On sums and products of combinatorial cubes

We obtain several lower bounds on the product set of combinatorial cubes, as well as some non–trivial upper estimates for the multiplicative energy of such sets.     

风电场地形绕流的CFD结果确认研究

掌握复杂地形区域的风能分布对风电场微观选址至关重要.为把CFD技术应用于风场中实际地形的风流动模拟,本文选择三种具有实验数据的典型地形进行数值计算,并对数值结果进行确认研究.文中简述了不同网格和不同湍流模型对旋涡位置和速度分布的影响,并探讨了为增加风能利用率,如何确定风力机的最佳安装位置.     

角锥棱镜腔Nd:YAG/Cr4+:YAG被动锁模激光器的研究

理论分析并数值模拟了腔内光强随角锥棱镜旋转的变化,实验证明在角锥棱镜腔Nd:YAG/Cr4 :YAG被动锁模激光器中,偏振耦合输出得到了锁模深度和锁模几率近乎100%的线偏振被动锁模脉冲输出.通过旋转角锥棱镜改变偏振耦合输出、调节腔内光强,可以得到被动锁模和被动调Q两种状态的脉冲输出,脉冲能量166.5 mJ/pulse,脉冲动静比高达59.7%.     

Hilbert space compression and exactness of discrete groups

We show that the Hilbert space compression of any (unbounded) finite-dimensional CAT(0) cube complex is 1 and deduce that any finitely generated group acting properly, co-compactly on a CAT(0) cube complex is exact, and hence has Yu's Property A. The class of groups covered by this theorem includes free groups, finitely generated Coxeter groups, finitely generated right angled Artin groups, finitely presented groups satisfying the B(4)-T(4) small cancellation condition and all those word-hyperbolic groups satisfying the B(6) condition. Another family of examples is provided by certain canonical surgeries defined by link diagrams.     

New regular embeddings of n‐cubes Qn

We investigate highly symmetrical embeddings of the n‐dimensional cube Q_n into orientable compact surfaces which we call regular embeddings of Q_n. We derive some general results and construct some new families of regular embeddings of Q_n. In particular, for n = 1, 2,3(mod 4), we classify the regular embeddings of Q_n which can be expressed as balanced Cayley maps. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 297–312, 2004     

角锥后向反射器的数值模拟研究

鉴于实际应用的需要，考虑角锥反射器的二面角加工误差，采用矩阵光学和矢量运算方法，建立了一套适合于数值模拟的角锥反射器的后向反射数学模型，给出了角锥后向反射器光束变换及衍射传输的公式和数值模拟计算方法。分别针对理想角锥后向反射器和有二面角加工误差的角锥反射器，研究了反射光束的传输特性，分桥了入射角和传输距离对近场和远场能量分布的影响。根据卫星搭载角锥反射器的特殊要求，讨论了速差补偿方法和设计等问题，并针对卫星姿态控制的两种情况，分别提出了速差补偿的设计方案。     

On Orthogonal Latin <Emphasis Type="Italic">p</Emphasis>-Dimensional Cubes

We give a construction of p orthogonal Latin p-dimensional cubes (or Latin hypercubes) of order n for every natural number n ≠ 2, 6 and p ≥ 2. Our result generalizes the well known result about orthogonal Latin squares published in 1960 by R. C. Bose, S. S. Shikhande and E. T. Parker.     

切削微角锥棱镜型超高定向反射膜的分析与测试

采用几何光学法对切削微角锥棱镜薄膜结构单元的反射特性进行理论分析,采用光学仿真软件对该结构单元的反光性能进行模拟验证,并与传统微角锥棱镜薄膜结构单元进行对照.结果表明,理论中,当平行光垂直于结构底面入射并忽略吸收时,该切削结构薄膜单元可实现完全定向反射,而相同条件下,传统微角锥棱镜结构薄膜单元定向反射率为66.7%.模拟仿真的定向反射率分别是92.3%和62.4%.建立了薄膜定向反射率测量方法,对具有上述两种结构单元的薄膜样品的定向反射率进行测试,测试结果分别为67.8%和39.5%.