Continuous time random walks and the Cauchy problem for the heat equation

We deal with anomalous diffusions induced by continuous time random walks - CTRW in ?ⁿ. A particle moves in ?ⁿ in such a way that the probability density function u(·, t) of finding it in region Ω of ?ⁿ is given by ∫_Ωu(x, t)dx. The dynamics of the diffusion is provided by a space time probability density J(x, t) compactly supported in {t ≥ 0}. For t large enough, u satisfies the equation

$$u\left( {x,t} \right) = \left[ {\left( {J - \delta } \right)*u} \right]\left( {x,t} \right)$$

, where δ is the Dirac delta in space-time. We give a sense to a Cauchy type problem for a given initial density distribution f. We use Banach fixed point method to solve it and prove that under parabolic rescaling of J, the equation tends weakly to the heat equation and that for particular kernels J, the solutions tend to the corresponding temperatures when the scaling parameter approaches 0.

     

The lowest electronic states of Ne2 +, Ar2 + and Kr2 +: comparison of theory and experiment

Non-relativistic configuration interaction (CI) ab initio calculations using large basis sets have been carried out to determine the potential curves of the first electronic states of Ne₂ ⁺, Ar₂ ⁺ and Kr₂ ⁺. The spin—orbit interaction was treated assuming that the spin—orbit coupling constant is independent of the internuclear separation (R). For Ar₂ ⁺, calculated dissociation energies and equilibrium separations are in good agreement with experimental results. The calculations for Ne₂ ⁺ suggest that the lowest vibrational level of the I(1/2u) ground state observed by threshold photoelectron spectroscopy by Hall et al. [1995, J. Phys. B: At. molec. opt. Phys., 28, 2435] and assigned to either ν = 0 or ν = 2 actually corresponds to ν = 4. The calculations also predict the I(1/2g) state of Ne₂ ⁺ and Ar₂ ⁺ to possess a double-well potential and that of Kr₂ ⁺ to be repulsive at short range and to only possess a single shallow well at large internuclear separation. The ab initio calculations provide an explanation for the observation made by Yoshii et al. [2002, J. chem. Phys., 117, 1517] that Kr₂ ⁺ and Xe₂ ⁺ dissociate after photoemission from the II(1/2u) state to the I(1/2g) state whereas Ar₂ ⁺ does not.     

On weighted inequalities for singular integrals

In this note we consider singular integrals associated to Calderón-Zygmund kernels. We prove that if the kernel is supported in then the one-sided condition, , is a sufficient condition for the singular integral to be bounded in , , or from into weak- if . This one-sided condition becomes also necessary when we require the uniform boundedness of the singular integrals associated to the dilations of a kernel which is not identically zero in . The two-sided version of this result is also obtained: Muckenhoupts condition is necessary for the uniform boundedness of the singular integrals associated to the dilations of a general Calderón-Zygmund kernel which is not the function zero either in or in .

     

Symbolic Dynamics of the Two-Well Duffing Equation

At weak force range the two-well Duffing equation has a closed bifurcation region in theparameter plane, inside which there are many different periodic windows. By means ofone-dimensional and two-dimensional symbolic dynamics, these periodic windows and thedynamical behavior of chaotic attractors are analyzed systematically.     

Cu、Zn-SOD酶模型化合物催化O-2歧化作用的研究

本文采用ＮＢＴ法,利用７２１分光光度计,在ｐＨ＝７．８的条件下,测定了前文所合成的含Ｎ、Ｏ的Ｓ的Ｓｃｈｉｆｆ碱及其铜（Ⅱ）、锌（Ⅱ）配合物催化Ｏ２＾－歧化的活性,并探讨了平均抑制率与浓度的关系。     

若丹明B荧光增强二硫化碳高阶受激喇曼散射

 利用若丹明B乙醇溶液的荧光改变了二硫化碳的一至三阶Stokes喇曼谱线的强度分布,选择性地增强了三阶Stokes喇曼谱线。在泵浦功率密度为~560MW^.cm^-2时,对染料摩尔浓度分别为~10^-5、cm^-5散射池和~10^-4、1cm散射池进行实验,观察到二硫化碳的三阶Stokes喇曼谱线与染料激光形成的共振增强现象及、二阶Stokes喇曼谱线的部分或完全耗尽。     

铝球弹丸高速正撞击薄铝板穿孔研究

 低地球轨道上的航天器易受到微流星体及空间碎片的超高速撞击，导致其严重的损伤甚至灾难性的失效。撞击损伤特性研究是航天器防护设计的一个重要问题。通过铝球弹丸超高速正撞击薄铝板的实验研究和数值模拟，证明了AUTODYN-2D软件数值模拟预测薄铝板超高速撞击穿孔直径的有效性。通过对弹丸直径、弹丸撞击速度和薄铝板厚度影响薄铝板超高速撞击穿孔直径的数值模拟，以及利用实验结果和数值模拟结果拟合的曲线，得到了铝球弹丸超高速撞击薄铝板的穿孔规律以及影响薄铝板超高速撞击穿孔直径的主要因素。     

含改性松香的丁二醇二缩水甘油醚固化反应动力学研究

设计了含改性松香无苯环的环氧固化体系和无松香的对照体系,分别是无松香体系Ⅰ：丁二醇二缩水甘油醚（BDGE）和甲基六氢苯酐（MeHHPA）;无规体系Ⅱ：丙烯酸松香（AR）、BDGE和MeHHPA;有规体系Ⅲ：丙烯酸松香基环氧树脂（ARE,由AR和BDGE预聚而来）和MeHHPA。对三体系的固化反应应用动态示差扫描量热仪（DSC）进行了研究,利用KAS法求得不同转化率下的表观活化能,通过整个反应过程反应活化能的变化,得到了三体系反应的内在机理,结果发现松香基的引入及引入顺序都对固化反应产生影响。     

氮气中空心阴极放电条纹的发光特性

利用发射光谱法,在氮气环境下研究了圆柱型空心阴极放电条纹的特性。测量得到了气压为20 Pa,放电电流为1.3 mA时条纹区的发射光谱,结果表明发射光谱主要为氮分子的第一正带系(B3П_g →A3П_u)和 第二正带系(C3П_u→B3П_g )。利用双原子光谱发射理论,计算得到了氮分子振动温度的空间分布特性。结果表明光谱线强度呈周期性分布,明纹中心处的谱线强度高于暗纹中心处的谱线强度。明纹中心处的N₂分子振动温度为3 500～4 400 K,并且从阴极到阳极,明纹中心处光谱线强度和分子振动温度逐渐下降。同时测量得到了放电电流为1.0和1.5 mA时的发光条纹特性,研究了放电电流对条纹特性的影响。随着放电电流的增加,明纹中心处的分子振动温度升高,条纹间距增加。另外,利用测量得到的发光条纹,计算得到了条纹区的平均约化电场强度为44～49 m-1·Pa-1,并且由阴极向阳极逐渐降低。对于揭示气体放电中发光条纹的形成机理和促进空心阴极放电的稳定性有重要的参考价值。