Near-infrared photonic crystals with higher-order bandgaps generated by two-photon photopolymerization

Three-dimensional photonic crystals with bandgaps of 1.5-2.3 mum in wavelength and with gap/midgap ratios of as much as 18% were generated efficiently by two-photon photopolymerization in a liquid resin. From 0.5-1.1-mW femtosecond-pulsed 540-nm light, woodpile structures consisting of 40 layers of elliptically shaped rods spaced at 350-500 nm were fabricated by focusing with a 1.3-N.A. objective. The high degree of correlation in these structures allowed the suppression of infrared transmission by as much as 50% as well as the observation of higher-order bandgaps. We also investigated the decrease in the gap wavelength on reduction of layer spacing, in-plane rod spacing, and rod size.     

Recurrence relations for semilocal convergence of a fifth-order method in Banach spaces

In this paper, we study the semilocal convergence for a fifth-order method for solving nonlinear equations in Banach spaces. The semilocal convergence of this method is established by using recurrence relations. We prove an existence-uniqueness theorem and give a priori error bounds which demonstrates the R-order of the method. As compared with the Jarratt method in Hernández and Salanova (Southwest J Pure Appl Math 1:29–40, 1999) and the Multi-super-Halley method in Wang et al. (Numer Algorithms 56:497–516, 2011), the differentiability conditions of the convergence of the method in this paper are mild and the R-order is improved. Finally, we give some numerical applications to demonstrate our approach.     

一类函数增量的局部渐近性质

文章研究了一类函数增量的局部渐近性质,发现这类函数增量的局部渐近性对于一元实函数,二元及多元实函数,向量值函数和复函数在一定条件下都会保持不变,进而提出了两个相关的猜想:此类函数增量的渐近性是关于函数变换的拓扑不变量。     

1D atom localization via probe absorption spectrum in a four-level cascade-type atomic system

We present a simple scheme of atom localization in a subwavelength domain via manipulation of probe absorption spectrum in a four-level atomic system. Due to the joint quantum interference induced by the standing-wave and radio-frequency driving fields, the localization peak position and number as well as the conditional position probability can be controlled by properly adjusting the system parameters. The proposed scheme may provide a promising way to achieve high-precision and high-resolution 1D atom localization.     

On the convergence of <Emphasis Type="Italic">s</Emphasis>-dependent GFR conjugate gradient method for unconstrained optimization

In this paper, the authors present an s-dependent conjugate gradient method for unconstrained optimization problem and make two different kinds of estimations of upper bounds of β _k with respect to \(\beta_{k}^{\mathrm{FR}}\) which are called dependent ratio. The global convergence of s-dependent GFR conjugate gradient method using several step-size rules is obtained.     

Hydrothermal-assisted ion exchange synthesis and photoluminescence of Li+ and Eu3+ co-doped NaLa(WO4)2 as near-UV type red phosphors

A series of Li⁺ and Eu³⁺ co-doped double tungstate NaLa(WO₄)₂ (NLW) red phosphors have been successfully synthesized by an ion exchange method under a hydrothermal condition. The effects of Li⁺ doping concentration on the crystal structure, morphology and photoluminescence properties were investigated using the XRD, TEM and photoluminescence (PL) measurements. The results reveal that the samples have phase-pure scheelite structure and adopt spherical particle morphology. Furthermore, room temperature PL spectrum shows that the optical brightness is highly dependent on the concentration of doping Li⁺, which is determined by ion exchange duration and the precursor concentration of LiNO₃. As 5% Li⁺ ions was introduced into the crystal lattice, the emission intensity was enhanced by more than 10-fold as compared with the pristine one. Moreover, the co-doping of Li⁺ can substantially improve the effective excitation of the NaLa(WO₄)₂:Eu³⁺ phosphors under near-UV region.     

斜光轴面内位移测量的数字散斑相关法研究

以工程环境中远距离位移和位移场的光学测量为研究课题,分析了远距离斜光轴成像时,像模糊和成像位置变化对白光数字散斑相关方法产生的影响,给出了这两种影响的误差理论计算公式。提出使用参考测量技术克服斜光轴成像位置变化带来影响,给出一种新的远距离斜光轴高精度测量面内位移的方法,在2～50m处作静载挠度测量,其最大相对误差小于1％,测量精度在实验室环境和工程测量环境中都得到了验证。该方法无需共轴光路的测量环境要求,特别适用于桥梁、高速公路立交桥的静载挠度测量等工程应用。使用高速图像采集卡,该方法可应用于斜光轴动态位移测量,拓展了数字散斑相关方法的应用范围。     

Demixing of amphiphile–polymer mixtures investigated using density functional theory

We construct a functional for amphiphile–polymer mixtures and investigate the demixing transition by using a proposed version of density functional theory. It is found that increase of the amphiphilic size ratio and polymer length can effectively promote phase separation of the systems. Phase diagrams are plotted to clarify these influences. The results provide an effective way of controlling the stability of the fluid–fluid phase equilibrium of the mixtures.     

Geometric, topological and differentiable rigidity of submanifolds in space forms

Let M be an n-dimensional submanifold in the simply connected space form F ^n+p (c) with c + H ² > 0, where H is the mean curvature of M. We verify that if M ⁿ (n ≥ 3) is an oriented compact submanifold with parallel mean curvature and its Ricci curvature satisfies Ric _M ≥ (n ? 2)(c + H ²), then M is either a totally umbilic sphere, a Clifford hypersurface in an (n + 1)-sphere with n = even, or ${\mathbb{C}P^{2} \left(\frac{4}{3}(c + H^{2})\right) {\rm in} S^{7} \left(\frac{1}{\sqrt{c + H^{2}}}\right)}$ C P 2 4 3 ( c + H 2 ) in S 7 1 c + H 2 . In particular, if Ric _M > (n ? 2)(c + H ²), then M is a totally umbilic sphere. We then prove that if M ⁿ (n ≥ 4) is a compact submanifold in F ^n+p (c) with c ≥ 0, and if Ric _M > (n ? 2)(c + H ²), then M is homeomorphic to a sphere. It should be emphasized that our pinching conditions above are sharp. Finally, we obtain a differentiable sphere theorem for submanifolds with positive Ricci curvature.     

Fabrication and magnetic properties of Ni-Zn nanowire arrays

Ni-Zn nanowire arrays, with diameters of approximately 60 nm and lengths of around 40 μm, were fabricated by electrodeposition in porous anodic aluminum oxide templates at different electric potentials. X-ray diffraction observations demonstrated that the isolated nanowires had polycrystalline structure and that their phases changed with the deposition potential. The amount of deposited zinc in the nanowires increased with the deposition potential, whereas the amount of nickel decreased. Magnetic measurements showed that there was a gradual change of magnetism from isotropic to anistropic with increasing potential amplitude and that the coercivity reached a maximum value in the nanowire deposited at −1.35 V.