This work, structured in two main parts, is devoted to the parabola topic. In the first, the elements of a parabola are reviewed by linking the definition of intersection of a plane and a cone with a ...locus of the plane. The necessary transformations for the calculation of the elements as a curve in space are pointed out as well as historical notes and properties of light are included. In the second part, the applications in teaching at a high school level or university courses are explained. A project based on the reflection of light is proposed that seeks to connect various subjects in line with the new educational paradigm of development of key competencies, joining different fields of knowledge. For university courses, applications of linear algebra are obtained in the establishment of relationships between analytical geometry in the rotation and translation of planes, and the dihedral system that is taught in technical drawing subjects. As a conclusion, it is obtained that the teaching of the parabola from different approaches allows a complete learning of diverse fields of knowledge, even of different topics of mathematics, an essential factor in the development of thought at any educational level.
It was shown by J. C. Langer and D. A. Singer in their influential 2007 paper 5 that real algebraic curves can be interpreted as trajectories of meromorphic quadratic differentials defined on ...appropriate Riemann surfaces. The goal of this note is to suggest a more elementary approach to this problem that is based on the classical complex analysis. To demonstrate how our approach works, we apply it to the simplest non-trivial case of real algebraic curves; i.e. to conics.
Area between a parabola and two tangent lines de la Rosa, Félix Martínez
International journal of mathematical education in science and technology,
10/2021, Letnik:
52, Številka:
9
Journal Article
Recenzirano
The goal of this note is to obtain the area enclosed between a parabola and two tangent lines using visual arguments. The first step that we have to follow, in order to do that, is noticing that the ...area between a parabola and a tangent line only depends on the leading coefficient of the quadratic function of the parabola. Finally, the intersection of two parabolas with the vertices on x-axis and equal leading coefficients is the key to obtain the result.
The experimental proof that near-field radio communication channels based on orbital angular momentum (OAM) are naturally isolated is presented. In near-field zone, we show that two antennas, built ...for producing a beam with the same value of OAM, have a good throughput. On the other hand, antennas of different types, i.e., built for generating beams with different OAM values, including a standard l = 0 antenna, exhibit a good modal isolation .
ABSTRAKPada studi ini dilakukan analisis penambahan batang metal berbentuk persegi di dalam feed horn piramida antena reflektor parabola untuk meningkatkan performansi gain, beamwidth dan side lobe ...level. Kebutuhan utama antena radar maritim adalah memiliki gain yang besar ≥ 27 dB, beamwidth kecil ≤ 2o, dan side lobe level yang rendah ≤ -30 dB. Oleh karena itu, perlu diajukan teknik desain antena parabola dengan penambahan batang metal berbentuk persegi di dalam feed horn piramida untuk meningkatkan performasi gain, beamwidth dan side lobe level. Hasilnya dapat meningkatkan gain antena reflektor parabola menjadi 36,9 dB, memperkecil beamwidth menjadi 1,9o dan menekan side lobe level menjadi 31,4 dB. Hasil studi ini mengkonfirmasi bahwa teknik desain dengan menambahkan batang metal persegi di dalam feed horn piramida antena reflektor parabola dapat meningkatkan performasi gain, beamwidth dan side lobe level lebih baik dibandingkan desain tanpa penambahan batang metal persegi.Kata kunci: antena parabola, feed horn piramida, antena radar maritim, gain ABSTRACTIn this study, an analysis of the addition of square-shaped metal rods was carried out in the pyramid feed horn of a parabolic reflector antenna to increase gain, beamwidth and side lobe level performance. The main requirement for a maritime radar antenna is to have a large gain ≥ 27 dB, a small beamwidth of ≤ 2o, and a low side lobe level of ≤ -30 dB. Therefore, it is necessary to propose a parabolic antenna design technique with the addition of a rectangular metal rod inside the pyramidal feed horn to improve gain, beamwidth and side lobe level performance. The result can increase the gain of the parabolic reflector antenna to 36.9 dB, reduce the beamwidth to 1.9o and suppress the side lobe level to 31.4 dB. The results of this study confirm that the design technique by adding a square metal rod in the pyramid feed horn of a parabolic reflector antenna can improve gain, beamwidth and side lobe level performance better than the design without the addition of square metal rods.Keywords: parabolic antenna, pyramid feed horn, maritime radar antenna, gain
In this paper, the nonlinear vibration and dynamic buckling responses of the sinusoid, parabola, and cylindrical CNT-reinforced panels with piezoelectric layer stiffened by a CNT-reinforced stiffener ...system in uniform temperature change with a piezoelectric layer are presented. An improved homogenization technique for the x- or y-direction CNT-reinforced stiffener system is utilized to determine the total stiffnesses of the considered structures. The higher-order shear deformation theory (HSDT) in conjunction with the von Kármán nonlinearities is adopted to formulate the motion equations, while the stress function for complex curvature panels is estimated using the like-Galerkin procedure. The nonlinear equation of motion is acquired by utilizing the Lagrange function and Euler-Lagrange's equations. The numerical examples use the Runge-Kutta technique to acquire the nonlinear time-amplitude curves, and the critical dynamic buckling load is determined using the Budiansky-Roth criterion. These examples evaluate the effects of stiffeners, piezoelectric layer, material, and geometrical parameters on the nonlinear vibration and dynamic buckling responses of the panels.
•Nonlinear dynamic responses of the CNT-reinforced stiffened panels are studied.•Sinusoid, parabola, and cylindrical panels with piezoelectric layer are mentioned.•The improved smeared stiffener technique for CNT-reinforced stiffeners is presented.•The like-Galerkin procedure is applied to estimate the approximate stress function.•HSDT, Euler-Lagrange's equation, and Runger-Kutta method are used.
This paper further explores multiple discrete-continuous extreme value (MDCEV) models. MDCEV models are widely used for time-use analysis because they can accommodate the diminishing marginal utility ...with respect to time consumption and benefit from simple closed-form likelihood expressions for estimation, while considering the overall constraints of time resource. However, all of the existing models adopt a monotonically increasing form of utility function, which does not accommodate possible non-monotonic utilities with respect to time-use. This paper further develops the MDCEV model by firstly introducing utility functions with a form of parabola to capture non-monotonic preferences in time allocation behaviors. A corresponding simple and computationally efficient forecasting algorithm to predict the time-use of individuals is also developed. The proposed MDCEV model with parabolic utilities is applied to analyze time-use decisions among a variety of outdoor non-mandatory activities on weekends using data from the 2019 American Time Use Survey. The proposed model is compared with traditional MDCEV models to show its ability to describe non-monotonic preferences in time-use in association with various explanatory variables. This paper makes an initial attempt to specify non-monotonic utilities for time-use analysis, but further studies are required to develop more sophisticated non-monotonic utility formulation to improve the goodness-of-fit of the model.
The compressive resistance of concrete in new structures is usually characterized on the basis of tests performed on concrete cylinders or cubes under relatively rapid loading conditions. Although ...efficient for material characterization, these tests do not acknowledge a number of phenomena potentially influencing the compressive resistance of concrete in actual structures. For this reason, when performing a structural analysis, strength reduction factors are usually considered in codes of practice modifying the uniaxial strength of material tests. In this paper, a detailed investigation of the influence of material brittleness and internal stress redistributions on the structural response of reinforced concrete members is presented. This work is based on a number of theoretical considerations and supported by the experimental results of more than 400 reinforced concrete columns tested with or without eccentricity and gathered from the literature. The results show the pertinence of considering a brittleness factor in the calculation of the structural resistance of reinforced concrete columns and compression zones of beams. The results of this work are eventually formulated in terms of code‐like proposals, currently considered in the draft of the new Eurocode 2 (prEN 1992‐1‐1:2018).
La investigación en Educación Matemática suele centrarse en compartir los resultados de la aplicación de instrumentos de obtención de información. Si bien dichos instrumentos suelen describirse en la ...sección de metodología, el proceso de su desarrollo no suele ser muy transparente para el lector. En esta investigación el objetivo es abordar dicha problemática y describir con todo detalle el proceso de generación de un cuestionario, basado en el modelo MTSK, para la exploración del conocimiento del profesor acerca de la parábola, entendida como cónica. Se presenta el diseño de un instrumento de carácter cualitativo que permite hacer una aproximación al conocimiento matemático del profesor acerca de la parábola, poniendo énfasis tanto en el uso de la teoría, como de la triangulación, interna y externa, como elementos clave en el diseño metodológico. El principal aporte fue determinar pautas para el diseño de cuestionarios basados en el modelo MTSK, las cuales pueden ser tomadas en cuenta al margen de los contenidos matemáticos.
•The influence of the parameters of the spherical and aspheric MLAs on the luminance efficiencywe were investigated. High fill factor parabola curve MLAs was introduced to improve the light ...out-coupling efficiency of OLED.•Geometric ray tracing was employed to investigate and optimize the tructure parameters of spherical and aspheric MLAs, such as the curved profile, the base shape, the fill factor, the aspect ratio (the ratio of height to diameter), and the material refractive index of the MLAs.•The experimental results are consistent with the trend of the simulation results, and show that the maximum light out-coupling efficiency of OLED improvement is 49 %.
Aspheric microlens arrays (MLAs) are introduced on glass substrate to improve the light out-coupling efficiency (LOCE) of organic light-emitting diode (OLED). Geometric ray tracing was employed to simulate the improved effects and optimize the structure parameters of the MLAs pattern. The simulation results show that when the parameters of MLAs as follows, the curved profile is parabola, the base shape is hexagon, the fill factor is 1, the aspect ratio is 0.6, and the material refractive index should be match to that of the substrate of the OLED, which can improve LOCE maximum.
Poly-dimethyl-siloxane (PDMS) parabola curve MLAs films ware fabricated by maskless lithography technique and template replication. The experimental results show that the MLAs can improve the LOCE and the trends of the experimental results agree with the simulation results. A maximum increase of 49 % in the coupling efficiency was achieved.
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