Triangle Type Research Articles

Rectangle-triangle soft-matter quasicrystals with hexagonal symmetry.

Aperiodic (quasicrystalline) tilings, such as Penrose's tiling, can be built up from, e.g., kites and darts, squares and equilateral triangles, rhombi- or shield-shaped tiles, and can have a variety of different symmetries. However, almost all quasicrystals occurring in soft matter are of the dodecagonal type. Here we investigate a class of aperiodic tilings with hexagonal symmetry that are based on rectangles and two types of equilateral triangles. We show how to design soft-matter systems of particles interacting via pair potentials containing two length scales that form aperiodic stable states with two different examples of rectangle-triangle tilings. One of these is the bronze-mean tiling, while the other is a generalization. Our work points to how more general (beyond dodecagonal) quasicrystals can be designed in soft matter.

The APR triangle: A practical zone in the Glissonean approach to laparoscopic anatomical right hepatectomy

An understanding of vascular anatomy is crucial for the safe performance of laparoscopic anatomical liver excision. We discovered a triangular zone during the laparoscopic right liver surgery and termed this zone the APR triangle. The purpose of this study was to determine the probability of the existence of the APR triangle and elucidate its various forms. Analyzed three-dimensional image reconstructions of 66 individuals who underwent liver surgery and calculated the statistics for various types of APR triangles under various grouping settings. The APR triangle was present in the majority of cases, with right hepatic vein trunk type in 68% and right hepatic vein branch type in 21%, respectively. The angle between the right anterior and right posterior hepatic pedicles (AP&PP) was at most between 45 and 90° (74%). There was a 35% chance that at least one of the AP&PP was longer than 2 cm, and a 39% chance that both were. The right posterior pedicle first branch would appear at the bifurcation of AP&PP in 13% only. The APR triangle is objectively present and may represent a practical zone for performing laparoscopic right hepatic anatomical resection more simply and safely.

Mechanical Strength Evaluation of a Yoroi-Coil Structured Non-Circular REBCO Pancake Coil in High Magnetic Field

In order to achieve a high intensity and compact multifunctional air-core cyclotron, the behavior of non-circular coils in a high magnetic field at 4.2 K were investigated. Two types of isosceles triangle shaped double-pancake coils: a coil with reinforcement by Yoroi-coil (Y-based oxide superconductor and reinforcing outer integrated coil) structuring and a coil without reinforcement, were manufactured and their behaviors were observed when current was applied to each coil in a high magnetic field. The non-reinforcement coil showed in 10 T external magnetic field that the superconducting properties of the coil were partially lost and a voltage generated in the coil winding was observed when the applied current exceeded 160 A. After disassembling this coil, it was found that the superconducting tape in the coil winding was plastically deformed and permanently bent at the corners. The reinforced coil due to Yoroi-coil structuring was powered up to the coil current of 300 A in a magnetic field of 14 T. A voltage of 0.3 mV was observed when the coil current was 277 A, and the excitation was terminated when the voltage reached 0.6 mV at 300 A. The coil winding, after the current flowing up to 300 A in 14 T field, indicated that the deformation of it was significantly limited. It was confirmed that the Yoroi-coil type structural reinforcement, even for triangular coils, has sufficient mechanical strength under the conditions of our air-core cyclotron.

A direct method for generating rogue wave solutions to the (3+1)-dimensional Korteweg-de Vries Benjamin-Bona-Mahony equation

In this paper, we provide a generating mechanism to obtain rogue wave solutions from N soliton of Hirota's bilinear method. Based on the long wave limit method, the phase parameters are reconstructed to generating rogue wave solutions of Korteweg–de Vries Benjamin-Bona-Mahony equation. The rogue wave solutions are expressed explicitly in rational forms. Besides fundamental pattern of rogue waves, the triangle or pentagon pattern have been revealed. Both types of triangle and pentagon patterns are resolved upon different choices of free parameters introduced.

Mechanical and Acoustic Properties of Alloys Used for Musical Instruments.

Music should be integrated into our daily activities due to its great effects on human holistic health, through its characteristics of melody, rhythm and harmony. Music orchestras use different instruments, with strings, bow, percussion, wind, keyboards, etc. Musical triangles, although not so well known by the general public, are appreciated for their crystalline and percussive sound. Even if it is a seemingly simple instrument being made of a bent metal bar, the problem of the dynamics of the musical triangle is complex. The novelty of the paper consists in the ways of investigating the elastic and dynamic properties of the two types of materials used for musical triangles. Thus, to determine the mechanical properties, samples of material from the two types of triangles were obtained and tested by the tensile test. The validation of the results was carried out by means of another method, based on the modal analysis of a ternary system; by applying the intrinsic transfer matrix, the difference between the obtained values was less than 5%. As the two materials behaved differently at rupture, one having a ductile character and the other brittle, the morphology of the fracture surface and the elementary chemical composition were investigated by scanning electron microscopy (SEM) and analysis by X-ray spectroscopy with dispersion energy (EDX). The results were further transferred to the finite element modal analysis in order to obtain the frequency spectrum and vibration modes of the musical triangles. The modal analysis indicated that the first eigenfrequency differs by about 5.17% from one material to another. The first mode of vibration takes place in the plane of the triangle (transverse mode), at a frequency of 156 Hz and the second mode at 162 Hz, which occurs due to vibrations of the free sides of the triangle outside the plane, called the torsion mode. The highest dominant frequency of 1876 Hz and the sound speed of 5089 m/s were recorded for the aluminum sample with the ductile fracture in comparison with the dominant frequency of 1637 Hz and the sound speed of 4889 m/s in the case of the stainless steel sample, characterized by brittle fracture.

Dynamic Analysis of the Musical Triangles—Experimental and Numerical Approaches

This paper addresses the experimental and numerical dynamic analysis of curved bars used as percussion musical instruments. These structures are known as triangles, being made of various metal materials. The study was based on the experimental analysis of the dynamic response over time and the frequency of three types of triangles, different in material and size. Subsequently, finite element analysis of the same structures modeled with the SimCenter 12 program was performed. The results were compared, highlighting the contribution of material type and geometry in obtaining vibration modes, frequency spectrum, and structural damping coefficient. Between the experimental and the numerical analysis, the obtained errors were below 2.2% in terms of their natural frequencies. The study also highlights the complementarity of the two methods in understanding the vibration modes of triangles.

Error Analysis on Triangle Type Functions Concerning Extremum Values in Ordinary High SchoolMathematics Teaching

Error Analysis on Triangle Type Functions Concerning Extremum Values in Ordinary High SchoolMathematics Teaching

Hybrid balance theory: Heider balance under higher-order interactions.

Heider's balance theory in signed networks, which consists of friendship or enmity relationships, is a model that relates the type of relationship between two people to the third person. In this model, there is an assumption of the independence of triadic relations, which means that the balance or imbalance of one triangle does not affect another and the energy only depends on the number of each type of triangle. There is evidence that in real network data, in addition to third-order interactions (Heider balance), higher-order interactions also play a role. One step beyond the Heider balance, the effect of quartic balance has been studied by removing the assumption of triangular independence. The application of quartic balance results in the influence of the balanced or imbalanced state of neighboring triangles on each specific one. Here, a question arises as to how the Heider balance is affected by the existence of quartic balance (fourth order). To answer this question, we presented a model which has both third- and fourth-order interactions and we called it a hybrid balance theory. The phase diagram obtained from the mean-field approximation shows there is a threshold for higher-order interaction strength, below which a third-order interaction dominates and there are no imbalance triangles in the network, and above this threshold, squares effectively determine the balance state in which the imbalance triangles can survive. The solution of the mean-field indicates that we have a first-order phase transition in terms of the random behavior of agents (temperature) which is in accordance with the Monte Carlo simulation results.

The mechanical and repair behavior of damaged carbon/carbon composites

With the aim of understanding the effect of defect types on the mechanical performance of carbon/carbon (C/C) composites, three kinds of defects such as circle arc, square, and triangle shapes were prefabricated on their surfaces. The results show that the prefabricated defects damage the flexural strength of C/C composites compared to the pristine sample (101 ± 6 MPa). The flexural strength of C/C decreased by 30.84%, 45.84%, and 42.58% corresponding to the circle arc, square, and triangle type defects respectively. The defect-repair method with Ni-based solder as the additive was employed to repair the damaged C/C composites. After repair, the stress concentration of C/C composites decreases, and there is a good connection between carbon fiber and the repaired solder so that the load can be transferred continuously, therefore the flexural strength of C/C composites can be improved by 20–28%.

Investigating the Impact of Triangle and Quadrangle Mesh Representations on AGV Path Planning for Various Indoor Environments: With or Without Inflation

In a factory with different kinds of spatial atmosphere (warehouses, corridors, small or large workshops with varying sizes of obstacles and distribution patterns), the robot’s generated paths for navigation tasks mainly depend on the representation of that environment. Hence, finding the best representation for each particular environment is necessary to forge a compromise between length, safety, and complexity of path planning. This paper aims to scrutinize the impact of environment model representation on the performance of an automated guided vehicle (AGV). To do so, a multi-objective cost function, considering the length of the path, its complexity, and minimum distance to obstacles, is defined for a perfect circular robot. Unlike other similar studies, three types of representation, namely quadrangle, irregular triangle, and varying-size irregular triangle, are then utilized to model the environment while applying an inflation layer to the discretized view. Finally, a navigation scenario is tested for different cell decomposition methods and an inflation layer size. The obtained results indicate that a nearly constant coarse size triangular mesh is a good candidate for a fixed-size robot in a non-changing environment. Moreover, the varying size of the triangular mesh and grid cell representations are better choices for factories with changing plans and multi-robot sizes due to the effect of the inflation layer. Based on the definition of a metric, which is a criterion for quantifying the performance of path planning on a representation type, constant or variable size triangle shapes are the only and best candidate for discretization in about 59% of industrial environments. In other cases, both cell types, the square and the triangle, can together be the best representation.

Tiling a tubule: how increasing complexity improves the yield of self-limited assembly

The ability to design and synthesize ever more complicated colloidal particles opens the possibility of self-assembling a zoo of complex structures, including those with one or more self-limited length scales. An undesirable feature of systems with self-limited length scales is that thermal fluctuations can lead to the assembly of nearby, off-target states. We investigate strategies for limiting off-target assembly by using multiple types of subunits. Using simulations and energetics calculations, we explore this concept by considering the assembly of tubules built from triangular subunits that bind edge to edge. While in principle, a single type of triangle can assemble into tubules with a monodisperse width distribution, in practice, the finite bending rigidity of the binding sites leads to the formation of off-target structures. To increase the assembly specificity, we introduce tiling rules for assembling tubules from multiple species of triangles. We show that the selectivity of the target structure can be dramatically improved by using multiple species of subunits, and provide a prescription for choosing the minimum number of subunit species required for near-perfect yield. Our approach of increasing the system’s complexity to reduce the accessibility of neighboring structures should be generalizable to other systems beyond the self-assembly of tubules.

INTELLECTUAL MAPS AS A MEANS OF MATH COMPETENCE DEVELOPMENT OF PRIMARY EDUCATION APPLICANTS

The article presents the mathematical competence of primary education applicants as one of the key competence. The state of the analyzed issue is outlined in the framework of the current modernization of primary education. Intellectual maps are viewed as one of the promising ways of forming mathematical competence of primary school students. The investigated problem is analyzed, the essence of concept “intellect-map” (mental map, map of mind, load map, map of knowledge, mind map, associative map) is found out. Attention is accented on theoretical positions of scientific works of the British psychologist Tony Buzan, who made a significant contribution to the advancement of the technology of use of mind map in education. It is marked that mental maps are an effective instrument that provides structuring and maintenance of information in student’s memory for further effective application. The basic practical aspects of creation of intellectual maps are expounded, that it is presented in the book of Tony Buzan “Mind Map Mastery: The Complete Guide to Learning and Using the Most Powerful Thinking Tool in the Universe”. Three basic characteristics of map of knowledge are highlighted. Seven basic steps of development of intellectual map are described based on rules of their construction. The row of cloudy services is presented for creation of mental maps. The templates of intellectual maps are given, created in a visual environment Ayoa (before iMindMap). The article proposes the algorithm for introduction mind map into the educational process of initial school that contains three stages: acceptance, application, adaptation. The features of producting and use of mental maps in the math lessons are described for clear structuring and systematization of geometrical material. The examples of use of intellectual map are considered during the study of topics the “Geometrical figures” in a 1 grade, “Polygonal. Perimeter of polygonal” in 2 grade and “Types of triangles” in 4 grade. Methodology of work with these maps on the different stages of math lesson in primary school is offered.

Position and orientation of hyoid bone in mouth breathing children: a cephalometric study

Introduction: The importance of the hyoid bone is associated with its unique anatomical position. The hyoid bone is the only bone in the facial skeleton that attaches to other bones only with the help of muscles. Aim: The aim of this article is to make a cephalometric analysis of the craniofacial anatomy and position of the hyoid bone in children with mixed dentition who have difficult nasal breathing, habitual mouth breathing and a control group of nasal breathing children. Materials and methods: A total of 120 lateral cephalograms of children with mixed dentition were analyzed. The examined X-rays were divided into three groups: 50 lateral cephalograms of children with difficult nasal breathing; 18 lateral cephalograms of children with a habitual mouth breathing and 52 lateral cephalograms of nasal breathing children. To determine the position of the hyoid bone we used the method of Bibby and Preston.1 Results: When comparing the type of the hyoid triangle we found the presence of a statistically significant difference (χ2 = 24.97; p <0.001). In 84% of the children with nasal breathing difficulties there is a negative hyoid triangle and in only 16.00% a positive hyoid triangle. In the nasal breathing children, the positive triangle occurs in 84.60% of cases. In children with habitual mouth breathing the distribution is almost even. A significant difference was found when comparing the height of the negative triangle in children with nasal breathing difficulties and nasal breathing children (t = 6.06; p <0.001). Conclusion: In mouth breathing children there is a lower and posterior position of the hyoid bone compared to nasal breathing children. The negative triangle is characteristic for children, who have difficult nasal breathing, whereas the positive triangle is specific for nasal breathing children.

Magnetic Structures of Electron Systems on the Extended Spatially Completely Anisotropic Triangular Lattice near Quantum Critical Points

We examine magnetic structures of electron systems on an extended triangular lattice that consists of two types of bond triangles with electron transfer energies t_l and t'_l (l = 1, 2, and 3), respectively. We examine the ground state in the mean-field theory when t_1 = t'_1, focusing on collinear states with two sublattices. It is shown that when the imbalance of the spatial anisotropies of the two triangles is large, up-up-down-down (uudd) phases are stable, and the most likely ground states of the lambda-(BETS)_2FeCl_4 system are the Neel state with the modulation vector (\pi/c,\pi/a) and a uudd state, where c = a_1 = a'_1 and a = (a_2+a'_2)/2, with a_1, a_1', a_2, and a_2' being the lattice constants of the bonds with t_1, t'_1, t_2, and t'_2, respectively. These results are consistent with those from the classical spin system. In addition, this study reveals behaviors near the quantum critical point, which cannot be reproduced in the localized spin model. As the imbalance of the spatial anisotropies increases, the U_c of the Neel state increases, and that of the uudd state decreases. In the phase diagrams containing areas of the paramagnetic state, the Neel state with (\pi/c,\pi/a), and a uudd state, their boundaries terminate at a triple point, near which all the transitions are of the first order. The phase boundary between the antiferromagnetic phases does not depend on U, and the transition is of the first order everywhere on the boundary. By contrast, the transitions from the two antiferromagnetic phases to the paramagnetic phase are of the second order, unless the system is close to the triple point.

Attitude of Elementary Stage Students Towards Animation Software as Innovative Strategy to Ensure Learning Outcomes in Mathematics

Abstract: Over the period of years, there has been a much emphasis on the attainment of minimum levels of learning by the students. The act ( RTE- 2009) emphasises on child friendly learning activities without fear and anxiety. Learning outcomes at elementary stage is a document having list of grade wise learning outcomes. Researchers and policy makers across the globe are interested in improving learning outcomes in fear free environment, with aid of technology and digital innovative. The present paper is an attempt to create Pawtoon (animation software) as innovative strategy to ensure learning outcomes on basis of identifying types of triangle in mathematics at elementary stage. The purpose of this paper is to study the attitude of students towards Pawtoon as improving the learning outcomes. The sample of the study include 31 VII grade students (15 boys 16 girls) selected in random manner. Findings of the study revealed that both boys and girls showed positive response for pawoon on basis of identifying types of triangle in mathematics. Further, response towards animation software among students is positive. Based on results, conclusions has been drawn that animation software as innovative strategies can ensure learning outcomes in overall holistic and comprehensive manner.

Breaking degeneracies with the Sunyaev-Zeldovich full bispectrum

Non-Gaussian (NG) statistics of the thermal Sunyaev-Zeldovich (tSZ) effect carry significant information which is not contained in the power spectrum. Here, we perform a joint Fisher analysis of the tSZ power spectrum and bispectrum to verify how much the full bispectrum can contribute to improve parameter constraints. We go beyond similar studies of this kind in several respects: first of all, we include the complete power spectrum and bispectrum (auto- and cross-) covariance in the analysis, computing all NG contributions; furthermore we consider a multi-component foreground scenario and model the effects of component separation in the forecasts; finally, we consider an extended set of both cosmological and intra-cluster medium parameters. We show that the tSZ bispectrum is very efficient at breaking parameter degeneracies, making it able to produce even stronger cosmological constraints than the tSZ power spectrum: e.g. the standard deviation on σ8 shrinks from σPS(σ8)=0.35 to σBS(σ8)=0.065 when we consider a multi-parameter analysis. We find that this is mostly due to the different response of separate triangle types (e.g. equilateral and squeezed) to changes in model parameters. While weak, this shape dependence is clearly non-negligible for cosmological parameters, and it is even stronger, as expected, for intra-cluster medium parameters.

Computational analysis of three lamp close conduit water disinfection UV reactor

The purpose of ultraviolet (UV) disinfection is to bring to end the growth and procreation of microorganism. UV reactors are used for the UV disinfection of the drinking water. Our goal of the current research work was properly locating the positions of the UV lamps in a three-lamp close conduit water disinfection UV reactor. Three positions of UV lamps are based on vertices of the four basic types of triangles (Equilateral, Right angle, Scalene and Isosceles). The objective function for optimized lamp positioning was Reduction Equivalent Dose (RED). To ascertain efficient UV dose delivery to pathogen, water disinfection UV reactors was simulated with the aid of computational fluid dynamics. The computational investigation was achieved employing ANSYS® Fluent 15.0 academic version. The turbulent flow was modeled using standard k−e model, fluence rate (FR) was modeled using UVCalc3D model and pathogen transport was modeled using discrete phase model. The scalene lamp positioning results in highest RED value and isosceles lamp positioning results in lowest RED value. There is meager difference between the RED values of equilateral and scalene lamp positioning. Moreover, we found two lamps on the upstream side and one lamp on the downstream side results in better UV disinfection. The proposed methodology for the three-lamp model provides useful insights to the design and optimization of close conduit water disinfection UV reactor. This research work has evaluated, for the first time, a systematic methodology for three-lamp positioning to ameliorate the performance of UV reactor and has revitalized the comprehension about the contribution of FR distribution within the UV reactor.

Reduction of Magnetic Flux Density of Parallel Overhead Power Lines by Optimization of Phase Wires Hanging Order

Overhead power lines are one of the largest sources of the low-frequency magnetic fields. Such magnetic fields occur the harmful effects on human health and other biological objects. The current size of the security zones doesn’t provide a safe level of the magnetic flux density outside them. Therefore, the task of reducing the magnetic flux density value of the overhead power lines outside the security zone is urgent. Some overhead power lines have sections where two lines pass parallel to each other at a short distance. For such lines the method of phase wires hanging order optimization can be applied. For efficiency comparison of different hanging orders was chose two types of electricity pylons: portal (PB330-7) and triangular (P330-3). The cases both lines done by the same pylons were investigated. Analyze of different hanging orders efficiency was performed by mathematical simulation using MATLAB software. The magnetic flux density computation inside the security zone and outside it was done by a specialized simplified methodology of power lines electric and magnetic fields calculation. It is shown that in case of identical phase wires hanging order and the same currents direction of two parallel lines there is a significant increasing of magnetic flux density value at the border of the security zone and outside it for both types of the electricity pylons. It is determined that with a certain hanging order it is possible to achieve a significant reduction of the magnetic flux density value. For lines with electricity pylons of a portal type (PB330-7) the most efficient is the mirror order. It allows to obtain a decreasing of magnetic flux density more than 30 percent at the security zone border and more than 50 percent outside it. For pylons of a triangle type (P330-3) the most efficient is the nonsymmetrical order. It provides the decreasing of magnetic flux density up to 20 percent. In case of opposite currents direction, the most efficient is the same hanging order for both types of electricity pylons. It is shown that optimal phase wires hanging order allows to decrease the magnetic flux density value outside the security zone border, to reduce the distance to border of the area with safe level of the magnetic flux density, to increase the phase current value at which the magnetic flux density value reaches the safe level within the security zone.

AUTOMATIC SEGMENTATION AND INDICATORS MEASUREMENT OF THE VOCAL FOLDS AND GLOTTAL IN LARYNGEAL ENDOSCOPY IMAGES USING MASK R-CNN

In present clinic practice of otolaryngology, otolaryngologists utilized laryngoscopy to diagnose the larynx lesion of patients preliminarily. Nevertheless, it was challenging for otolaryngologists to interpret the detailed information from laryngoscopy videos comprehensively. In this paper, we proposed Mask R-CNN deep learning algorithm to segment the regions of the vocal folds and glottal from laryngoscopy videos, and self-built algorithm to calculate measured indicators including the length and curvature of vocal folds, the angle of glottal, the area of vocal folds and glottal, and the triangle type composed of vocal folds and glottal. Moreover, in order to provide otolaryngologists critical and immediate medical information during diagnosis, we also provided visualized information, which is labeled on the laryngoscopy images to meet all the needs in clinical practice. From the result of this research, the precision of segmentation has reached a high rate of 90.4% on average. It shows that the model not only achieves great performance in segmentation, but also further proved the indicators are accurate enough to be considered in practical diagnosis. In the future, it is possible for the proposed model to be applied in more kinds of laryngoscopy analyses for more comprehensive diagnosis, which would make a positive influence toward the clinical practice of otolaryngology.

Application of hierarchical structures based on binary matrices with the generalized arithmetic of Pascal’s triangle in route building problems

The paper describes a method for constructing binary matrices based on Pascal’s triangle. It provides the definitions of vertical and horizontal generatrices, consisting of binary elements, and the recurrent rule of Pascal’s triangle, with the help of which a binary matrix is formed. The possibility of parametrization of generatrices is shown by identifying a combinatorial root word, called a generatrix pattern, in terms of word combinatorics. A comparative analysis is provided with the method of generalizing Pascal’s triangle using reduction modulo a prime. Combinatorial differences are shown. Discrete mathematical objects (an integer lattice and combinatorial lattice paths) are described. The paper provides the definitions of lattice paths and describes specific types of paths - the Motzkin paths and the McMahon paths. It gives some combinatorial properties of the Motzkin paths. A method for mapping a binary matrix of the Pascal triangle type to the set of points of an integer combinatorial lattice is described. A method for constructing and predicting the qualitative characteristics of navigation routes by combining binary matrices and integer lattices is developed. Possibilities of parametrization of a binary matrix and an integer lattice, taking into account practical problems, are presented.