一阶变系数线性微分方程系统的Hyers-Ulam稳定性

通过基解矩阵的指数二分性证明了一阶变系数微分方程的Hyers-Ulam稳定性,推广了已有结论.

Abstract：

S. M. Jung investigated the Hyers-Ulam stability of a system of first order linear differential equations with constant coefficients by discussing the eigenvalues of matrix. Using the exponential dichotomy of fundamental solution matrix, this paper proves the Hyers-Ulam stability of first-order differential equations with variable coefficients and generalizes the previous conclusions.     

微量穴醚(2.2.2)测定方法初探

用紫外分光光度法研究微量穴醚(2.2.2)的检测方法,并将该方法用于氟[18F]脱氧葡萄糖中微量穴醚(2.2.2)测定.将适量苯甲醛加入硝酸铅缓冲溶液中配制储备液,使溶液在250 nm检测波长处的吸收曲线为一平台,用储备液和微量穴醚(2.2.2)配制供试液,用紫外分光光度法检测.穴醚(2.2.2)的线性范围为1.0～10.0 μg/mL,相关系数0.999 5,平均回收率为100.5%(n=5),相对标准偏差为2.24%,方法检出限(3d)为0.15μg/mL.该方法用于氟[18F]脱氧葡萄糖中微量穴醚(2.2.2)测定,结果良好.该方法精密度高,准确性好,可用于微量穴醚(2.2.2)测定.

Abstract：

A method for the determination of trace cryptand 222 by ultraviolet spectrometry was researched. As benzaldehyde and complex of lead cryptand 222 possess the same ultralviolet absorbance peak and their maximum absorbance wavelength are both 250 nm, proper amount of benzaldehyde and lead nitrate was added to the citric acid buffer solution (pH=6.4) for preparing storage solution, and the ultralviolet absorbance curve of the storage solution was made a platform about 250 nm detection wavelength.Trace cryptand 222 was added to the storage solution, and trace complex of lead cryptand 222 was detected by ultraviolet spectrometry for quantitative determination of trace cryptand 222. This method kept in good linearity from 1.0 to 10.0 μg/mL of cryptand 222 concentration with a correlation coefficient of 0. 999 5, a recovery of 100.5% (n=5), a relative standard deviation of 2.24% and a limit of quantification of 0.15 μg/mL. This method has been successfully applied in determination of trace cryptand 222 of [18F]-fluorodeoxyglucose with satisfactory results. This method is simple, accurate and suitable for determination of trace cryptand 222.     

一类p-Laplacian方程非零解的存在性

通过运用变分方法和分析技巧,在超二次条件和非二次条件下获得了p-Laplacian方程Dirichlet边值问题解的存在性结果.

Abstract：

The existence results are obtained for solutions of Dirichlet boundary value problem for a class of p-Lapla-eian equations by using the variational method and analytic technique under the superquadratie condition and the non-quadratic condition.     

一类拟线性椭圆系统的多重解

利用上下解方法和强极大值原理研究了一类拟线性椭圆系统正解的存在性问题.用山路引理研究了该椭圆系统在次临界增长条件下解的多重性问题.

Abstract：

Using upper-lower solution method and strong maximum principle,the existence of positive solutions is considered for a class of quasilinear elliptic systems.By means of mountain pass lemma,the multiplicity of solutions is considered for the related systems with subcritical growth condition.     

弱条件下马氏链收敛速度的界

以m-骨架(m≥1)代替1-骨架,计算出马氏链Ф的几何收敛速度的界,从而推广了已有结论.

Abstract：

Assume that φ is a time-homogeneous discrete-time Markov chain with m-skeleton φm on the state space [0, ∞). Meyn and Tweedie have studied the bounds on convergence rates of Markov chains φ with conditions of 1-skeleton. This paper is an attempt to weaken those conditions, that is, it manages to change 1-skeleton into m-skeleton. At the same time, it calculates the bounds on geometric convergence rates of Markov chain φ with weak conditions of m-skeleton (m ≥ 1) in order to generalize the result ofM-eyn and Tweedie.     

杜鹃花色素的提取及稳定性研究(英文)

[Objective] The aim of this study was to further investigate and utilize the natural anthocyanidin from Rhododendron L. [Method] Using Rhododendron L. with four different colors including white, pink, red and purple as the test materials, its anthocyanidin extraction methods were analyzed in this study to evaluate the spectral properties and its stability of various anthocyanidin. [Result] The anthocyanidin from Rhododendron L. was perfectly extracted by methanol with 1% concentrated hydrochloric acid (V/V) and had better stability in this extraction solution. The further experiment in vitro indicated that the anthocyanidin from Rhododendron L. became stable with pH value of 0-3, but could not resistant to high temperature or strong light, and the alkaline condition had also great effects on its stability. [Conclusion] The methanol with 1% concentrated hydrochloric acid (V/V) has the best effect for extraction, and the anthocyanidin from Rhododendron L. is more stable in low temperature, weak light and acid conditions.     

有机硼酸基团对铝缓蚀作用的研究

采用自组装技术、交流阻抗法研究了对巯基苯硼酸对铝在3.5% NaCl溶液中的腐蚀行为.实验表明,随着对巯基苯硼酸浓度的变化和组装时间的不同缓蚀效率有所不同.当对巯基苯硼酸浓度为3.2×10~(-3) mol/L,组装时间为12 h时腐蚀电流最小,缓蚀效率最高,达98%以上.

Abstract：

The corrosion behavior of aluminum with 4-mercaptophenyl-boronic acid in a 3.5% NaCl solution was studied, using the self-assembly technology and EIS (electrochemical impedance spectroscopy).The efficiency of corrosion inhibition was found to vary with the concentration of 4-mercaptophenyl-boronic acid and the assembly time. A 4-mercaptophenyl-boronic acid concentration of 3.2×10~(-3) mol/L in combination with an assembly time of 12h was the optimum condition, under which the corrosion current was the smallest and efficiency was the highest (98%).     

Effects of Carboxymethylcelluloses （CMC） on Some Hydraulic Properties of Sandy Soil

The property of hydrophilic polymers capable absorbing huge volumes of water led to many practical applications of these new materials in arid regions for improving the water retention in sandy soils. Effects of four carboxymethylcelluloses (CMC), mixed at various rates with the sandy soil, on the water-holding capacity and hydraulic conductivity (KS ) when leached with distilled water (simulating rain), tap water, and saline water were evaluated. The maximum water absorption of CMCs ranged between 80 and 100 kg ? kg-1 of polymer; however, the absorbent swelling capacity decreased significantly with increasing the salt concentration in the solution. The water absorption capacity of CMCs decreased significantly when incorporated in the sandy soil compared to that of the absorbent alone. Application of CMC increased significantly the available water content up to 3 ± 0.5 times. All soils treated with CMCs showed a significant lower in KS compared to the control soil. Meanwhile, KS was found increased with increasing the salt concentration in the leaching solution. This understanding of characteristics of the absorbents and the interactions among absorbents, soil, and irrigation water quality would be of help in water management of sandy soil.     

Simulation of water and nitrogen dynamics as affected by drip fertigation strategies

The aim of drip fertigation is synchronising the application of water and nutrients with crop requirements, and maintaining the proper concentration and distribution of nutrient and water in the soil. The wetting patterns and nutrient distributions under drip fertigation have been proved to be closely related to the fertigation strategies. In order to find out the critical factors that affect the nutrient distribution under different drip fertigaiton strategies, a computer simulation model HYDRUS2D/3D was used to simulate the water and nitrate distribution for various fertigation strategies from a surface point source. Simulation results were compared with the observed ones from our previous studies. A 15° wedge-shaped plexiglass container was used in our experiment to represent one-twenty-fourth of the complete cylinder. The height of container is 40 cm, and the radius is 41 cm. The ammonium nitrate solution was added through a no. 7 needle connected to a Mariotte tube with a flexible hose. The soil water content, nitrate and ammonium concentrations were measured. The comparison of simulated and observed data demonstrated that the model performed reliably. The numerical analysis for various fertigation strategies from a surface point source showed that:(1) The total amount of irrigation water, the concentration of the fertilizer solution and the amount of pure water used to flush the pipeline after fertilizer solution application are the three critical factors influencing the distribution of water and fertilizer nitrogen in the soil.(2) The fresh water irrigation duration prior to fertigation has no obvious effect on nitrate distribution. The longer flushing time period after fertigation resulted in nitrate accumulation closer to the wetting front. From the point of avoiding the possibility of nitrate loss from the root zone, we recommended that the flushing time period should be as shorter as possible.(3) For a given amount of fertilizer, higher concentration of the fertilizer applied solution reduces the potential of nitrate leaching in drip irrigation system. While, lower concentration of the fertilizer solution resulted in an uniform distribution of nitrate band closer to the wetted front.     

黎曼流形上弱向量似变分不等式解的存在性

在黎曼流形上分别给出了伪不变凸函数和弱向量似变分不等式的概念.研究这类弱向量似变分不等式和向量优化问题弱有效解之间的关系.利用最大元定理证明了弱向量变分不等式解的存在性,并给出了向量优化问题弱有效解存在的条件.

Abstract：

The definitions of pseudo-invex function and weak vector variation-like inequality on Riemannian manifolds are presented. The relationship between this kind of weak vector variation-like inequalities and the weak efficient solution of vector optimization problems is obtained. By using the maximum element theorem, the existence theorem for weak vector variational-like inequalities defined on Riemannian manifolds is given. Moreover, the conditions for the existence of weak efficient solution to vector optimization problems are presented.