFe、SiO2和P

四硼酸锂为熔剂 ,钴为内标 ,高温熔融法对铁矿石进行均一处理 ,X射线荧光光谱法测定铁矿石中TFe、Si O2 和 P,取得满意结果。     

Jordan-Wigner Approach to Dynamic Correlations in 2D Spin-1/2 Models

We discuss the dynamic properties of the square-lattice spin-1/2 XY model obtained using the two-dimensional Jordan-Wigner fermionization approach. We argue the relevance of the fermionic picture for interpreting the neutron scattering measurements in the two-dimensional frustrated quantum magnet Cs₂CuCl₄.     

New Exact Solutions for (2+1)-Dimensional Breaking Soliton Equation

New exact solutions in terms of the Jacobi elliptic functions are obtained to the (2+1)-dimensional breaking soliton equation by means of the modified mapping method. Limit cases are studied, and new solitary wave solutions and triangular periodic wave solutions are obtained.     

High resolution study of the six lowest doubly excited vibrational states of PH2D

The five lowest doubly excited deformational vibrational bands ν₄ + ν₆, 2ν₆, ν₃ + ν₄, ν₃ + ν₆, and 2ν₃ of PH₂D have been recorded for the first time using a Bruker 120 HR interferometer with a resolution 0.0033 cm⁻¹ and analysed. Some transitions belonging to a very weak band 2ν₄ have been also assigned. From the fit 24 and 86, respectively, diagonal and resonance interaction parameters were obtained which reproduce 1089 upper energy levels obtained from more than 4600 assigned transitions with the rms deviation of 0.00059 cm⁻¹.     

A new constructive method for solving singular integral equations

In this paper, a new method for the approximate solution of linear singular integral equations defined on smooth closed curves is proposed and justified.     

Preparation of nanosized Bi<Subscript>2</Subscript>WO<Subscript>6</Subscript> using different content of starting materials and their photoactivities

A series of nanosized Bi₂WO₆ catalysts was synthesized using various starting materials, and they were characterized by X-ray diffractometry, transmission electron microscopy, and diffuse reflectance spectroscopy. Rhodamine-B (RhB) photodegradation in aqueous medium was employed as a probe reaction to test the photoactivity of the as-prepared samples. Dependence of the photocatalytic activities on different contents of the starting materials was examined under visible irradiation (λ > 400 nm). The sample prepared in the following conditions: reaction time 24 h, the pH of the solution 7, the Bi³⁺ amount in the start precipitates 5 mmol — exhibited the highest photochemical activity when the hydrothermal temperature was settled at 180°C. Published in Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 2, pp. 243–249, Martch–April, 2009.     

Applications of operator identities to the multiple q-binomial theorem and q-Gauss summation theorem

In this paper, we first give an interesting operator identity. Furthermore, using the q-exponential operator technique to the multiple q-binomial theorem and q-Gauss summation theorem, we obtain some transformation formulae and summation theorems of multiple basic hypergeometric series.     

Photoelectrochemical cells using metal-decorated carbon nanotube electrodes

We fabricated the photoelectrochemical (PEC) cells using n-type TiO₂ and metal (Pt, Pd)-decorated carbon nanotubes (CNTs) as an anode and a cathode, respectively. Photovoltaic effects were clearly observed. Compared with conventional PEC cell with Pt cathode, a larger photo-voltage was found in the PEC cells with the metal-decorated CNT cathode due to p-type semiconducting properties of CNTs. Additionally, we connected two PEC cells in series to decompose water into oxygen and hydrogen. Indeed, the connected PEC cells yielded the photo-voltage of about 1.35 V, which is larger than 1.23 V required for water splitting. This result demonstrates the possibility of hydrogen generation using the connected PEC cells without an external bias.