Compared with commercial polyolefin membranes, polyacrylonitrile (PAN) membrane prepared by electrostatic spinning has higher porosity, electrolyte uptake, thermal stability, and lithium-ion conductivity, etc. However, poor mechanical performance has largely limited the application of electrospun PAN separators. In this study, PAN/polyimide (PI) composite membrane is prepared by electrostatic spinning to improve the mechanical and electrochemical performances. Scanning electron microscopy, thermal analysis method, and electrochemical methods were used for evaluation of the electrospun composite membrane. The results show that the composite membrane possesses good thermal stability and exhibits better mechanical performance than pristine PAN membrane (increasing by 1.1 times in tension strength). The addition of PI can increase porosity and fluid absorption rate obviously. In addition, the composite membrane has high ionic conductivity (18.77 × 10−4 S/cm), wide electrochemical window (about 4.0 V), and excellent cycling performance. It can retain a discharge specific capacity of 153 mA h/g even after 50 cycles at 0.5 C. The electrospun PAN/PI membrane may be a promising candidate for lithium-ion battery separators.

We consider the nonlinear and ill-posed inverse problem where the Robin coefficient in the Laplace equation is to be estimated using the measured data from the accessible part of the boundary. Two regularisation methods are considered — viz. L2 and H1 regularisation. The regularised problem is transformed to a nonlinear least squares problem; and a suitable regularisation parameter is chosen via the normalised cumulative periodogram (NCP) curve of the residual vector under the assumption of white noise, where information on the noise level is not required. Numerical results show that the proposed method is efficient and competitive.

In this paper, preconditioned iterative methods for solving two-dimensional space-fractional diffusion equations are considered. The fractional diffusion equation is discretized by a second-order finite difference scheme, namely, the Crank-Nicolson weighted and shifted Grünwald difference (CN-WSGD) scheme proposed in [W. Tian, H. Zhou and W. Deng, A class of second order difference approximation for solving space fractional diffusion equations, Math. Comp., 84 (2015) 1703-1727]. For the discretized linear systems, we first propose preconditioned iterative methods to solve them. Then we apply the D’Yakonov ADI scheme to split the linear systems and solve the obtained splitting systems by iterative methods. Two preconditioned iterative methods, the preconditioned generalized minimal residual (preconditioned GMRES) method and the preconditioned conjugate gradient normal residual (preconditioned CGNR) method, are proposed to solve relevant linear systems. By fully exploiting the structure of the coefficient matrix, we design two special kinds of preconditioners, which are easily constructed and are able to accelerate convergence of iterative solvers. Numerical results show the efficiency of our preconditioners.

We consider a Robin inverse problem associated with the Laplace equation, which is a severely ill-posed and nonlinear. We formulate the problem as a boundary integral equation, and introduce a functional of the Robin coefficient as a regularisation term. A conjugate gradient method is proposed for solving the consequent regularised nonlinear least squares problem. Numerical examples are presented to illustrate the effectiveness of the proposed method.

An efficient numerical method is proposed for the solution of Love's integral equation

where c > 0 is a small parameter, by using a sinc Nyström method based on a double exponential transformation. The method is derived using the property that the solution ƒ(x) of Love's integral equation satisfies ƒ (x) → 0.5 for x ∈ (−1, 1) when the parameter c → 0. Numerical results show that the proposed method is very efficient.

The most important crustal growth on Earth occurred at ~2.7 Ga, but the North China Craton (NCC) is characterized by prevalent development of ~2.5 Ga juvenile crust, with relatively rare records of ~2.7 Ga crustal growth. The Fuping Complex in the middle segment of the Trans-North China Orogen (TNCO) between the Eastern and Western blocks of the NCC is composed mainly of ~2.5 Ga Fuping tonalitic–trondhjemitic–granodioritic (TTG) gneisses and Longquanguan augen gneisses, ~2.1 Ga Nanying granitic gneisses and the Wanzi supracrustal rocks. Previous studies have suggested one major phase of crustal growth at ~2.5 Ga, possible intracrustal recycling at ~2.1 Ga and the presence of older rocks in the Fuping Complex, but there has been no record of ~2.7 Ga crustal growth. The Fuping TTG gneisses are dominated by stromatic migmatite, and new U–Pb dating of magmatic zircons from two stromatic migmatite samples yielded three different ages: (1) 2.75 Ga, which is the oldest age obtained from the Fuping TTG gneisses, (2) 2.54 Ga, which just falls in the published zircon U–Pb age range of 2.53 to 2.47 Ga for the Fuping TTG gneisses, and (3) 2.11 Ga, which is almost the same as the age of the Nanying granitic gneisses. Therefore, there are two generations of TTG gneisses in the Fuping Complex. Importantly, both of the 2.75 and 2.54 Ga zircons have the highest εHf(t) values, almost equal to the contemporaneous depleted mantle. This indicates high contributions of juvenile material to the two generations of TTG gneisses. In contrast, the 2.11 Ga zircons have apparently low εHf(t) values of −0.47 to +2.04, just falling in between 2.55 and 2.75 Ga continental crust values. This strongly suggests the reworking of the two generations of TTG gneisses at 2.1 Ga. Zircon U–Pb and Hf isotopes convincingly reveal two major phases of crustal growth in the Fuping Complex at ~2.7 and ~2.5 Ga, the same as in the northern and southern segments of the TNCO, and also confirm one major phase of intracrustal recycling at ~2.1 Ga, which may be responsible for the Nanying granitic gneisses.

In this study we report on the correlation between bacteriology and disease severity staging by computed tomography (CT) for chronic sinusitis. When patients with chronic sinusitis underwent functional endoscopic sinus surgery (FESS), swab specimens were taken from the ipsilateral middle meati and ethmoid sinuses under endoscope guidance. The severity of chronic sinusitis was evaluated by pre-operative CT scans. The CT scans were staged by the Lund and Mackay system. The scores for the frontal, anterior ethmoid and maxillary sinuses and for the ostiomeatal complex were added. The culture rates were correlated with the added scores. Between November 1998 and January 2003, 79 pairs of specimens were collected from 79 patients whose CT scans were done within a day before FESS. The culture rates of middle-meatus specimens were moderately correlated with the scores, but those of ethmoid sinus specimens were negatively correlated with the scores. If Staphylococcus epidermidis and corynebacteria were considered normal flora, the bacteriology of the middle meatus was highly correlated with the CT scores. This study shows that culture rates of middle-meatal specimens tended to increase with the severity of chronic sinusitis.

High-quality GaP, GaP@GaN and GaN@GaP nanowires were grown by a convenient vapor deposition technique. The wire-like and two-layers structures of GaP@GaN and GaN@GaP core-shell nanowires were clearly resolved using X-ray powder diffraction and high-resolution transmission electron microscopy (HRTEM) and their growth directions were identified. Photoluminescence intensity of GaP@GaN nanowires increased as temperature increased. The result was interpreted by the piezoelectric effect induced from lattice mismatch between two semiconductor layers. An unexpected peak at 386 cm-1 was found in the Raman spectra of GaN@GaP and assigned to a surface phonon mode due to the interface. Detailed synthetic conditions and possible growth mechanisms of those nanowires were proposed.

In this study we report on the correlation between the bacteriology of the middle meatusand ethmoid sinus in chronic sinusitis. When patients with chronic sinusitis underwent functional endoscopicsinus surgery (FESS), swab specimens were taken from the middle meati before surgery. After removing the ethmoid bullae, swab specimens were taken from the ethmoid sinuses. Between November 1998 and February 2001, 186 pairs of middle meatal and ethmoid sinus specimens were collected from 186 patients. No bacteria were cultured from either specimen in 32 patients. The same bacteria were cultured from both specimens in another 60 patients. The culture results differed between the middle meatal and ethmoid sinus specimens in the remaining 94 patients. There was a significant difference between culture rates of 63.4 per cent for middle meatal specimens and 76.3 per cent for the ethmoid sinus specimens. In analysing bacterial species, significantly more aerobic Gram negative bacteria were cultured from the ethmoid sinus specimens than from the middle meatalspecimens. This study shows that the bacteriology of the middle meatus was different from that of the ethmoid sinus. Therefore, the bacteriological findings in the middle meati may not reflect the real bacteriology in chronic sinusitis.

Experiments have shown that the third-order nonlinear spectrum of trans- polyacetylene has two peaks at 0.6 eV and 0.9 eV respectively. None of the existing theories can give a quantitatively satisfying interpretation. A new theory is proposed in this paper by considering the excitation-dependent damping, and the theoretical results agree with the observed spectrum very well.