对偶Brunn-Minkowski不等式的逆

20世纪80年代Milman曾指出:反向Brunn-Minkowski不等式是凸几何的一个深刻的结果.考虑了对偶情况,建立了一个反向的对偶Brunn-Minkowski不等式.进一步,均值积分差的反向对偶Brunn-Minkowski型不等式也被建立.     

基于《基本要求》的新建本科院校大学物理实验教学模式研究

针对新建本科院校大学物理实验教学的现状,结合教育部高等学校物理基础课程教学指导分委员会制定的《理工科类大学物理实验课程教学基本要求》,按照"能力培养+成本最小化与效益最大化"的原则,构建了"一个目标、五个模块"的大学物理实验分层次教学课程体系,对大学物理实验"多元化、交互式"的教学模式进行了研究与探讨.     

Synthesis, Crystal Structure and Band Structure of Eu3Sn5 with Arachno-type Zintl Anions

A new polar intermetallic compound, Eu3Sn5, has been synthesized by solid-state reaction of the corresponding pure elements in a stoichiometric ratio in a welded tantalum tube at high temperature. Its crystal structure was established by single-crystal X-ray diffraction. Eu3Sn5 crystallizes in orthorhombic, space group Cmcm with a = 10.466(11), b = 8.445(8), c = 10.662(12) , V = 942.4(17) 3, Z = 4, Mr = 1049.33, Dc = 7.396 g/cm3, μ = 32.578 mm-1, F(000) = 1756, the final R = 0.0236 and wR = 0.0472 for 535 observed reflections with I > 2σ(I). Its structure belongs to the modified Pu3Pd5 type. It is isostructural with Sr3Sn5 and Ba3Sn5, featuring [Sn5] square pyramidal clusters described as "arachno" according to the Wade-Mingos electron counting rules. The europium cations are located at the voids between the square pyramidal clusters. Results of the extended Hückel band structure calculations indicate that Eu3Sn5 is metallic.     

新建本科院校仪器分析教学的改革与探索

仪器分析课程是化学、药学、食品等专业的一门专业基础课,对培养符合产业界和社会需要的专门人才起着非常重要的作用。基于新建本科院校的功能定位,对仪器分析课程教学改革的跟进具有重要的意义。以重庆第二师范学校为例,在加强与当地企业联合制定教学内容、引入新型“翻转课堂”教学模式,结合企业考核员工指标,注重过程评价方式等方面进行了初步的探讨。期望可以为培养实践能力较强的应用型人才开辟新的路径。     

A note on the multilinear singular integral operators

Lp(Rn) boundedness is considered for the multilinear singular integral operator defined by TAf(x) = ∫Rn Ω(x - y)/|x - y|n 1 (A(x) - A(y) - (△)A(y)(x - y))f(y)dy,where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈ Lipα(Sn-1) (0 ＜α≤ 1) and implies the Lp(Rn) (1 ＜ p ＜ oo) boundedness for the operator TA. Some endpoint estimates are also established.     

Measurement of spatial object''''s exterior attitude based on linear CCD

It is difficult to realize real-time measurement of exterior attitude by the traditional systems based on the area image sensor which have conflict between speed and accuracy.The subsystem for three-dimensional (3D) coordinate rcconstruction of point target (S3DCRPT) which is composed of three one-dimensional (1D) cameras based on linear charge-coupled device (CCD) can determine the distant light spots' spatial position. The attitude angle of the measured object is determined by the spatial solution while the coordinate reconstruction is separately carried on by the S3DCRPT with some point cooperation targets (PCTs) on the measured object. A new optical system is designed to solve the interference problem with one-to-one relationship between the PCTs and the S3DCRPT optical subsystems,which improves the measurement accuracy and saves space. The mathematical model of the attitude measurement is established,and partial and global calibrations are realized for the multi-camera attitude measurement system.The test results show the feasibility of the exterior attitude measurement based on linear CCD.     

An endpoint estimate for maximal multilinear singular integral operators

A weak type endpoint estimate for the maximal multilinear singular integral operator T*Af(x)=supε＞0|(f)(x-y)＞ε (Ω(x-y)/(|x-y|(n 1)))(A(x)-A(y)-▽A(y)(x-y))f(y)dy| is established, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, and A has derivatives of order one in BMO(Rn). A regularity condition on Ω which implies an LlogL type estimate of T*A is given.