Cohen–Macaulay Modules in Dimension >s and Results on Local Cohomology

Let (R,𝔪) be a local ring and s ≥ ?1. Using the notion of M-sequence in dimension > s, we introduce Cohen–Macaulay modules in dimension > s. Among other things concerning Cohen–Macaulay modules in dimension > s, some finiteness results of the support and the associated primes of local cohomology modules are investigated.     

A Generalization of Weak Law of Large Numbers

Kolmogorov's weak law of large numbers for i.i.d. random variables is generalized to a larger class distributions and to a wide class of normalizing sequences. The result is extended to maximal sums of negatively associated identically distributed random variables.     

Existence and uniqueness of the entropy solution of a stochastic conservation law with a Q-Brownian motion

In this paper, we prove the existence and uniqueness of the entropy solution for a first-order stochastic conservation law with a multiplicative source term involving a $Q$-Brownian motion. After having defined a measure-valued weak entropy solution of the stochastic conservation law, we present the Kato inequality, and as a corollary, we deduce the uniqueness of the measure-valued weak entropy solution, which coincides with the unique weak entropy solution of the problem. The Kato inequality is proved by a doubling of variables method; to that purpose, we prove the existence and the uniqueness of the strong solution of an associated stochastic nonlinear parabolic problem by means of an implicit time discretization scheme; we also prove its convergence to a measure-valued entropy solution of the stochastic conservation law, which proves the existence of the measure-valued entropy solution.     

Estimation of partial linear error-in-variables models for ρ<Superscript>−</Superscript>-mixing dependence data

Consider the partly linear regression model Y = xβ + g(t) + e where the explanatory x is erroneously measured, and both t and the response Y are measured exactly, the random error e is ρ⁻-mixing. Let be a surrogate variable observed instead of the true x in the primary survey data. Assume that in addition to the primary data set containing N observations of , which is ρ⁻-mixing data sets, an independent validation data containing n observations of is available. The exact observations on x may be obtained by some expensive or diffcult procedures for only a small subset of subjects enrolled in the study. In this paper, inspired by Berberan-Santos et al. [J. Math. Chem. 37 (2005)101], a semiparametric method with the primary data is employed to obtain the estimators of β and g(·) based on the least squares criterion with the help of validata. The proposed estimators are proved to be strongly consistent.      

直链型与支链型疏水缔合水凝胶的机械性能与溶胀行为

以丙烯酰胺(AM)为亲水单体,脂肪醇聚氧乙烯醚丙烯酸酯(AEO-AC-n-m,n为疏水端烷基链碳的数目,m为亲水端PEG链的长度,n,m=13,5;10,5;13,10)为疏水单体,十二烷基硫酸钠(SDS)为表面活性剂,过硫酸钾(KPS)为引发剂,通过胶束聚合制备了3种聚丙烯酰胺-co-脂肪醇聚氧乙烯醚丙烯酸酯(AM-co-AEO-AC)疏水缔合水凝胶.以疏水烷基链为直链的疏水单体AEO-AC-13-5合成的直链型水凝胶的网络结构均匀且强度高,其形态在水中可维持180 d.而以疏水烷基链为支链的疏水单体AEO-AC-10-5与AEO-AC-13-10合成的支链型水凝胶的机械性能较弱,60 d内即溶解于水中.在相同条件下,直链型水凝胶断裂时的最大应力是支链型水凝胶的4~5倍.利用弹性橡胶理论中的新胡克方程计算了直链型和支链型水凝胶的有效交联密度ν0和有效交联点间的分子量Mc.     

同异反动态关联分析方法

在B型关联分析基础上给出了同异反同一度和综合同一度的概念,论证了同异反动态关联分析的性质及其求解方法。为研究事物的发展态势提供了一种动态分析方法     

电感耦合等离子体原子发射光谱法(ICP-OES)测定铍铀伴生矿石中的铍

建立了电感耦合等离子体原子发射光谱法(ICP-OES)测定铍铀伴生矿石中的铍的方法,研究了酸溶-碱熔融法溶样过程中加入的焦硫酸钾,对ICP-OES法测定铍铀伴生矿石中的铍含量产生的基体干扰问题。主要阐述消除基体干扰的一些措施。从实验数据可知,控制称样量、焦硫酸钾加入量、定容体积和加标稀释倍数,能够有效消除焦硫酸钾对ICP-OES法测定结果的基体干扰,6次平行测定结果的相对标准偏差为3.4%,加标回收率为98.7%~104.4%,实验表明,方法准确、可靠。