Penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions

The penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions is investigated in this paper. Since this class of nonlinear slip boundary conditions include the subdifferential property, the weak variational formulation is a variational inequality problem of the second kind. Using the penalty finite element approximation, we obtain optimal error estimates between the exact solution and the finite element approximation solution. Finally, we show the numerical results which are in full agreement with the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Multidimensional stability of planar waves for delayed reaction-diffusion equation with nonlocal diffusion

In this paper, we consider the multidimensional stability of planar waves for a class of nonlocal dispersal equation in $n$--dimensional space with time delay. We prove that all noncritical planar waves are exponentially stable in $L^{\infty}(\RR^n )$ in the form of $\ee^{-\mu_{\tau} t}$ for some constant $\mu_{\tau} =\mu(\tau)>0$( $\tau >0$ is the time delay) by using comparison principle and Fourier transform. It is also realized that, the effect of time delay essentially causes the decay rate of the solution slowly down. While, for the critical planar waves, we prove that they are asymptotically stable by establishing some estimates in weighted $L^1(\RR^n)$ space and $H^k(\RR^n) (k \geq [\frac{n+1}{2}])$ space.     

纳米复合永磁Pr9Fe74Co12B5Snx(x=0, 0.5)的磁化行为与磁黏滞性

用熔体快淬法制备了纳米复合永磁样品Pr₉Fe₇₄Co₁₂B₅ 与Pr₉Fe₇₄Co₁₂B₅Sn_0.5，分析了样品的起始磁化、反磁化过程，测得样品的总磁化率、可逆磁化率以及样品的磁黏滞性.结果表明，两样品在室温下均表现为单一硬磁相磁化行为，在低温下表现为双相行为，且由于添加Sn后使晶粒均匀化从而导致样品低温下的双相行为更加明显.添加Sn后引起样品中软磁相含量和软磁相晶粒尺寸的增加，使磁化反转中可逆磁化部分增多，且使反磁化形核场降低.磁黏滞性研究表明，热激活体积与软磁相晶粒的大小有关. 关键词： 纳米复合永磁 磁化反转 磁粘滞     

List star edge coloring of k-degenerate graphs

A star edge coloring of a graph is a proper edge coloring such that every connected 2-colored subgraph is a path with at most 3 edges. Deng et al. and Bezegová et al. independently show that the star chromatic index of a tree with maximum degree $\Delta$ is at most $?\frac{3\Delta }{2}?$, which is tight. In this paper, we study the list star edge coloring of $k$-degenerate graphs. Let $c{h}_{st}^{\prime }\left(G\right)$ be the list star chromatic index of $G$: the minimum $s$ such that for every $s$-list assignment $L$ for the edges, $G$ has a star edge coloring from $L$. By introducing a stronger coloring, we show with a very concise proof that the upper bound on the star chromatic index of trees also holds for list star chromatic index of trees, i.e. $c{h}_{st}^{\prime }\left(T\right)\le ?\frac{3\Delta }{2}?$ for any tree $T$ with maximum degree $\Delta$. And then by applying some orientation technique we present two upper bounds for list star chromatic index of $k$-degenerate graphs.     

Persistence properties and wave‐breaking criteria for the Geng‐Xue system

Considered herein is a two‐component Novikov equations (called Geng‐Xue system for short) with cubic nonlinearities. The persistence properties and some unique continuation properties of the solutions to the system in weighted L_p spaces are established. Moreover, a wave‐breaking criterion for strong solutions is determined in the lowest Sobolev space by using the localization analysis in the transport equation theory, and we also give a lower bound for the maximal existence time.     

基于回波平移序列的快速三维磁共振温度成像方法

高强度聚焦超声（HIFU）是一种无创的热消融疗法，为保证其安全性和有效性，需要一种精度高、速度快的测温方法在其治疗过程中对温度进行监控.基于质子共振频率位移（PRFS）的磁共振温度成像（MRT）对温度具有较高的灵敏度，且与温度具有良好的线性关系，因此常被用于引导HIFU治疗.然而在实际应用中，HIFU治疗的最大隐患在于可能造成表皮灼伤，并且灼伤区域可能与焦点区域相隔较远.因此MRT的监控范围十分重要.本文基于三维回波平移成像序列，结合可控混叠的空间并行成像技术，实现了时间分辨率为3 s的快速三维温度成像.为了验证该方法的精度，本文首先设计了仿体降温实验，利用光纤温度计验证回波平移序列测温的准确度和精确度.然后在室温条件下扫描离体猪肉组织，对比加速前后的MRT的测温精确度.在HIFU加热条件下扫描离体猪肉组织，对比加速前后的MRT的测温准确度.结果显示，本文提出的方法可以在3 s内完成三维温度精准测量，对于HIFU治疗的安全监控具有重要意义.     

低钾血症对颅脑创伤患者预后的影响

目的 探讨低钾血症在颅脑创伤患者中的发病情况及其与预后的关系。方法 2010 年6月至2013 年6 月共有168 例住院期间出现低钾血症且年龄≥18 岁的颅脑创伤患者纳入研究。依据低钾血症严重程度的不同,将患者分成轻度组（3.00mmol/L≤血钾＜3.50mmol/L）、中度组（2.50mmol/L≤血钾＜3.00mmol/L）和重度组（血钾＜2.50mmol/L）,各组均采用患者血钾的最低值进行数据分析。高钠血症和低磷血症分别被定义为血钠＞147.00mmol/L 和血磷＜0.80mmol/L。结果 受试患者的血钾在1.10~3.40mmol/L,平均2.90mmol/L。当血钾出现最低值时,与其余两组比较,重度组患者具有更高的血钠和更低的血磷水平（均P＜0.01）。与轻度组（10.5%）或中度组（25.7%）相比,重度组患者的病死率（82.1%）显著上升（均P＜0.01）。多变量逻辑回归分析结果显示,低格拉斯哥昏迷评分（OR=1.28,95%CI=1.12~1.42,P＜0.01）、低血钾（OR=5.57,95%CI=2.76~10.93,P＜0.01）、低血磷（OR=2.76,95%CI=1.11~7.25,P＜0.01）以及高血尿素氮（OR=1.16,95%CI=1.07~1.24,P＜0.01）是导致患者死亡的独立危险因素。结论 颅脑创伤患者是出现低钾血症的高危人群,重度低钾血症的患者更容易合并高钠血症和低磷血症。重度低钾血症和低磷血症是颅脑创伤患者死亡的独立危险因素。     

q-Gronwall不等式及其在分数阶q-微分方程的应用

利用q-微积分的性质,得到时间测度q上的Gronwall不等式;并利用该推广的不等式分别讨论带有Riemann-Liouville和Caputo分数阶导数的q-微分方程的解对分数阶导数的阶数和初值的依赖性.     

Stability constants of metal complexes of macrocyclic ligands with pendant donor groups

Abstract

In our studies of the stability constants of metal complexes, we have investigated a number of macrocyclic ligands with pendant donor groups. The ligands are characterized by the fact that they have nitrogen donors in the macrocyclic ring and oxygen or sulfur donors in the pendant arms. These ligands represent seven different macrocycles, and by varying the pendant donor groups, ten different ligands are indicated. The affinities of these ligands for fifteen metal ions will be described. The Fe(III) complex of triazanonane with o-hydroxypyridyl or o-hydroxybenzyl pendant donor groups are the most stable ferric complexes ever reported. The In(III) complex of triazacyclononane with pendant mercaptoethyl donor groups, is exceptionally stable. Also, the Ca(II) complex of DOTA probably has the highest stability of any calcium(II) complex. These, and other comparisons will be made on the basis of the thermodynamic stability constant data for the ligands described.     

金属-半导体异质结构纳米晶的可控制备和光谱调控

本文简要综述了金属-半导体异质结构纳米晶的设计、可控制备和物性研究的相关工作.设计了异相成核与生长、选择硫化和种子介导液相外延生长3种不同的方法并以此制备了多种金属-半导体异质结构纳米晶,对其中所涉及的反应机制进行了论述,并简要探讨了金属-半导体异质结构纳米晶的热稳定性、表面等离子共振活性、荧光特性以及异质界面的电荷转移和保持能力.