Triangle Type Research Articles

Star-triangle type relations from 2d mathcal{N} = (0, 2) USp(2N) dualities

Inspired by the gauge/YBE correspondence this paper derives some star-triangle type relations from dualities in 2d mathcal{N} = (0, 2) USp(2N) supersymmetric quiver gauge theories. To be precise, we study two cases. The first case is the Intriligator-Pouliot duality in 2d mathcal{N} = (0, 2) USp(2N) theories. The description is performed explicitly for N = 1, 2, 3, 4, 5 and also for N = 3k + 2, which generalizes the situation in N = 2, 5. For N = 1 a triangle identity is obtained. For N = 2, 5 it is found that the realization of duality implies slight variations of a star-triangle relation type (STR type). The values N = 3, 4 are associated to a similar version of the asymmetric STR. The second case is a new duality for 2d mathcal{N} = (0, 2) USp(2N) theories with matter in the antisymmetric tensor representation that arises from dimensional reduction of 4d mathcal{N} = 1 USp(2N) Csáki-Skiba-Schmaltz duality. It is shown that this duality is associated to a triangle type identity for any value of N. In all cases Boltzmann weights as well as interaction and normalization factors are completely determined. Finally, our relations are compared with those previously reported in the literature.

Design of multilayer microfluidic paper chip and its visual detection of pesticide residues

With the increase of China's grain production, the use of pesticides is gradually increasing. Traditional pesticide detection takes a long time and requires expensive experimental instruments, which is not conducive to the rapid and accurate detection of pesticide residues in the field. To solve this problem, this paper proposes a visual detection method of pesticide residues based on multi-layer microfluidic paper chips. The internal channel structure of paper chip is designed from the perspective of efficient mixing. Through the simulation of the mixed effect of three kinds of staggered channel structures, which are arc type, triangle type, and ladder type, the "ladder-type h-0.3, s-2.6" is selected as the best-staggered structure, and the mixing strength is 0.91534. The best simulation structure was tested by a colored reagent, and the image processing of 15 test results was carried out with MATLAB. The average mixing strength was 0.84, and the and the standard deviation was 0.022. The visual detection experiment of acetamiprid and profenofos in cabbage samples was carried out by using the device，The detection range of acetamiprid was 4~72 μg/kg, and the detection range of profenofos was 3~54 μg/kg . The recovery of acetamiprid was 75%~85%, and the recovery of profenofos was 80%~90%. The detection range and recovery rate indicate that the device has high repeatability and accuracy in the actual sample detection

Rolling gaits of a strut-actuated six-strut spherical tensegrity

A tensegrity is a self-stressed pin-jointed system consisting of tensile members and compressive members. As its shape can be actively controlled by changing the prestress of its members, it has great potential to be used as a shape-controllable locomotive system. Particularly, the six-strut spherical tensegrity has been studied intensively as a rolling locomotive system. In this study, the rolling gaits of a strut-actuated six-strut spherical tensegrity are investigated. Specifically, a mathematical model for generating the rolling gaits of locomotive spherical tensegrities is presented, and a numerical method combining dynamic relaxation method and genetic algorithm is used to solve the model. Various rolling gaits for the strut-actuated six-strut locomotive spherical tensegrity are identified using this approach. Two basic types of touching-ground triangles, two basic distributions of payload, and six cases for the numbers of used active struts are considered. Several rolling gait primitives are noted, their motion features analyzed, and a simple path-generating strategy is proposed based on idealized rolling gait primitives. A physical prototype of the strut-actuated six-strut locomotive tensegrity is manufactured, and experiments are conducted to verify the rolling gaits and locomotion paths generated by the proposed methods.

CT Diagnosis of the Fracture of Anterior Nasal Spine.

To study anterior nasal spine fractures, including the incidence, missed diagnosis rates, and relationship with shapes using computed tomography (CT). Two hundred cases of axial CT images performed for maxillofacial trauma were reviewed. The incidence, correct, and missed diagnosis rates of anterior nasal spine fractures were studied. The relationship between the fracture and the shape of the anterior nasal spine was also analyzed. The rate of anterior nasal spine fractures was 22.00% (44 of 200). The diagnostic accuracy was 4.55% (2 of 44) and the missed diagnosis rate was 95.45% (42 of 44). The fracture rates of the double rod, single rod, triangle, and irregular anterior nasal spine were 33.85% (22 of 65), 32.26% (10 of 31), 12.24% (12 of 98), and 0.00% (0 of 6), respectively. The double and single rod types of anterior nasal spine were most likely to be fractured than the type of triangle (χ2 = 11.05, 6.67, P < .0167). No fracture was found in the irregular type of anterior nasal spine. Anterior nasal spine fractures are not rare and the high missed diagnostic rate results from unfamiliarity with the structure. Double and single rod types of anterior nasal spines are easy to fracture. Bony reconstruction and thin thickness of CT images are necessary for diagnosis.

The Mathematics of the Viereckschanzen of the La Tène Culture

The development of script-using ancient civilizations and their achievements in sciences such as astronomy and mathematics have been well researched. Illiterate cultures were able to attain an adequate level of knowledge and transferred this knowledge to succeeding generations via oral tradition and mnemonic artefacts. The constructions of the square ditched enclosures (Viereckschanzen) of the last phase of the La Tene period (LT D, 150-1 BC) are documentations of the mathematical knowledge of this culture and served as a kind of mnemonic artefact. The constructions comprise the application of Pythagorean theorem (in terms of Pythagorean triangles) and square-root approximation triangles. Via these types of triangles, convex quadrangles are constructed (i.e., trapezium, parallelogram, rectangle, kite, lozenge, and square). The constructions were laid out in the terrain on the basis of a consistent ‘Babylonian/Egyptian’ metrology.

Identifying hazardous obstructions within an intersection using unmanned aerial data analysis

Intersections are places where two or more roadways intersect with one another. Federal Highway Administration (FHWA) quoted that more than fifty percent of crashes occur at or near intersections. An at-grade intersection is more accident prone compared to grade separated intersections. Intersection-related crashes are almost 335-times more likely to occur as compared to non-intersection-related crashes caused by vehicles turned with obstructed views. Approach and departure sight triangles are two types of sight triangles that are considered to provide clear visibility for drivers entering and exiting an intersection. Presently, there is no common practice followed by transportation or public work agencies other than considering accident history and public complaints as indicators for the need to improve intersection conditions. This approach warrants a safe and rapid methodology that can effectively identify obstructions within the intersection sight triangles. Unmanned aerial vehicles coupled with close range photogrammetry (UAV-CRP) technology offers a safe, quick, and efficient alternative for obstruction identification compared to traditional methods. In this study, a UAV based methodology is developed to identify obstructions in intersections from the 3-dimensional models developed using the imagery collected from unmanned aerial surveys. Two case studies including a T-intersection and a railroad crossing were considered to demonstrate the developed methodology. This research successfully validated the developed UAV methodology by analyzing departure sight triangles at T-intersection and approach sight triangles at railroad crossing. It is expected to be applied in many other civil engineering applications that are deemed critical due to the presence of obstructions and can potentially save human lives.

Path integration in large-scale space and with novel geometries: Comparing vector addition and encoding-error models.

Path integration is thought to rely on vestibular and proprioceptive cues yet most studies in humans involve primarily visual input, providing limited insight into their respective contributions. We developed a paradigm involving walking in an omnidirectional treadmill in which participants were guided on two sides of a triangle and then found their back way to origin. In Experiment 1, we tested a range of different triangle types while keeping the distance of the unguided side constant to determine the influence of spatial geometry. Participants overshot the angle they needed to turn and undershot the distance they needed to walk, with no consistent effect of triangle type. In Experiment 2, we manipulated distance while keeping angle constant to determine how path integration operated over both shorter and longer distances. Participants underestimated the distance they needed to walk to the origin, with error increasing as a function of the walked distance. To attempt to account for our findings, we developed configural-based computational models involving vector addition, the second of which included terms for the influence of past trials on the current one. We compared against a previously developed configural model of human path integration, the Encoding-Error model. We found that the vector addition models captured the tendency of participants to under-encode guided sides of the triangles and an influence of past trials on current trials. Together, our findings expand our understanding of body-based contributions to human path integration, further suggesting the value of vector addition models in understanding these important components of human navigation.

Estimate the number of triangles in real-world graph streams

Estimating the number of triangles in the graph streams is the basis of data mining, which aims to design an efficient graph stream algorithm to estimate the number of triangles in graph. Real-world graph is a multi-layer graph encompassing multiple distinct types of connectivity. The state-of-the-art approaches that counting triangles mainly focus on a general graph and cannot be applied for multi-layer graph, since duplicated edges across different layers exist. In this paper, we give the concept of several triads and triangles under the multilayer network, which truly reflect the real-world network topology. And we design a new two-stage sample algorithm based on reservoir sampling and triad sampling under real-world graph streams which solve the problem of more data brought by multi-layer networks. The algorithm is also a one-pass algorithm, and it can calculate the number of all types of triangles at the same time. We analyze the expectation and variance of the estimations and show that the algorithm is unbiased and stable. Our experimental results demonstrate that algorithm has good time efficiency and accuracy.

Review design of wind load analysis structures guyed tension in the Bogor repeater radio frequency antenna towers

The purpose of this study is to analyze the wind load on the Repeater Radio Frequency (RRF) antenna tower, the wind load is viewed from an angle of 0° to the towing cable to the largest angle on the two types of antenna towers, triangle and rectangular. Both types will produce different wind loads so that we can find out which load is the biggest from a combination of wind directions. The research method is by empirical analysis, calculating the wind load alone while other loads are not counted. As a result of wind loads, the tension cable and load direction correspond to each section and then the resultant values of force and direction will arise. And finally, the force is changed to lift and the anchor will hold the force. The results; The use of triangle antenna towers is more beneficial, especially the wind load that occurs is smaller, thus the construction costs are also smaller. The lifting power of a triangle antenna anchor tower is lighter around 1393.971N or 1.393971kN than that of a square antenna anchor tower lift of around 1971.373N or 1.971373kN.

A ROBÓTICA COMO UM INSTRUMENTO FACILITADOR DE ENSINO:UMA APLICAÇÃO NO ESTUDO DE TRIÂNGULOS

Robotics currently occupies a prominent position in the educational scenario, used as a new teaching methodology, it is inserted in many schools. As this is a new technology investment tends to be high and consequently there are still schools that did not have access to this method. With this in mind, our goal was to propose a project that combines low cost and yet provides a great benefit in student learning. Our work was developed following the Free Robotics methodology that uses the Arduino UNO board, as it is a low cost material and easy to work. The constructed project will have the following functions: read the three-segment measurement using an ultrasonic sensor (HC-SR04), verify whether or not these measurements form a triangle, and form, classify the triangle's type, calculate its perimeter, its area and finally also provide the values of the internal angles of the triangle.

Types of triangle in Hamiltonian triangulations and an application to domination and k-walks

We investigate the minimum number t0(G) of faces in a Hamiltonian triangulation G so that any Hamiltonian cycle C of G has at least t0(G) faces that do not contain an edge of C. We prove upper and lower bounds on the maximum of these numbers for all triangulations with a fixed number of facial triangles. Such triangles play an important role when Hamiltonian cycles in triangulations with 3-cuts are constructed from smaller Hamiltonian cycles of 4-connected subgraphs. We also present results linking the number of these triangles to the length of 3-walks in a class of triangulation and to the domination number.

Multiple solution problems and mathematical thinking: Wasan geometry example

Wasan geometry flourished in Edo period of Japan as arty, multiple solutioned and systematic. Teachers are not open and papers are not evaluated. Multiple solutions are seen in parallel with advanced mathematics thinking. 80 middle school and 37 high school pre service math teachers were given a Wasan problem and grouped according to correct answers, different answers, and originality. 24 different answers (equality of diagonals of a square, symmetry, equality of tangent lines, auxiliary lines and auxiliary shapes, cosines’ theorem, tan (67.5), similarities, types of triangles etc.) were detected. Answers were also coded for composite answers (who include two different rules), or simple one ways, first answers, similar solution ways and 5-6 different solutions.

The effect of aperture shape, angle of incidence and polarization on shielding effectiveness of metallic enclosures

Apertures and slots of the enclosures come into prominence for heat allocation, ventilation, I/O cable, etc. These slots and apertures induce the coupling route of electromagnetic interference (EMI) from the inside to outside. So, electromagnetic shielding is usually used to decrease the emissions or to the progress of equipment immunity. In this paper, an effect of an aperture shape on the performance of electrical shielding effectiveness has been investigated by means of simulation. Rectangular, square, circular, equilateral triangle and hexagonal shape apertures that have a constant area of 5625 mm2 have been studied in addition to polarization type of applied electromagnetic field. It has been observed that ESE depends on the electric field direction and plane wave polarization and rectangular shape aperture has more effective ESE performance than square, circular, equilateral triangle and hexagonal type apertures. Rectangular shaped aperture has approximately 43 dB better performance than equilateral triangle one for whole frequency band of 100 MHz to 1GHz. Rectangular, square, circular, hexagonal and equilateral triangle type apertures have been ranked from best performance to the worst with respect to their ESE. There have been considerable findings that can be useful for enclosure designers about the effect of angle of incidence and polarization angle.

Complete flat cone metrics on punctured surfaces

We prove that each complete flat cone metric on a surface with regular or irregular punctures can be triangulated with finitely many types of triangles. We derive the Gauss-Bonnet formula for this kind of cone metrics. In addition, we prove that each free homotopy class of paths has a geodesic representative.

Misconception of triangle concept through epistemological mathematics belief

Triangle topics have been studied since preschool. However, there are still pre-services teachers who do not understand the triangle concept. This descriptive qualitative study aims to trace the understanding of the base and the altitude of the triangle concept. A total of 30 pre-service teachers of elementary school were assigned to solve the problem on the triangle topic. Futhermore, an interview was conducted to explore the subject’s understanding of the triangle concept. The results revealed that the base of the triangle was understood as the horizontal side of the triangle, located at the bottom or one of the longest sides of the triangle. The altitude of the triangle was an vertical side of the right triangle or a distance between the base of the triangle and the vertex before it. Misconception of triangle concept was due to the given examples of triangles limited to the right triangle, the equilateral triangle, and the isosceles of triangle. Varying samples which represent all types of triangles and varied problem will build the understanding concept of the base and altitude of the triangle correctly.

Целочисленные треугольники, уравнение Пелля и многочлены Чебышева

In this paper we consider some types of integer triangles: “almost equilateral”, rectangular “almost isosceles”, rectangular “whose angle is almost 300”. The description is reduced to Pell’s equation. We state the theory of Pell’s equation on the basis of an “iterated matrix”. Powers of this matrix are expressed in terms of Chebyshev polynomials.

Two Pentavanadate-based Organic-inorganic Materials with Third-order NLO Properties

Two isolated organic-inorganic pentavanadate-based hybrids, \({\rm[H_2N(CH_3)_2]_{6.34}[V^V(\mu_3-O)_4V^{IV}_4O_5(SO_4)_4]\cdot(SO_4)_{0.67}\cdot(DMF)\cdot[HN(CH_3)_2]_{1.66}}\)(1) and [(HN)2(CH2)2(CH3)4][VV(μ3-O)4V4IVO5(SO4)4][H2N(CH3)2]3·(DMF)· [HN(CH3)2]0.5(2)(DMF=N,N-dimethylformamide) have been synthesized under solvothermal conditions and structu-rally characterized. In compound 1, three adjacent basic units form a triangle type cluster. The symmetric double-layer exists in compound 2. The study of the third-order nonlinear optical(NLO) properties for the two compounds demonstrates that the two-photon absorption(TPA) cross-section σ values of compounds 1 and 2 are 1372 and 1228 GM, respectively, indicating that both compounds may have potential application in optical field.

Delaunay mesh simplification with differential evolution

Delaunay meshes (DM) are a special type of manifold triangle meshes --- where the local Delaunay condition holds everywhere --- and find important applications in digital geometry processing. This paper addresses the general DM simplification problem: given an arbitrary manifold triangle mesh M with n vertices and the user-specified resolution m (&lt; n ), compute a Delaunay mesh M * with m vertices that has the least Hausdorffdistance to M. To solve the problem, we abstract the simplification process using a 2D Cartesian grid model, in which each grid point corresponds to triangle meshes with a certain number of vertices and a simplification process is a monotonic path on the grid. We develop a novel differential-evolution-based method to compute a low-cost path, which leads to a high quality Delaunay mesh. Extensive evaluation shows that our method consistently outperforms the existing methods in terms of approximation error. In particular, our method is highly effective for small-scale CAD models and man-made objects with sharp features but less details. Moreover, our method is fully automatic and can preserve sharp features well and deal with models with multiple components, whereas the existing methods often fail.

Two-dimensional tessellation by molecular tiles constructed from halogen\u2013halogen and halogen\u2013metal networks

Molecular tessellations are often discovered serendipitously, and the mechanisms by which specific molecules can be tiled seamlessly to form periodic tessellation remain unclear. Fabrication of molecular tessellation with higher symmetry compared with traditional Bravais lattices promises potential applications as photonic crystals. Here, we demonstrate that highly complex tessellation can be constructed on Au(111) from a single molecular building block, hexakis(4-iodophenyl)benzene (HPBI). HPBI gives rise to two self-assembly phases on Au(111) that possess the same geometric symmetry but different packing densities, on account of the presence of halogen-bonded and halogen–metal coordinated networks. Sub-domains of these phases with self-similarity serve as tiles in the periodic tessellations to express polygons consisting of parallelograms and two types of triangles. Our work highlights the important principle of constructing multiple phases with self-similarity from a single building block, which may constitute a new route to construct complex tessellations.

Deepening students understanding of triangle topic through ‘application’ component of ELPSA (Experience, Language, Pictorial, Symbol and Application) framework

ELPSA (Experience, Language, Pictorial, Symbol and Application) is a learning framework that was introduced as a sequence of a learning process which presents mathematical ideas through lived experience, mathematical conversation, visual stimuli, symbolic notation and the application of applied knowledge. Employing the “application” component of ELPSA framework in the mathematics classroom emphasizes how the understanding of certain material can be applied to a new situation. This study investigates the learning process during the class activity about the triangle. The study was conducted in one of the junior high school in Central Lombok, West Nusa Tenggara. The data were collected from teaching and learning videos and students’ work during the learning processes in the classroom. We transcribed and analysed the video as well as looked at the students’ works. The result shows that the activity of composing a 2D shape from various types of triangle support students in deepening their understanding about the types of triangles. Also, the activity of composing 2D shape can be a promising foreground for students in their following learning about the area of the composite figure.