The absorption and thermal behaviors of PET-SiO2 nanocomposite films

In this paper, to improve properties of Poly(ethylene terephthalate) (PET) in thermal stability and barrier to water, the films of PET, PET with micronmeter Silica/Polystyrene (SiO₂/PS) composites (SPET) and PET with nano-SiO₂/PS composites (SNPET) are prepared and their water absorption and thermal stable behaviors are investigated.In the samples, silica load is optimized as 2 wt%, at which silica not only disperses well but also forms the tough morphology in PET as investigated by SEM. The nanoeffect and thermal degradation behaviors of SNPET are firstly presented.The water absorption experiments for the samples show that the maximum absorption water weight percentage (C_∞) and the pseudo-diffusion coefficient (D) of water reduce with SiO₂ particle size varying from 440 nm to 40 nm, and the barrier property to water of SNPET is superior to those of pure PET and SPET. At the minimum silica size of 40 nm, the C_∞ and D of SNPET approach the minimum values that are 0.946% and 7.075 × 10⁻¹³ m² s⁻¹, respectively. Fixing SiO₂ size at 40 nm, with un-modified SiO₂ and modified SiO₂, the core-shell SiO₂/PS nanocomposite particles are more effective on keeping PET from absorbing water. With the increase in nano-SiO₂ load, the C_∞ and D of SNPET films reduce, proving that the nano-SiO₂ particles can inhibit water absorption. When amorphous SNPET films are annealed at 130 °C, their C_∞ and D quickly decrease with the increase in annealing time, stating that the crystallized SNPET also retards the water absorption or diffusion in PET. Under oversaturated oxygen atmosphere, the C_∞ and D of amorphous PET and SNPET, and crystallized SNPET samples are higher than those of corresponding samples without flowing oxygen, showing that oxygen promotes the films to absorb water.TGA results show that SNPET keeps similar thermal degradation behavior under the conditions of with and without both water and oxygen. But SNPET is more thermally stable than PET.     

Stopping rules,permutation invariance and sufficiency principle

In the context of sequential (point as well as interval) estimation, a general formulation of permutation-invariant stopping rules is considered. These stopping rules lead to savings in the ASN at the cost of some elevation of the associated risk—a phenomenon which may be attributed to the violation of the sufficiency principle. For the (point and interval) sequential estimation of the mean of a normal distribution, it is shown that such permutation-invariant stopping rules may lead to a substantial saving in the ASN with only a small increase in the associated risk.Work partially supported by (i) Office of Naval Research, Contract Number N00014-85-K-0548, and (ii) Office of Naval Research, Contract Number N00014-83-K-0387.     

The distribution and the exact percentage points for Wilks'L mvc criterion

Summary Wilks'L _mvc is the likelihood ratio criterion for testing the hypothesis that the mean values are equal, the variances are equal and the covariances are equal, in ap-variate normal population. In this article the exact null distribution as well as the exact percentage points are given for the first time. The distribution is obtained for the most general cases and the inverse tables, namely, the values ofu for given values ofF(u) are computed for the values ofF(u)=0.01, 0.02, 0.05 and for the various values ofn andp whereF(u) is the exact distribution function of the test statistic,n=N−1 andN is the sample size. The exact tables are given forp=2, 3, 4, 5, 6, 7, 8, 9.     

The distribution of the sphericity test criterion

The exact distribution of Mauchly's sphericity test criterion W = |S|/[trS/p]^p, when S is the sum of product matrix from a sample of size N taken from a p-variate normal population, is obtained using contour integration and methods similar to those of Nair and Box. Tables of percentage points for p = 4(1)10, α = 0.01 and 0.05, and various values of N (including small) are given and comparisons made with approximate percentage points using methods of Box, Mauchly, Tukey and Wilks, and Davis.     

稳幅范围,稳幅精度与De—Qing电路的设计

De—Qing电路的设计历来都是从它的稳定工作的必要条件出发,求得网络元件参数。本文从理论分析证明De-Qing工作有一限制的范围,这一范围既决定于所选元件参数,更大程度上取决于设计者所期望的稳幅精度。     

Percentage Points of the Largest Among Student's T Random Variable

Let us consider k( 2) independent random variables U₁, . . . ,U_k where U_i is distributed as the Student's t random variable with a degree of freedom m_i, i=1, . . . ,k. Here, m₁, . . . ,m_k are arbitrary positive integers. We denote m=(m₁, . . . ,m_k) and U_k:k=max {U₁, . . . ,U_k}, the largest Student's t random variable. Having fixed 0< <1, let a a(k,) and h_m h_m (k,) be two positive numbers for which we can claim that (i) ^k(a)–^k(–a)=1–, and (ii) P{–h_m U_k:k h_m}=1–. Then, we proceed to derive a Cornish–Fisher expansion (Theorem 3.1) of the percentage point h_m. This expansion involves a as well as expressions such as _i=1 ^k m_i ^–1, _i=1 ^km_i ^–2, and _i=1 ^k m_i ^–3. The corresponding approximation of h_m is shown to be remarkably accurate even when k or m₁, . . . ,m_k are not very large.     

尼龙6,6膜的电驱动透过性

电驱动条件下膜分离性能的研究对膜在微流控芯片等微小器件中的应用具有重要的指导意义.研究了界面聚合的尼龙6,6膜的电驱动分离性能,并考察了电场强度、通电时间和温度等操作条件对SO42-和Cl-离子透过性能的影响.结果表明尼龙6,6膜具有较好的SO24-和Cl-离子透过性能,并且透过性能差异不大,离子透过百分比随电场强度和通电时间的增加而增加,而随温度的增加基本保持不变.而对FITC标记的甘氨酸和赖氨酸则能完全截留,截留分子量在500左右,具有部分纳滤膜性质.该膜可望应用于微型器件中氨基酸等有机与生物大分子的电驱动分离和浓缩.     

定量计算水表面张力系数及其温度变化率

应用饱和蒸汽压下单元液体的玻尔兹曼因子方程,导出了表面张力系数及其温度变化率的数学公式;依据数学公式定量计算的理论结果与实测值高度吻合;证实了简洁的数学公式,可以在很宽的温度范围内准确地描述表面张力随温度的变化而变化的自然规律.     

Percentage problems in bridging courses

Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging courses. In this method, the information from a word problem about percentages is presented in a two-way table. Such a table gives a logical structure to the problem and provides an algorithm for finding a simple equation for the unknown value of interest. The use of this procedure is illustrated by several examples of different levels of difficulty. The method can be applied to many types of percentage problems, so it is quite universal.     

Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation

The nonlinear behaviors and vibration reduction of a linear system with a nonlinear energy sink(NES)are investigated.The linear system is excited by a harmonic and random base excitation,consisting of a mass block,a linear spring,and a linear viscous damper.The NES is composed of a mass block,a linear viscous damper,and a spring with ideal cubic nonlinear stiffness.Based on the generalized harmonic function method,the steady-state Fokker-Planck-Kolmogorov equation is presented to reveal the response of the system.The path integral method based on the Gauss-Legendre polynomial is used to achieve the numerical solutions.The performance of vibration reduction is evaluated by the displacement and velocity transition probability densities,the transmissibility transition probability density,and the percentage of the energy absorption transition probability density of the linear oscillator.The sensitivity of the parameters is analyzed for varying the nonlinear stiffness coefficient and the damper ratio.The investigation illustrates that a linear system with NES can also realize great vibration reduction under harmonic and random base excitations and random bifurcation may appear under different parameters,which will affect the stability of the system.