共形平坦黎曼流形中具有平行第二基本形式的超曲面

In this paper, we prove the followingTheorem. Let Cⁿ⁺¹ ( n >5 ) be a conformally flat Riemannian anifola of dimension n + 1 . If Mn is a hypersurface immersed isometrically in Cⁿ⁺¹ over which the second fundamental form is covariant constant, then there are three posible cases only:I . locally Mⁿ= S^p×S^q×S^r, p+q+r=n;Ⅱ . locally Mⁿ=S^p×S^q, p + q = n , where S^k is k- dimensional Riemannian space of constant curvature;III. Mⁿ is umbilical and conformally flat. Moreover, if Mⁿ is connected and complete, then the result holds globally.     

混流式水轮机准三元流动分析及性能予估基础上的水电站过渡过程仿真

本文根据电站参数用计算机予设计转轮后进行其性能予估，并在此基础上进行过渡过程仿真，其结果与用实验得到的综合特性曲线进行仿真的计算结果比较，在较高效率区结果符合很好，低效率区有一定缺陷，但不失为一种在没有合适转轮及其综合特性曲线情况下进行电站过渡过程预测计算的方法。     

Modeling of Coesterification Process for Biodegradable Poly(Butylene Succinate‐co‐Butylene Terephthalate) Copolyesters

Comprehensive mathematical model based on the kinetics and thermodynamic equations is developed to examine a coesterification concept of biodegradable aliphatic‐aromatic copolyesters, poly(butylene succinate‐co‐butylene terephthalate) (PBST). The simulation results for batch process are validated with pilot experimental data. The continuous process is further studied to figure out the coesterification performance of succinic acid (SA) and terephthalic acid (TPA) with different reaction activities and thermodynamic properties in terms of reaction efficiency, small molecular evaporation and product quality. There is a compromise between the operating conditions of the two systems of SA/1,4‐butanediol (BDO) and TPA/BDO. Proper pressure reduction is beneficial to reaction efficiency and product quality. The way to increase reaction efficiency by raising temperature is limited due to the serious evaporation of reactants. Influenced by the solid–liquid equilibrium and the slow reaction rate of TPA, the esterification of acid needs sufficient residence time to complete.     

Determination of the minimum sample size for the transmission load of a wheel loader based on multi-criteria decision-making technology

The present paper aims to provide a new approach in estimating the minimum sample size of the transmission load of a wheel loader under multiple operating conditions based on multi-criteria decision-making (MCMD) technology. Extreme load values (ELVs) and load cycles under multi-operating conditions are carefully considered, and the mean and the standard deviation of ELVs and the fatigue life are the three criteria selected for estimating the sample size. Using MCMD, the weight values of the three criteria are determined, where the eigenvector and entropy information methods, together with linear combination weighting, are adopted. The optimal minimum sample size (MSS) is estimated based on the feasible values determined by the three criteria and their corresponding weight values. As an example, the load time history of the semi-axle of a wheel loader is analyzed in detail. As the ELVs and load cycles are studied, the optimal MSS can properly represent the load characteristics. The objectivity and validity of the optimal MSS are assured using the combination of the eigenvector and entropy information methods.     

从分子运动论看连续介质气体动力学和稀薄气体的新特性

首先，综述了根据分子运动论对连续介质极限气体行为的最近研究．它表明：经典的连续气体动力学是不完整的；用分子运动论分析在连续介质极限时一些重要情况得到气体的正确行为是必不可免的．即，除了特殊的情况，甚至在平均自由程变为零的极限下热传导方程不能描述静止气体温度场；文中给出了根据分子运动论导出的温度场的正确方程组和边界条件及其具体应用．还用同轴圆筒间的包含气体凝聚相的气体流场的渐近分析，论证了经典连续气体动力学方程组的不完整性．其次，综述了最近几年发现的稀薄气体流动的新特性．如在凸体周围速度分布函数的不连续性及它与Ｓ层的关系，加热平板边缘周围引起的流动，有周期性温度分布的管道内产生的单方向流动．     

关于欧氏空间中共形平坦超曲面的变形问题

1.n 1维欧氏空间E~(n 1)中超曲面V~n的变形问题一直是为人们所研究的.如所知,E~n在E~(n 1)中的等距浸入是可变形的,且其变形依赖于n个单参数的任意函数.紧致的正常曲率黎曼流形S~n在E~(n 1)中等距浸入必为超球面,即是不可变形的.Bepбеций,л.л.曾讨论了四维欧氏空间E~4中一个主法曲率为零,且另外二个主法曲率不相等的共形平坦超曲面M~3的局部安装结构.本文的目的在于确定E~(n 1)中局部为可变形的共形平坦超曲面M~n的几何特征,给出其分类,并证实E~(n 1)中紧致的共形平坦超曲面M~n的刚性.主要结果为     

木质纤维素纳米纤丝制备及形态特征分析

以阔叶树材杨木木粉为原料,始终保持纤维处在水润涨的状态下,利用亚氯酸钠在酸性条件下脱除木质素,氢氧化钾脱除半纤维素,然后借助高强度超声波的空化作用,依次制备了综纤维素、纯化纤维素及木质纤维素纳米纤丝(WCNF).通过傅里叶变换红外吸收光谱(FTIR)、X射线衍射(XRD)、扫描电镜(SEM)对WCNF制备过程中的化学组分、晶型结构、结晶度及形态特征变化进行了表征,并进一步利用图像分析系统对WCNF的直径分布进行了测量统计.结果表明,WCNF的主要成分为纤维素,其晶型结构仍为纤维素Ⅰ型,结晶度为65.68%,较之原料木粉提高了12.33%.所得纤丝的直径集中分布在5～32nm之间,长度大于10μm,长径比高于300,纤丝间相互交织成网状缠结结构.WCNF的高结晶度、高长径比、纳米尺度、网状缠结结构,显示其为一种十分理想的增强增韧材料.     

An Integral Equality on the Laplace-Beltrami Operator

Let M be an n-dimensional Riemanniaii manifold of class C^r(r> 2)> and D \subset M be a regular oriented domain on M with boundary \partial D, and W_2,0^2(D) denote the Sobolev space defined on D with the property that every u \in W_2,0^2(D) vanishes at \partial D,i. e., $u|_\partial D=0$. Let (\alpha_=\alpha \beta) be the symmetric matrix of the positive definite metric of M,and $\nabla _\alpha$ denote the operator of the covariant derivative with respect to $\alpha _\alpha \beta$. For any $u \in C^\infty(M)$, it is convenient to define $u_\alpha=\nabla_\alpha u,u_\alpha \beta=\nabla_\alpha u_\beta$ $u^\alpha=a^\alpha\beta=a^\alpha\gamma \nabla_\gamma u^\beta.(1 \leq \alpha,\beta,\gamma \leq n)$ In this paper we establish the following Theorem. Let $u \in W_2,0^2(D)$ . Then $\int_D{u^\alpha \beta u_\alpha \beta dV}=\int_D{(\Delta u)^2dV}+\int_D{Ric(du,du)dV}-\int_\partial D{(\nabla_Nu)^2\Omega ds}$ where $\Delta$ is the Laplace-Beltrami operator, Ric (du, du) is the Ricci curvature of M with respect to the vector field du, \nabla_N is the directional derivative in the direction of the exterior normal vector N at $\partial D$ is the mean curvature of \partial D in M.     

Inverse Functions of Number Theoretic Functions (II)

In this paper^[1] we defined the weak and the strong left inverse functions of f and the weak and the strong right inverse functions of f.In the present paper we shall give their definitions by means of the primitive recursion or the limited minimal or maximal operator. The principal results are: