A triangular exploration

2021 ◽  
Vol 105 (564) ◽  
pp. 501-506
Author(s):  
Prithwijit De ◽  
Gerry Leversha
Keyword(s):  
Angle Bisector ◽  
Internal Angle

In this Article we study the following problem: Let ΔABC be an acute-angled triangle. Let the points D, E, F on the sides BC, CA and AB, respectively, be such that AD is the median from A, BE is the internal angle bisector of ∠ABC, and CF is the altitude from C. This is shown in Figure 1.

scholarly journals DESCRIPTIONS OF NEW SPECIES OF NORTH AMERICAN HETEROCERA, WITH NOTES

1887 ◽  
Vol 19 (8) ◽  
pp. 145-147
Author(s):  
Henry Edwards
Keyword(s):  
New Species ◽  
North American ◽  
Bright Orange ◽  
Golden Yellow ◽  
Basal Half ◽  
Internal Angle

Allied to F. denudata, but differing greatly in important particulars, Fore wings are bright shining seal-brown, deep orange along the costa for the basal half. At the middle of the wing at base in a narrow denuded space, and the internal angle is also devoid of scales, but much more narrowly so than in denudata. The transparent space is golden yellow in shade. Lower wings transparent golden yellow, with very bright but dark opalescent reflection. The margin and spot at the extremity of cell dark brown. Antennæ bluish black, orange brown at the base. Head, disk of thorax, and the upper portion of the abdominal segements, black. Eyes black, palpi with black at their base. Front of head, collar, sides and base of thorax, posterior edges of abdominal segments bright orange. Feet and legs wholly orange without any black bands.

scholarly journals Better Wettability of Pandanus Utilis Alkaline Treated Fibres Tead to Higher Tensile Strengths of Composites.

2021 ◽  
Author(s):  
Laurent L'Entete ◽  
Hareenanden Ramasawmy
Keyword(s):  
Tensile Strength ◽  
Composite Materials ◽  
Carbon Footprint ◽  
Fibre Length ◽  
Natural Fibre ◽  
Engineering Properties ◽  
Aggressive Treatment ◽  
High Carbon ◽  
Reinforcing Agent ◽  
Internal Angle

Abstract Composite materials made with synthetic fibres like E-glass, Kevlar or carbon have helped to provide a wide array of products to society with specific engineering properties. However, these materials have a high carbon footprint as well as being non-biodegradable. The use of natural fibre, as a substitution to these man-made fibres, has been studied and encouraging results are being obtained.In this study, the use of ‘Pandanus utilis’ fibre as a reinforcing agent in plastic was investigated with the aim of exploring specific properties such as the tensile strength of the fibre, its wettability and the effect of fibre length after treating the fibre with two different NaOH solutions. Results have shown that better reinforcement was obtained for the composites (11.10 ± 2.53MPa) with fibres subjected to a more aggressive treatment (2.5%NaOH for 2h) compared to the composite made with fibres having maximum tensile strength (168 ± 12MPa at 0.5% NaOH for 14h), due to a better hydrophilicity of the alkaline treated fibre (87.37° internal angle). Within the range of short chopped fibre length tested (6 to 15 mm), it was shown that there was a general decrease in the tensile strength of the composite.

scholarly journals Maxillomandibular Plane Angle Bisector (MM) Adjunctive to Occlusal Plane to evaluate Anteroposterior Measurement of Dental Base

2012 ◽  
Vol 13 (4) ◽  
pp. 539-544
Author(s):  
Chanamallappa R Ganiger ◽  
KU Cariappa ◽  
AR Yusuf Ahammed
Keyword(s):  
Clinical Significance ◽  
Orthodontic Treatment ◽  
Clinical Usefulness ◽  
Occlusal Plane ◽  
Reference Plane ◽  
Plane Angle ◽  
B Values ◽  
Angle Bisector ◽  
Lateral Cephalograms ◽  
Relationship Of

ABSTRACT Aim This study was undertaken to analyze the clinical usefulness of the maxillomandibular bisector, its reproducibility, its validity and its relationship to the functional occlusal plane, the bisecting occlusal plane and the nature of its cant. Materials and methods Thirty pretreatment lateral cephalograms, each of adolescents (above 18 years of age) and children (10- 12 years), seeking orthodontic treatment were randomly selected and the Wits technique of anteroposterior measurement was used to compare A-B values measured to the new plane with those measured to the functional occlusal plane (FOP) and to the traditional or bisecting occlusal plane (BOP). Results Present study showed that MM bisector plane is more reproducible and valid reference plane, than the FOP and BOP. Conclusion A new plane, geometrically derived from the dental base planes, has been tested as an occlusal plane substitute for the measurement of anteroposterior jaw relationships. It lies close to but at an angle and inferior to the traditional occlusal planes and is highly reproducible at all times. Clinical significance Maxillomandibular planes angle bisector may be a useful adjunct for the cephalometric assessment of sagittal relationship of the patient. How to cite this article Ganiger CR, Nayak USK, Cariappa KU, Ahammed ARY. Maxillomandibular Plane Angle Bisector (MM) Adjunctive to Occlusal Plane to evaluate Anteroposterior Measurement of Dental Base. J Contemp Dent Pract 2012; 13(4):539-544.

scholarly journals Angle Bisector Algorithm and Modified Dynamic Programming Algorithm for Dubins Traveling Salesman Problem

2021 ◽  
Author(s):  
Eswara Venkata Kumar Dhulipala
Keyword(s):  
Euclidean Distance ◽  
Travelling Salesman Problem ◽  
Dynamic Programming Algorithm ◽  
Constant Factor ◽  
Programming Algorithm ◽  
Worst Case ◽  
Angle Bisector ◽  
Set Of Points ◽  
The Given ◽  
Tour Length

A Dubin's Travelling Salesman Problem (DTSP) of finding a minimum length tour through a given set of points is considered. DTSP has a Dubins vehicle, which is capable of moving only forward with constant speed. In this paper, first, a worst case upper bound is obtained on DTSP tour length by assuming DTSP tour sequence same as Euclidean Travelling Salesman Problem (ETSP) tour sequence. It is noted that, in the worst case, \emph{any algorithm that uses of ETSP tour sequence} is a constant factor approximation algorithm for DTSP. Next, two new algorithms are introduced, viz., Angle Bisector Algorithm (ABA) and Modified Dynamic Programming Algorithm (MDPA). In ABA, ETSP tour sequence is used as DTSP tour sequence and orientation angle at each point $i_k$ are calculated by using angle bisector of the relative angle formed between the rays $i_{k}i_{k-1}$ and $i_ki_{k+1}$. In MDPA, tour sequence and orientation angles are computed in an integrated manner. It is shown that the ABA and MDPA are constant factor approximation algorithms and ABA provides an improved upper bound as compared to Alternating Algorithm (AA) \cite{savla2008traveling}. Through numerical simulations, we show that ABA provides an improved tour length compared to AA, Single Vehicle Algorithm (SVA) \cite{rathinam2007resource} and Optimized Heading Algorithm (OHA) \cite{babel2020new,manyam2018tightly} when the Euclidean distance between any two points in the given set of points is at least $4\rho$ where $\rho$ is the minimum turning radius. The time complexity of ABA is comparable with AA and SVA and is better than OHA. Also we show that MDPA provides an improved tour length compared to AA and SVA and is comparable with OHA when there is no constraint on Euclidean distance between the points. In particular, ABA gives a tour length which is at most $4\%$ more than the ETSP tour length when the Euclidean distance between any two points in the given set of points is at least $4\rho$.

scholarly journals LEARNING HYPERPLANES THAT CAPTURES THE GEOMETRIC STRUCTURE OF CLASS REGIONS

2013 ◽  
pp. 7-12
Author(s):  
PRAMOD PATIL ◽  
ALKA LONDHE ◽  
PARAG KULKARNI
Keyword(s):  
Decision Tree ◽  
Decision Trees ◽  
Geometric Structure ◽  
Gini Index ◽  
Decision Tree Algorithm ◽  
Top Down ◽  
Angle Bisector ◽  
Eigen Value ◽  
Tree Algorithms ◽  
Left And Right

Most of the decision tree algorithms rely on impurity measures to evaluate the goodness of hyperplanes at each node while learning a decision tree in a top-down fashion. These impurity measures are not differentiable with relation to the hyperplane parameters. Therefore the algorithms for decision tree learning using impurity measures need to use some search techniques for finding the best hyperplane at every node. These impurity measures don’t properly capture the geometric structures of the data. In this paper a Two-Class algorithm for learning oblique decision trees is proposed. Aggravated by this, the algorithm uses a strategy, to evaluate the hyperplanes in such a way that the (linear) geometric structure in the data is taken into consideration. At each node of the decision tree, algorithm finds the clustering hyperplanes for both the classes. The clustering hyperplanes are obtained by solving the generalized Eigen-value problem. Then the data is splitted based on angle bisector and recursively learn the left and right sub-trees of the node. Since, in general, there will be two angle bisectors; one is selected which is better based on an impurity measure gini index. Thus the algorithm combines the ideas of linear tendencies in data and purity of nodes to find better decision trees. This idea leads to small decision trees and better performance.

Roman Britain in 1961

1962 ◽  
Vol 52 (1-2) ◽  
pp. 160-199
Keyword(s):  
Roman Britain ◽  
Internal Angle

Destruction by gravel-working of the successive fort and fortlet at Llystyn, Caernarvonshire (JRS xlviii, 130; L, 210–1) is nearly complete. (a) In the retentura of the fort four further barracks lay each side of the via decumana. The NW and NE gates had double carriageways between flanking towers, like the SE gate, and there were internal angle- and interval-turrets of timber, (b) The fortlet (fig. 10), whose gate lay on the SW, was asymmetrically planned, with a quadrangle SE of the unmetalled axial street and parallel blocks to NW of it.

Study of Sintering of Iron Powder Bars Processed by Equal Channel Angular Pressing

2014 ◽  
Vol 802 ◽  
pp. 404-408 ◽  
Author(s):  
Mônica Paula Ribeiro ◽  
Marcio Ferreira Hupalo ◽  
Selauco Vurobi ◽  
Osvaldo Mitsuyuki Cintho
Keyword(s):  
Iron Powder ◽  
Equal Channel Angular Pressing ◽  
Volume Fraction ◽  
Substantial Reduction ◽  
Microstructural Characterization ◽  
Porosity Evolution ◽  
Angular Pressing ◽  
Internal Angle ◽  
Quantitative Stereology ◽  
1045 Steel

The main aim of this work is to show porosity evolution during application of various processing conditions to a high-purity (99.7 wt.%) iron powder, including compacting, sintering and equal channel angular pressing (ECAP). Iron powder bars with dimensions of 8x8x30 mm and 8x8x10 mm were axially pressed with pressures ranging from 100MPa to 250MPa, followed by sintering at 1100oC during 30 minutes under argon atmosphere. Sintered bars were processed by ECAP at room temperature in a single pass, using a SAE 1045 steel die with an internal angle of 120o. Microstructural characterization was performed by light optical microscopy (LOM) and quantitative stereology. ECAP processing resulted in a substantial reduction in the porosity levels for specimens pressed at 100 MPa and 150 MPa. The sample compacted with 150MPa and processed by ECAP with back-pressure showed the lowest volume fraction of porosity. Higher compacting pressures caused an increase in porosity levels. This result is explained by presence of cracks prior to ECAP and the concurrent action of severe stress-strain states during extrusion.

An Internal Angle Guidance Law with Impact Angle and Time Constraints

2021 ◽  
pp. 5559-5570
Author(s):  
Liang Yong ◽  
Zhang You’an ◽  
Yan Shi
Keyword(s):  
Impact Angle ◽  
Time Constraints ◽  
Guidance Law ◽  
Internal Angle

An Investigation into Optimized Ti-6Al-4V Titanium Alloy Equal Channel Angular Extrusion Process

2013 ◽  
Vol 479-480 ◽  
pp. 181-186 ◽  
Author(s):  
Dyi Cheng Chen ◽  
Yi Ju Li ◽  
Gow Yi Tzou
Keyword(s):  
Plastic Deformation ◽  
Titanium Alloy ◽  
Deformation Behavior ◽  
Equal Channel Angular Extrusion ◽  
Extrusion Process ◽  
Process Conditions ◽  
Rigid Plastic ◽  
Die Geometry ◽  
Plastic Deformation Behavior ◽  
Internal Angle

The shear plastic deformation behavior of a material during equal channel angular (ECA) extrusion is governed primarily by the die geometry, the material properties, and the process conditions. This paper employs the rigid-plastic finite element (FE) to investigate the plastic deformation behavior of Ti-6Al-4V titanium alloy during ECA extrusion processing. Under various ECA extrusion conditions, the FE analysis investigates the damage factor distribution, the effective stress-strain distribution, and the die load at the exit. The relative influences of the internal angle between the two die channels, the friction factors, the titanium alloy temperature and the strain rate of billet are systematically examined. In addition, the Taguchi method is employed to optimize the ECA process parameters. The simulation results confirm the effectiveness of this robust design methodology in optimizing the ECA processing of the current Ti-6Al-4V titanium alloy.

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