Eigenvalues of Random Power law Graphs

Many graphs arising in various information networks exhibit the "power law" behavior -the number of vertices of degree k is proportional to k^-# for some positive #. We show that if # > 2.5, the largest eigenvalue of a random power law graph is almost surely(1+ o(1))?m (1+ o(1))\sqrt{m} where m is the maximum degree. Moreover, the klargest eigenvalues of a random power law graph with exponent # have power law distribution with exponent 2# if the maximum degree is sufficiently large, where k is a function depending on #, mand d, the average degree. When 2<#< 2.5, the largest eigenvalue is heavily concentrated at cm^3-# for some constant c depending on # and the average degree. This result follows from a more general theorem which shows that the largest eigenvalue of a random graph with a given expected degree sequence is determined by m, the maximum degree, and [(d)\tilde] \tilde{d} , the weighted average of the squares of the expected degrees. We show that the k-th largest eigenvalue is almost surely (1+ o(1))?{m_k} (1+ o(1))\sqrt{m_k} where m_k is the k-th largest expected degree provided m_k is large enough. These results have implications on the usage of spectral techniques in many areas related to pattern detection and information retrieval.     

Singular integrals with rough kernels along real-analytic submanifolds in

mapping properties will be established in this paper for singular Radon transforms with rough kernels defined by translates of a real-analytic submanifold in .

     

A Note on π-Engel Conditions

In this paper we show that the weakly -Engel conditions are closely related to the existance of normal -complements; while the -Engel conditions are closely related to the -nilpotent groups.AMS Subject Classification (2000): 20D20     

In-situ Synthesis of Copper Phthalocyanine in Silica Xerogel Matrix

Using a newly developed in-situ syntheses technique during sol-gel process, copper phthalocyanine (CuPc) is synthesized in-situ in silica xerogel matrix homogeneously. It has been confirmed by UV-Vis and IR spectroscopies that the copper ions which existed in the form of complex-ions [Cu(H₂O)₄]²⁺ and [CuCl₄]^2– in the stages of sol and wet gel were destroyed in the heat treatment process, meanwhile the copper phthalocyanine molecules were synthesized in-situ gradually during the wet gel to xerogel transition. The dimerization phenomenon of CuPc in the composite is suppressed greatly because the in-situ synthesized CuPc molecules were well isolated in the micro-pores of the xerogel matrix. The doping concentration of Copper phthalocyanine in sol-gel derived matrix can be enhanced also by this in-situ synthesis method.     

On the Distribution of Long-Term Time Averages on Symbolic Space

The pressure was studied in a rather abstract theory as an important notion of the thermodynamic formalism. The present paper gives a more concrete account in the case of symbolic spaces, including subshifts of finite type. We relate the pressure of an interaction function to its long-term time averages through the Hausdorff and packing dimensions of the subsets on which has prescribed long-term time-average values. Functions with values in ^d are considered. For those depending only on finitely many symbols, we get complete results, unifying and completing many partial results.     

氮化铟p型掺杂的第一性原理研究

采用基于密度泛函理论(DFT)的总体能量平面波超软赝势法，对Mg，Zn，Cd掺杂InN的32原子超原胞体系进行了几何结构优化，从理论上给出了掺杂和非掺杂体系的晶体结构参数，其中非掺杂体系的理论值与实验值符合很好. 计算了掺杂InN晶体的结合能，总体态密度、集居数，差分电荷密度，并对此做了细致的分析. 计算结果表明，相对于Zn和Cd，Mg_In在InN中的溶解度会更大，并能提供更多的空穴态，非常有利于InN的p型掺杂. 关键词： 氮化铟 p型掺杂 电子结构 第一性原理     

多层介质膜脉冲宽度压缩光栅与超短脉冲作用时的性能分析

基于啁啾脉冲放大技术的超短脉冲激光系统是提供超快、超强激光的重要途径，具有良好输出波形和高损伤阈值的多层介质膜脉冲宽度压缩光栅是获得高峰值功率脉冲激光的关键. 基于傅里叶谱变换方法和严格模式理论，分析了多层介质膜光栅(MDG)在超短脉冲作用下的光学特性. 结果表明，当MDG的反射带宽小于具有高斯分布的入射脉冲的频谱宽度时，-1级反射脉冲呈非对称高斯分布，其前沿出现振荡，并且-1级反射脉冲能量开始剧烈下降. 讨论了MDG结构参数对其反射带宽的影响. 分析了MDG与超短脉冲作用时的近场光分布，对提高其抗激光损 关键词： 脉冲压缩光栅 傅里叶谱变换 模式理论 损伤阈值     

左右手系材料界面处全反射行为的特性

基于电磁场理论，推导了左右手系材料界面处发生全反射时的物理特性，分析了相位变化情况.提出利用左右手系材料构成周期性结构，观测全反射时介质中隐失波干涉的实验设想，并从理论上计算了干涉条纹的分布. 关键词： 左手材料 负折射率 全反射 隐失波     

MgF2单晶的THz光谱研究

利用THz时域光谱技术对MgF₂晶体(样品1)和MgF₂：Co晶体(样品2)在0.5—2.5 THz的吸收特性进行了研究.在0.5—2.5 THz波段，样品1吸收系数α(ν)随频率ν增加而增大，最大值为24 cm^-1.样品2的吸收系数比样品1大得多，Co掺杂使晶格吸收带边向低频移动，而且样品2在1.9 THz有吸收峰，吸收系数达到70 cm^-1，由此求出F^--Co²⁺离子键伸缩振动的键力常数K为3.40×10^-2　N/cm.这一结果表明，THz光谱分析有可能成为研究晶体化学键的一种重要手段.利用光学常数之间的关系计算了两个样品在0.5—2.5 THz的介电函数的实部ε₁(ν)，得到样品1的ε₁(ν)值在4.67至4.73之间，样品2的ε₁(ν)值在4.62至5.01之间. 关键词： THz辐射 光谱 2晶体')" href="#">MgF₂晶体     

基于双核模型对超重元素合成机制的研究

在双核模型基础上，考虑了熔合与准裂变的竞争，通过数值法求解主方程，计算了⁵⁰Ti，⁵⁸Fe+²⁰⁸Pb，²⁰⁹Bi这4个反应系统通过冷熔合反应合成超重元素的激发函数，得到了与实验比较符合的结果.计算了不同入射能量时各角动量分波对熔合概率和超重核存活概率的影响以及对蒸发剩余截面的贡献.这些结果对进一步理解超重核的合成机制有重要意义. 关键词： 超重元素 双核模型 熔合反应 蒸发剩余截面