Approximation of maxillary arch shape by mathematical functions

2009 ◽  
Author(s):  
Vilma Ardzijauskaite
Keyword(s):  
Mathematical Functions ◽  
Maxillary Arch ◽  
Arch Shape

scholarly journals Relationship between Maxillary Arch Shape and Maxillary Labial Bone Dimensions: A Pilot Study

2021 ◽  
Author(s):  
Ahmad Assari ◽  
Shereen Shokry ◽  
Dana Al-Senan ◽  
Tasnim Alsbaih ◽  
Mada Alanazi ◽  
...  
Keyword(s):  
Wall Thickness ◽  
Alveolar Bone ◽  
The Other ◽  
Cone Beam ◽  
Facial Bone ◽  
Anterior Portion ◽  
Significant Difference ◽  
Bone Dimensions ◽  
Maxillary Arch ◽  
Arch Shape

Abstract OBJECTIVE: To determine whether there is any relationship between the thickness of the labial alveolar bone wall in the anterior portion of the maxilla and arch shape.MATERIALS AND METHODS: Thirty patients (age, 12–53 years) were selected from archived cone beam computed tomography (CBCT) cases. All maxillary front teeth were present in all the cases. The distance between the cementoenamel junction (CEJ) and the facial bone crest and the thickness of the labial alveolar bone wall at distances of 1, 3, and 5 mm apical to the facial bone crest were measured.RESULTS: The distance between the CEJ and the facial bone crest ranged from 2.24 mm and 3.08 mm. No significant differences were found between the thickness of the bone wall at 1, 3, and 5 mm apical to the crest. A significant difference was found between the U-shaped arch on one side and the V-shaped and square-shaped arches on the other side. The U-shaped arch and labial bone wall thickness were correlated at the 1-mm distance (F = (8, 276) = 3.24, p = 0.002). U-shaped and V-shaped arches were common in women, whereas square-shaped arches were common in men (χ2 = 105.5, p = 0.000).CONCLUSION: Our study is the first to associate arch shape and labial alveolar bone wall thickness.CLINICAL RELEVANCE: The association between the U-shaped arch and bone wall thickness may constitute a new indicator for the tendency of the labial alveolar bone to resorb after extraction and placement of endo-osseous implants.

Dental arch changes comparison between expander with differential opening and fan-type expander: a randomized controlled trial

2020 ◽  
Author(s):  
Camila Massaro ◽  
Guilherme Janson ◽  
Felicia Miranda ◽  
Aron Aliaga-Del Castillo ◽  
Fernando Pugliese ◽  
...  
Keyword(s):  
Randomized Controlled Trial ◽  
Controlled Trial ◽  
Dental Arch ◽  
Maxillary Expansion ◽  
Nasal Bridge ◽  
Arch Width ◽  
Randomized Controlled ◽  
Permanent Molar ◽  
Maxillary Arch ◽  
Arch Shape

Summary Objectives To compare posterior crossbite correction frequency and dentoalveolar changes of the expander with differential opening (EDO) and the fan-type expander (FE). Trial design Two-arm parallel randomized controlled trial. Methods Forty-eight patients from 7 to 11 years of age were allocated into two groups. Twenty-four patients were treated with the EDO and 24 patients were treated with the FE. Block randomization was performed. The study was single blind. Digital dental models were acquired before treatment and 6 months after rapid maxillary expansion. The primary outcomes were crossbite correction rate and maxillary arch width changes. Secondary outcomes were interincisal diastema, arch perimeter, length, size and shape, and mandibular dental arch changes. Results The final sample comprised 24 patients (13 female and 11 male; mean initial age of 7.62 years) in the EDO group and 24 patients (14 female and 10 male; mean initial age of 7.83 years) in the FE group. The crossbites were corrected in 100 per cent of subjects from EDO group and in 75 per cent of patients in FE group. EDO showed greater increases in maxillary intermolar region (P < 0.001), while the FE demonstrated greater increases in the intercanine distance (P = 0.008). Increase in mandibular inter-first permanent molar distance was slightly greater in the EDO group (mean difference of 0.8 mm). Changes in arch length and perimeter were similar in both groups. Both expanders changed the maxillary arch shape. The post-treatment arch shape was larger in the anterior region for FE and in the posterior region in the EDO group. Harms Discomfort during activation was reported by 54 per cent of the participants. A temporary change in the nasal bridge was reported by one patient from FE group. Conclusions Maxillary arch width and shape changes were distinct between the EDO and the FE. Greater transversal increases of the anterior and posterior regions were observed for the FE and the EDO, respectively. A slightly greater mandibular spontaneous expansion was observed for the EDO only at the molar region. Trial registration NCT03705871.

Risk assessment models with functionally different influences on natural and technical systems

2020 ◽  
Vol 89 ◽  
pp. 8-19
Author(s):  
V. A. Minaev ◽  
◽  
N. G. Topolsky ◽  
A. O. Faddeev ◽  
R. O. Stepanov ◽  
...  
Keyword(s):  
Risk Assessment ◽  
Differential Equations ◽  
Research Area ◽  
Practical Implementation ◽  
Model Assessment ◽  
Mathematical Functions ◽  
Effective Response ◽  
Risk Assessment Models ◽  
Technical Systems ◽  
Material Values

Introduction. The complex combination of natural and technogenic factors that lead to dangerous threats to the health and life of the population, as well as to material values, creates a need to develop special mathematical models for risk assessment in the relevant territories. Herewith it is important to take into account the significant differences between these factors. The new areas of research are models that describe natural and technogenic risks using differential equations that reflect different types of functions. The article presents the development of this research area. Goals and objectives. The goal of the article is to create a model for risk assessment in natural and technical systems (PTS), based on taking into account the influences of different natural and technogenic factors on them. Objectives include justification, construction and practical implementation of the mathematical model of risk assessment in the form of differential equations system. Methods include interpretation of the considered influences on PTS in terms of risks and assessment of the dynamic interaction of natural and technogenic factors in the form of inhomogeneous differential equations. Results and discussion. Solutions for models of assessing complex natural and technogenic risks in relation to two cases that differ in NTS are found: functionally different external natural and technogenic influences on PTS, which are understood as their type, in which the effects of both natural and technogenic factors are described by different mathematical functions. Conclusions. The first model considers parabolic (reflecting threats whose intensity gradually decreases with distance from the epicenter) and linear types of influences (reflecting sudden threats). The second model considers parabolic and hyperbolic (reflecting threats, the intensity of which decreases sharply over time) types of influences. It is concluded that it is necessary to create a special computer album of complex influences on the PTS in order to prevent "replay" of various situations and develop the most effective response to emerging dangers from the EMERCOM units and other structures. Key words: model, assessment, natural and technogenic risks, functionally different influences, counteraction, EMERCOM units.

scholarly journals Global Image Thresholding Adaptive Neuro-Fuzzy Inference System Trained with Fuzzy Inclusion and Entropy Measures

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 286 ◽  
Author(s):  
Athanasios Bogiatzis ◽  
Basil Papadopoulos
Keyword(s):  
Fuzzy Inference System ◽  
Fuzzy Inference ◽  
Initial Step ◽  
Local Area ◽  
Mathematical Functions ◽  
Inference System ◽  
Neuro Fuzzy ◽  
Entropy Measures ◽  
Complex Procedure ◽  
Artificial Neural Network Ann

Thresholding algorithms segment an image into two parts (foreground and background) by producing a binary version of our initial input. It is a complex procedure (due to the distinctive characteristics of each image) which often constitutes the initial step of other image processing or computer vision applications. Global techniques calculate a single threshold for the whole image while local techniques calculate a different threshold for each pixel based on specific attributes of its local area. In some of our previous work, we introduced some specific fuzzy inclusion and entropy measures which we efficiently managed to use on both global and local thresholding. The general method which we presented was an open and adaptable procedure, it was free of sensitivity or bias parameters and it involved image classification, mathematical functions, a fuzzy symmetrical triangular number and some criteria of choosing between two possible thresholds. Here, we continue this research and try to avoid all these by automatically connecting our measures with the wanted threshold using some Artificial Neural Network (ANN). Using an ANN in image segmentation is not uncommon especially in the domain of medical images. However, our proposition involves the use of an Adaptive Neuro-Fuzzy Inference System (ANFIS) which means that all we need is a proper database. It is a simple and immediate method which could provide researchers with an alternative approach to the thresholding problem considering that they probably have at their disposal some appropriate and specialized data.

scholarly journals A Unified Mathematical Formalism for First to Third Order Dielectric Response of Matter: Application to Surface-Specific Two-Colour Vibrational Optical Spectroscopy

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 153 ◽  
Author(s):  
Christophe Humbert ◽  
Thomas Noblet
Keyword(s):  
Dielectric Response ◽  
Structure And Properties ◽  
Linear Optics ◽  
Third Order ◽  
Mathematical Functions ◽  
Sum Frequency ◽  
Non Linear Optics ◽  
Non Linear ◽  
Light Excitation

To take advantage of the singular properties of matter, as well as to characterize it, we need to interact with it. The role of optical spectroscopies is to enable us to demonstrate the existence of physical objects by observing their response to light excitation. The ability of spectroscopy to reveal the structure and properties of matter then relies on mathematical functions called optical (or dielectric) response functions. Technically, these are tensor Green’s functions, and not scalar functions. The complexity of this tensor formalism sometimes leads to confusion within some articles and books. Here, we do clarify this formalism by introducing the physical foundations of linear and non-linear spectroscopies as simple and rigorous as possible. We dwell on both the mathematical and experimental aspects, examining extinction, infrared, Raman and sum-frequency generation spectroscopies. In this review, we thus give a personal presentation with the aim of offering the reader a coherent vision of linear and non-linear optics, and to remove the ambiguities that we have encountered in reference books and articles.

scholarly journals Molariform Mesiodens in Primary Dentition

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Sachin B. Mangalekar ◽  
Tajammul Ahmed ◽  
M. Zakirulla ◽  
Halawar Sangmesh Shivappa ◽  
F. B. Bheemappa ◽  
...  
Keyword(s):  
Rare Case ◽  
Treatment Plan ◽  
Permanent Dentition ◽  
Primary Dentition ◽  
Occlusal Surface ◽  
Radiographic Examination ◽  
Supernumerary Tooth ◽  
Dentigerous Cysts ◽  
Delayed Eruption ◽  
Maxillary Arch

Mesiodens is a midline supernumerary tooth commonly seen in the maxillary arch, and incidence of molariform mesiodens in the maxillary midline is rare in permanent dentition and extremely uncommon in primary dentition. A midline supernumerary tooth in the primary dentition can cause ectopic or delayed eruption of permanent central incisors which will further alter occlusion and may compromise esthetics and formation of dentigerous cysts. This paper reports a rare case of the presence of a molariform mesiodens in the primary dentition. On clinical and radiographic examination, flaring of the primary central incisors was seen, with a molariform mesiodens consisting of multiple lobes or tubercles on the occlusal surface with the well-formed root. The treatment plan consisted of the extraction of the supernumerary tooth and regular observation of permanent central incisors for proper eruption and alignment.

scholarly journals Tables of the Mathematical Functions

1965 ◽  
Vol 19 (92) ◽  
pp. 696
Author(s):  
J. W. W. ◽  
Harold T. Davis
Keyword(s):  
Mathematical Functions
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