石英晶体板非线性高频振动的拓展伽辽金法分析

针对考虑几何和材料非线性的石英晶体板厚度剪切振动和弯曲振动的方程组,利用扩展伽辽金法对该方程组进行转化和求解,分别获得了强烈耦合的厚度剪切振动模态和弯曲振动模态的频率响应关系,绘制了不同振幅比和不同驱动电压影响下的频率响应曲线图。数值计算结果表明可以选取石英晶片的最佳长厚比尺寸来避免两种模态的强烈耦合。驱动电压的变化将引起石英晶体谐振器厚度剪切振动频率的明显改变,必须将振动频率的漂移值控制在常用压电声波器件的允许值之内。扩展伽辽金法对石英晶体板非线性振动方程组的求解为非线性有限元分析和偏场效应分析奠定了基础。     

Stabilized Nonconforming Mixed Finite Element Method for Linear Elasticity on Rectangular or Cubic Meshes

Based on the primal mixed variational formulation, a stabilized nonconforming mixed finite element method is proposed for the linear elasticity on rectangular and cubic meshes. Two kinds of penalty terms are introduced in the stabilized mixed formulation, which are the jump penalty term for the displacement and the divergence penalty term for the stress. We use the classical nonconforming rectangular and cubic elements for the displacement and the discontinuous piecewise polynomial space for the stress, where the discrete space for stress are carefully chosen to guarantee the well-posedness of discrete formulation. The stabilized mixed method is locking-free. The optimal convergence order is derived in the $L^2$-norm for stress and in the broken $H^1$-norm and $L^2$-norm for displacement. A numerical test is carried out to verify the optimal convergence of the stabilized method.     

Asymmetric Total Syntheses,Stereostructures, and Cytotoxicities of Marine Bromotriterpenoids Aplysiol B (Laurenmariannol) and Saiyacenol A

There are marine cytotoxic bromotriterpenoids, named the thyrsiferol family that are structurally characterized by some tetrahydropyran (THP) and tetrahydrofuran (THF) rings. The thyrsiferol family belongs to natural products that are often difficult to determine their stereostructures even by the current, highly advanced spectroscopic methods, especially in acyclic systems including stereogenic tetrasubstituted carbon centers. In such cases, it is effective to predict and synthesize the possible stereostructures. Herein, to elucidate ambiguous stereostructures and unassigned absolute configurations of aplysiol B, laurenmariannol, and saiyacenol A, members of the thyrsiferol family, we carried out their asymmetric chemical syntheses featuring 6-exo and 5-exo oxacyclizations of epoxy alcohol precursors and 6-endo bromoetherification of a bishomoallylic alcohol. In this paper, we report total assignments of their stereostructures through their asymmetric chemical syntheses and also their preliminary cytotoxic activities against some tumor cells. These results could not have been achieved without depending on asymmetric total synthesis.     

On the Brauer p-dimension of Henselian discrete valued fields of residual characteristic p > 0

Let $(K,v)$ be a Henselian discrete valued field with residue field $\stackrel{?}{K}$ of characteristic $p>0$, and ${\text{Brd}}_p(K)$ be the Brauer p-dimension of K. This paper shows that ${\text{Brd}}_p(K)\ge n$ if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=p^n$, for some $n\in \mathbb{N}$. It proves that ${\text{Brd}}_p(K)=\infty$ if and only if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=\infty$.     

NUMERICAL SIMULATION OF FIBROBLAST DUROTAXIS MIGRATION INDUCED BY STIFFNESS GRADIENT OF SUBSTRATE1)

建立了一种细胞趋硬性迁移的理论模型和有限元分析框架,为连续变刚度人工基质的试验设计提供理论依据。考虑了细胞体的黏弹性属性,以及细胞与基质间的配受体动态反应过程,并以配受体合成时间为时间步长,将细胞运动方程化为静力学形式进行求解。对有限元过程提出一种动约束,便于消除其结构矩阵的奇异性。结果表明,模型能够模拟黏着斑内部力的快速波动现象,细胞的运动速度与观测数据一致,可有效模拟20,h以上的长时程问题。     

Simultaneous determination of 75 abuse drugs including amphetamines,benzodiazepines, cocaine,opioids, piperazines,zolpidem and metabolites in human hair samples using liquid chromatography–tandem mass spectrometry

A liquid chromatography–tandem mass spectrometric method for the simultaneous determination of 75 abuse drugs and metabolites, including 19 benzodiazepines, 19 amphetamines, two opiates, eight opioids, cocaine, lysergic acid diethylamide, zolpidem, three piperazines and 21 metabolites in human hair samples, was developed and validated. Ten‐milligram hair samples were decontaminated, pulverized using a ball mill, extracted with 1 mL of methanol spiked with 28 deuterated internal standards in an ultrasonic bath for 60 min at 50°C, and purified with Q‐sep dispersive solid‐phase extraction tubes. The purified extracts were evaporated to dryness and the residue was dissolved in 0.1 mL of 10% methanol. The 75 analytes were analyzed on an Acquity HSS T3 column using gradient elution of methanol and 0.1% formic acid and quantified in multiple reaction monitoring mode with positive electrospray ionization. Calibration curves were linear (r ≥ 0.9951) from the lower limit of quantitation (2–200 pg/mg depending on the drug) to 2000 pg/mg. The coefficients of variation and accuracy for intra‐ and inter‐assay analysis at three QC levels were 4.3–12.9% and 89.2–109.1%, respectively. The overall mean recovery ranged from 87.1 to 105.3%. This method was successfully applied to the analysis of 11 forensic hair samples obtained from drug abusers.     

Synthesis and Structure Determination of SCM-15: A 3D Large Pore Zeolite with Interconnected Straight 12×12×10-Ring Channels

A new germanosilicate zeolite named SCM-15 (Sinopec Composite Material No. 15), the first zeolite containing a 3-dimensional (3D) channel system with interconnected 12-, 12-, and 10-ring channels (pore sizes: 6.1×7.2, 6.1×7.4, and 5.2×5.9 Å), has been synthesized using neutral 4-pyrrolidinopyridine as organic structure-directing agents (OSDAs). Its structure has been determined by combining single-crystal electron diffraction (SCED) and synchrotron powder X-ray diffraction (SPXD) data. The unique open framework structure of SCM-15 is related to that of FOS-5 ( BEC ), ITQ-7 ( ISV ), PKU-16 ( POS ), ITQ-26 ( IWS ), ITQ-21, Beta polymorph B, and SU-78B, since all these framework structures can be constructed from similar chains which are connected through shared 4-ring or double 4-ring (d4r) units. Based on this relation, six topologically reasonable 3D large or extra-large pore hypothetical zeolites are predicted.     

The improvement of numerical modeling in the solution of incompressible viscous flow problems using finite element method based on spherical Hankel shape functions

In this paper, the finite element method with new spherical Hankel shape functions is developed for simulating 2‐dimensional incompressible viscous fluid problems. In order to approximate the hydrodynamic variables, the finite element method based on new shape functions is reformulated. The governing equations are the Navier‐Stokes equations solved by the finite element method with the classic Lagrange and spherical Hankel shape functions. The new shape functions are derived using the first and second kinds of Bessel functions. In addition, these functions have properties such as piecewise continuity. For the enrichment of Hankel radial basis functions, polynomial terms are added to the functional expansion that only employs spherical Hankel radial basis functions in the approximation. In addition, the participation of spherical Bessel function fields has enhanced the robustness and efficiency of the interpolation. To demonstrate the efficiency and accuracy of these shape functions, 4 benchmark tests in fluid mechanics are considered. Then, the present model results are compared with the classic finite element results and available analytical and numerical solutions. The results show that the proposed method, even with less number of elements, is more accurate than the classic finite element method.