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In this article, we mainly investigate continuity, monotonicity and differentiability for the first eigenvalue of the p-Laplace operator along the Ricci flow on closed manifolds. We show that the first p-eigenvalue is strictly increasing and differentiable almost everywhere along the Ricci flow under some curvature assumptions.
In particular, for an orientable closed surface, we construct various monotonic quantities and prove that the first p-eigenvalue is differentiable almost everywhere along the Ricci flow without any curvature assumption, and therefore derive
a p-eigenvalue comparison-type theorem when its Euler characteristic is negative. 相似文献
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75.
用质子化学移位 ,自扩散系数和核磁弛豫方法研究了正十二烷基磺酸钠(SDSN) ,正十六烷基三甲基溴化铵 (CTAB)和TritonX 1 0 0等 3种类型表面活性剂及其在溶液中生成的胶团的动态行为 .3种体系的化学移位 ,自扩散系数和自旋 晶格弛豫时间 (T1) ,自旋 自旋弛豫时间 (T2 )均在临界胶团浓度 (cmc)附近有明显的转折点 ,并在 5~ 1 0倍cmc左右时趋向平衡 .T1和T2值的测量表明TritonX 1 0 0分子在溶液中的浓度低于cmc时进行着快速的各向同性运动 .生成胶团后 ,胶团核中的疏水碳氢链紧密堆积使其CH2 和CH3 基团进行着偏离极限窄化条件的运动 .而胶团核外的亲水醚氧长链则进行着相对自由的运动 .但是由于胶团中的分子密集 ,亲水长链产生局部缠结引起T1和T2 值变短 .SDSN和CTAB生成的胶团核内的碳氢链的状态和TritonX 1 0 0的相同 . 相似文献
76.
Jia-Yong Wu 《Annals of Global Analysis and Geometry》2018,54(4):541-549
In this paper, we prove a new Myers’ type diameter estimate on a complete connected Reimannian manifold which admits a bounded vector field such that the Bakry–Émery Ricci tensor has a positive lower bound. The result is sharper than previous Myers’ type results. The proof uses the generalized mean curvature comparison applied to the excess function instead of the classical second variation of geodesics. 相似文献
77.
Huang YP Zhang L Zhang L Luo L Zhao S Yu JY 《The journal of physical chemistry. B》2007,111(20):5640-5647
Synthesis, characterization, and interfacial properties of hydroxy-substituted alkyl benzenesulfonates, sodium 2-hydroxy-3-decyl-5-octylbenzenesulfonate (C10C8OHphSO3Na) and 2-hydroxy-3-octyl-5-decylbenzenesulfonate (C8C10OHphSO3Na), are reported. The dynamic dilational properties of the surfactants are expounded by means of oscillating the bubble/drop method at both water-air and water-decane interfaces. The distinct maxima appear in dilational modulus vs time curves in some cases, which is believed to be attributed to the change of surfactant conformation and the arrangement of surface layer. Our results show that the measurement of dynamic interfacial dilational properties is a powerful tool to probe the structure of the surfactant adsorption film. 相似文献
78.
利用核磁共振化学位移变化, 自旋-自旋弛豫和2D NOESY(two-dimensional nuclear Overhauser enhancement spectroscopy)研究了一系列新合成的双取代烷基苯磺酸盐的胶束化. 结果表明, 邻位取代的是正烷烃链, 间位取代的是支烷烃链. 而且, 邻位取代的烷烃链越长, 参与形成胶束疏水核表面层的亚甲基个数越多. 因此, 每个分子在饱和吸附的油水界面上的面积越大. 间位取代的分支链在胶束疏水核中堆积得没有邻位取代的正烷烃链紧密. 分支链越短, 堆积得越不紧密. 描述了胶束中分子的相对排列. 相似文献
79.
Bao-dong Ma Lei Zhang Bao-yu Gao Lu Zhang Sui Zhao Jia-Yong Yu 《Colloid and polymer science》2011,289(8):911-918
The dynamic dilational properties of branched alkyl benzene sulfonates at the air–water and decane–water interfaces were investigated
by drop shape analysis, and their lamella stability was measured. The influences of time, dilational frequency, and bulk concentration
on surface dilational elasticity and dilational viscosity were expounded. The results show that the molecular interaction
controls the nature of adsorption film during lower concentration range and the film behaves elastic in nature. During higher
concentration range, the diffusion-exchange process controls the dynamic dilational properties and the surface film shows
remarkable viscoelasticity. An increase in hydrophobic chain length enhances the molecular interaction, which results in the
increase of dilational parameters and lamella stability. The data correlation suggests that the ability to form a stable lamella
is linked to the intrinsic surface dilational elasticity. 相似文献
80.
界面张力弛豫法研究不同结构破乳剂油水界面扩张粘弹性 总被引:3,自引:0,他引:3
采用界面张力弛豫法研究了支链破乳剂AE121和直链破乳剂SP169在正癸烷-水界面上的扩张粘弹性质,并与小幅周期振荡法获得的结果进行了比较.阐述了两种破乳剂的扩张模量随扩张频率和破乳剂浓度的变化规律.研究发现,在低频率处,两种破乳剂的扩张模量均接近于零;在中间频率范围内,扩张模量随扩张频率的增加而增大;在高频率处,扩张模量的幅度接近于极限扩张弹性.在中间频率范围内,扩张模量随破乳剂浓度增大,在接近临界胶束浓度处出现一个极大值;同时还发现,界面上和界面附近的微观弛豫过程的数目随破乳剂浓度增加而增大,其贡献也呈规律性变化. 相似文献