Study on optical nonlinearities of ZnO-Nb_2O_5-TeO_2 glass with time-resolved four-wave mixing technique

We investigated nonlinear optical properties of ZnO-Nb2O5-TeO2 glass excited by a femtosecond laser with time-resolved four-wave mixing (FWM) technique. The unusual FWM signals were observed in samples with ZnO dopant. The mechanism for the optical nonlinearities was discussed.

Mixed Monotone Iterative Technique and Boundary Value Problem for a Class of Impulsive Integro-Differential Equations

In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.

Progress on the Use of Stable Isotope Techniques in Catchment Hydrograph Separation: A Review

Hydrograph separation is a fundamental catchment descriptor,revealing information about sources of water in runoff generation processes. The water isotopes are ideal tracers in studying hydrological processes since the isotope fractionation produces a natural labeling effect within the hydrologic cycle. The water isotope technique has become one of effective means for investigating complex hydrologic system on a catchment scale. This paper reviews the progress on the use of stable water isotope techniques in catchment hydrograph separation in last decades. Also,the isotope mixing model for hydrograph separation and its uncertainties are explained in detail. In future research,there are three hot issues in the use of isotopic hydrograph separation（ IHS） ： integrating new approaches into IHS,calibration and verification of IHS model and IHS application in large river basins.

Synthesis of Poly[(3-octanoylpyrrole-2,5-diyl)-p-(N,N-dimethylamino)benzylidene] and Its Properties by Nitrogen Ion Implantation

A novel soluble π-conjugated polymer, poly[(3-octanoylpyrrole-2,5-diyl)-p-(N,N-dimethylamino)benzylidene](POPDMABE), was synthesized firstly by the condensation of 3-octanoylpyrrole with para-dimethylaminobenzaldehyde. The chemical structure of the polymer was characterized by FTIR and 1H NMR spectrometries. The polymer is a potential nonlinear optical(NLO) material. According to the function of optical forbidden band gap(E_g) and photon energy(hν), the optical forbidden band gaps of the polymer before and after ion implantation were calculated. The resonant third-order nonlinear optical properties of POPDMABE before and after ion implantation were also studied by using the degenerate four-wave mixing(DFWM) technique at 532 nm. When the energy is 25 keV and the dose is 2.2×10 17 ions/cm 2, the {polymer′s} optical forbidden band gap is about 1.63 eV which is smaller than that of the non-implanted sample(1.98 eV) and the resonant third-order NLO susceptibility of POPDMABE is about 4.3×10 -7 esu, 1 order of magnitude higher than that of the non-implanted sample(4.1×10 -8 esu). The results show that nitrogen ion implantation is an effective method to improve the resonant third-order NLO property of the polymer.

EXISTENCE OF SOLUTIONS FOR MIXED MONOTONE IMPULSIVE VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACES

This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mixed monotone iterative technique and Monch fixed point theorem, Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained. Finally, an example is worked out.

MIXED MONOTONE ITERATIVE TECHNIQUES FOR SEMILINEAR EVOLUTION EQUATIONS IN BANACH SPACES

This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.