能用例证法来证明几何定理吗?

本文提出了证明平面几何定理的例证法。根据这一方法,想判定一个几何命题是否为真,只需近似地验证一个数值曲特例就行了。这个特例仅依赖于该几何命题在某种规范形式下表述的长度l以及命题中自由变量的个数s,可以非常简单地表示出来,与几何命题的内容无关。同时还证明了该类平面几何判定问题所需的并行时间是l_s的一个多项式。     

考虑意外事件对交通流影响的元胞自动机交通流模型

在NaSh模型的基础上,考虑交通事故和养护路段等意外事件对高速公路交通流的影响,建立了有意外事件影响的在车道管制下的高速公路交通流元胞自动机模型,并进行数值模拟. 研究发现:意外事件对高速公路交通流有明显影响,并且意外事件对交通流的影响在某一密度值范围内尤其明显,且意外事件堵塞点在第一车道比在第二车道对交通流的影响小;同时,在该密度值范围内,意外事件堵塞时间和堵塞路段长度越长,对交通流的影响就越大. 关键词： 元胞自动机 交通流 意外事件     

非晶态ZrO_2镶嵌的超细CeO_2催化HCl氧化

采用不同方法制备了铈锆复合氧化物催化剂用于催化HCl氧化反应。自发沉积策略制备的CeO_2@ZrO_2催化剂中,超细CeO_2纳米粒子均匀的镶嵌于非晶态ZrO_2中。CeO_2粒子显著的"尺寸效应"使得该催化剂具有更高的Ce~(3+)和氧空位浓度,而较高的Ce~(3+)和氧空位浓度使得催化剂具有优异的低温氧化还原性能和储释氧能力。催化性能测试表明,CeO_2@ZrO_2催化剂展现出最好的催化活性(1.90 gCl2·gcat~(-1)·h~(-1)),同时CeO_2粒子周围非晶态的ZrO_2阻碍CeO_2的高温烧结,提高了该催化剂的稳定性。     

Hölder Continuity of the Saddle Point Set for Real-Valued Functions

This paper is concerned with Hölder continuity of the solution to a saddle point problem. Some new su?cient conditions for the uniqueness and Hölder continuity of the solution for a perturbed saddle point problem are established. Applications of the result on Hölder continuity of the solution for perturbed constrained optimization problems are presented under mild conditions. Examples are given to illustrate the obtained results.     

Conjugation of quantum dots with graphene for fluorescence imaging of live cells

It is difficult to achieve fluorescent graphene-quantum dots (QDs) conjugation because graphene quenches the fluorescence of the QDs. In the present study, the conjugation of graphene (reduced graphene oxide, RGO) with QDs via a bridge of bovine serum albumin (BSA) provides a novel highly fluorescent nano probe for the first time. BSA capped QDs are firmly grafted onto polyethylenimine (PEI)/poly(sodium 4-styrenesulfonate) (PSS) coated RGO (graphene-QDs) via electrostatic layer by layer assembly. The strong luminescence of the graphene-QDs provides a potential for non-invasive optical in vitro imaging. The graphene-QDs are used for in vitro imaging of live human carcinoma (Hela) cells. Graphene-QDs could be readily up-taken by Hela cells in the absence of specific targeting molecules, e.g., antibodies or folic acid, and no in vitro cytotoxicity is observed at 360 μg mL(-1) of the graphene-QDs. The results for the imaging of live cells indicated that the cell-penetrating graphene-QDs could be a promising nano probe for intracellular imaging and therapeutic applications.     

化学交联聚乙烯醇改性纤维素碱性阴离子交换复合膜的制备与性能

高稳定性碱性阴离子交换膜的制备已成为碱性固体电解质膜研究领域的一大热点.本文通过聚乙烯醇化学交联改性制备出了季铵化羟乙基乙氧基纤维素碱性阴离子交换膜（PVA/QHECE）.采用傅里叶变换红外（FTIR）光谱、热重（TG）分析、交流（AC）阻抗等方法考察了复合膜的分子结构、热稳定性、耐碱稳定性及离子电导率等性能.详尽考察了交联时间、交联剂含量、聚合物组成对成膜力学强度、含水率以及OH^-电导率的影响.实验结果表明:随着交联时间的增加,膜的溶胀率降低,力学强度随之增强,而离子电导率随膜含水率的降低没有发生明显变化,室温下OH^-的电导率在3.26×10^-4-4.44×10^-4S·cm^-1范围内变化.热重分析结果显示:掺入42.9%的QHECE时,膜的热分解温度达260℃.此外,将PVA/QHECE膜在6 mol·L^-4 KOH浓碱溶液中80℃浸渍处理168 h,膜的电导率从4.90×10^-4S·cm^-1提高到9.68×10^-4S·cm^-1,而膜的外观和力学强度以及含水率未发生明显变化,这一结果表明该膜具有很好的耐碱化学稳定性,有望作为一种新型的碱性燃料电池用离子交换膜.     

Study on connections of the MFS, Trefftz method, indirect BIEM and invariant MFS in the three-dimensional Laplace problems containing spherical boundaries

Following the success of a study on the method of fundamental solutions using an image concept [13], we extend to solve the three-dimensional Laplace problems containing spherical boundaries by using the three approaches. The case of eccentric sphere for the Laplace problem is considered. The optimal locations for the source distribution to include the foci in the MFS are also examined by using the image concept in the 3D problems. Whether a free constant is required or not in the MFS is also studied. The error distribution is discussed after comparing with the analytical solution derived by using the bispherical coordinates. Besides, the relationship between the Trefftz bases and the singularity in the MFS for the three-dimensional Laplace problems is also addressed. It is found that one source of the MFS contains several interior and exterior Trefftz sets through a degenerate kernel. On the contrary, one single Trefftz base can be superimposed by some lumped sources in the MFS through an indirect BIEM. Based on this finding, the relationship between the fictitious boundary densities of the indirect BIEM and the singularity strength in the MFS can be constructed due to the fact that the MFS is a lumped version of an indirect BIEM.     

关于p(kp+1)(kp+2)阶的单群

本文证明了:对于任何一个正整数n存在一个正整数m,使得对任何正整数k≤n及任何素数p≥m,阶为p(k_p+1)(k_p+2)的单群都必须同构于LF(2,p+1)或LF(2,2p+1)。     

脉冲激光沉积法制备高温压电薄膜0.20 BiInO$lt;sub$gt;3$lt;/sub$gt;-0.80PbTiO$lt;sub$gt;3$lt;/sub$gt;$lt;strong$gt;$lt;font color="#ff0000"$gt;$lt;font color="#ff0000"$gt;（已撤稿）$lt;/font$gt;$lt;/font$gt;$lt;/strong$gt;

采用脉冲激光沉积法制备了0.20BiInO₃-0.80PbTiO₃（20BI-PT）高温压电薄膜,并与0.15BiInO₃-0.85PbTiO₃（15BI-PT）样品进行了比较研究. X射线衍射谱显示,20BI-PT样品100峰出现了明显的劈裂,显示样品具有更高的四方对称性. FESEM图显示,20BI-PT样品中出现了部分111取向的三角形晶粒. 20BI-PT样品的铁电剩余极化（P_r）为～28 μC/cm²,矫顽场（E_c）为～120 kV/cm,相较15BI-PT样品,P_r略有增加,但同时E_c也有增加. 20BI-PT样品的横向压电系数（e_31,f）约为–4.7±0.6 C/m²,和15BI-PT相比几乎一样. 介电温度谱显示,20BI-PT 样品的居里温度比15BI-PT增加了约30 ℃,达590 ℃,且介电峰没有明显的频率依赖性. Rayleigh分析显示,20BI-PT样品中内在本征因素及可翻转畴对介电非线性的贡献和15BI-PT基本相同,但是外在因素的贡献没有15BI-PT的贡献大,这可能和20BI-PT样品中晶粒111相对取向率较高有关. 关键词： 薄膜 脉冲激光沉积 铁电 压电     

三乙醇胺改性Cu/Zn/Al类水滑石衍生氧化物催化合成气制备低碳醇

采用共沉淀法制备Cu/Zn/Al类水滑石前驱体,并用配体三乙醇胺(TEA)对其进行改性。前驱体经焙烧后成功获得TEA改性的Cu/Zn/Al催化剂。借助XRD、FTIR、H2-TPR、CO-TPD及SEM等方法对催化剂进行表征,并将其应用于合成气制备异丁醇的活性评价反应中。结果表明,TEA的加入能够改变催化剂形貌,使催化剂表面呈松散絮状结构。TEA可使类水滑石前驱体的结构发生膨胀,其焙烧获得的催化剂中有明显的晶格扭曲和晶格缺陷。TEA对催化剂结构的改变有利于Cu/Zn/Al催化剂中CuO组分的氢还原和CO在催化剂表面的化学吸附,从而促进异丁醇的合成。当TEA的添加比例为nTEA/nZn=0.5时,TEA改性的Cu/Zn/Al催化剂的催化效果达到最佳。