Triangle Height Research Articles

Evaluation of Interdental Papilla Regeneration Using Injectable Hyaluronic Acid: A Clinical Study.

This study aimed to assess the efficacy of hyaluronic acid (HA) gel injections in deficient papillae and record the effects for four weeks. Fifteen deficient class 1 papilla sites according to Nordland and Tarnow classification were included. After scaling and root planing, 0.5 ml HA gel was injected into the papillae. Measurements of black triangle height (BTH) and black triangle area (BTA) from the contact point to the most coronal level of the visible papilla tip weredone on the clinical photographs using ImageJ software at baseline, one week, and four weeks postoperatively, and a comparison was made. Descriptive data were examined using the mean and standard deviation (SD). Paired t-test was used for intragroup comparisons, with p-values <0.05 considered significant. All the data analysis was done using SPSS software version 25.0. There was a mean decrease in the BTA from baseline (0.54 mm2), one week (0.13 mm2), to four weeks (0.26 mm2) with a slight loss of papilla volume from the first week to the fourthweek, and this decrease in area was statistically significant. A mean decrease in the BTH throughout the follow-ups from baseline (1.36 mm) to the first week (0.30 mm) to the fourth week (0.73) was recorded with a slight loss of papilla volume from the first week to the fourthweek, and this decrease in height was also statistically significant (p < 0.05). However, the decrease in the BTA and BTH recorded was more from baseline to the first week as compared to baseline to the fourth week postoperatively. HA gel is an effective treatment for minimally invasive papilla augmentation, particularly in class I Nordland and Tarnow papilla deficits.

Natural convection of viscoplastic fluids in a triangular enclosure

This study extends the analysis of natural convection in a viscoplastic fluid to flow within a triangular enclosure. The finite-element approach provided a numerical solution to the continuity, momentum, and energy equations. The governing parameters for this problem are the Rayleigh number, (Ra=104−106), yield number, (Y=0−Ymax), aspect ratio, (HL=0.5−2.5), and slope angle, (∅=0−π2). The influence of these parameters on the heat and mass transfer, morphology of yielded/unyielded regions, and fluid flow were thoroughly examined. The results show that two opposing factors influence the flow behavior and heat transmission within the triangular enclosure. The proximity of the walls restricts the convective movement, leading to reduced heat transfer. However, the proximity of hot and cold sources increases the temperature gradient and heat transfer. The unique influence of the viscoplastic material properties, particularly the yield stress, further distinguishes the heat transfer in this triangular enclosure from other geometries. The results indicate that an increase in the Rayleigh number mitigates the effects of yield stress to some extent. However, the accumulation of unyielded material at the triangular apex hinders convection flow. Furthermore, the viscoplastic fluid flow and heat transfer changed significantly with changes in triangle height. In particular, the maximum yield stress increased by more than 100 % as the aspect ratio increased from 0.5 to 2.5. A change in the slope angle causes a continuous transition from subcritical to supercritical bifurcation, significantly affecting the morphology of the yielded and unyielded areas, and the maximum (critical) yield number. Finally, correlations were developed to predict the Nusselt number and maximum yield stress in all cases.

Mixing of powders under periodic shear stress: effect of initial filling level

Powder Mixing continues being of great importance in the field of particle technology because of the challenge to get homogeneous mixtures at a large scale. However, it is still moderately understood because of the complexity of designing 3D experiments that consider all the factors affecting the powder flow and powder mixing, hindering the acquisition of enough data that would provide a basic conception of powder behavior. This study involves a simple granular material mixing system of low friction that has five walls, where two of them are high friction moving walls following a cyclic function, and the others are non-friction static walls. The purpose was to create a complete set of 3D experiments of powder distribution to have a better insight into the inside mixing behavior as a function of the initial powder filling level. Experiments at different filling heights were run, obtaining the best mixing at the highest filling level. It was obtained a non-mixing zone with a triangle shape highly affected by the column particle weight. The increase of the vertical component of the resultant force produced by the acrylic motion walls causes a high momentum transfer in the x, y and z directions resulting in a decrease in the no-mixing zone. It was found an asymptotic behavior of the triangle height as a function of the initial filling height of the powders which indicates that values above a limited initial filling level will not have a significant effect on the triangle. A filling height increment of 100 % from 3.81 to 7.62 cm causes an increase in the mixing of 4.44 %. DEM simulations for mixing in the low-shear equipment were run to compare the experimental work

Use of Injectable Hyaluronic Acid Gel and Injectable Platelet-rich Fibrin in the Treatment of Gingival Black Triangles: A Randomized Clinical Trial

Purpose: The current study aimed to compare the efficacy of injectable hyaluronic acid gel and injectable platelet rich fibrin, either alone or combined; for the reconstruction of defective interdental papilla using clinical approaches. Subjects and Methods: A total sample size of eighteen class I and class II deficient interdental papillae sites were randomly divided in 3 groups. Group 1 included 6 sites that were treated by 0.2ml hyaluronic acid gel injection. Group 2 included 6 sites that were treated by injectable platelet-rich fibrin (i-PRF). Group 3 included 6 sites that were treated by a combination of 0.2ml hyaluronic acid gel injection and iPRF. Each deficient papilla received 3 injections; at 0, 3and 6 weeks intervals. The height of black triangles was recorded at baseline before injection procedure, at each injection interval and during follow ups. Results: A statistically significant difference in all three groups was found in the mean of the black triangle height records between the five time intervals, mainly between baseline and 6 months follow up. Conclusion: Hyaluronic acid injections and injectable platelet rich fibrin can be an alternative non-invasive treatment method for gingival black triangles.

Use of Injectable Hyaluronic Acid Gel and Injectable Platelet-rich Fibrin in the Treatment of Gingival Black Triangles: A Randomized Clinical Trial

Purpose: The current study aimed to compare the efficacy of injectable hyaluronic acid gel and injectable platelet rich fibrin, either alone or combined; for the reconstruction of defective interdental papilla using clinical approaches. Subjects and Methods: A total sample size of eighteen class I and class II deficient interdental papillae sites were randomly divided in 3 groups. Group 1 included 6 sites that were treated by 0.2ml hyaluronic acid gel injection. Group 2 included 6 sites that were treated by injectable platelet-rich fibrin (i-PRF). Group 3 included 6 sites that were treated by a combination of 0.2ml hyaluronic acid gel injection and iPRF. Each deficient papilla received 3 injections; at 0, 3and 6 weeks intervals. The height of black triangles was recorded at baseline before injection procedure, at each injection interval and during follow ups. Results: A statistically significant difference in all three groups was found in the mean of the black triangle height records between the five time intervals, mainly between baseline and 6 months follow up. Conclusion: Hyaluronic acid injections and injectable platelet rich fibrin can be an alternative non-invasive treatment method for gingival black triangles.

On the Resolution of Triangular Meshes

AbstractIt is generally agreed that the resolution of a regular quadrilateral mesh is the side length of quadrilateral cells. There is less agreement on the resolution of triangular meshes, exacerbated by the fact that the numbers of edges or cells on triangular meshes are approximately three or two times larger than that of vertices. However, the geometrical resolution of triangular meshes, that is, maximum wavenumbers or smallest wavelengths that can be represented on such meshes, is a well defined quantity, known from solid state physics. These wavenumbers are related to a smallest common mesh cell (primitive unit cell), and the set of mesh translations that map it into itself. They do not depend on whether discrete degrees of freedom are placed on vertices, cells or edges. For equilateral triangles the smallest wavelength equals twice the triangle height. Resolutions of quadrilateral and triangular meshes approximately agree if they have the same numbers of vertices.

Chain Decompositions of q, t-Catalan Numbers: Tail Extensions and Flagpole Partitions

This article is part of an ongoing investigation of the combinatorics of $q,t$-Catalan numbers $\textrm{Cat}_n(q,t)$. We develop a structure theory for integer partitions based on the partition statistics dinv, deficit, and minimum triangle height. Our goal is to decompose the infinite set of partitions of deficit $k$ into a disjoint union of chains $\mathcal{C}_{\mu}$ indexed by partitions of size $k$. Among other structural properties, these chains can be paired to give refinements of the famous symmetry property $\textrm{Cat}_n(q,t)=\textrm{Cat}_n(t,q)$. Previously, we introduced a map that builds the tail part of each chain $\mathcal{C}_{\mu}$. Our first main contribution here is to extend this map to construct larger second-order tails for each chain. Second, we introduce new classes of partitions called flagpole partitions and generalized flagpole partitions. Third, we describe a recursive construction for building the chain $\mathcal{C}_{\mu}$ for a (generalized) flagpole partition $\mu$, assuming that the chains indexed by certain specific smaller partitions (depending on $\mu$) are already known. We also give some enumerative and asymptotic results for flagpole partitions and their generalized versions.

Impact of Variation in Interleaflet Triangle Height Between Fused Leaflets in the Functionally Bicuspid Aortic Valve on Hemodynamics and Tissue Biomechanics

AbstractThere is fusion between two leaflets in functionally bicuspid (bileaflet) aortic valves with trisinuate aortic root. The degree of fusion inversely correlates with variation in the interleaflet triangle height (“commissural height”). We aimed to determine the hemodynamics and biomechanical response in the thoracic aorta due to variations in the commissural height between fused leaflets in a bicuspid aortic valve with raphe. A three-dimensional (3D) aortic valve model was reconstructed using cardiac magnetic resonance (CMR) imaging from a patient with a normal trileaflet aortic valve. Fluid–structure interaction (FSI) simulations were used to investigate the effect of variation in commissural height between the coronary leaflets with leaflet fusion, and this was contrasted to a case with a normal trileaflet valve. Phase-contrast CMR was used for validation of the simulated hemodynamics. The aorta and leaflet tissues were treated as hyperelastic materials. In the normal trileaflet aortic valve, two counter-rotating vortex cores develop within the root at peak systole and interact with the walls of the ascending aorta. However, in the bicuspid aortic valve with fusion between the coronary leaflets, the vortex system becomes more asymmetric. This correlates with more recirculation of flow toward the fusion side of the aortic root. The peak velocity, pressure gradient, wall shear stress, and strain levels increase approximately linear with decreasing commissural height and increasing leaflet fusion. Decreasing interleaflet triangle height between the fused leaflets in bicuspid aortic valves with raphe results in linear elevation of wall shear stress at the sinutubular junction and proximal ascending aorta.

Reconstruction of Interdental Papilla in Esthetic Zone using Hyaluronic Acid Gel: A Clinical Prospective Study

Introduction: Interdental papilla deficiency or black triangles are considered to be one of the most challenging dilemmas in esthetic dentistry. Various invasive techniques with less success have been introduced for interdental papilla regeneration. So, to overcome the limitations a non-invasive technique with greater predictability and patient comfort has been introduced using Hyaluronic acid gel (HA). In the present study, the efficacy of 2% Hyaluronic acid gel on interdental papilla enhancement was evaluated clinically along with photographic analysis (Image J Software) and its effect on gingival fibroblast cell culture lines was observed.&#x0D; Aim: To evaluate the changes in buccal triangle dimensions i.e. buccal triangle area (BTA), buccal triangle width (BTW), buccal triangle height (BTH) at baseline and 6 months using commercially available 2% HA gel and to check the effect of HA on proliferative abilities of gingival fibroblast cell culture lines.&#x0D; Materials and Methods: 60 sites in 15 patients were selected and were randomly divided into test and control group. The Test Group received commercially available 2% HA gel and the control group received saline as a placebo. All the clinical measurements, photographs were taken at 3 weeks, 3 months and 6 months and comparisons among test and control groups were done both for clinical measurements and Image J analysis of photographs for interdental papilla enhancement. MTT assay and XTTT assay was done to check the effect of 2% HA gel on proliferative abilities of gingival fibroblast in cell culture lines.&#x0D; Results: HA treated sites showed gradual and constant improvement in interdental papilla enhancement while the control sites did not show any improvement. Complete interdental papilla reconstruction was seen in 63.3% of test sites at 6 months and 365 of test sites showed partial interdental papilla reconstruction. HA gel has a positive effect on the proliferative and migratory abilities of gingival fibroblast.&#x0D; Conclusion: HA is a noninvasive voluminizing alternative treatment modality for interdental papilla deficiency. It is biocompatible as it does not cause an adverse reaction. HA gel has a strong effect on the migratory and proliferative abilities of gingival fibroblasts.

A novel amnion-chorion allograft membrane combined with a coronally advanced flap: a minimally invasive surgical therapy to regenerate interdental papillary soft tissue recession - a six-month postoperative image analysis-based clinical trial.

ObjectivesLoss of the interdental papilla is multi-factorial and creates a multitude of problems. Autogenous connective tissue/biomaterial-based regeneration has been attempted for decades to reconstitute the black space created due to the loss of papilla. The aim of this present study was to regenerate papillary recession defects using an amnion-chorion membrane (ACM) allograft and to evaluate the clinical outcome up to six months postoperatively.Materials and MethodsTwenty patients with 25 Nordland and Tarnow’s Class I/II interdental papillary recession defects were treated with ACM and coronal advancement of the gingivo-papillary unit via a semilunar incision on the labial aspect followed by a sulcular incision in the area of interest. A photographic image analysis was carried out using the GNU Image Manipulation software program from the baseline to three and six months postoperatively. The black triangle height (BTH) and the black triangle width (BTW) were calculated using the pixel size and were then converted into millimeters. The mean and standard deviation values were determined at baseline and then again at three and six months postoperatively. The probability values (P˂0.05 and P≤0.01) were considered statistically significant and highly significant, respectively. An analysis of variance and post hoc Bonferroni test were carried out to compare the mean values.ResultsOur evaluation of the BTH and BTW showed a statistically and highly significant difference from the baseline until both three and six months postoperatively (P=0.01). A post hoc Bonferroni test disclosed a statistically significant variance from the baseline until three and six months postoperatively (P˂0.05) and a non-significant difference from three to six months after the procedure (P≥0.05).ConclusionAn ACM allograft in conjunction with a coronally advanced flap could be a suitable minimally invasive alternative for papillary regeneration.

Minimally invasive therapy for reconstruction of lost interdental papilla by using injectable hyaluronic acid filler.

Background and Aim:Reconstruction of interdental papillae (IDP) is among the most difficult periodontal therapy. Papillary recession is multifactorial, and several surgical, nonsurgical, and minimally invasive techniques have been suggested. The purpose of this study was to evaluate the clinical application of injectable hyaluronic acid (HA) gel for the reconstruction of IDP in Nordland and Tarnow's Class I and II papillary recession cases.Materials and Methods:In the present in vivo clinical trial, 7 patients (2 males, 5 females) with 25 defects were selected. A volume of 0.2 ml HA gel was injected at the respective areas and massaged for 2–3 min. Photographs were obtained, and the assessment of the data was performed clinically (CP-GM, interproximal width [IPW]) and by Image analysis software (black triangle height [BTH], black triangle width [BTW]). Comparison of mean values was performed using the analysis of variance, followed by Post hoc Bonferroni test. Value of P ≤ 0.05 was considered statistically significant.Results:Application of HA gel for the reconstruction of IDP was successful in 6 months. CP-GM, BTH, IPW, and BTW showed a statistically significant difference from baseline to 3 and 6 months interval (P = 0.01). Post hoc Bonferroni test for CP-GM, BTH, BTW, and IPW revealed a statistically significant difference from baseline to 3 months (P ≤ 0.05) and 6 months (P ≤ 0.05) and a nonsignificant difference at 3–6 months (P ≥ 0.05).Conclusion:Injectable HA gel is a promising minimally invasive therapy for enhancing papillary esthetics.

Interdental papilla reconstruction using injectable hyaluronic acid: A 6 month prospective longitudinal clinical study.

The objective of this study was to assess the efficacy of Hyaluronic Acid (HA) on interdental papilla (IDP) loss in the esthetic zone. Twenty one subjects (14 females and 7 males) from those referred for treatment of IDP loss at Periodontics postgraduate clinics at the Jordan University of Science and Technology. A total of 86 interdental sites (58 sites in the maxillary jaw and 28 sites in the mandibular jaw) were treated and followed up. A 0.2 ml of Hyaluronic acid was injected in each receded IDP site and injections were repeated after 21 days. Papilla sites were evaluated and statistically analyzed. At the 3 week interval the mean reduction of black triangle (BT) height was 0.17 mm (8% reduction) (P-value <0.001), at the 3 month interval there was a mean reduction of BT height of 0.83 mm (39% reduction) (P-value <0.001). At 6 months however, the reduction in BT height was 0.62 mm (29% reduction) (P-value <0.001). Within the limitations of this study, it can be concluded that the use of commercially available HA gel for the treatment of interdental papillae loss may have promising results over the first 6 months after injection. The maximum improvement in black triangles was at 3 months after injection with a reduction of improvement between 3 and 6 months. Clinical Relevance Helping clinician to take evidence based decision while considering Hyaluronic acid injection as a short term nonsurgical treatment modality for interdental papilla loss.

The investigation of the stress-strain state of beam crossings with a truss-form supporting element of the operating pipeline

The areas of application and advantages of the over-ground piping or pipe section layout are given. The classification according to the design features of the most common systems of overhead pipeline crossings on the basis of generalization of scientific publications and experience of pipeline construction are considered. The authors indicate the ranges of the effective spans for rectilinear single-span and multi-span crossings without compensators of longitudinal strains (with the fixed ends) and also in multi-span systems with compensators depending on the diameter of pipes, nominal pipe wall thickness and brand of pipe steel for gas, oil and oil-products pipelines respectively. The description of the design of beam systems of overhead pipeline crossings with a truss-form supporting element of the operating pipeline is given and the procedure for estimating their stress-strain state is suggested. According to the constructed cargo and unit calculation schemes of the truss with a cross-section in the form of an isosceles triangle (height – 3 m, width – 2.02 m) the stiffness coefficients of elastic-malleable supports is determined. The selection of cross-sections of truss members is carried out, the required deflections of the pipeline and the emerging internal force factors (bending moments and reactions of elastic-malleable supports) at the points where the pipeline rests on the truss are found. The strength of the pipeline to the action of the maximum bending moment is checked and the possibility of the cross-water layout of the beam crossing of the gas pipeline is shown. This is the gas pipeline with the length of . It has compensators with a truss-form supporting element which eliminates the use of intermediate supports. Thus, it was shown that the truss makes it possible to double or triple the length of the span using no intermediate supports and preserving sufficient horizontal rigidity.

Giant Magnetoimpedance Effect Modified by Transverse Shape Anisotropy in Fe-Based Amorphous Ribbon

The magnetoimpedance (MI) effect on the text Fe-based ribbon with different sizes of triangle transverse structures has been investigated. The initial susceptibility ( $\chi _{\mathbf {i}}$ ) and the MI ratio along the width (T-MI) and length (L-MI) directions as a function of the triangle height ( ${h}$ ) were measured and discussed. The text T-MI and $\chi _{\mathbf {i}}$ along the width direction increase with the increase in ${h}$ , while the text L-MI and $\chi _{\mathbf {i}}$ along the length direction decrease with the increase in ${h}$ . These behaviors are mainly attributed to the variation of the effective shape anisotropy ( ${K} _{\mathbf {eff}}$ ) and the corresponding magnetization process, in which ${K} _{\mathbf {eff}}$ mainly originates from the competition of demagnetization effects along the width and length directions. The triangle structures changed the demagnetization fields along the two directions. Thus, the effective shape anisotropy, permeability, and MI were varied. This article also provides an idea to fabricate the MI sensor by introducing transverse shape anisotropy.

Comparison of Connective Tissue Graft and Platelet Rich Fibrin as Matrices in A Novel Papillary Augmentation Access: A Randomized Controlled Clinical Trial.

Objective The present study was a randomized controlled clinical trial with the aim of evaluating the increase in papillary height and reduction in black triangle height obtained by the novel papillary augmentation access with either connective tissue graft (CTG) or platelet-rich fibrin (PRF) as matrix from baseline to 6 months. Materials and Methods A total number of 20 sites with Nordland and Tarnow’s Class I, I-II and II interdental papillary loss were recruited into the study. The sites were randomly allocated with 10 sites per group into either: Group A (control group) or Group B (test group) which utilizes the same technique with CTG or PRF as matrix, respectively. The clinical parameters such as PPD (probing pocket depth) and CAL (clinical attachment level) at the surgical site, plaque score (FMPS), bleeding scores (FMBS), interdental papillary height (PH) and black triangle height (BTH), along with visual analog score by dentist (VAS-D) and by patient (VAS-P) were evaluated at baseline and at 6 months. Results In both CTG and PRF groups, all the primary and secondary outcome variables such as PH, BTH, VAS-D and VAS-P showed statistically significant improvement from baseline to 6 months ( p ≤0.05) within the group. On comparison at 6 months, there were no differences in the papillary height between the groups. However, the BTH has significantly reduced in the CTG group than the PRF group. Similarly, the VAS-D significantly improved in the CTG group than the PRF group ( p = 0.010) at 6 months. Conclusion The study demonstrates that the proposed papillary augmentation access with CTG and PRF was successful in managing the unaesthetic interdental papillary loss, with CTG showing better results in terms of reduction of black triangle than PRF.

A framework for visualising road design prior to construction using driving simulation technologies

This paper proposes a framework where road designs can be visualised in a virtual reality environment prior to any physical construction. A software algorithm for generating computer graphics models automatically enables this framework to be effective. Key road design parameters such as the number of lanes, shoulder length, speed limits, turn angles, etc., must first be identified and then a computer program is developed to build computer graphics models based on these parameters. The generated computer graphics will include triangle meshes, textures, and height maps which can be rendered within a virtual reality environment. When used in conjunction with driving simulation technologies, the program also enables road designers to drive on their road being designed. Any implementation of this framework will be the most effective if it is incorporated with an existing road design process. Additionally, a case study is presented in order to demonstrate an implementation of the proposed framework.

Assessment of body parameters' symmetry in child violinists.

Playing violin may lead to overload of the locomotor system. The aim of this study was to assess body parameters for trunk symmetry in child violinists and compare with the control group. We analyzed body posture of 101 children aged 7-12 years, mean age 11.09 ± 9.46, 49 child violinists and control group of 52 children. We found statistically significant differences for the difference in depth of the lower corners of scapulae and upper posterior spina iliaca, though greater asymmetries were found in the clinical control group. The remaining parameter values are close to significance, which may suggest that the process of postural change among the children had just started and that the existing asymmetries were easy to correct. We found positive correlation between body height and the difference in distance of the lower corners of scapulae from the spine: OL (p= 0.029, correlation coefficient value was 0.167) and the Thales triangle height: (p= 0.018, correlation coefficient was 0.214). Position maintained while playing the violin changed some parameters characterizing the curvature of the spine in frontal plane. We found the importance of detailed analysis of children body posture and its critical assessment.

小学生は高さをどのようにとらえているのか : 「日常的経験から得た高さ」と「平面図形における三角形の高さ」との関連

小学生は高さをどのようにとらえているのか : 「日常的経験から得た高さ」と「平面図形における三角形の高さ」との関連

The Study of the Ageing Impact on Workability and Hardness of the Samples Made of Alloy VV751P (Ni-15Co-10Cr) after Selective Laser Sintering

Work is focused on study of workability changing of heat resistant nickel-based Ni-15Co-10Cr alloy produced by selective laser sintering from metal powder. Experimental research of HRC hardness changing was provided on plate samples 2х10х30 mm after sintering and typical heat treatment for this alloy. Heat treatment was: annealing at temperature of 1,000oС during 1.5 hours, and then at the temperature of 1,180oC for 2.5 h – 3 h. After that samples were treated in a furnace for 50 – 60 minutes at the temperature of 1,050oС. Then they were cooled-off to the temperature of 1,000oС during 50 – 60 minutes. After that they were further quenched at ambient temperature. After quenching the samples were subjected to ageing at the temperature of 850oC during 3, 6, 9, 12 and 15 hours. The bending and measurement of triangle height was proposed for work ability assessment of samples. Increased hardness was found with duration of ageing. Work ability grew up with duration of ageing but where was a gap of workability for 9 hours ageing. Calibration of sintered parts and samples are recommended to perform after quenching and ageing at 850oC no longer 6 hours.

Prediction of the Spinning Triangle Height in Ring Frame Using Artificial Neural Networks

Prediction of the Spinning Triangle Height in Ring Frame Using Artificial Neural Networks