关于Haar 酉元的一个注记

设M 是一个Ⅱ₁ 型因子, τ 是M 的正规的、忠实的迹态, U ∈ M 是一个Haar 酉元, p ∈ M是一个投影, τ (p) = (1/n) (n > 3, n ∈ Z), p 和U 自由. 我们用初等方法证明了若pUp = wh 是pUp 的极分解, 则w 也是一个Haar 酉元且w 和h 是自由的. 我们还给出了pUp 的矩的刻画.     

ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES

Let X(1)= {X(1)(s), s ∈ R+ } and X(2)= {X(2)(t), t ∈ R+ } be two independent nondegenerate diusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X(1)and X(2)are studied. More generally, let E1, E2 ■(0, ∞) and F  Rd be Borel sets. A necessary condition and a suffcient condition for P{X(1)(E1) ∩ X(2)(E2) ∩ F = φ} 0 are proved in terms of the Bessel-Riesz type capacity and Hausdor measure of E1 ×E2 ×F in the metric space(R+ ×R+ ×Rd, ρ), where ρ is an unsymmetric metric defined in R+ × R+ × Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.     

A new high accuracy non-polynomial tension spline method for the solution of one dimensional wave equation in polar co-ordinates

In this paper, we propose a new three-level implicit nine point compact finite difference formulation of O(k² + h⁴) based on non-polynomial tension spline approximation in r-direction and finite difference approximation in t-direction for the numerical solution of one dimensional wave equation in polar co-ordinates. We describe the mathematical formulation procedure in details and also discuss the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.     

一种基于极坐标编码的果蝇优化算法

针对果蝇优化算法易陷入早熟收敛、收敛速度慢、寻优精度低的缺点,提出一种基于极坐标编码的果蝇优化算法.为提高果蝇优化算法的寻优精度,采用极坐标编码的形式,以增加单个母体寻优空间表示方法的多样性,并使种群中的个体,在围绕个体的整个超球体内随机搜索,使个体的搜索范围更加广泛.在迭代寻优过程中,根据适应度值和概率调整极角,逐渐降低观测结果的不确定性.通过9个基准测试函数,对基于极坐标编码的果蝇优化算法进行仿真实验,结果表明了算法在收敛性和稳定性方面,优于其它5个优化算法,测试结果验证了极坐标编码方法的有效性和可行性.     

Effect of Alcohols on the CMC and Thermodynamic Functions of Anionic Surfactants in DMF/Long‐Chain Alcohol Using Microcalorimetric Method

The critical micelle concentration (CMC) of two kinds of anionic surfactant (including sodium laurate (SLA) and sodium dodecyl sulfate (SDS)) in mixed alcohol and N, N‐dimethyl formamide solvent (DMF) were investigated through measuring power‐time curves by titration microcalorimetry. From data of the lowest point and the area of the power‐time curves, their CMC and ΔH _m ⁰ can be obtained. According to standard thermodynamic equations, ΔG _m ⁰ and ΔS _m ⁰ also can be calculated. For different surfactant, the influences of the carbon number and the concentration of alcohol on the CMC and standard thermodynamic functions are different in DMF polar medium. These thermodynamic functions for micelle formation can be further interpreted.     

A modification to the Peng–Robinson-fitted equation of state for pure substances

In this work we present two modifications to the Peng–Robinson-Fitted equation of state where pure component parameters are regressed to vapor pressure and saturated liquid density data. The first modification (PR-f-mod) is a method that enhances the equation of state pure component property predictions through simple temperature dependent pure component parameters. In the second modification (PR-f-prop) we propose a temperature dependency for co-volume b in the repulsive parameter of the EoS, and revise the temperature function in the attractive term. The agreement with experimental data for 72 pure substances, including highly polar compounds, is remarkably good. We obtain average absolute deviations in saturated liquid density of less than 1% for all substances studied.     

Lp-dual Quermassintegral sums

In this paper,we first introduce a concept of L_p-dual Quermassintegral sum function of convex bodies and establish the polar projection Minkowski inequality and the polar projection Aleksandrov-Fenchel inequality for L_p-dual Quermassintegral sums.Moreover,by using Lutwak's width-integral of index i,we establish the L_p-Brunn-Minkowski inequality for the polar mixed projec- tion bodies.As applications,we prove some interrelated results.     

Suzuki cross-coupling reactions using reverse-phase glass beads in aqueous media

Reverse-phase glass beads have been employed in Suzuki reactions to provide, in aqueous media, a route to diverse polar substrates in good yield and with low levels of palladium leaching.     

Sobolev空间中的几个不等式的推广

本文将Sobolev空间中的Clarkson不等式的几个引理作了适当的推广,并给出了证明.     

Number of lattice points in the hyperbolic cross

An asymptotic formula for the number of points of an arbitrary lattice in the hyperbolic cross is obtained. Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 363–369, March, 1998. The authors wish to thank Professors N. M. Korobov and V. I. Nechaev for their attention and useful discussions.