published_or_final_version / abstract / Dentistry / Master / Master of Philosophy

O problema de reconstruir uma função f a partir de um número finito de valores conhecidos f(x0), f(x1), ..., f(xn) aparece com frequência em modelagem matemática. Em geral, não é possível determinar f completamente a partir de f(x0), f(x1), ..., f(xn), mas, em muitos casos de interesse, podemos encontrar aproximações razoáveis para f usando interpolação, que consiste em determinar uma função (um polinômio, ou uma função racional ou trigonométrica, etc) g que satisfaça g(xi) = f(xi); i = 0, 1, ..., n: Na prática, a função interpoladora g é avaliada em precisão finita e o valor final computado de g(x) pode diferir do valor exato g(x) devido a erros de arredondamento. Essa diferença pode, inclusive, ultrapassar o erro de interpolação E(x) = f(x) - g(x) em várias ordens de magnitude, comprometendo todo o processo de aproximação. A estabilidade numérica de um algoritmo reflete sua sensibilidade em relação a erros de arredondamento. Neste trabalho apresentamos uma análise detalhada da estabilidade numérica de alguns algoritmos utilizados no cálculo de interpoladores polinomiais ou racionais que podem ser postos na forma baricêntrica. Os principais resultados deste trabalho também estão disponíveis em língua inglesa nos artigos - Mascarenhas, W e Camargo, A. P., On the backward stability of the second barycentric formula for interpolation, Dolomites research notes on approximation v. 7 (2014) pp. 1-12. - Camargo, A. P., On the numerical stability of Floater-Hormann\'s rational interpolant, Numerical Algorithms, DOI 10.1007/s11075-015-0037-z. - Camargo, A. P., Erratum: On the numerical stability of Floater-Hormann\'s rational interpolant\", Numerical Algorithms, DOI 10.1007/s11075-015-0071-x. - Camargo, A. P. e Mascarenhas, W., The stability of extended Floater-Hormann interpolants, Numerische Mathematik, submetido. arXiv:1409.2808v5 / The problem of reconstructing a function f from a finite set of known values f(x0), f(x1), ..., f(xn) appears frequently in mathematical modeling. It is not possible, in general, to completely determine f from f(x0), f(x1), ..., f(xn) but, in several cases of interest, it is possible to find reasonable approximations for f by interpolation, which consists in finding a suitable function (a polynomial function, a rational or trigonometric function, etc.) g such that g(xi) = f(xi); i = 0, 1, ..., n: In practice, the interpolating function g is evaluated in finite precision and the final computed value of g(x) may differ from the exact value g(x) due to rounding. In fact, such difference can even exceed the interpolation error E(x) = f(x)-g(x) in several orders of magnitude, compromising the entire approximation process. The numerical stability of an algorithm reflect is sensibility with respect to rounding. In this work we present a detailed analysis of the numerical stability of some algorithms used to evaluate polynomial or rational interpolants which can be put in the barycentric format. The main results of this work are also available in english in the papers - Mascarenhas, W e Camargo, A. P., On the backward stability of the second barycentric formula for interpolation, Dolomites research notes on approximation v. 7 (2014) pp. 1-12. - Camargo, A. P., On the numerical stability of Floater-Hormann\'s rational interpolant, Numerical Algorithms, DOI 10.1007/s11075-015-0037-z. - Camargo, A. P., Erratum: On the numerical stability of Floater-Hormann\'s rational interpolant\", Numerical Algorithms, DOI 10.1007/s11075-015-0071-x. - Camargo, A. P. e Mascarenhas, W., The stability of extended Floater-Hormann interpolants, Numerische Mathematik, submetido. arXiv:1409.2808v5

No description available.

More than half of the women aged from 45-55 suffer from menopausal symptoms which can seriously affect the quality of life of the midlife women. The menopause transition has become a very active research area in healthy aging in the last several decades. In recent years, more and more women have turned to traditional Chinese medicine (TCM) to manage their menopausal symptoms. Among various Chinese medicine formulae, Er-Xian Decoction (EXD) is one of the most acceptable Chinese medicine formulae to relieve menopausal symptoms. Although EXD is popular in the management of menopausal symptoms, its effectiveness has not been evaluated by strictly designed clinical study. A systematic review was conducted to evaluate the current evidence to assess the efficacy and safety of EXD as a basic formula for menopausal symptoms. A total of 12 randomized controlled trials (RCTs) were included for further analysis. The results of these studies suggested that EXD was more effective than the control interventions, which included various HRT and other Chinese herbal medicine. Seven of the studies compared EXD with HRT and the meta-analysis seemed to suggest that EXD as a basic formula was superior to hormone replacement therapy. However, the included studies were insufficient in methodological quality and had a high probability of bias. A double-blind randomized controlled clinical trial was then conducted to assess the efficacy and safety of EXD for menopausal symptoms. Of 557 recruited women, 108 subjects were eligible to participate in the study and 101 subjects finished the study. Comparisons between placebo and EXD groups were conducted by using an analysis of covariance (ANCOVA) with baseline as covariate. EXD granules when compared with placebo significantly reduced the frequency and severity of hot flushes and night sweats. EXD compared with placebo significantly reduced the frequency of hot flushes (P=0.041) and the hot flush severity score (P=0.016). Superiority of EXD over placebo was also observed in greater improvement in total scores of MRS (P=0.028) and MENQOL questionnaires (P=0.021). There were no differences between EXD and placebo group in serum hormones and bone markers. There were no serious adverse events and the safety indices of whole blood counts, renal and liver functions were normal before and after the treatment. Both EXD and placebo were well tolerated. In summary, this Chinese herbal formula EXD was found to be superior to placebo in reducing hot flushes and improving menopausal symptoms in Hong Kong perimenopausal women. It was well tolerated, with no serious adverse events noted during the study period. / published_or_final_version / Chinese Medicine / Doctoral / Doctor of Philosophy

No description available.

There is no abstract available for this thesis. / Department of Art

目的：通过对柴胡桂枝汤从古至今文献的整理，了解柴胡桂枝汤的应用规律，并对其方证应用做出归纳、总结。 方法：在充分收集资料的基础上，对各类相关文献进行整理、归类，分为方论类文献、医论类文献、本草类文献、临床观察类文献和医案类文献。根据不同文献特点提取相共不同信息。其中前三类文献以文义阐释和解读为主进行归纳总结；余下两类文献则以数据统计为主进行频次分析，从统计数据中提取疾病谱、典型指征等信息。 结果：一. 通过文献阐释方药含义，对柴胡桂枝汤病机、方义、适应证进行了初步归纳、总结；二．通过文献数据统计、分析，对柴胡桂枝汤疾病谱、适应证、适应体质作了详细归纳。 结论：一．柴胡桂枝汤病机：太少两感、营卫不和 适应证型：太少两枝轻证 偏虚证 二．从典型指征、患者体质状态和疾病谱对柴胡桂枝汤方证作如下 表述： （一） 1.王证（典型指征）：恶寒、肢节烦疼、发热、喜呕、腹痛、胸闷气短； 2.兼证（重要指征）：纳呆、神疲乏力、口干、口苦脇痛、往来寒热、汗出。 （二）适合体质：体虚、气郁之人 （三）疾病谱： 1.外感类疾病：如小儿外感热病、产后发热等 2.体痛类疾病：如坐骨神经痛、颈椎病等 3.心腹痛类疾病：冠心病、慢性胃炎、膜腺炎等。 4.神志相关类疾病：如更年期综合征、癫痫等。 關鍵詞：柴胡桂枝汤 方证研究 太少两戚 医案文献

O problema de reconstruir uma função f a partir de um número finito de valores conhecidos f(x0), f(x1), ..., f(xn) aparece com frequência em modelagem matemática. Em geral, não é possível determinar f completamente a partir de f(x0), f(x1), ..., f(xn), mas, em muitos casos de interesse, podemos encontrar aproximações razoáveis para f usando interpolação, que consiste em determinar uma função (um polinômio, ou uma função racional ou trigonométrica, etc) g que satisfaça g(xi) = f(xi); i = 0, 1, ..., n: Na prática, a função interpoladora g é avaliada em precisão finita e o valor final computado de g(x) pode diferir do valor exato g(x) devido a erros de arredondamento. Essa diferença pode, inclusive, ultrapassar o erro de interpolação E(x) = f(x) - g(x) em várias ordens de magnitude, comprometendo todo o processo de aproximação. A estabilidade numérica de um algoritmo reflete sua sensibilidade em relação a erros de arredondamento. Neste trabalho apresentamos uma análise detalhada da estabilidade numérica de alguns algoritmos utilizados no cálculo de interpoladores polinomiais ou racionais que podem ser postos na forma baricêntrica. Os principais resultados deste trabalho também estão disponíveis em língua inglesa nos artigos - Mascarenhas, W e Camargo, A. P., On the backward stability of the second barycentric formula for interpolation, Dolomites research notes on approximation v. 7 (2014) pp. 1-12. - Camargo, A. P., On the numerical stability of Floater-Hormann\'s rational interpolant, Numerical Algorithms, DOI 10.1007/s11075-015-0037-z. - Camargo, A. P., Erratum: On the numerical stability of Floater-Hormann\'s rational interpolant\", Numerical Algorithms, DOI 10.1007/s11075-015-0071-x. - Camargo, A. P. e Mascarenhas, W., The stability of extended Floater-Hormann interpolants, Numerische Mathematik, submetido. arXiv:1409.2808v5 / The problem of reconstructing a function f from a finite set of known values f(x0), f(x1), ..., f(xn) appears frequently in mathematical modeling. It is not possible, in general, to completely determine f from f(x0), f(x1), ..., f(xn) but, in several cases of interest, it is possible to find reasonable approximations for f by interpolation, which consists in finding a suitable function (a polynomial function, a rational or trigonometric function, etc.) g such that g(xi) = f(xi); i = 0, 1, ..., n: In practice, the interpolating function g is evaluated in finite precision and the final computed value of g(x) may differ from the exact value g(x) due to rounding. In fact, such difference can even exceed the interpolation error E(x) = f(x)-g(x) in several orders of magnitude, compromising the entire approximation process. The numerical stability of an algorithm reflect is sensibility with respect to rounding. In this work we present a detailed analysis of the numerical stability of some algorithms used to evaluate polynomial or rational interpolants which can be put in the barycentric format. The main results of this work are also available in english in the papers - Mascarenhas, W e Camargo, A. P., On the backward stability of the second barycentric formula for interpolation, Dolomites research notes on approximation v. 7 (2014) pp. 1-12. - Camargo, A. P., On the numerical stability of Floater-Hormann\'s rational interpolant, Numerical Algorithms, DOI 10.1007/s11075-015-0037-z. - Camargo, A. P., Erratum: On the numerical stability of Floater-Hormann\'s rational interpolant\", Numerical Algorithms, DOI 10.1007/s11075-015-0071-x. - Camargo, A. P. e Mascarenhas, W., The stability of extended Floater-Hormann interpolants, Numerische Mathematik, submetido. arXiv:1409.2808v5

No description available.

IFE, the Interactive Formula Editor is an experimental system designed, developed and implemented to propose a different approach to handle mathematical formulae. Its main characteristics are: (1) Interactive creation and edition of a mathematical formula, (2) Tex-form output for a printed version of a formula, and (3) Ability to generate a new set of characters by means of a character editor. Mathematical symbols are provided and adjusted by the system, automatically. The system also, guides the user during the formula description because it knows the syntax of the graphical representation. The system seems to be complete and perform well. The listing of the program is included, as are suggestions for further development.