Mean width inequalities for isotropic measures

In this paper, we establish Barthe’s mean width inequalities for continuous isotropic measures by a direct approach rather than using the Brascamp–Lieb inequality. The following results are obtained: among the convex hulls of the support of isotropic measures on S ^n–1, the regular simplex inscribed in the Euclidean unit ball has maximal ?-norm; in the dual situation, there is a reverse result for their polar bodies. Moreover, the case of even isotropic measures is also investigated.     

Extreme properties of quermassintegrals of convex bodies

In this paper, we establish two theorems for the quermassintegrals of convex bodies, which are the generalizations of the well-known Aleksandrov’ s projection theorem and Loomis-Whitney’ s inequality, respectively. Applying these two theorems, we obtain a number of inequalities for the volumes of projections of convex bodies. Besides, we introduce the concept of the perturbation element of a convex body, and prove an extreme property of it.     

往复射流分散与超声分散对纳米碳管在不饱和聚酯中分散效果的研究

分别采用超声分散法和本课题组研究的新技术-往复射流分散法对一系列含不等量多壁纳米碳管的前驱体混合物进行了分散,并将其固化制得了不同的复合材料.其中,前驱体混合液的粘度通过旋转粘度计测定,并使用扫描电镜观测最终所得复合材料中纳米碳管的分布状态.检测结果表明,一方面,往复射流分散工艺相对于超声分散更有利于纳米碳管在聚合物中的分散,而且碳管的分散均匀程度随工作次数的增加而有所提升.但另一方面,前驱体混合液的粘度同时亦随之大幅度下降,而这将减弱后续的前驱体固化过程的工艺性.     

Statistical Properties of a Ring Laser with Injected Signal and Backscattering

The Statistical Properties of a homogeneously broadened ring laser with an injected signal are investigated and the normalized two-mode intensity auto-and cross-correlation functions are calculated by a full saturation laser theory with backscattering.The theoretical predictions are in good agreement with the experimental measurements.Further inverstigation reveals that the backscattering can reduce the fluctuations in the system while the full saturation effect plays a major role when the laser is operated above threshold.It is also quite important to notice that the injected signal can drive the weak mode from incoherent light to coherent light.     

内部爆炸载荷作用下混凝土动力响应的数值模拟

 目前,采用实验方法对爆炸载荷破坏效应进行全面、准确描述仍是一个难题。运用ANSYS/LS-DYNA非线性显式动力学有限元程序,采用流固耦合算法,对混凝土在内部爆炸载荷作用下的空腔形成和发展规律等动力响应问题进行了数值模拟。通过实际算例,比较研究了混凝土敷设钢板与否对成坑大小、损伤区、压力云图以及应力时程曲线等的影响,进一步研究了有钢板加固时混凝土在爆炸荷载作用下的破坏机理。研究表明：采用流固耦合算法可以避免由于物质的大变形引起的单元畸变和网格消蚀等问题,提高了计算效率;很好地模拟了混凝土内部爆炸时,中心爆炸空腔压缩面和自由面的拉伸层裂破坏过程,且与理论计算值吻合较好;通过表面敷设钢板,可以减小混凝土的拉应力峰值,抑制混凝土中裂纹的发展,从而提高其防震塌能力以及结构的完整性。     

Lp截面体

通过利用Brunn-Minkowski-Firey混合体积及对偶混合体积理论,研究了Lp-截面体和对偶混合体积的相互关系,建立了关于正规化Lp-径向加及Lp-径向线性组合的Lp-截面体的Brunn-Minkowski形不等式及其隔离形式,且获得了算子Ip的一些性质.     

对偶L_p-质心体与Fourier变换

对p>0,Lutwak,Yang和Zhang引进了R~n中一个凸体K的对偶L_p~-质心体Γ_(-p)K.本文研究Γ_(-p)KΓ_(-p)L是否必定蕴涵vol_n(K)≤vol_n(L)的问题.我们的结果是Lutwak(p=1的情形)及Grinberg和Zhang(p>1的情形)关于L_(p~-)质心体算子Γ_p的类似问题的结果的对偶形式.     

基于降低污垢热阻的复合强化传热研究

复合强化传热的换热系数的增加通常要比单独使用其中的任何一种技术高,但过分增长的污垢热阻会轻而易举地将对流换热系数提高的效果加以抵消。将振动看作不仅仅意味着噪声与元件损坏的能量表达方式,就有可能利用流体诱导的传热元件振动扰动水流,提高对流换热系数;同时,用振动变形清除传热表面积垢,降低污垢热阻,从而形成一种复合强化传热的新方法。     

关于地质时间本质的思考

通过对新疆北部志留—泥盆系界线的讨论，以及对乌吐布拉克组的地层归属问题的探讨，和国际志留—泥盆系界线的理论根据的浅析，提出地质时间本质的含义。     

Inequalities for Edge Lengths and Volumes of Two Simplexes

In this paper, a class of geometric inequalities for the edge lengths and volumes of two n-dimensional simplexes are established. As a corollary, a generalization to several dimensions of the Neuberg–Pedoe inequality is given.