ARCH在財務分析近來頗受重視，然而實務在建構ARCH模式時參數估計值很難有效估計，而且參數數字本身亦常存在不確定性，其原因可能來自時間數列資料的模糊的性質。利用此一假性的數值來建構模式影響預測，也可能擴大預測結果和實際狀況的誤差，很難讓一般投資者使用並判斷。本文在建構ARCH模式中，加入模糊邏輯概念，以符合實際情況在建構ARCH模式時參數動態的不確定性。嘗試以模糊數的來建構股價加權指數FUZZY ARCH模式，進一步預測，並與ARCH模式作比較分析。 / ARCH is more emphasized in financial analysis recently. However, it is difficult to estimate the parameters of ARCH model in practice. Because of the fuzzy property in time series , there exists the uncertainty in the parameters. Use the fictitious value to construct model and forecast the model will make the errors largely between the forecasts and the practical ones. In this thesis, we add the concept of the fuzzy logic to construct the ARCH model in order to conform the real situation. Also, an analysis of the stock data is provided.

Doctor Scientiae - DSc / Determining arch perimeter is of importance in both a clinical setting, where it is used to determine space requirements, as well as in an epidemiological setting where it is used to describe large populations. Physical measurement of arch perimeter is time consuming and may be prone to operator errors when done on study casts and even more so in a clinical situation. The use of a simple mathematical model to predict arch perimeter, using a few measurements that can be done easily and reliably, would be of great use to the practitioner.

Magister Scientiae Dentium - MSc(Dent) / The aim of this study was to determine whether there are changes in the interdental arch widths and arch lengths of the mandibular and maxillary arches during nonextraction and extraction orthodontic treatment. The records of 78 patients treated by one orthodontist were used for this study. Three treatment groups were selected: a nonextraction group (Group NE), a group treated with extraction of maxillary and mandibular first premolars (Group 44), and a group treated with extraction of maxillary first premolars and mandibular second premolars (Group 45). The arch width measurements were measured in the inter-canine, inter-premolar and inter-molar areas. The arch length was measured as the sum of the left and right distances from mesial anatomic contact points of the first permanent molars to the contact point of the central incisors or to the midpoint between the central incisor contacts, if spaced.Statistical analysis included descriptive statistics of the data, analysis of the correlation matrices, Wilcoxon Signed Rank tests and Kruskal-Wallis tests of the changes which occurred during treatment. The intercanine widths in the mandible and maxilla increased during treatment in all three groups, with the extraction groups showing a greater increase than Group NE (p<0.05). In Group NE the mandibular arch length increased (p>0.05), while the maxillary arch length remained essentially unchanged. Both extraction groups showed decreases in arch length in the dentitions (p<0.05), with greater decreases occurring in the maxilla. The difference in arch length change between the two extraction groups was not significant (p<0.05). The inter-canine arch width increased in all three treatment groups, more so in the two extraction groups. From this it is evident that extraction treatment does not necessarily lead to narrowing of the dental arches in the canine region. The inter-second premolar arch width decreased in both extraction groups. Non-extraction treatment resulted in an increase in the inter-premolar and inter-molar arch widths. / South Africa

<p>The aim of this study was to determine whether there are changes in the interdental arch widths and arch lengths of the mandibular and maxillary arches during nonextraction and extraction orthodontic treatment. The records of 78 patients treated by one orthodontist were used for this study. Three treatment groups were selected: a nonextraction group (Group NE), a group treated with extraction of maxillary and mandibular first premolars (Group 44), and a group treated with extraction of maxillary first premolars and mandibular second premolars (Group 45). The arch width measurements were measured in the inter-canine, inter-premolar and inter-molar areas. The arch length was measured as the sum of the left and right distances from mesial anatomic contact points of the first permanent molars to the contact point of the central incisors or to the midpoint between the central incisor contacts, if spaced.</p> <p>Statistical analysis included descriptive statistics of the data, analysis of the correlation matrices, Wilcoxon Signed Rank tests and Kruskal-Wallis tests of the changes which occurred during treatment. The intercanine widths in the mandible and maxilla increased during treatment in all three groups, with the extraction groups showing a greater increase than Group NE (p&lt / 0.05). In Group NE the mandibular arch length increased (p&lt / 0.05), while the maxillary arch length remained essentially unchanged. Both extraction groups showed decreases in arch length in the dentitions (p&lt / 0.05), with greater decreases occurring in the maxilla. The difference in arch length change between the two extraction groups was not significant (p&gt / 0.10). The inter-canine arch width increased in all three treatment groups, more so in the two extraction groups. From this it is evident that extraction treatment does not necessarily lead to narrowing of the dental arches in the canine region. The inter-second premolar arch width decreased in both extraction groups. Non-extraction treatment resulted in an increase in the inter-premolar and inter-molar arch widths.</p>

<p>The aim of this study was to determine whether there are changes in the interdental arch widths and arch lengths of the mandibular and maxillary arches during nonextraction and extraction orthodontic treatment. The records of 78 patients treated by one orthodontist were used for this study. Three treatment groups were selected: a nonextraction group (Group NE), a group treated with extraction of maxillary and mandibular first premolars (Group 44), and a group treated with extraction of maxillary first premolars and mandibular second premolars (Group 45). The arch width measurements were measured in the inter-canine, inter-premolar and inter-molar areas. The arch length was measured as the sum of the left and right distances from mesial anatomic contact points of the first permanent molars to the contact point of the central incisors or to the midpoint between the central incisor contacts, if spaced.</p> <p>Statistical analysis included descriptive statistics of the data, analysis of the correlation matrices, Wilcoxon Signed Rank tests and Kruskal-Wallis tests of the changes which occurred during treatment. The intercanine widths in the mandible and maxilla increased during treatment in all three groups, with the extraction groups showing a greater increase than Group NE (p&lt / 0.05). In Group NE the mandibular arch length increased (p&lt / 0.05), while the maxillary arch length remained essentially unchanged. Both extraction groups showed decreases in arch length in the dentitions (p&lt / 0.05), with greater decreases occurring in the maxilla. The difference in arch length change between the two extraction groups was not significant (p&gt / 0.10). The inter-canine arch width increased in all three treatment groups, more so in the two extraction groups. From this it is evident that extraction treatment does not necessarily lead to narrowing of the dental arches in the canine region. The inter-second premolar arch width decreased in both extraction groups. Non-extraction treatment resulted in an increase in the inter-premolar and inter-molar arch widths.</p>

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Masonry arch bridges still play an important role in the transportation infrastructure today in the United Kingdom. Previous research has mainly focused on the load carrying capacity in the span direction. The three dimensional behaviour is often investigated by simplifying into two dimensions with modified arch parameters but these simplified analyses cannot represent all aspects of behaviour. Spandrel wall failure in some railway masonry arch bridges has raised concerns recently, and this is one aspect which cannot be modelled in two dimensions. This thesis presents a research which attempts to model the interaction behaviour between arch, backfill and spandrel wall with the aim of representing the three dimensional nature of real bridges. It mainly focuses on the spandrel wall defects under increasing load, including crack development across the wall and longitudinal cracks in the arch barrel underneath spandrel wall. Experimental results from the laboratory tests on engineering blue brick and a hydraulic premixed mortar as well as brickwork masonry specimens are presented. Numerical analysis was initially performed on these brickwork masonry specimens for validation. Three dimensional FE models were proposed for both small and large scale bridges. The general behaviour of the small scale bridge under rolling load and large scale bridge under increasing load were studied. Reasonable agreement between the FE analyses and experimental results from previous literature was obtained, indicating the model validated for small masonry specimens could be scaled up to full-scale bridges. A series of computer models were constructed to investigate the relationship between a range of geometric and material parameters and the lateral behaviour of arch bridges. The backfill depth and spandrel wall thickness have greatest impact on both bridge strength and lateral behaviour. The fill properties also have an importance influence on the load carrying capacity. This provides an indication of which bridge should be more closely monitored for spandrel wall defects. Separate FE models was constructed to simulate existing longitudinal cracks found in the arch barrel for old bridges and the influence of strengthening of spandrel wall with tie bars. The general behaviour under a concentrated load is studied and discussed. It has been demonstrated that it is possible to effectively model the three dimension behaviour of masonry arch bridges and in particular, spandrel wall failures.

OBJECTIVES: The objective of this research is to evaluate variation of mandibular arch forms at different heights and to determine if there is any correlation between occlusal arch and sub-gingival arch forms. METHODS: 44 subjects were selected based on the inclusion criteria and their CBCTs then were imported to Mimics software (Materialise NV, Belgium) and traced. Each tooth was sliced midsection at 4 different heights: Occlusal, CEJ, Apex and 5mm apical to the apex. At occlusal level the midpoint of the crown was calculated mesiodistally as well as buccolingually. Subsequently, midpoints between the buccal and lingual plates were located for every tooth between and including the first molars. The points were connected forming 4 splines, which then were exported to Geomorph software (cran.r-project.org, Geomorph package, Dean Adams author, Iowa State 2015) for shape statistical analysis. RESULTS: The variation in the arch form among subjects is significantly smaller in the Occlusal and CEJ level. The variation at apical and basal bone levels are higher than the variation at CEJ and occlusal levels. However, variation between apical and basal bone levels are minimal. CONCLUSIONS: Mandibular dental arch form demonstrate more variation apically. It may be concluded that dental arch form variation should be considered when using standardized arch forms for different patients. The subgingival arch forms cannot be predicted from occlusal arch form. Occlusal arch shape and form may not be an indication of basal bone arch form. More information needed for detection of correlation between occlusal arch and sub-gingival arch forms.

Introduction: Dento-alveolar anomalies associated with Orofacial clefts (OFCs) can present with a wide range of variation. This vast diversity makes it difficult to pinpoint their specific etiology. For instance, differentiating anomalies that arise as a consequence of the physical effects of the cleft itself or from the same biological processes that result on clefting, from those that likely occur as a sequela from the surgical repair is a challenge. One approach that can aid this differentiation is to study if first degree relatives of children with clefts whom themselves do not have an overt cleft but may carry genetic cleft risk, are more likely to present some of these anomalies. If so, the elevated risk on these seemingly unaffected relatives will indicate that the particular anomaly arises as a consequence of the molecular pathways that give rise to cleft risk rather than from the physical consequences of the cleft or the surgical repairs. Understanding the different etiological factors underlying dental anomalies within the cleft phenotypic spectrum is a fundamental step for prevention and better management of such anomalies. Amongst the most common dento-alveolar anomalies seen in children born with OFC are tooth size-arch length discrepancies and dento-alveolar shape irregularities, mostly studied in the maxillary arches. Such arch irregularities lead to moderate or severe malocclusions. It is not well known if unaffected family members (UFM) of children with clefts are also susceptible to such dento-alveolar shape irregularities and thus their etiology is not well understood. This study aims to characterize 3D variation in dento-alveolar shape as part of the cleft phenotypic spectrum in UFMs of individuals with OFCs compared to controls with no history of OFC. Methods: A total of 760 maxillary and 760 mandibular casts were digitally scanned using a NextEngine Laser scanner and digitized by two raters with 92 landmarks for maxilla and 94 landmarks for mandible, covering gingival margins and occlusal surfaces via Landmark Editor Software. A reliability of 88.15% was obtained for an interrater agreement error of less than 1mm for all landmarks obtained. 3D coordinates were extracted and registered using a Procrustes fit procedure. Procrustes residuals were analyzed via canonical variate analyses to capture differences in 3D shape between cases and controls. Of the 760 maxillary individuals attempted, 535 (Cases N=133, Controls=402) had all 92 landmarks and 688 (Cases=192, Controls496) had at least 40 landmarks in the canine to canine region. Of the 760 mandibular individuals attempted, 434 (Cases N=99, Controls=335) had all 94 landmarks and 611 (Cases=180, Controls=431) had at least 40landmarks in the canine to canine region. Thus analyses were done separately for each subsample. Results: Case-control differences were not significant (P=0.11) for overall maxillary dental arch shape. However, for the maxillary canine to canine dataset, significant differences were found (P=0.02 for raw Procrustes distance, P<0.0001 for Mahalanobis distance). Case-control differences were significant (P=0.02) for overall mandibular dental arch shape. Significant shape differences were also found for the mandibular canine to canine dataset (P=0.01 for raw Procrustes distance, P<0.0001 for Mahalanobis distance). In other words, there is better separation between cases and controls for the mandibular dataset compared to the maxillary dataset (P=0.11 for the maxillary full arch). Cases had maxillary and mandibular anterior dentitions that were overall retrusive, with anterior teeth that significantly tapered towards the incisal third with larger interproximal incisal embrasures and height to width rations that deviate from ideal ratios (i.e. width is ~70% of the height) due to an overall decrease in crown height. Also, incisal edges seem to flare outwards from the arch line when compared to controls. Moreover, case arch forms trend towards a “v” shape, resembling a Bonwill-Hawley arch shape compared to a “u” shape in the controls. Conclusions: Upper anterior, lower anterior and overall arch shape significantly differ between UFM of individuals with OFC and controls. The most significant differences were located in the maxillary and mandibular anterior dentitions, where cases were more retrusive overall with incisal edges that were tapered and flared, displaying large embrasures and tapered and flared, displayed large embrasures when compared to controls. The phenotypic differences identified in this study contribute to the understanding of the cleft phenotypic spectrum aiding future studies of cleft etiology and cleft risk prediction.