MULTIPLE PERIODIC SOLUTIONS TO SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATION WITH INFINITE DELAY

This paper is concerned with the existence of positive periodic solutions to a second order functional differential equation with infinite delay.Under the appropriate conditions,some existence and multiplicity of positive periodic solutions are derived by an abstract fixed-point theorem.     

Effect of different doped elements on visible light absorption and ultraviolet light emission on Er3+:Y3Al5O12

In this progress report, seven kinds of novel carefully designed and fabricated up-conversion luminescence agents, Er³⁺:Y₃Al₅O₁₂, Er³⁺:Yb_nY_3?nAl₅O₁₂, Er³⁺:Y₃B_aAl_5?aO₁₂, Er³⁺:Y₃Ga_bAl_5?bO₁₂, Er³⁺:Y₃Al₅N_xO_12?x, Er³⁺:Y₃Al₅F_yO_12?y and Er³⁺:Yb_nY_3?nB_aGa_bAl_5?a?bN_xF_yO_12?x?y, are successfully synthesized using sol–gel methods. After that, their corresponding photocatalysts, Er³⁺:Y₃Al₅O₁₂/TiO₂, Er³⁺:Yb_nY_3?nAl₅O₁₂/TiO₂, Er³⁺:Y₃B_aAl_5?aO₁₂/TiO₂, Er³⁺:Y₃Ga_bAl_5?bO₁₂/TiO₂, Er³⁺:Y₃Al₅N_xO_12?x/TiO₂, Er³⁺:Y₃Al₅F_yO_12?y/TiO₂ and Er³⁺:Yb_nY_3?nB_aGa_bAl_5?a?bN_xF_yO_12?x?y/TiO₂, are also prepared by sol–gel coating process. The obtained up-conversion luminescence agents and photocatalysts were characterized by using XRD, XPS, SEM, UV–vis and fluorescence spectrophotometer. Synchronously, several kinds of organic dyes are used to test their photocatalytic degradation using prepared photocatalysts. It indicates that the up-conversion luminescence ability of Er³⁺:Y₃Al₅O₁₂ can be improved obviously through doping of some elements. And then, the photocatalytic activity of TiO₂ is markedly enhanced by modified up-conversion luminescence agents which can transform much visible light into ultraviolet light.     

Sonocatalytic degradation of organic dyes and comparison of catalytic activities of CeO2/TiO2, SnO2/TiO2 and ZrO2/TiO2 composites under ultrasonic irradiation

The CeO₂/TiO₂, SnO₂/TiO₂ and ZrO₂/TiO₂ composites were prepared by dispersing various nano-sized oxides (CeO₂, SnO₂, ZrO₂ and TiO₂) with ultrasound and mixing TiO₂ with CeO₂, SnO₂ and ZrO₂, respectively, in boiling water in a molar ratio of 4:1, followed by calcining temperature 500 °C for 60 min. Then a series of sonocatalytic degradation experiments were carried out under ultrasonic irradiation in the presence of CeO₂/TiO₂, SnO₂/TiO₂ and ZrO₂/TiO₂ composites and nano-sized TiO₂ powder. Also, the influences of heat-treatment temperature and heat-treatment time on the sonocatalytic activities of CeO₂/TiO₂, SnO₂/TiO₂ and ZrO₂/TiO₂ composites, and of irradiation time and solution acidity on the sonocatalytic degradation of Acid Red B were investigated by UV–vis spectra. It was found that the sonocatalytic degradation of Acid Red B shows significant variation in rate and ratio that decreases in order: CeO₂/TiO₂ > SnO₂/TiO₂ > TiO₂ > ZrO₂/TiO₂ > SnO₂ > CeO₂ > ZrO₂, and the corresponding ratios of Acid Red B in aqueous solution are 91.32%, 67.41%, 65.26%, 41.67%, 28.34%, 26.75% and 23.33%, respectively. And that the degradation ratio is only 16.67% under onefold ultrasonic irradiation. Because of the good degradation efficiency, this method may be an advisable choice for the treatment of non- or low-transparent wastewaters in the future.     

Amplified spontaneous emission and power amplification in high-power DF laser systems

Amplified spontaneous emission （ASE） always occurs in high-power DF laser systems with master oscillator-power amplifier （MOPA） configuration. ASE not only reduces the energy extraction efficiency of the laser system, but also negatively influences its heat management. The interaction between the ASE flux and the coherent laser flux, as well as the effect of ASE on cuboid DF amplifiers, is studied using a finite difference method and an iterative arithmetic. In addition, the influence of ASE on coherent laser amplification is discussed in detail.     

Configuration of an optical waveguide interconnect mesh network based on EOPCB

<正>An optical waveguide interconnect mesh network scheme for parallel multiprocessor systems based on an electro-optical printed circuit board(EOPCB) with multimode polymer waveguide is proposed.The system consists of 2×2 processor element chips interconnected in a mesh network configuration.An additional layer with optical waveguide structure is embedded in a conventional printed circuit board to construct the EOPCB.Vertical cavity surface emitting laser(VCSEL)/positive intrinsic-negative(PIN) arrays are applied as the optical transmitters/receivers.Three 1×12 VCSEL/PIN parallel optical transmitting/receiving modules are used to provide 32 input/output optical channels required by the 2×2 chip-to-chip optical mesh interconnect system.The data rate in each optical channel is 3.125 Gbps and thus 10 Gbps parallel optical interconnect link for each direction of a chip is obtained.The optical signals from a processor element chip can be transmitted to another chip through optical waveguide interconnect embedded in the board.Thus the optical interconnect mesh network for parallel multiprocessor system can be implemented.     

The effect of the Kerr nonlinearity on the transmission through the nanoslit gold film

This paper has made a theoretical study of enhanced transmission through a gold grating with arrays of subwavelength slits filled with nonlinear Kerr medium. The results of the research are based on rigorous finite-difference time domain calculations. The resonance transmission peaks in the investigated wavelength range are produced as a result of the surface plasmon resonance collaborated with the localized waveguide resonance. The paper also gives a detailed analysis of the influence exerted by various fa...     

Research on the mechanics of underwater supersonic gas jets

An experimental research was carried out to study the fluid mechanics of underwater supersonic gas jets. High pressure air was injected into a water tank through converging-diverging nozzles (Laval nozzles). The jets were operated at different conditions of over-, full- and under-expansions. The jet sequences were visualized using a CCD camera. It was found that the injection of supersonic air jets into water is always accompanied by strong flow oscillation, which is related to the phenomenon of shock waves feedback in the gas phase. The shock wave feedback is different from the acoustic feedback when a supersonic gas jet discharges into open air, which causes screech tone. It is a process that the shock waves enclosed in the gas pocket induce a periodic pressure with large amplitude variation in the gas jet. Consequently, the periodic pressure causes the jet oscillation including the large amplitude expansion. Detailed pressure measurements were also conducted to verify the shock wave feedback phenomenon. Three kinds of measuring methods were used, i.e., pressure probe submerged in water, pressure measurements from the side and front walls of the nozzle devices respectively. The results measured by these methods are in a good agreement. They show that every oscillation of the jets causes a sudden increase of pressure and the average frequency of the shock wave feedback is about 5–10 Hz.     

A HYBRID METHOD FOR SOLVING VARIATIONAL INEQUALITY PROBLEMS

§ 1　IntroductionThe problem of finding a point x* ∈S such that〈F(x* ) ,x -x* 〉≥ 0 for all x∈ S,(VIP)where S is a nonempty closed convex subset of Rn,F is a mapping from Rninto itself,and〈.,.〉denotes the inner productin Rn,is called the variational inequality problem and hasbeen widely used to study various equilibrium models arising in economic,operations re-search,transportation and regional sciences[1 ,2 ] .Many iterative methods for (VIP) havebeen developed,for example,project…     

Preparation and Characterization of Cu_3V_2O_7(OH)_2·2H_2O Hollow Spheres from Na_2V_6O_16·3H_2O Nanobelts

Monoclinic Cu3V2O7(OH)2·2H2O(copper polyvanadate) hollow spheres were prepared with Na2V6O16· 3H2O nanobelts as V-precursor by hydrothermal method. The purity and structure of the products were characterized by X-ray powder diffraction(XRD), Fourier transform infrared(FTIR) spectroscopy, Raman spectroscopy, thermogra-vimetric analysis(TGA) and X-ray photoelecton spectroscopy(XPS). The morphology and size were observed by scanning electron microscopy(SEM). We found that the Kagomé staircase-structural copper...     

WEIGHTED INEQUALITIES FOR MULTILINEAR POTENTIAL TYPE OPERATORS

The author derives a kind of weighted norm inequalities which relate the multilinear potential type integral operators to the corresponding maximal operators.