边界吸收效应对非定常剪切弥散的影响

采用延迟扩散方程［７，９］描述了具有边界吸收条件下，非定常剪切流动中的剪切弥散特性．给出了记忆函数、中心位移函数的控制方程．特例分析结果表明：所采用的模型方程是合理的；边界吸收效应使得纵向浓度分布具有后倾的趋势．这主要是由于边界吸收使得低速强剪切区浓度减少，剪切弥散贡献减少，从而污染物对流速度高于断面的平均速度．     

Inverse-Definiteness of the Fourth-Order Symmetric Differential Operator （Ⅰ）

Abstract   We give a linear symmetric differential operator L defined by

Entropy,Periodicity, and Graphs with Zero Euler Characteristic

Let G be a graph which contains exactly one simple closed curve. We prove that a continuous map f : G → G has zero topological entropy if and only if there exist at most k ≤ |(Edg(G) End(G) 3)/2] different odd numbers n1,...,nk such that Per(f) is contained in ∪i=1^k ∪j=0^∞ ni2^j, where Edg(G) is the number of edges of G and End(G) is the number of end points of G.     

On（N,U）-Coherence of Modules and Rings

Let U be a flat right R-module and N an infinite cardinal number.A left R-module M is said to be (N,U)-coherent if every finitely generated submodule of every finitely generated M-projective module in σ[M] is (N,U)-finitely presented in σ[M].It is proved under some additional conditions that a left R-module M is (N,U)-coherent if and only if Л^Ni∈I U is M-flat as a right R-module if and only if the (N,U)-coherent dimension of M is equal to zero.We also give some characterizations of left (N,U)-coherent dimension of rings and show that the left N-coherent dimension of a ring R is the supremum of (N,U)-coherent dimensions of R for all flat right R-modules U.     

An Arc as the Inverse Limit of a Single Bonding Map of Type N on [0,1]

Let I = [0, 1], c ₁, c ₂ ∈ (0, 1) with c ₁ < c ₂ and f : I⊸I be a continuous map satisfying: are both strictly increasing and is strictly decreasing. Let A = {x ∈ [0, c ₁]∣f(x) = x}, a=max A, a ₁ =max(A\{a}), and B = {x ∈ [c ₂, 1]∣f(x) = x}, b=minB, b ₁ =min(B\{b}). Then the inverse limit (I, f) is an arc if and only if one of the following three conditions holds: (1) If c ₁ < f (c ₁) ≤ c ₂ (resp. c ₁ ≤ f (c ₂) < c ₂), then f has a single fixed point, a period two orbit, but no points of period greater than two or f has more than one fixed point but no points of other periods, furthermore, if A≠φ and B≠φ, then f (c ₂) > a (resp. f (c ₁) < b). (2) If f (c ₁) ≤ c ₁ (resp. f (c ₂) ≥ c ₂), then f has more than one fixed point, furthermore, if B≠φ and A\ {a} ≠φ, f (c ₂) ≥ a or if a ₁ < f (c ₂) < a, f ² (c ₂) > f (c ₂), (resp. f has more than one fixed point, furthermore, if A≠φ and B\{b}≠φ, f (c ₁) ≤ b or if b < f (c ₂) < b ₁, f ² (c ₁) < f (c ₁)). (3) If f (c ₁) > c ₂ and f (c ₂) < c ₁, then f has a single fixed point, a single period two orbit lying in I\(u, v) but no points of period greater than two, where u, v ∈ [c ₁, c ₂] such that f (u) = c ₂ and f (v) = c ₁. Supported by the National Natural Science Foundation of China (No. 19961001, No. 60334020) and Outstanding Young Scientist Research Fund. (No. 60125310)     

一维无限深势阱中粒子运动的路径积分解法

用路径积分的分析方法求得了一维无限深势阱中粒子的传播函数,并由传播函数导出了粒子的波函数和能量,展示了路径积分与传统方法的等价性,同时还介绍了一种有用的数学函数——雅可比θ_3函数．     

激光二极管泵浦双频固体激光器

研制了0~1.5GHz频差的LD泵浦双频固体激光器。利用端面泵浦和F-P标准具的选模作用得到单频连续输出,在单频基础上将λ/4波片加入谐振腔中,造成本征光频率分裂,实现频差连续可调的双频激光输出。采用琼斯矩阵分析光在腔内的本征值及本征向量,实现了定量分析模在腔内的相位延迟和偏振状态,定量计算双频频差大小。     

多个侧向链对横向量子线传输性质的调制

利用递推格林函数方法，研究了与多个量子点间无相互作用的量子链相耦合的横向量子线的电子输运特性，发现量子链上格点的个数N_U与侧向无限或有限量子链个数N对横向量子线输运性质的不同调制规律.由计算可知，利用格林函数可以方便的对传输构型及传输链中的格点数进行调解，从而得到各种人为量子器件的输运性质. 关键词： 递推格林函数 无限链 有限链 电子输运     

参变过程中的群速延迟对晶体匹配长度的影响

基于能量守恒和三波耦合波方程,建立了超短脉冲在参变过程中二次谐波产生时的I类和II类相位匹配条件、基波与谐波之间的群速延迟时间、以及群速失配对晶体长度限制的理论基础。以负单轴非线性光学晶体CsLiB6O10为例,分析和数值计算了超短脉冲宽度为100fs时,谐波的群速匹配长度随基波波长变化的规律。研究结果表明在I类相位匹配条件下,基波波长为642nm时,群速延迟最小,相应的群速匹配晶体长度最长为19.1mm;在II类相位匹配条件下,基波波长为767nm,群速延迟最小,群速匹配长度最长为0.89mm。     

光纤中高斯型伪随机序列码偏振度的理论分析和实验研究

推导了准单色光波情况下高斯脉冲伪随机序列偏振度的简洁数学表达式.理论分析结果表明,偏振度与差分群延迟之间的关系与线路啁啾和光纤色散无关,并且此关系可以由光信号频谱半宽度Δω和分光比γ唯一确定.用10 Gbit/s 7级m序列归零码进行的实验表明:实验结果与理论推导基本一致,从而验证了推导公式的正确性.