Three critical points theorem and its application to quasilinear elliptic equations

In this paper, we prove a Pucci-Serrin type three critical points theorem for continuous functionals and study its application to quasilinear elliptic equations with natural growth.     

Kinetics study of the photopolymerisation of donor/acceptor pairs using the differential photocalorimetric technique and the relation of the kinetics data to hydrogels formation

The differential photocalorimetric technique was used to study the rates of photopolymerisation initiated by donor/acceptor pairs with N-vinylpyrrolidinone (NVP) as the donor, and the acceptors were a series of N-hydroxy alkylmaleimides including N-hydroxymethyl maleimide (HMMI), N-(2-hydroxy) ethylmaleimide (HEMI), N-(3-hydroxy) propylmaleimide (HPrMI) and N-(5-hydroxy) pentylmaleimide (HPMI). HPMI/NVP system displays the highest rate of polymerisation followed by HMMI/NVP and then HPrMI/NVP, with HEMI/NVP giving the lowest rate.These donor/acceptor pair systems were subsequently used to initiate the polymerisation of NVP under the influence of UV radiation. With the exception of the HEMI/NVP system, the other three systems produced polymers with characteristics pertaining to that of hydrogel. A previously proposed mechanism (Proceedings of the RadTech Asia ’01 Conference, Kunming, China, 2001, pp. 182–201) was used to explain such phenomenon.     

A DERIVATIVE-FREE ALGORITHM FOR UNCONSTRAINED OPTIMIZATION

In this paper a hybrid algorithm which combines the pattern search method and the genetic algorithm for unconstrained optimization is presented. The algorithm is a deterministic pattern search algorithm,but in the search step of pattern search algorithm,the trial points are produced by a way like the genetic algorithm. At each iterate, by reduplication,crossover and mutation, a finite set of points can be used. In theory,the algorithm is globally convergent. The most stir is the numerical results showing that it can find the global minimizer for some problems ,which other pattern search algorithms don＇t bear.     

p阶平均曲率算子Dirichlet问题的无穷多个解

§ 1　 IntroductionSince the Mountain Pass Theorem came out,the existence of nontrivial solutions,pos-sibly multiple,ofnonlinear elliptic equations has been extensively studied.In this paper,weconsider the following Dirichlet problem for p-(generalized) mean curvature operator:-div((1 +| u|2 ) p- 22 u) =f(x,u) ,　 x∈Ω,u∈ W1 ,p0 (Ω ) , (1 .1 )whereΩ is a bounded domain in Rn(n>p>1 ) with smooth boundary Ω.First let us recall the following Dirichletproblem for p-Laplacian:-Δpu≡ -div…     

Effect of temperature on the physical properties of 1-butyl-3-methylimidazolium based ionic liquids with thiocyanate and tetrafluoroborate anions,and 1-hexyl-3-methylimidazolium with tetrafluoroborate and hexafluorophosphate anions

The effect of temperature on the physical properties of some ionic liquids was investigated. Density, refractive index, surface tension, dynamic and kinematic viscosities of 1-butyl-3-methylimidazolium based ionic liquids with thiocyanate and tetrafluoroborate, and 1-hexyl-3-methylimidazolium with tetrafluoroborate and hexafluorophosphate anions were measured at various temperatures (density from T = (278.15 to 363.15) K, refractive index from (293.15 to 343.15) K, surface tension from (283.15 to 333.15) K, dynamic viscosity from (283.15 to 368.15) K, and kinematic viscosity from (298.15 to 363.15) K). The volumetric properties for the ionic liquids were also calculated from the experimental values of the density at T = 298.15 K. The Vogel–Fulcher–Tammann (VFT) equation was applied to correlate experimental values of dynamic and kinematic viscosities as a function of temperature. As well, the relation between density and refractive index was correlated satisfactorily with several empirical equations such as Lorentz–Lorenz, Dale–Gladstone, Eykman, Oster, Arago–Biot, Newton and Modified–Eykman. Finally, the relation between surface tension and viscosity was investigated and the parachor method was used to predict density, refractive index and surface tension of the ionic liquids.     

椰胡声功率级的半消声室测试

椰胡是具有地方特色的拉弦乐器之一,多用于演奏广东音乐和广东戏曲、曲艺的伴奏。但对其发声强度一直未进行过科学的测试。本文介绍在华南理工大学半消声室内参照ISO(GB)标准对椰胡声功率级的测量工作。由两位资深乐师分别用两把椰胡在pp,mp,f和ff力度下演奏单音、音阶和乐曲,对每一把椰胡的每一测试内容,由十通道测试设备同步测试中心频率为100～10000 Hz的1/3倍频带声压级谱,通过计算获得每把椰胡在演奏每项内容时的声功率级和动态范围。通过对两把椰胡的测试结果进行平均,获得该乐器在演奏上述内容时的典型声功率级数值及频谱。文中并将半消声室内的测试结果与混响室内的测试结果相对比,探讨测试环境对测试结果的影响。民族乐器发声强度及其频谱特性的获得是开展民族音乐厅堂音质研究的基础。     

中国筝的声功率级测试

筝是中国古老的弹弦乐器。但迄今为止,对其声功率级一直未进行科学的测定。本文在一混响室内根据ISO及GB标准,对二十一弦筝的声功率级进行了首次测定。两位资深乐师在混响室内分别演奏各自的乐器,通过围绕乐师和乐器布置的四通道测试设备,对筝所辐射的声功率级和动态范围进行测定。测试结果表明,中国筝在以不同力度演奏单音、音阶和乐曲时所辐射的声功率级及其频率特性均有所不同。考虑到乐器演奏音阶时所辐射的声功率级及其动态范围与演奏乐曲时的声功率级接近,并且,音乐的空间感也大都在乐器以f力度演奏乐曲的强音标志乐段时最为显著,故此我们建议中国筝所辐射的声功率级用其以f力度演奏音阶时的平均声功率级表示。本文测试的两架中国筝以f力度演奏音阶时的平均声功率级为85.9dB。文中不仅首次公布了中国筝声功率级的测试结果,并且所介绍的测试方法对其它乐器声功率级测试也具有借鉴意义。民族乐器所辐射的声音性能的确定是民族音乐厅堂音质研究的基础。     

Infinitely many solutions of dirichlet problem for <Emphasis Type="Italic">p</Emphasis>-mean curvature operator

The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator: is considered, where Θ is a bounded domain in R ⁿ (n>p>1) with smooth boundary ∂Θ. Under some natural conditions together with some conditions weaker than (AR) condition, we prove that the above problem has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if . Supported by the National Natural Science Foundation of China (10171032) and the Guangdong Provincial Natural Science Foundation (011606).     

球形木素基离子交换树脂的合成及其对Cr3+的吸附特性

以木素磺酸钙为原料,利用反相悬浮聚合技术在一种价廉无毒的介质相中制备出球状木质素基离子交换树脂,并讨论了它对Cr3 的吸附性能。结果表明,树脂对低浓度Cr3 的吸附效果好,前期吸附速度快,40min后吸附速率趋缓;升高温度能明显提高前期吸附速率,饱和吸附量约为60mgCr3 /g干树脂,而且树脂在较宽的弱酸性范围内表现出良好的吸附性能。