带有临界指数的椭圆方程多重正解的存在性

采用变分方法考虑了一类带有临界指数和有限个奇点的椭圆方程正解的存在性问题,利用临界点理论可以得到V(x)的每一个奇点都可以产生一个正解.     

The parameterization of 2-channel orthogonal multifilter banks with some symmetry

For the 2-channel orthogonal multiwavelet systems with symmetric center γ/2, we give the parameterization of the associated multifilter banks, whether γ is odd or even. When γ is odd, we obtain the similar results to Jiang’s, for the case that γ is even, we transform the parameterization of the multifilter banks into the one of the case that γ is odd, then by the previous results and inverse transforms, we derive the corresponding results. Using the parameterization of the multifilter banks, we easily reconstruct the Chui-Lian multiwavelet systems with support [0,2] and [0,3]. Moreover, a new orthogonal multiwavelet system with symmetric center 2 is obtained, and the corresponding multiscaling function has approximation order 2.     

磁性热敏聚合物微球的制备及磁感应控制释放行为

采用种子乳液聚合法在Fe3O4纳米粒子表面聚合包覆N-异丙基丙烯酰胺(NIPAM)与α-甲基丙烯酸(MAA)的共聚物,制备了磁性热敏聚合物微球Fe3O4/P(NIPAM-co-MAA).利用广角X射线衍射仪(WAXD)、透射电子显微镜(TEM)、zeta粒度仪(DLS)、热重分析(TGA)、振动样品磁力计(VSM)及比表面积测试仪(BET)等对微球的结构与形貌进行了表征,通过紫外-可见光分光光度法(UV-Vis)研究了微球对水溶性模型药物罗丹明B(RhB)的负载和磁感应控制释放行为.结果表明,微球粒径为80～200 nm,比表面积约为30.04m2/g,平均孔径约为24.50 nm;微球中聚合物含量约为73 wt%,磁粒子含量约为20 wt%,饱和磁感应强度为16.49 emu/g,其体积相转变温度(VPTT)约为37.5℃.RhB在微球中的装载量可以达到16.38 mg/g;在外加交变磁场作用下,RhB在模拟肠液和胃液中的磁感应释放量分别达到10.47和13.02 mg/g.     

基于F-P腔干涉的膜片式光纤微机电系统压力传感器

基于法布里-帕罗腔的干涉原理,采用微机电系统技术加工制作了一种光纤微机电系统压力传感器.采用浓硼扩散自停止腐蚀和磁控溅射的方法,制备厚度为6 μm、机械灵敏度为0.502 μm/MPa的传感器敏感膜.基于强度解调技术,利用干涉腔的反射功率与压力的关系对压力进行解调.分析了腔长变化对反射率的影响,确定传感器线性工作点的波长,建立稳定的压力传感测试系统.测试结果表明,该传感器压强最小分辨率为62 Pa,灵敏度达到0.51 nW/KPa,具有良好的线性度、灵敏度和重复性,适用于人体内压力测量和口腔义齿压力测量.     

On lattice profile of the elliptic curve linear congruential generators

Lattice tests are quality measures for assessing the intrinsic structure of pseudorandom number generators. Recently a new lattice test has been introduced by Niederreiter and Winterhof. In this paper, we present a general inequality that is satisfied by any periodic sequence. Then, we analyze the behavior of the linear congruential generators on elliptic curves (EC-LCG) under this new lattice test and prove that the EC-LCG passes it up to very high dimensions. We also use a result of Brandstätter and Winterhof on the linear complexity profile related to the correlation measure of order $k$ to present lower bounds on the linear complexity profile of some binary sequences derived from the EC-LCG.     

Eigenvalue problems on Riemannian manifolds with a modified Ricci tensor

In this paper, we study the eigenvalue problems on a Riemannian manifold with a modified Ricci tensor. We obtain some sharp lower bound estimates for the first eigenvalue of Laplacian. We also prove some rigidity theorems for the Riemannian manifold with some suitable conditions.     

双星图的IC-着色

研究了双星图的IC-着色问题,得到了双星图极大IC-着色的一些必要条件.利用这些必要条件,得到了双星图的极大IC-着色至多有两类着色方案,并确定了双星图在其中一种情况下的IC-指数.     

Source-type solution to nonlinear Fokker-Planck equation in one dimension

In this paper, we consider the following equation ut=(um)xx+(un)x, with the initial condition as Dirac measure. Attention is focused on existence, nonexistence, uniqueness and the asymptotic behavior near (0,0) of solution to the Cauchy’s problem. The special feature of this equation lies in nonlinear convection effect, i.e., the equation possesses nonlinear hyperbolic character as well as degenerate parabolic one. The situation leads to a more sophisticated mathematical analysis. To our knowledge, the solvability of singular solution to the equation has not been concluded yet. Here based on the previous works by the authors, we show that there exists a critical number n0=m+2 such that a unique source-type solution to this equation exists if 0≤n相似文献   

Low frequency phononic band structures in two-dimensional arc-shaped phononic crystals

The low frequency phononic band structures of two-dimensional arc-shaped phononic crystals (APCs) were studied by the transfer matrix method in cylindrical coordinates. The results showed the first phononic band gaps (PBGs) of APCs from zero Hz with low modes. Locally resonant (LR) gaps were obtained with higher-order rotation symmetry, due to LR frequencies corresponding to the speeds of acoustic waves in the materials. These properties can be efficiently used in a structure for low frequencies that are forbidden, or in a device that permits a narrow window of frequencies.     

Numerical solution of variational inequalities for pricing Asian options by higher order Lagrange–Galerkin methods

Asian options prices can be modelled in the Black–Scholes framework leading to two-factor models depending on the asset price, the average of the asset price and the time. They can also involve inequality constraints, as in the case of Amerasian options, leading to variational inequalities (VI). In the first section, we completely describe the pricing model for fixed-strike Eurasian and Amerasian options and list some properties satisfied by the option value function. Then, since no solutions in closed form are known, we deal with the numerical solution of the above problems proposing a general methodology: an iterative algorithm for the VI, combined with higher order Lagrange–Galerkin methods for partial differential equations. Finally, numerical results are shown.