New conditions on absolute stability of uncertain Lur'e systems and the maximum admissible perturbed bound

Email: fhao{at}buaa.edu.cn Received on April 5, 2006; Accepted on September 10, 2006 The robust absolute stability problem for structured uncertainLur'e systems is considered in this paper by using Popov criterionand extended strictly positive real lemma. The conditions onrobust absolute stability for Lur'e systems with structureduncertainties are established in terms of multilinear matrixinequalities. An estimate of the maximum bound of all admissibleperturbations is given by a generalized eigenvalue problem.Finally, a numerical example is worked out to illustrate theefficiency of the main results.     

On the limiting behavior of the maximum partial sums for arrays of rowwise NA random variables

Let {Xni, 1 ≤ n,i ＜∞} be an array of rowwise NA random variables and {an, n ≥ 1} a sequence of constants with 0 ＜ an ↑∞. The limiting behavior of maximum partial sums 1/an max 1≤k≤n| kΣi=1 Xni| is investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [1] and Hu and Chang [2].     

Potential theory of truncated stable processes

For any , a truncated symmetric α-stable process is a symmetric Lévy process in with a Lévy density given by for some constant c. In this paper we study the potential theory of truncated symmetric stable processes in detail. We prove a Harnack inequality for nonnegative harmonic functions of these processes. We also establish a boundary Harnack principle for nonnegative functions which are harmonic with respect to these processes in bounded convex domains. We give an example of a non-convex domain for which the boundary Harnack principle fails. The research of Panki Kim is supported by Research Settlement Fund for the new faculty of Seoul National University. The research of Renming Song is supported in part by a joint US-Croatia grant INT 0302167.     

Maximum number of colorings of (2k,k2)‐graphs

Let consist of all simple graphs on 2k vertices and edges. For a simple graph G and a positive integer , let denote the number of proper vertex colorings of G in at most colors, and let . We prove that and is the only extremal graph. We also prove that as . © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 135–148, 2007     

Hapten heterology for a specific and sensitive indirect enzyme-linked immunosorbent assay for organophosphorus insecticide fenthion

Five haptens with different spacer-arm attachment sites on the structure of the organophosphorus insecticide fenthion were designed and synthesized. All of the haptens were conjugated with ovalbumin (OVA) for the coating antigen, and three haptens containing all or most of the structure of fenthion were conjugated with bovine serum albumin (BSA) for the immunogen. Six polyclonal antisera were raised against the three BSA conjugates, and 30 antibody/coating conjugate combinations were selected for studies of assay sensitivity and specificity for fenthion. The study revealed the best combination with high sensitivity (I₅₀ of 0.08 ng mL⁻¹) and high assay specificity, which indicated that when structural difference between the analyte and an immunizing hapten is less than that between a coating hapten and the immunizing hapten, a high sensitive enzyme-linked immunosorbent assay (ELISA) in the heterologous system may stand a good chance to be developed. The immunity results showed that heterology in the hapten spacer-arm attachment site of the immunogen could achieve a remarkable improvement in the quantity, sensitivity, and/or specificity of antibody, and that the moiety of an analyte, which is the same as the moiety near/on the immunizing spacer-arm hapten attachment site, contributes greatly to the interaction of antibody and hapten.     

三氨基三硝基苯基高聚物粘结炸药热力学性质的理论计算研究

高聚物粘结炸药(PBX)的热力学性质是用于炸药结构响应、安全性评估、数值模拟分析等的重要参数.由于PBX结构的多尺度特性,完全采取实验方法精细表征这些参数存在巨大的挑战.本文运用第一性原理和分子动力学计算的方法,系统研究了三氨基三硝基苯(TATB)基高聚物粘结炸药的热力学参数和界面热传导性质.利用散射失配模型研究了TATB与聚偏二氟乙烯(PVDF)界面的热传导过程,发现热导率随温度升高而上升,并且在高温情况下接近于定值.基于分子动力学获得的TATB热导率并结合界面热导率,分析了PBX炸药的热导与颗粒尺寸的关系,当颗粒尺寸大于100 nm时,界面热阻对于PBX热导率的影响有限.     

MoO_3/Si界面区钼掺杂非晶氧化硅层形成的第一性原理研究

采用基于密度泛函理论的第一性原理计算方法,通过模拟MoO_3/Si界面反应,研究了MoO_x薄膜沉积中原子、分子的吸附、扩散和成核过程,从原子尺度阐明了缓冲层钼掺杂非晶氧化硅(a-SiO_x(Mo))物质的形成和机理.结果表明,在1500 K温度下, MoO_3/Si界面区由Mo, O, Si三种原子混合,可形成新的稳定的物相.热蒸发沉积初始时, MoO_3中的两个O原子和Si成键更加稳定,同时伴随着电子从Si到O的转移,钝化了硅表面的悬挂键. MoO_3中氧空位的形成能小于SiO_2中氧空位的形成能,使得O原子容易从MoO_3中迁移至Si衬底一侧,从而形成氧化硅层;替位缺陷中, Si替位MoO_3中的Mo的形成能远远大于Mo替位SiO_2中的Si的形成能,使得Mo容易掺杂进入氧化硅中.因此,在晶硅(100)面上沉积MoO_3薄膜时, MoO_3中的O原子先与Si成键,形成氧化硅层,随后部分Mo原子替位氧化硅中的Si原子,最终形成含有钼掺杂的非晶氧化硅层.     

On Entropic Uncertainty Relations for Measurements of Energy and Its “Complement”

Heisenberg's uncertainty principle in application to energy and time is a powerful heuristics. This statement plays an important role in foundations of quantum theory and statistical physics. If some state exists for a finite interval of time, then it cannot have a completely definite value of energy. It is well known that the case of energy and time principally differs from more familiar examples of two non‐commuting observables. Since quantum theory was originated, many approaches to energy–time uncertainties have been proposed. Entropic way to formulate the uncertainty principle is currently the subject of active researches. Using the Pegg concept of complementarity of the Hamiltonian, uncertainty relations of the “energy–time” type are obtained in terms of Rényi and Tsallis entropies. Although this concept is somehow restricted in scope, derived relations can be applied to systems typically used in quantum information processing. Both the state‐dependent and state‐independent formulations are of interest. Some of the derived state‐independent bounds are similar to the results obtained within a more general approach on the basis of sandwiched relative entropies. The developed method allows us to address the case of detection inefficiencies.     

稀土（Ce,Gd）掺杂CdS的第一性原理研究

采用第一性原理赝势平面波法中的LDA+U的方法对稀土(Ce,Gd)掺杂CdS的光电性质进行了计算与分析. 结果表明: Ce, Gd掺杂后, CdS的晶格常数增大, 费米面附近的能带明显增多、变密, 禁带宽度有所增大. Ce和Gd的f态的强局域性使体系产生磁有序性. 稀土掺杂后CdS的静态介电常数增大而反射率明显降低. 以上结果表明稀土元素的掺入能有效调制CdS的光电性质.     

时间尺度上Herglotz变分原理及其Noether定理

Herglotz变分原理的作用量是由微分方程定义的,不仅可以描述所有经典变分原理能够描述的动力学过程,还可以对经典变分原理不能适用的非保守系统或耗散系统进行变分描述．时间尺度上微积分理论提供了一种可同时研究离散系统和连续系统的有效方法．本文结合Herglotz变分原理和时间尺度微积分理论来研究时间尺度上的Herglotz变分原理及其Noether定理．首先,给出时间尺度上Lagrange系统的Herglotz变分原理．其次,根据Herglotz变分原理和Dubois-Reymond引理,推导出时间尺度上Lagrange系统的Herglotz变分问题的运动微分方程．再次,基于时间尺度上Hamilton-Herglotz作用量在群的无限小变换下的不变性,给出Noether对称性的定义并导出其Noether等式．最后,建立了时间尺度上Lagrange系统的Herglotz变分问题的Noether定理,给出了连续和离散两种情况下基于Herglotz变分问题的Noether守恒量．文末举例说明结果的应用．