Search results for: torus

Authors: Pakkinee Chitsakul

Abstract:

In this article, we would like to show that there is no cut point of any point in a plane, but there exists the cut locus of a point in a flat torus. By the results, we would like to determine the structure of cut locus of a flat torus.

Keywords: cut locus, flat torus, geodesics

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Authors: Raka Aldy Nugraha, Kiwah Andanni, Aditya Indra Pratama, Aswin Guntara

Abstract:

Background: Torus palatinus is a bony protuberance in the hard palate. Sex and race are considered as influencing factors for the development of torus palatinus. Hence, the objective of this study was to determine the prevalence and characteristics of torus palatinus and its correlation with sex and ethnicity among Western Indonesian Population. Methods: We conducted a descriptive and analytical study employing cross-sectional design in 274 new students of Universitas Indonesia. Data were collected by using consecutive sampling method through questionnaire-filling and direct oral examination. Subject with racial background other than indigenous Indonesian Mongol were excluded from this study. Data were statistically analyzed using chi square test for categorical variables whereas logistic regression model was employed to assess the correlation between variables of interest with prevalence of torus palatinus. Results: Torus palatinus were found in 212 subjects (77.4%), mostly small in size (< 3 mm) and single in number, with percentage of 50.5% and 90.6%, respectively. The prevalence of torus palatinus were significantly higher in women (OR 2.88; 95% CI: 1.53-5.39; p = 0.001), dominated by medium-sized and single tori. There was no significant correlation between ethnicity and the occurrence of torus palatinus among Western Indonesian population. Conclusion: Torus palatinus was prevalent among Western Indonesian population. It showed significant positive correlation with sex, but not with ethnicity.

Keywords: characteristic, ethnicity, Indonesia, mongoloid, prevalence, sex, Torus palatinus

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Authors: Preethy Mary Donald, Renjith George

Abstract:

Oral tori are localized non-neoplastic protuberances of maxilla and mandible. Torus palatinus (TP) is found on the midline of the roof of mouth existing as single growth or in clusters. Torus mandibularis(TM) is located on the lingual aspect of the mandible commonly between canine and premolar region. Etiology of their presence was not clear and was found to be multifactorial. Their variations in relation to age, gender, ethnicity and also the characteristics of TP and TM have become the interest of multiple studies. The objectives of this study were to determine the prevalence of torus palatinus (TP) and torus mandibularis (TM) among patients who have visited outpatient department, Faculty of Dentistry, Melaka Manipal Medical College. 108 patients were examined for the presence of oral tori at the outpatient department, Faculty of Dentistry, Melaka-Manipal Medical College. Factors such as age, gender, ethnicity of the patients and size, shape, location of the oral tori were studied. For TP, Malays (62.96%) have been found to have the highest prevalence than Chinese (43.3%) and Indians (35.71%). For TM, Chinese (7.46%) had predominated compared to Malays (7.41%) and Indians (0%). There is no significant association between occurrence of TP and TM with age, gender and ethnicity. For Torus palatinus, the most common size was Grade 1(1-3mm), most common location was molar region, and the most common shape was spindle. For Torus mandibularis, the most frequent location was canine premolar region and exists in unilateral single or bilateral single fashion. The overall prevalence rates were 47.2% for TP and 6.48% for TM. However, there is no significant association between occurrence of TP and TM with age, gender and ethnicity. The results showed variations in clinical characteristics and support the findings that occurrence of tori is a dynamic phenomenon which is multifactorial owing to the environmental factors such as stress from occlusion and dietary habits. It could be due to the genetic make-up of the individual.

Keywords: torus palatinus, torus mandibularis, age, gender

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Authors: Bhavini Pandya

Abstract:

This paper considers Hη: T2 → T2 the Perturbed Cerbelli-Giona map. That is a family of 2-dimensional nonlinear area-preserving transformations on the torus T2=[0,1]×[0,1]= ℝ2/ ℤ2. A single parameter η varies between 0 and 1, taking the transformation from a hyperbolic toral automorphism to the “Cerbelli-Giona” map, a system known to exhibit multifractal properties. Here we study the multifractal properties of the family of maps. We apply a box-counting method by defining a grid of boxes Bi(δ), where i is the index and δ is the size of the boxes, to quantify the distribution of stable and unstable manifolds of the map. When the parameter is in the range 0.51< η <0.58 and 0.68< η <1 the map is ergodic; i.e., the unstable and stable manifolds eventually cover the whole torus, although not in a uniform distribution. For accurate numerical results we require correspondingly accurate construction of the stable and unstable manifolds. Here we use the piecewise linearity of the map to achieve this, by computing the endpoints of line segments which define the global stable and unstable manifolds. This allows the generalized fractal dimension Dq, and spectrum of dimensions f(α), to be computed with accuracy. Finally, the intersection of the unstable and stable manifold of the map will be investigated, and compared with the distribution of periodic points of the system.

Keywords: feed forward, gradient descent, neural network, integral equation

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Authors: Ibrahim Alsendid, Rob Sturman, Benjamin Sharp

Abstract:

In this paper, we consider a family of 2-dimensional nonlinear area-preserving transformations on the torus. A single parameter η varies between 0 and 1, taking the transformation from a hyperbolic toral automorphism to the “Cerbelli-Giona” map, a system known to exhibit multifractal properties. Here we study the multifractal properties of the family of maps. We apply a box-counting method by defining a grid of boxes Bi(δ), where i is the index and δ is the size of the boxes, to quantify the distribution of stable and unstable manifolds of the map. When the parameter is in the range 0.51< η <0.58 and 0.68< η <1 the map is ergodic; i.e., the unstable and stable manifolds eventually cover the whole torus, although not in a uniform distribution. For accurate numerical results, we require correspondingly accurate construction of the stable and unstable manifolds. Here we use the piecewise linearity of the map to achieve this, by computing the endpoints of line segments that define the global stable and unstable manifolds. This allows the generalized fractal dimension Dq, and spectrum of dimensions f(α), to be computed with accuracy. Finally, the intersection of the unstable and stable manifold of the map will be investigated and compared with the distribution of periodic points of the system.

Keywords: Discrete-time dynamical systems, Fractal geometry, Multifractal behaviour of the Perturbed map, Multifractal of Dynamical systems

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Authors: S. Altmeyer, B. Hof, F. Marques, J. M. Lopez

Abstract:

We present numerical simulations concerning the reversal of spiraling vortices in short highly counter-rotating cylinders. Increasing the differential cylinder rotation results in global flow-inversion is which develops various different and complex flow dynamics of several quasi-periodic solutions that differ in their number of vortex cells in the bulk. The dynamics change from being dominated of the inner cylinder boundary layer with ’passive’ only responding outer one to be dominated by the outer cylinder boundary layer with only responding inner one. Solutions exist on either two or three tori invariant manifolds whereby they appear as symmetric or asymmetric states. We find for either moderate and high inner cylinder rotation speed the quasiperiodic flow to consist of only two vortex cells but differ as the vortices has opposite spiraling direction. These both flows live on 2-tori but differ in number of symmetries. While for the quasi-periodic flow (q^a_2) at lower rotation speed a pair of symmetrically related 2-tori T2 exists the quasi-periodic flow (q^s_2) at higher rotation speeds is symmetric living on a single 2-torus T2. In addition these both flows differ due to their dominant azimuthal m modes. The first is dominated by m=1 whereas for the latter m=3 contribution is largest. The 2-tori states are separated by a further quasi-periodic flow (q^a_3) living on pair of symmetrically related 3-tori T3. This flow offers a ’periodical’ competition between a two and three vortex cell states in the bulk. This flow is also an m=1 solution as for the quasiperiodic flows living on the pair of symmetrically-related 2-tori states. Moreover we find hysteresis resulting in coexisting regions of different quasiperiodic flows q^s_2 and q^a_3 with increasing and decreasing the differential rotation.

Keywords: transition, bifurcation, torus, symmetries

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Authors: Patricia Shirley Almeida Prado, Liz Brito, Selma Paixão Argollo, Gracie Moreira, Leticia Matos Sobrinho

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Diffuse idiopathic skeletal hyperostosis (DISH) is a degenerative bone disease also known as Forestier´s disease and ankylosing hyperostosis of the spine is characterized by a tendency toward ossification of half the anterior longitudinal spinal ligament without intervertebral disc disease. DISH is not considered to be osteoarthritis, although the two conditions commonly occur together. Diagnostic criteria include fusion of at least four vertebrae by bony bridges arising from the anterolateral aspect of the vertebral bodies. These vertebral bodies have a 'dripping candle wax' appearance, also can be seen periosteal new bone formation on the anterior surface of the vertebral bodies and there is no ankylosis at zygoapophyseal facet joint. Clinically, patients with DISH tend to be asymptomatic some patients mention moderate pain and stiffness in upper back. This disease is more common in man, uncommon in patients younger than 50 years and rare in patients under 40 years old. In modern populations, DISH is found in association with obesity, (type II) diabetes; abnormal vitamin A metabolism and also associated with higher levels of serum uric acid. There is also some association between the increase of risk of stroke or other cerebrovascular disease. The DISH condition can be confused with Heterotopic Ossification, what is the bone formation in the soft tissues as the result of trauma, wounding, surgery, burnings, prolonged immobility and some central nervous system disorder. All these conditions have been described extensively as myositis ossificans which can be confused with the fibrodysplasia (myositis) ossificans progressive. As in the DISH symptomatology it can be asymptomatic or extensive enough to impair joint function. A third confusion osteoarthritis disease that can bring confusion are the enthesopathies that occur in the entire skeleton being common on the ischial tuberosities, iliac crests, patellae, and calcaneus. Ankylosis of the sacroiliac joint by bony bridges may also be found. CASE 1: this case is skeletal remains presenting skull, some vertebrae and scapulae. This case remains unidentified and due to lack of bone remains. Sex, age and ancestry profile was compromised, however the DISH pathognomonic findings and diagnostic helps to estimate sex and age characteristics. Moreover to presenting DISH these skeletal remains also showed some bone alterations and non-metrics as fusion of the first vertebrae with occipital bone, maxillae and palatine torus and scapular foramen on the right scapulae. CASE 2: this skeleton remains shows an extensive bone heterotopic ossification on the great trochanter area of left femur, right fibula showed a healed fracture in its body however in its inteosseous crest there is an extensive bone growth, also in the Ilium at the region of inferior gluteal line can be observed some pronounced bone growth and the skull presented a pronounced mandibular, maxillary and palatine torus. Despite all these pronounced heterotopic ossification the whole skeleton presents moderate bone overgrowth that is not linked with aging, since the skeleton belongs to a young unidentified individual. The appropriate osteopathological diagnosis support the human identification process through medical reports and also assist with epidemiological data that can strengthen vulnerable anthropological estimates.

Keywords: bone disease, DISH, human identification, human remains

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Authors: Adriano Losso, Birgit Dämon, Stefan Mayr

Abstract:

In vascular plants, water flows from roots to leaves in a metastable state, and even a small perturbation of the system can lead a sudden transition from the liquid to the vapor phase, resulting in xylem embolism (cavitation). Xylem embolism, induced by drought stress and/or freezing stress is caused by the aspiration of gaseous bubbles into xylem conduits from adjacent gas-filled compartments through pit membrane pores (‘air seeding’). At water potentials less negative than the threshold for air seeding, the surface tension (γ) stabilizes the air-water interface and thus prevents air from passing the pit pores. This hold is probably also true for conifers, where this effect occurs at the edge of the sealed torus. Accordingly, it was experimentally demonstrated that γ influences air seeding, but information on the relevance of this effect under field conditions is missing. In this study, we analyzed seasonal changes in γ of the xylem sap in two conifers growing at the alpine timberline (Picea abies and Pinus mugo). In addition, cut branches were perfused (40 min perfusion at 0.004 MPa) with different γ solutions (i.e. distilled and degassed water, 2, 5 and 15% (v/v) ethanol-water solution corresponding to a γ of 74, 65, 55 and 45 mN m-1, respectively) and their vulnerability to drought-induced embolism analyzed via the centrifuge technique (Cavitron). In both species, xylem sap γ changed considerably (ca. 53-67 and ca. 50-68 mN m-1 in P. abies and P. cembra, respectively) over the season. Branches perfused with low γ solutions showed reduced resistance against drought-induced embolism in both species. A significant linear relationship (P < 0.001) between P12, P50 and P88 (i.e. water potential at 12, 50 and 88% of the loss of conductivity) and xylem sap γ was found. Based on this correlation, a variation in P50 between -3.10 and -3.83 MPa (P. abies) and between -3.21 and -4.11 MPa (P. mugo) over the season could be estimated. Results demonstrate that changes in γ of the xylem sap can considerably influence a tree´s resistance to drought-induced embolism. They indicate that vulnerability analyses, normally conducted at a γ near that of pure water, might often underestimate vulnerabilities under field conditions. For studied timberline conifers, seasonal changes in γ might be especially relevant in winter, when frost drought and freezing stress can lead to an excessive embolism.

Keywords: conifers, Picea abies, Pinus mugo, timberline

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