Theoretical and Numerical Investigation of Fractional Partial Differential Equations

近年来，分数阶偏微分方程(FPDEs)在数学模型中的应用受到越来越广泛的关注。不同的FPDEs模型已被应用到越来越多的领域中，包括：材料，力学，以及生物系统等，并且发现FPDEs在研究一些具有记忆过程、遗传性质以及异质材料时比整数阶方程模型更有优势。FPDEs在数学建模上取得的进展，激发了人们研究数值算法的兴趣。 本文从理论和数值计算两方面对分数阶扩散方程(FDEs)及其相关问题进行深入研究，主要内容包括以下三个方面： 我们引进了一类新的利用分数阶导数定义的分数阶空间，并证明了此类空间与传统的分数阶Sobolev空间在范数意义下是等价的。利用这些结果我们导出了FDEs初边值问题的弱...The use of fractional partial differential equations (FPDEs) in mathematical models has become increasingly popular in recent years. Different models using FPDEs have been proposed in more and more fields, covering materials, mechanical, and biological systems, and it's found that FPDEs gain the advantage over the classical one in modeling some materials with memory, heterogeneity or inheritable c...学位：理学博士院系专业：数学科学学院信息与计算数学系_计算数学学号：1902006015316

分数阶Nernst-Planck 方程的有限差分/谱元法求解

Nernst-Planck 方程是用来描述在离子浓度梯度rC 及电场rV 共同存在的情况下，穿过渗透膜 的离子(如钙，钾，钠，氯，镁等) 流J 的方程。但是，计算Nernst-Planck 方程的数值解会遇 到一些困难。本文考虑用以描述神经细胞中离子反常扩散现象的电缆型简化的分数阶Nernst- Planck 方程，提出了一个时间有限差分/空间谱元法对该方程进行数值求解。我们给出了数值方 法的详细构造过程以及实现方法。结果表明数值解在空间方向上具有指数阶收敛精度，在时间 方向上具有2-alpha阶精度。最后，通过计算一个具有实际背景参数的问题说明所提方法的潜在应 用。国家自然科学基金(10531080)；973“高性能科学计算研究”项目(2005CB321703)；福建省自然科学 基金(S0750017)

A Finite Difference/Spectral Element Method for the Fractional Nernst-Planck Equation

nErnST-PlAnCk方程是用来描述在离子浓度梯度C及电场V共同存在的情况下,穿过渗透膜的离子(如钙,钾,钠,氯,镁等)流J的方程。但是,计算nErnST-PlAnCk方程的数值解会遇到一些困难。本文考虑用以描述神经细胞中离子反常扩散现象的电缆型简化的分数阶nErnST-PlAnCk方程,提出了一个时间有限差分/空间谱元法对该方程进行数值求解。我们给出了数值方法的详细构造过程以及实现方法。结果表明数值解在空间方向上具有指数阶收敛精度,在时间方向上具有2？α阶精度。最后,通过计算一个具有实际背景参数的问题说明所提方法的潜在应用。The Nernst-Planck equation describes the flux of ions(for example,calcium,potassium, sodium,chloride,and magnesium etc.)through a diffusive membrane under the influence of both the ionic concentration gradient ▽C and electric potential ▽V.However,numerical approximations to the Nernst-Planck equation suffer from several diffculties.In this paper,we first briefly recall the derivation of the fractional Nernst-Planck equation in a cable-like geometry,which describes the anomalous diffusion in the movement of the ions in a neuronal system.Then a method combining finite differences in time and spectral element methods in space is proposed to numerically solve the underlying problem.The detailed construction and implementation of the method are presented.Our numerical experiences show that the convergence of the proposed method is exponential in space and (2-α)-order in time.Finally,a practical problem with realistic physical parameters is simulated to demonstrate the potential applicability of the method.国家自然科学基金(10531080);973“高性能科学计算研究”项目(2005CB321703);福建省自然科学基金(S0750017)---

design and implementation of multi-role requirement review system

需求质量对于软件产品质量有至关重要的影响,而需求评审是保证需求质量的有效手段之一.目前的需求评审存在效率低、问题发现率不高、评审结果难以被有效处理等问题.在对需求特性进行研究,以及对实际项目中人员角色及其关注点进行调研的基础上,开发了多角色的需求评审系统MRRS.MRRS系统为每类角色的评审人员提供有针对性的评审指标体系,依照预设算法对评审结果进行量化处理,以GUl形式展示结果,为项目决策提供支持.应用了MRRS系统后,评审效率提高一倍以上

A survey on clinical communication competence of psychiatric nurses in Guangdong Province (广东省精神科护士临床沟通能力调查分析)

Objective To investigate the clinical communication competence of psychiatric nurses in Guangdong Province and its influencing factors, and provide reference for the improvement of communication skills among psychiatric nurses. Methods A cross-sectional study using general information scale and the Clinical Communication Competency Scale (CCCS) was conducted to 667 psychiatric nurses in Guangdong Province. Results The total score of CCCS was (3. 99±0. 57) , dimensions arranged by scores from the highest to the lowest were: team communication (4. 15±0. 62), verbal communication (4. 01±0. 59), affective perception (4. 00±0. 60), Non-verbal communication (3. 99±0. 61), emotional support (3. 95±0. 63) and communication in difficult situations(3. 92±0. 60). The main factors influencing the clinical communication competence of psychiatric nurses were age, professional title, job title and job seniority (P<0. 05). Conclusion Findings of the study indicated a high level of team communication competence of psychiatric nurses , however relatively low level of emotional support and communication in difficult situations were found. Targeted training program should be carried out to improve the clinical communication competence of psychiatric nurses in Guangdong Province (目的 调查广东省精神科护士的临床沟通能力水平并分析其影响因素, 为管理层提高精神科护士沟通能力提供参考依据。方法 采用方便抽样的方法, 使用一般资料问卷及临床沟通能力量表对广东省31所医院667名精神科护士进行横断面调查。结果 广东省精神科护士的沟通能力总分为(3. 99±0. 57)分。各维度得分从高到低依次是团队沟通能力(4. 15±0. 62)分, 基本语言沟通能力(4. 01±0. 59)分, 情感感知能力(4. 00±0. 60)分, 基本非语言沟通能力(3. 99±0. 61)分, 情感支持能力(3. 95±0. 63)分, 困难情景沟通能力(3. 92±0. 60)分。精神科护士的年龄、职称、职务及工作年限是影响其临床沟通能力得分的主要因素, 差异具有统计学意义(P<0. 05)。结论 广东省精神科护士的团队沟通能力较好, 但情感支持和困难情景沟通能力较弱, 提示医院管理层需要针对性地进行沟通能力培训, 从而提高精神科护士的临床沟通能力。

A survey on clinical communication competence of psychiatric nurses in Guangdong Province (广东省精神科护士临床沟通能力调查分析)

Objective To investigate the clinical communication competence of psychiatric nurses in Guangdong Province and its influencing factors, and provide reference for the improvement of communication skills among psychiatric nurses. Methods A cross-sectional study using general information scale and the Clinical Communication Competency Scale (CCCS) was conducted to 667 psychiatric nurses in Guangdong Province. Results The total score of CCCS was (3. 99±0. 57) , dimensions arranged by scores from the highest to the lowest were: team communication (4. 15±0. 62), verbal communication (4. 01±0. 59), affective perception (4. 00±0. 60), Non-verbal communication (3. 99±0. 61), emotional support (3. 95±0. 63) and communication in difficult situations(3. 92±0. 60). The main factors influencing the clinical communication competence of psychiatric nurses were age, professional title, job title and job seniority (P<0. 05). Conclusion Findings of the study indicated a high level of team communication competence of psychiatric nurses , however relatively low level of emotional support and communication in difficult situations were found. Targeted training program should be carried out to improve the clinical communication competence of psychiatric nurses in Guangdong Province (目的 调查广东省精神科护士的临床沟通能力水平并分析其影响因素, 为管理层提高精神科护士沟通能力提供参考依据。方法 采用方便抽样的方法, 使用一般资料问卷及临床沟通能力量表对广东省31所医院667名精神科护士进行横断面调查。结果 广东省精神科护士的沟通能力总分为(3. 99±0. 57)分。各维度得分从高到低依次是团队沟通能力(4. 15±0. 62)分, 基本语言沟通能力(4. 01±0. 59)分, 情感感知能力(4. 00±0. 60)分, 基本非语言沟通能力(3. 99±0. 61)分, 情感支持能力(3. 95±0. 63)分, 困难情景沟通能力(3. 92±0. 60)分。精神科护士的年龄、职称、职务及工作年限是影响其临床沟通能力得分的主要因素, 差异具有统计学意义(P<0. 05)。结论 广东省精神科护士的团队沟通能力较好, 但情感支持和困难情景沟通能力较弱, 提示医院管理层需要针对性地进行沟通能力培训, 从而提高精神科护士的临床沟通能力。

头颈部动脉支架植入围手术期患者血清NETs标志物的动态变化（Dynamic Changes in Serum NETs Markers during the Perioperative Period in Patients Undergoing Head and Neck Arterial Stent Implantation）

目的 探讨头颈部动脉支架植入后血清中性粒细胞外陷阱（neutrophil extracellular traps，NETs）标志物瓜氨酸化组蛋白3（citrullinated histone 3，cit-H3）及髓过氧化物酶（myeloperoxidase，MPO）水平随时间变化的规律。 方法 前瞻性连续纳入因头颈部动脉粥样硬化性大动脉狭窄行支架植入术的患者，分别于术前空腹24 h内，术后6、12、24、48 h采集患者静脉血，测定血清cit-H3及MPO水平。采用经Greenhouse-Geisser校正的单因素重复测量方差分析，比较患者围手术期不同时间点血清cit-H3及MPO水平的动态变化趋势。根据支架植入部位（颅内 vs. 颅外）、支架植入数目（1个 vs. 2个）、责任血管是否为症状性狭窄，以及手术时脑梗死是否处于急性期（病程≤14 d），对血清cit-H3及MPO水平的变化进行亚组分析。 结果 本研究共纳入48例患者，平均年龄为（61.8±8.4）岁，男性42例（87.5%）。在整体患者中，血清cit-H3在术前及术后6、12、24、48 h的水平分别为（54.50±6.48）ng/mL、（56.73±6.50）ng/mL、（71.27±7.35）ng/mL、（53.53±17.35）ng/mL和（52.22±5.45）ng/mL；血清MPO在术前及术后6、12、24、48 h的水平分别为（25.45±6.67）ng/mL、（26.29±6.75）ng/mL、（28.28±7.68）ng/mL、（31.55±9.09）ng/mL和（28.68±7.61）ng/mL，两者术后水平均呈现先升高后降低趋势，整体差异均具有统计学意义（P=0.002；P=0.022）。颅外及颅内支架亚组、1个及2个支架亚组、症状性狭窄亚组及非急性期亚组的血清cit-H3水平均于术后12 h达到峰值。颅内支架亚组的血清MPO水平于术后12 h达到峰值，2个支架亚组、症状性狭窄亚组及非急性期亚组的血清MPO水平均于术后24 h达到峰值。 结论 头颈部动脉支架植入术后48 h内，血清NETs标志物cit-H3和MPO水平呈现先升高后恢复至术前水平的变化趋势，这种趋势在症状性狭窄患者中更显著。（Abstract: Objective To explore the dynamic changes over time in serum levels of neutrophil extracellular traps (NETs) markers—citrullinated histone 3 (cit-H3) and myeloperoxidase (MPO)—after head and neck arterial stent implantation. Methods Patients with atherosclerotic stenosis of the head and neck arteries who underwent stent implantation were prospectively and consecutively enrolled. Venous blood samples were collected from the patients within 24 hours of fasting before surgery, and at 6, 12, 24, and 48 hours after surgery to measure serum cit-H3 and MPO levels. One-way repeated measures analysis of variance with Greenhouse-Geisser correction was used to compare the dynamic changes in serum cit-H3 and MPO levels across different perioperative time points. Subgroup analyses of the changes in serum cit-H3 and MPO levels were conducted based on stent implantation site (intracranial vs. extracranial), number of stents implanted (1 vs. 2), whether the responsible vessel had symptomatic stenosis, and whether cerebral infarction was in the acute phase (disease duration≤14 days) at the time of surgery. Results A total of 48 patients were enrolled in this study with a mean age of (61.8±8.4) years, including 42 males (87.5%). Among all patients, the serum cit-H3 levels before surgery and at 6, 12, 24, and 48 hours after surgery were (54.50±6.48) ng/mL, (56.73±6.50) ng/mL, (71.27±7.35) ng/mL, (53.53±17.35) ng/mL, and (52.22±5.45) ng/mL, respectively. The serum MPO levels at the corresponding time points were (25.45±6.67) ng/mL, (26.29±6.75) ng/mL, (28.28±7.68) ng/mL, (31.55±9.09) ng/mL, and (28.68±7.61) ng/mL, respectively. Both markers showed a trend of increasing first and then decreasing, with statistically significant overall differences (P=0.002 for cit-H3; P=0.022 for MPO). In the extracranial and intracranial stent subgroups, the single and double stent subgroups, the symptomatic stenosis subgroup, and the non-acute phase subgroup, the serum cit-H3 levels peaked at 12 hours after surgery. The serum MPO levels peaked at 12 hours after surgery in the intracranial stent subgroup. However, in the double stent subgroup, the symptomatic stenosis subgroup, and the non-acute phase subgroup, the serum MPO levels peaked at 24 hours after surgery. Conclusions Within 48 hours after head and neck artery stent implantation, the serum levels of NETs markers cit-H3 and MPO showed an initial increase followed by a gradual return to preoperative levels. This trend was more pronounced in patients with symptomatic arterial stenosis.