A decomposition result for a class of polling models

Boxma and Groenendijk have shown that the workload in polling models decomposes into two independent variables. This paper demonstrates a different type of decomposition that has an explicit multi-dimensional form. This decomposition does not apply to all polling models, but does, for example, apply to models with constant switch-over times and either exhaustive or gated service disciplines. For such models, we show that the population of customers present in the system (represented by a vector indicating the number of customers at each queue) at key time points breaks into two independent subpopulations: (1) the population of customers present in the related model with zero switch-over times; (2) another population, which is particularly easy to analyze. This result has a number of theoretical and applied implications.     

n元等比级数

定义了n元等比数列、n元等比级数,给出了它们的通项公式及前n项和.并解决了多元等比级数的敛散性问题,求出了多元等比级数的和.指出了多元等比数列及多元等比级数在特殊情况下与一元等比数列及一元等比级数的一致性.     

广义风险过程中渐近方差的非参数估计

本文对广义风险过程中的渐近方差作了非参数估计,得出并证明了两个定理,为广义风险过程中破产概率的区间估计作了理论准备．     

Dependence of calculated electron effective attenuation lengths on transport mean free paths obtained from two atomic potentials

We report changes in electron effective attenuation lengths (EALs) resulting from use of transport mean free paths (TMFPs) obtained from the Dirac–Hartree–Fock (DHF) potential instead of the Thomas–Fermi–Dirac (TFD) potential in an algorithm used in the National Institute of Standards and Technology (NIST) Electron Effective‐Attenuation‐Length Database (SRD 82). TMFPs from the former potential are believed to be more reliable than those obtained from the latter potential. We investigated changes in the EALs for selected photoelectron and Auger‐electron lines in four elemental solids (Si, Cu, Ag, and W), for Si 2p photoelectrons of varying energy in SiO₂, and for photoelectrons excited by Al Kα X rays in four candidate gate‐dielectric materials (HfO₂, ZrO₂, HfSiO₄, and ZrSiO₄). For each material, we computed the change in the average EAL for a range of overlayer‐film thicknesses from zero to a maximum value corresponding to attenuation of the substrate signal to 10% of its original value. This EAL change was a maximum for electrons emitted normally from the surface and decreased monotonically with increasing emission angle. The maximum EAL change varied between ?4.4% and 2.6% for the three groups of materials. We found that the maximum EAL change correlated mainly with the TMFP change. We found that TMFP changes in other solids could generally lead to maximum EAL changes between ?2.6% and 1.9% for electron energies between 500 and 2000 eV. For lower energies, the maximum EAL changes could be larger for some solids. Our revised EALs for Si 2p photoelectrons in SiO₂ excited by Mg and Al Kα X rays agree within 0.5% with values reported by Seah and Spencer from a detailed analysis of SiO₂ film‐thickness measurements by XPS and other techniques. Copyright © 2006 John Wiley & Sons, Ltd.     

球面稳定同伦中的复合元素α1β1γs的非平凡性

本文证明:当p≥7任意奇素数,3≤s相似文献   

PEG-PLA嵌段共聚物的合成及~(13)C NMR对平均链段长度的测定

本文报道聚乙二醇(PEG)在辛酸亚锡存在下与丙交酯(LA)反应合成PEG-PLA嵌段共聚物,用~(13)C NMR测定了共聚物的结构,估算了平均链段长度.实验结果表明,L_(PEG)在反应过程中保持不变,而L_(PLA)随反应时间和LA在原料配比中含量的增加而增加,呈逐步聚合反应特点.对聚合反应机理作了推测.     

Electron microscope study of viscoelastic cationic surfactant systems

Some cationic surfactants such as cetyltrimethylammonium bromide (CTAB) show a very spectacular viscoelasticity in solution, in even very diluted states, with some aromatic substances added, such as salicylic acid. Formerly, the authors established that the remarkable solution behaviour was the result of the entanglement of such enormously elongated giant micelles, based on recognition of the existence of large aggregates, through direct observation of them as substantial images under the electron microscope.In this report, we further confirm the relation between micelle length and solution viscoelasticity after arbitrarily obtaining different size aggregates by altering the media pH, or by admixing shorter chain length surfactants than CTAB, which alone did not induce viscoelasticity.     

Fermi and Coulomb correlations in the 21 S state of the helium isoelectronic sequence

The Fermi and Coulomb holes of the 2¹ S state of the helium isoelectronic sequence are investigated. Several interesting differences between the results obtained and those which might be expected on the basis of the corresponding 2³ S state are pointed out and discussed.     

Influences of local polymer-solvent π-π-interaction on dynamics of phenyl ring rotation and its role on photophysics of conjugated polymer

In this report, the role of local polymer-solvent π-π-interaction on rotational dynamics of phenyl rings of poly[2-methoxy-5-(2′-ethyl-hexyloxy)-1,4-phenylenevinylene] (MEH-PPV) is examined by utilizing nuclear magnetic resonance (NMR) spectroscopy. We have found that an aromatic solvent can couple strongly with the phenyl rings via favorable local π-π-interaction, causing a restriction of the ring rotation. The dynamic process takes place at much faster rate in a non-aromatic solvent. NMR line shape analysis indicates the existence of two side chain configurations with relatively long life-time in toluene and pyridine while a single time-averaged configuration is detected in chloroform and tetrahydrofuran. Addition of chloroform or cyclohexane to a solution of MEH-PPV in toluene is accompanied by an increase of the rotational dynamics. This indicates that the expansion or collapse of main chain upon varying solvent quality play a minor role on the rotational dynamics. The relationship between the dynamics of ring rotation and photophysics of MEH-PPV in solution is discussed.