A measure of mutual complete dependence in discrete variables through subcopula

Siburg and Stoimenov [12] gave a measure of mutual complete dependence of continuous variables which is different from Spearman's ρ and Kendall's τ. In this paper, a similar measure of mutual complete dependence is applied to discrete variables. Also two measures for functional relationships, which are not bijection, are investigated. For illustration of our main results, several examples are given.     

Three‐Phase Barker Arrays

A 3‐phase Barker array is a matrix of third roots of unity for which all out‐of‐phase aperiodic autocorrelations have magnitude 0 or 1. The only known truly two‐dimensional 3‐phase Barker arrays have size 2 × 2 or 3 × 3. We use a mixture of combinatorial arguments and algebraic number theory to establish severe restrictions on the size of a 3‐phase Barker array when at least one of its dimensions is divisible by 3. In particular, there exists a double‐exponentially growing arithmetic function T such that no 3‐phase Barker array of size with exists for all . For example, , , and . When both dimensions are divisible by 3, the existence problem is settled completely: if a 3‐phase Barker array of size exists, then .     

一种通过梯形PPMgLN波导倍频实现带宽可调谐光源的理论研究

本文设计了一种梯形的周期极化掺镁铌酸锂(PPMgLN)波导,并通过在传播方向上引入温度梯度来拓宽其倍频(SHG)过程的泵浦光源可接收带宽。通过有限差分的光束传输法,计算波导的有效折射率,并进行波导尺寸的设计。结果表明,通过改变梯形波导不同位置的温度,使其形成一个温度梯度,可拓宽泵浦光源的波长可接收带宽。本文所设计的PPMgLN波导最大泵浦光源可接收带宽为C波段,即1 530~1 565 nm,该波导可倍频C波段,得到输出波段带宽为765~782.5 nm,温度调谐范围为30~150 ℃。     

NO分子宏观气体热力学性质的理论研究

采用量子统计系综理论,研究了基态NO分子宏观气体摩尔熵、摩尔内能、摩尔热容等热力学性质.首先应用课题组前期建立的变分代数法(variational algebraic method, VAM)计算获得了基态NO分子的完全振动能级,得到的VAM振动能级作为振动部分,结合欧拉-麦克劳林渐进展开公式的转动贡献,应用于经典的热力学与统计物理公式中,从而计算得到了1000-5000 K温度范围内NO宏观气体的摩尔内能、摩尔熵和摩尔热容.将不同方法计算得到的摩尔热容结果分别与实验值进行比较,结果表明基于VAM完全振动能级获得的结果优于其他方法获得的理论结果.振动部分采用谐振子模型对无限能级求和计算热力学性质的方法有一定的局限性,应当使用有限的完全振动能级进行统计求和.     

Synthesis and Characterization of Biodegradable Alternating Polyesteramides from Mixed Diamidediols and Sebacic Acid

A series of polyesteramide prepolymers[PrePEA（0/4,8）s] having mixed alternating bisesterdiamide units was synthesized via melt polycondensation from N,N＇-bis（2-hydroxyethyl）oxamide（0） and N,N＇-bis（2-hydroxyethyl）-adipamide（4） with sebacic acid（8） at different molar ratios.Chain extension of them was conducted with 2,2＇-（1,4-phenylene）-bis（2-oxazoline） and adipoyl biscaprolactamate as combined chain extenders.The chain extended polyesteramides[ExtPEA（0/4,8）s] were characterized by proton nuclear magnetic resonance（1H NMR）,gel permeation chromatography（GPC）,differential scanning calorimetry（DSC）,thermogravimetry analysis（TGA）,wide angle X-ray scattering,tensile test and enzymatic degradation.The results show that ExtPEA（0/4,8）s were crystalline polyesteramides.They had Tm up to 136.5 ℃ and initial decomposition temperature above 297.5 ℃.They crystallized in similar crystallites into Nylon-66 and degraded under the catalysis of protease or lipase.They are thermoplastic materials with tensile strength up to 21.5 MPa and elongation at break above 64.0％.     

不同分子量软链段的聚己内酯型聚氨酯扩链反应动力学研究

合成了一系列不同分子量的聚己内酯,进而制备异氰酸根封端的聚己内酯预聚体,用傅里叶变换红外光谱研究了不同分子量的聚己内酯预聚体与二元醇的扩链反应.扩链反应动力学研究结果表明:聚己内酯预聚体与二元醇的扩链反应均为二级反应;随着软链段反应物料分子量的增加,反应速率常数显著降低,但当分子量超过某一范围后,其对反应速率的影响逐渐减小,趋于不变.对于不同硬链段反应物料含量的扩链反应体系,硬链段反应物料含量越高,软链段反应物料分子量对反应速率的影响越明显,而且,当软链段反应物料分子量超过某一范围后,不同体系的反应速率常数间的差值趋于不变.Arrhenius方程中的指前因子(B)随软链段反应物料分子量的变化关系与速率常数对分子量的依赖关系相同;从反应速率常数对温度的依赖关系可见:表观活化能的直线斜率基本相同,扩链反应的活化能主要与官能团的反应活性相关.     

固定接触界面法向静弹性刚度

基于Hertz接触理论推导了两个微凸体之间互相作用的法向接触静弹性刚度.根据修正后的一个微接触点的平截面积尺寸分布,给出了界面的总法向接触静弹性条件刚度、总条件载荷的解析解.将法向静弹性刚度的解析解嵌入到有限元软件中,获得整机的理论模态.通过实验对解析解进行了定量验证.以机床结合部为研究对象,在理论振型与实验振型一致的...     

Multipliers,covers, and stem extensions for Lie superalgebras

Suppose that the underlying field is of characteristic different from 2 and 3. We first prove that the so-called stem deformations of a free presentation of a finite-dimensional Lie superalgebra L exhaust all the maximal stem extensions of L; up to equivalence of extensions. Then we prove that multipliers and covers always exist for a Lie superalgebra and they are unique up to superalgebra isomorphisms. Finally, we describe the multipliers, covers, and maximal stem extensions of Heisenberg superalgebras and model filiform Lie superalgebras.     

半格分次弱Hopf代数的$G$-Cleft扩张

本文首先将Clifford幺半群代数分解为交叉积的半格直和,然后将这个结果通过$H$-$G$-cleft扩张推广到所谓的$G$-交叉积上.     

ALGEBRAIC EXTENSION OF ＊-A OPERATOR

In this paper, we study various properties of algebraic extension of *-A operator.Specifically, we show that every algebraic extension of *-A operator has SVEP and is isoloid.And if T is an algebraic extension of *-A operator, then Weyl's theorem holds for f(T), where f is an analytic functions on some neighborhood of σ(T) and not constant on each of the components of its domain.