Inequalities and mathematical properties of uncertain variables

Uncertain variables are measurable functions from uncertainty spaces to the set of real numbers. In this paper, some important inequalities of uncertain variables, for example, extension of Jensen’s inequality, Liapounov’s inequality, and refined Markov inequalities are presented. In addition, some mathematical properties of uncertain variables are also given and proven.     

Global convergence of some modified PRP nonlinear conjugate gradient methods

Recently, similar to Hager and Zhang (SIAM J Optim 16:170–192, 2005), Yu (Nonlinear self-scaling conjugate gradient methods for large-scale optimization problems. Thesis of Doctors Degree, Sun Yat-Sen University, 2007) and Yuan (Optim Lett 3:11–21, 2009) proposed modified PRP conjugate gradient methods which generate sufficient descent directions without any line searches. In order to obtain the global convergence of their algorithms, they need the assumption that the stepsize is bounded away from zero. In this paper, we take a little modification to these methods such that the modified methods retain sufficient descent property. Without requirement of the positive lower bound of the stepsize, we prove that the proposed methods are globally convergent. Some numerical results are also reported.     

关于Newton级数的符号算子方法

In this paper, we present several expansions of the symbolic operator （1 ＋E）^x. Moreover, we derive some series transforms formulas and the Newton generating functions of {f（k）}.     

Improved luminescent properties of red-emitting Ca0.54Sr0.16Eu0.08Gd0.12(MoO4)0.2(WO4)0.8 phosphor for LED application by charge compensation

The red-emitting Ca_0.54Sr_0.16Eu_0.08Gd_0.12(MoO₄)_0.2(WO₄)_0.8 phosphor is improved in the emission charateristics by charge compensation, of which chromaticity coordinates (CIE) are x=0.66 and y=0.33. Three approaches to charge compensation are investigated, namely (a) 3Ca²⁺/Sr²⁺→2Eu³⁺/Gd³⁺+vacancy, (b) 2Ca²⁺/Sr²⁺→Eu³⁺/Gd³⁺+M⁺(M⁺ is a monovalent cation like Li⁺, Na⁺ and K⁺ employed as a charge compensator) and (c) Ca²⁺/Sr²⁺→Eu³⁺/Gd³⁺+N⁻ (N⁻ is a monovalent anion like F⁻, Cl⁻, Br⁻ and I⁻ employed as charge compensation ions). Through photoluminescent spectra analyzing the radiative and non-radiative relaxation mechanisms of luminescent system are obtained. Under 20 mA forward-bias current, one red-emitting LED is made by combining 390-405 nm-emitting LED chip and the phosphor. The red-emitting phosphor has broad prospects in LED application field.     

Improving the visible light photocatalytic activity of mesoporous TiO2 via the synergetic effects of B doping and Ag loading

B-doped together with Ag-loaded mesoporous TiO₂ (Ag/B–TiO₂) was prepared by a two-step hydrothermal method in the presence of boric acid, triblock copolymer surfactant, and silver nitrate, followed by heat treatment. The obtained samples were characterized by X-ray diffraction (XRD), high-resolution transmission electron microscopy (HRTEM), UV–vis diffuse reflectance spectroscopy, X-ray photoelectron spectroscopy (XPS), and nitrogen adsorption–desorption. It was revealed that all samples consist of highly crystalline anatase with mesoporous structure. For Ag/B–TiO₂, B was doped into TiO₂ matrix in the form of both interstitial B and substitutional B while Ag was deposited on the surface of B–TiO₂ in the form of metallic silver. Compared with the single B-doped or Ag-loaded TiO₂ one, mesoporous Ag/B–TiO₂ exhibits much higher visible light photocatalytic activity for the degradation of Rhodamine 6G, which can be ascribed to the synergistic effects of B doping and Ag loading by narrowing the band gap of the photocatalyst and preventing the fast recombination of the photogenerated charge carriers, respectively.     

Multi-wavelength metal-dielectric nonpolarizing beam splitters in the near-infrared range

A 21-layer multi-wavelength metal-dielectric nonpolarizing cube beam splitter was designed by use of an optimization method and theoretically investigated in the near-infrared range. The angular dependence of the reflectance and differential phases induced by reflection and transmission were presented. The simulation results revealed that the non-polarizing effect could be achieved for both the amplitude and phase characteristics at 1310 and 1550 nm. The differences between the simulated and the target reflectance of 50% are less than 2% and differential phases are less than 5°in the range 1300–1320 nm and 1540–1550 nm for both p- and s-components.     

Experimental research on an arbitrary pulse generation system for imaging VISAR

Imaging VISAR is an important diagnostic tool for a variety of shock-related phenomena in laser-driven experiments. To adapt to various types of shaped driven pulse, the imaging VISAR needs an illuminating light with good shaping capability. Here, a flexible laser probe system was experimentally studied. Being generated from a 1064-nm DFB laser, the continuous wave was modulated by a waveguide amplitude modulator driven by 10 GS/s arbitrary waveform generator. After being amplified by fiber amplifiers and Nd:YAG rod amplifiers, the signal pulse was frequency-converted to 532-nm green light by a thermally controlled LBO crystal with a final output energy larger than 10 mJ. Finally, the green light was coupled into a 1-mm core diameter, multimode fused silica optical fiber and propagated to the imaging VISAR. The probe laser could realize accurate pulse shaping with time resolution below 100 ps. Uniformity in intensity and capability of arbitrary pulse shaping provides great convenience for the analysis of experimental data.     

Theory of the Anderson transition in the quasiperiodic kicked rotor

We present the first microscopic theory of transport in quasiperiodically driven environments ("kicked rotors"), as realized in recent atom optic experiments. We find that the behavior of these systems depends sensitively on the value of a dimensionless Planck constant h: for irrational values of h/(4π) they fall into the universality class of disordered electronic systems and we describe the corresponding localization phenomena. In contrast, for rational values the rotor-Anderson insulator acquires an infinite (static) conductivity and turns into a "supermetal." We discuss the ensuing possibility of a metal-supermetal quantum phase transition.     

轴向分区双频磁绝缘线振荡器的数值模拟

 为了便于模式变换器的设计,达到双频微波都能集中辐射的目的,提出一种轴向分区的双频磁绝缘线振荡器,该器件束波互作用区为中间隔开、两端不同周期、不同深度的慢波结构,使电子在上下游与不同频率特性的慢波结构进行束波互作用,得到稳定的双频微波输出。使用2.5维全电磁粒子模拟软件进行数值模拟,在工作电压450 kV,电流40 kA条件下输出微波功率为1.4 GW,功率效率约为7%,输出的微波频率分别为1.25 GHz和1.65 GHz,两者频谱幅度相差约为1.5 dB,模式为TEM模。     

The magnetic properties of nanosized La<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ca<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>MnO<Subscript>3</Subscript> (0.5 ≤ <Emphasis Type="Italic">x</Emphasis> ≤ 0.8)

Magnetic properties of La_1−x Ca _x MnO₃ (0.5 ≤ x ≤ 0.8) samples with an equivalent average particle size ~50 nm prepared by a sol–gel method were investigated. The charge ordering (CO) transition that is observed in the bulks disappears and the ferromagnetic (FM) transition occurs in all the prepared samples. For all the samples, the spontaneous magnetization (M _S) value is much lower than the corresponding theoretic value, which shows that the majority of the sample is antiferromagnetic (AFM). However, the M _S value is much larger than the corresponding value reported by some other groups. The invisible of CO transition and the large M _S value can be attributed to the good connection among the adjacent particles. Moreover, the exchange bias (EB) phenomenon is observed except the x = 0.5 sample. With x increasing, the M _S value decreases and the EB field increases, which can be understood by considering the coexistence of FM phase with Mn³⁺–Mn⁴⁺ spin clusters in the shell and the AFM phase in the core of the nanoparticles.