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Botvynovska, Svitlana, Zhanetta Levina, and Hanna Sulimenko. "IMAGING OF A HYPERBOLIC PARABOLOID WITH TOUCHING LINE WITH THE PARABOLAL WRAPPING CONE." Management of Development of Complex Systems, no. 48 (December 20, 2021): 53–60. http://dx.doi.org/10.32347/2412-9933.2021.48.53-60.
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The paper is dedicated to architectural structures modeling by means of computer-graphics. Images on the monitor represent perspective. That’s why the images could be assessed from the most convenient points as viewer’s position is considered to be the perspective center. Non-rectilinear profile makes the structure the most impressive. The hyperbolic paraboloid surface is researched. Parabolas and hyperbolas are the only forms of its sections except for tangent planes cases. Parabolas as contact lines are reviewed. Hyperbolic paraboloid is an infinite surface that’s why only a portion of it could be modeled. Four link space zigzag ({4l} indicator) is its best representation. In such case the non-rectilinear profile should be represented as a curve of second order semicircular arc. Modeling of a limited section does not affect the final modeling because the {4l} representation makes the depiction of all surface in that frame of axis that have the identified hyperbolic paraboloid looks like a cone. The paper’s objective is development of imaging technique using parabolic contact lines to design hyperbolic paraboloid surface and applicable to several surfaces of the same construction. To do so, parameter analysis of the task is conducted, the applicable theory is identified, and the hyperbolic paraboloid imaging technique using the set profile line in the form of any curve of second order is conducted, namely the imaging technique for contact parabola and the set of hyperbolic paraboloids which it set forth. The set of plans that may contain the parabolic contact line set is two-parameter. However, in general, the position of those planes is remains unknown. Thus, the task is as follows: find the third point of the plane that intersects the given wrapping cone along the parabola when the two points are given. These two points must belong to the same forming line on the cone. The imaging requires 7 parameters whereas the hyperbolic paraboloid has 8 parameters. That’s why with one parabolic contact line and given wrapping cone of the second order one-parameter set of hyperbolic paraboloids could be imaged. The paper shows how to image the contact line if the profile line is given as a parabola, ellipse, or hyperbola. The portion of one hyperbolic paraboloid may imaged when the parameters are aligned and any other bisecant of same perspective line of shape. Two portions of parabola conjugated due to the joint wrapping cone hyperbolic paraboloid imaging is demonstrated.
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Zhu, Yuanchao, Dazhao Zhang, Yanlin Lai, and Huabiao Yan. "Shape adjustment of "FAST" active reflector." Highlights in Science, Engineering and Technology 1 (June 14, 2022): 391–400. http://dx.doi.org/10.54097/hset.v1i.493.
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Abstract. In this paper, the relevant working principle of "FAST" Chinese Eye is studied, and a mathematical model is established to solve the equation of the ideal paraboloid. The ideal paraboloid model is obtained by rotating the paraboloid around the axis in the two-dimensional plane. On this basis, the specific solutions of each question are discussed, and the parabolic equation, the receiving ratio of the feed cabin to the reflected signal, the numbering information and coordinates of the main cable node and other parameters are obtained. This paper for solving directly above the benchmark of spherical observation of celestial bodies when ideal parabolic equation, according to the geometrical optics to knowledge should be clear all the signals of the incoming signal after the ideal parabolic will converge to the focal point of basic rules, then through converting ideal parabolic model of ideal parabolic equation in a two-dimensional plane, An optimization model was established to minimize the absolute value of the difference between the arc length and the arc length of the parabola in the diameter of 300 meters. The known conditions were substituted into Matlab to solve the equation of the ideal parabola by rotating the parabola around the axis: . In order to determine the ideal paraboloid of the celestial body, a new spatial cartesian coordinate system is first established with the line direction between the celestial body and the spherical center as the axis, so that the observed object is located directly above the new coordinate system. The same model in question 1 is established to obtain the vertex coordinates of the ideal paraboloid at this time. Then the vertex coordinates are converted to the coordinates in the original space cartesian coordinate system by rotation transformation between space cartesian coordinate systems. The solution of its vertex coordinates (-49.5287, -37.0203, -294.1763).
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Acharya, Aviseka, Sonja Brungs, Yannick Lichterfeld, Jürgen Hescheler, Ruth Hemmersbach, Helene Boeuf, and Agapios Sachinidis. "Parabolic, Flight-Induced, Acute Hypergravity and Microgravity Effects on the Beating Rate of Human Cardiomyocytes." Cells 8, no. 4 (April 14, 2019): 352. http://dx.doi.org/10.3390/cells8040352.
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Functional studies of human induced pluripotent stem cell (hiPSC)-derived cardiomyocytes (hCMs) under different gravity conditions contribute to aerospace medical research. To study the effects of altered gravity on hCMs, we exposed them to acute hypergravity and microgravity phases in the presence and absence of the β-adrenoceptor isoprenalin (ISO), L-type Ca2+ channel (LTCC) agonist Bay-K8644, or LTCC blocker nifedipine, and monitored their beating rate (BR). These logistically demanding experiments were executed during the 66th Parabolic Flight Campaign of the European Space Agency. The hCM cultures were exposed to 31 alternating hypergravity, microgravity, and hypergravity phases, each lasting 20–22 s. During the parabolic flight experiment, BR and cell viability were monitored using the xCELLigence real-time cell analyzer Cardio Instrument®. Corresponding experiments were performed on the ground (1 g), using an identical set-up. Our results showed that BR continuously increased during the parabolic flight, reaching a 40% maximal increase after 15 parabolas, compared with the pre-parabolic (1 g) phase. However, in the presence of the LTCC blocker nifedipine, no change in BR was observed, even after 31 parabolas. We surmise that the parabola-mediated increase in BR was induced by the LTCC blocker. Moreover, the increase in BR induced by ISO and Bay-K8644 during the pre-parabola phase was further elevated by 20% after 25 parabolas. This additional effect reflects the positive impact of the parabolas in the absence of both agonists. Our study suggests that acute alterations of gravity significantly increase the BR of hCMs via the LTCC.
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Stojanov, V. V., S. J. Jgalli, and V. O. Stojanov. "THE CONSTITUENT ELEMENTS STRUCTURES COVERING OF HYPERBOLIC PARABOLOID." ACADEMIC JOURNAL Series: Industrial Machine Building, Civil Engineering 1, no. 48 (March 27, 2017): 54–61. http://dx.doi.org/10.26906/znp.2017.48.769.
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Hypar is a hyperbolic paraboloid representing translational ruled developable anti classical surface, i.e., the surface of negative Gaussian curvature. Shaping of the parabolic elements corresponds to buckling of the shell and the main tensile forces are arranged in the ascending direction of parabolas, and the main compression force - in the direction of the descending parabola. Composite materials are formed from the combination of two or more layered materials, each having very different properties. ANSYS Composite PrepPost software provides all the necessary functionality for the analysis of layered composite structures. The paper discloses a possibility of using for shell covering negative curvature. Design solutions into constituent elements structures and computations such structures are presented.
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Hayah, Ni, Bakri Mallo, and I. Nyoman Murdiana. "PROFIL PEMAHAMAN KONSEP MATEMATIKA DITINJAU DARI GAYA KOGNITIF FIELD INDEPENDENT (FI) DAN FIELD DEPENDENT (FD)." Aksioma 8, no. 2 (September 24, 2019): 137–50. http://dx.doi.org/10.22487/aksioma.v8i2.210.
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abstrak: Penelitian ini bertujuan untuk mendeskripsikan pemahaman konsep matematika siswa kelas XI SMA Negeri 2 Dampelas dalam menyelesaikan soal pada subpokok bahasan parabola ditinjau dari gaya kognitif Field Independent (FI) dan Field Dependent (FD). Jenis penelitian ini adalah penelitian kualitatif. Subjek dalam penelitian ini terdiri dari satu siswa yang bergaya kognitif FI dan satu siswa yang bergaya kognitif FD. Hasil dari penelitian ini yaitu saat menyajikan masalah, subjek FI dan FD menuliskan hal-hal yang diketahui dan ditanyakan. Selanjutnya dalam mengklasifikasi unsur-unsur parabola, subjek FI mengelompokkan unsur-unsur parabola menurut bentuk parabolanya yaitu parabola horizontal terbuka ke kanan. Kemudian dalam memberi contoh dan non-contoh pada setiap unsur-unsur parabola, subjek FI memberikan contoh dan non-contoh dari setiap unsur-unsur parabola yang diberikan. Kemudian menyajikan masalah persamaan parabola dalam representasi matematis, subjek FI dan subjek FD menyajikan persamaan parabola kedalam bentuk persamaan umum parabola. Kemudian menggunakan, memanfaatkan dan memilih prosedur tertentu dalam menentukan persamaan parabola, subjek FI menggunakan dan memilih persamaan umum parabola horizontal dan subjek FD menggunakan persamaan umum parabola walaupun subjek tidak mengetahui jenis persamaan umum parabola yang digunakan. Kemudian subjek FI menjelaskan kembali prosedur yang digunakan serta memberikan alasannya dengan menggunakan bahasanya sendiri dan subjek FD menjelaskan kembali prosedur yang digunakan walaupun dalam proses penyelesaiannya siswa belum memahami dengan baik langkah-langkah yang harus digunakan.
Kata Kunci: Profil; Pemahaman konsep matematika; Parabola;
abstract: This study aims to describe the understanding of mathematical concepts of class XI students of SMA 2 Dampelas in solving problems on the subject of the parabolic discussion reviewed from cognitive style of the Independent Field (FI) and Field Dependent (FD). This type of research is qualitative research. The subjects in this study consisted of one student who was in the cognitive style of FI and one student in the cognitive style of FD. The results of this study are when presenting a problem, FI and FD subject write things that are known and asked. Furthermore, in classifying parabolic elements, FI subjects classify parabolic elements according to their parabolic forms, namely horizontal parabola open to the right. Then in giving examples and non-examples of each parabolic element, the FI subject gives examples and non-examples of each parabolic element given. Then presenting the problem of parabolic equations in mathematical representations, the subject FI and subject FD present the parabolic equation in the form of a general parabolic equation. Then using, utilizing and selecting a particular procedure in determining the parabolic equation, FI subject uses and selects the general horizontal parabolic equation and the FD subject uses the general parabolic equation even though the subject does not know the type of general parabolic equation used. Then the FI subject explains the procedure used again and gives the reason using its own language and the FD subject explains the procedure used even though in the process of completion students do not understand the steps that must be used properly.
Keywords: Profile; Understanding of mathematical concepts; Parabolic
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Wang, Yanbo, Yingchang Xiong, Jianming Hao, Jiaqi He, Yuchi Liu, and Xinpeng He. "Active Control Model for the “FAST” Reflecting Surface Based on Discrete Methods." Symmetry 14, no. 2 (January 27, 2022): 252. http://dx.doi.org/10.3390/sym14020252.
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Radio telescopes are important for the development of society. With the advent of China’s Five-hundred-meter Aperture Spherical radio Telescope (FAST), adjusting the reflector panel to improve the reception ability is becoming an urgent problem. In this paper, an active control model of the reflector panel is established that considers the minimum sum of the radial offset of the actuator and the non-smoothness of the working paraboloid. Using the idea of discretization, the adjusted position of the main cable nodes, the ideal parabolic equation, and the expansion of each actuator are obtained by inputting the elevation and azimuth angle of the incident electromagnetic wave. To find the ideal parabola, a univariate optimization model is established, and the Fibonacci method is used to search for the optimal solution h=−0.33018 (offset in the direction away from the sphere’s center) and the focal diameter ratio f=0.4671 of the parabolic vertex. The ideal two-dimensional parabolic equation is then determined as x2−555.25z−166757.2=0, and the ideal three-dimensional paraboloid equation is determined to be z=(x2+y2)/555.25−300.33018. Moreover, the amount of the nodes and triangular reflection panels are calculated, which were determined to be 706 and 1325, respectively. The ratio reception of the working paraboloid and the datum sphere are 9.434% and 1.3898%, respectively. The latter is calculated through a ray tracing simulation using the optical system modeling software LightTools.
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Tang, Hongxin. "Parabolic Detection Algorithm of Tennis Serve Based on Video Image Analysis Technology." Security and Communication Networks 2021 (November 29, 2021): 1–9. http://dx.doi.org/10.1155/2021/7901677.
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At present, the existing algorithm for detecting the parabola of tennis serves neglects the pre-estimation of the global motion information of tennis balls, which leads to great error and low recognition rate. Therefore, a new algorithm for detecting the parabola of tennis service based on video image analysis is proposed. The global motion information is estimated in advance, and the motion feature of the target is extracted. A tennis appearance model is established by sparse representation, and the data of high-resolution tennis flight appearance model are processed by data fusion technology to track the parabolic trajectory. Based on the analysis of the characteristics of the serve mechanics, according to the nonlinear transformation of the parabolic trajectory state vector, the parabolic trajectory starting point is determined, the parabolic trajectory is obtained, and the detection algorithm of the parabolic service is designed. Experimental results show that compared with the other two algorithms, the algorithm designed in this paper can recognize the trajectory of the parabola at different stages, and the detection accuracy of the parabola is higher in the three-dimensional space of the tennis service.
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Sharma, N. K., Ashok Kumar Mishra, and P. Rajgopal. "Design of Low-Cost Solar Parabolic Through Steam Sterilization." International Journal of Biomedical and Clinical Engineering 10, no. 1 (January 2021): 50–60. http://dx.doi.org/10.4018/ijbce.2021010104.
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The objective of this study is to develop a low cost solar parabolic trough that can be used for steam sterilization of medical instruments in small clinics where electricity is scarce and expensive. On the basis of theoretical concepts of parabola and focus-balanced parabola, the assembly of ribs and reflector sheet with evacuated tube and heat pipe has been done. The parabolic trough has been mounted on a trolley so that it can be moved easily according to direction of sun light. The designed solar parabolic trough was integrated with pressure cooker under various setups and experiments were conducted to test whether sterilization is taking place or not. To validate sterilization process, tests were also conducted by placing the infected medical instruments. The solar parabolic trough developed was able to generate and maintain steam at 121 degrees Celsius at pressure 15 psig (101.3 kN/m2) for 15 minutes. The solar parabolic trough developed was effective in sterilizing the medical instruments.
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Stavek, Jiri. "Newton’s Parabola Observed from Pappus’ Directrix, Apollonius’ Pedal Curve (Line), Newton’s Evolute, Leibniz’s Subtangent and Subnormal, Castillon’s Cardioid, and Ptolemy’s Circle (Hodograph) (09.02.2019)." Applied Physics Research 11, no. 2 (February 25, 2019): 30. http://dx.doi.org/10.5539/apr.v11n2p30.
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Johannes Kepler and Isaac Newton inspired generations of researchers to study properties of elliptic, hyperbolic, and parabolic paths of planets and other astronomical objects orbiting around the Sun. The books of these two Old Masters “Astronomia Nova” and “Principia…” were originally written in the geometrical language. However, the following generations of researchers translated the geometrical language of these Old Masters into the infinitesimal calculus independently discovered by Newton and Leibniz. In our attempt we will try to return back to the original geometrical language and to present several figures with possible hidden properties of parabolic orbits. For the description of events on parabolic orbits we will employ the interplay of the directrix of parabola discovered by Pappus of Alexandria, the pedal curve with the pedal point in the focus discovered by Apollonius of Perga (The Great Geometer), and the focus occupied by our Sun discovered in several stages by Aristarchus, Copernicus, Kepler and Isaac Newton (The Great Mathematician). We will study properties of this PAN Parabola with the aim to extract some hidden parameters behind that visible parabolic orbit in the Aristotelian World. In the Plato’s Realm some curves carrying hidden information might be waiting for our research. One such curve - the evolute of parabola - discovered Newton behind his famous gravitational law. We have used the Castillon’s cardioid as the curve describing the tangent velocity of objects on the parabolic orbit. In the PAN Parabola we have newly used six parameters introduced by Gottfried Wilhelm Leibniz - abscissa, ordinate, length of tangent, subtangent, length of normal, and subnormal. We have obtained formulae both for the tangent and normal velocities for objects on the parabolic orbit. We have also obtained the moment of tangent momentum and the moment of normal momentum. Both moments are constant on the whole parabolic orbit and that is why we should not observe the precession of parabolic orbit. We have discovered the Ptolemy’s Circle with the diameter a (distance between the vertex of parabola and its focus) where we see both the tangent and normal velocities of orbiting objects. In this case the Ptolemy’s Circle plays a role of the hodograph rotating on the parabolic orbit without sliding. In the Plato’s Realm some other curves might be hidden and have been waiting for our future research. Have we found the Arriadne’s Thread leading out of the Labyrinth or are we still lost in the Labyrinth?
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Petkov, Emiliyan G. "Development and Implementation of NURBS Models of Quadratic Curves and Surfaces." Serdica Journal of Computing 3, no. 4 (January 11, 2010): 425–48. http://dx.doi.org/10.55630/sjc.2009.3.425-448.
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This article goes into the development of NURBS models of quadratic curves and surfaces. Curves and surfaces which could be represented by one general equation (one for the curves and one for the surfaces) are addressed. The research examines the curves: ellipse, parabola and hyperbola, the surfaces: ellipsoid, paraboloid, hyperboloid, double hyperboloid, hyperbolic paraboloid and cone, and the cylinders: elliptic, parabolic and hyperbolic. Many real objects which have to be modeled in 3D applications possess specific features. Because of this these geometric objects have been chosen. Using the NURBS models presented here, specialized software modules (plug-ins) have been developed for a 3D graphic system. An analysis of their implementation and the primitives they create has been performed.
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Pathan, Alex. "Euler’s and Barker’s equations: A geometric derivation of the time of flight along parabolic trajectories." Mathematical Gazette 92, no. 523 (March 2008): 39–49. http://dx.doi.org/10.1017/s0025557200182506.
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The parabolic orbit is rarely found in nature although the orbits of some comets have been observed to be very close to parabolic. The parabola is of interest mathematically because it represents the boundary between the open and closed orbit forms. An object moving along a parabolic path is on a oneway trip to infinity never being able to retrace the same orbit again. The velocity of such an object is the escape velocity and its total energy is zero.
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Chiuini, Michele. "The parabola of the parabolic arch." IABSE Symposium Report 104, no. 10 (May 13, 2015): 1–7. http://dx.doi.org/10.2749/222137815815775439.
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SANDI, EFRI, AODAH DIAMAH, and ARDI IMAM SANTOSO. "Desain Antena Reflektor Parabola untuk Aplikasi Radar Maritim dengan Rekayasa Feed Horn." ELKOMIKA: Jurnal Teknik Energi Elektrik, Teknik Telekomunikasi, & Teknik Elektronika 11, no. 2 (April 17, 2023): 451. http://dx.doi.org/10.26760/elkomika.v11i2.451.
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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
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Li, Jianhe, Honggang Li, Xiaoguang Guo, Renke Kang, and Shang Gao. "Effect of Wheel Path in Raster Grinding on Surface Accuracy of an Off-Axis Parabolic Mirror." Applied Sciences 13, no. 19 (October 9, 2023): 11096. http://dx.doi.org/10.3390/app131911096.
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Off-axis parabolic mirrors have extensive applications in X-ray optics, with the precision of their curvature directly impacting grazing-incidence focusing performance. Notably, the off-axis parabolic surface has non-rotating and non-symmetrical characteristics. Ultra-precision raster grinding utilizing a diamond wheel is a common method. Crucially, establishing an optimal wheel path stands as the key to ensuring surface accuracy during off-axis paraboloid grinding. In this study, according to the double curvature property of an off-axis parabolic surface, two different wheel paths were compared: one tracing the meridian direction (parabolic generatrix) and the other following the arc vector direction (arc). The results showed that the wheel path in raster grinding stepping along the arc vector direction can obtain a smaller scallop height and higher surface accuracy. The surface accuracy of one step along the arc vector direction is 9.6 μm, and that of the other step along the meridian direction is 32.6 μm. A model of the scallop height was established based on the relative relationship between adjacent wheel paths, and the error is within 5%. According to the correlation between scallop height and shape error, we conducted an analysis of the spatial distribution of shape errors under varying wheel paths. The wheel path that steps along the arc vector is more suitable for raster grinding of the off-axis paraboloid. The above study can provide theoretical guidance for the wheel path planning of off-axis parabolic mirrors with high surface accuracy.
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Schruth, David M. "Parabolic completions in gibbon duets may signal appreciation of projectile motion." Journal of the Acoustical Society of America 152, no. 4 (October 2022): A71. http://dx.doi.org/10.1121/10.0015580.
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Most gibbon species produce salient duet calls at daybreak. Duets start with low frequency barks by males, followed by the female great call, and end with a short, and often complex, male-dominated coda. The female great call itself typically climaxes via a crescendoing increase in pitch, tempo, or both and characteristically features bilaterally symmetrical parabolic structures, which can manifest both in the distribution of vocal units over time as well as in frequency. Male codas appear to anticipate and even complete many of these female-initiated parabolas. Employing spectrograms of species-typical great calls from nearly all gibbon species ( n = 12), I plotted coordinates of the upper-most frequency of each vocal unit. Using these x = time and y = frequency coordinates (plus x-differences), I tabulated the parabolas with the best possible second order polynomial fits for each species’ great call. Measures of parabolic fit for each call were then compared to quantitative locomotor estimates for each species. All forms of parabolic assessment had positive correlations with leaping bout percentages across species. These results indicate that gibbon duets may function to signal a fundamental understanding of parabolic shapes—presumably useful in landing airborne locomotor (especially leaping) bouts spanning canopy elements—enabling concordant execution of arboreally projectile acrobatics.
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Naufal, Muhamad, Tannie Wiyuna, Annisa Deutschlant Bintarum, and Ahmad Fakhri Burhanudin. "Desain Simulasi Gerak Parabola Sebagai Pemanfaatan Pembelajaran Fisika SMA Kelas X Menggunakan Pygame." Mitra Pilar: Jurnal Pendidikan, Inovasi, dan Terapan Teknologi 1, no. 2 (December 31, 2022): 155–70. http://dx.doi.org/10.58797/pilar.0102.08.
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Abstract In presenting learning media, teachers use various interesting simulations for their students. This research aims to develop learning media through interactive simulations on parabolic motion material. Parabolic motion is a two-dimensional motion that requires accurate analysis to understand it. Pygame is a Python programming language specifically written to make games. The development procedure uses a four-D model, which consists of the defining, designing, developing, and deploying stages. The results showed that interactive simulation learning media could be used for student learning media in analyzing the factors that influence parabolic motion. This shows that the developed simulation media is feasible to use in learning. However, further development needs to be carried out to obtain more interesting and more complete simulation media. The simulation results can be used as teaching materials in high school physics parabolic motion material. Abstrak Dalam menyajikan media pembelajaran, guru banyak memanfaatkan berbagai macam simulasi yang menarik bagi siswanya. Penelitian ini adalah penelitian pengembangan yang bertujuan untuk mengembangkan media pembelajaran berupa simulasi yang interaktif pada materi gerak parabola. Gerak parabola merupakan gerak dua dimensi yang membutuhkan analisis yang akurat dalam memahaminya. Pygame merupakan salah satu bahasa pemrograman python yang ditulis khusus untuk membuat game. Prosedur pengembangannya menggunakan model four-D yang terdiri dari tahap pendefinisian, perancangan, pengembangan, dan penyebaran. Hasil penelitian menunjukkan bahwa media pembelajaran simulasi interaktif dapat dipakai untuk media pembelajaran siswa dalam menganalisis faktor-faktor yang mempengaruhi gerak parabola. Hal ini menunjukkan bahwa pengembangan media simulasi yang dikembangkan layak digunakan dalam pembelajaran. Namun pengembangan lanjutan perlu dilakukan agar diperoleh media simulasi yang lebih menarik dan lebih lengkap. Hasil simulasi dapat digunakan sebagai bahan ajar di fisika SMA materi Gerak Parabola
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Guerrero-Turrubiates, Jose de Jesus, Ivan Cruz-Aceves, Sergio Ledesma, Juan Manuel Sierra-Hernandez, Jonas Velasco, Juan Gabriel Avina-Cervantes, Maria Susana Avila-Garcia, Horacio Rostro-Gonzalez, and Roberto Rojas-Laguna. "Fast Parabola Detection Using Estimation of Distribution Algorithms." Computational and Mathematical Methods in Medicine 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/6494390.
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This paper presents a new method based on Estimation of Distribution Algorithms (EDAs) to detect parabolic shapes in synthetic and medical images. The method computes a virtual parabola using three random boundary pixels to calculate the constant values of the generic parabola equation. The resulting parabola is evaluated by matching it with the parabolic shape in the input image by using the Hadamard product as fitness function. This proposed method is evaluated in terms of computational time and compared with two implementations of the generalized Hough transform and RANSAC method for parabola detection. Experimental results show that the proposed method outperforms the comparative methods in terms of execution time about93.61%on synthetic images and89%on retinal fundus and human plantar arch images. In addition, experimental results have also shown that the proposed method can be highly suitable for different medical applications.
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Najman, B. "Quasilinear parabolic-parabolic singular perturbations." Nonlinear Analysis: Theory, Methods & Applications 26, no. 2 (January 1996): 277–97. http://dx.doi.org/10.1016/0362-546x(94)00280-u.
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Alhafiz, Revi, Diswandi Nurba, and Devianti Devianti. "Modifikasi Pengering Efek Rumah Kaca (ERK) Atap Parabolik untuk Kacang Tanah (Arachis hypogaeai L.)." Jurnal Ilmiah Mahasiswa Pertanian 7, no. 2 (May 1, 2022): 480–89. http://dx.doi.org/10.17969/jimfp.v7i2.19796.
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Abstrak. Tujuan dari penelitian ini untuk melakukan desain dan rancang bangun serta pengujian fungsional terhadap pengering Efek Rumah Kaca (ERK) atap parabolik untuk kacang tanah (Arachis hypogaeai L.). Penelitian ini dilaksanakan pada bulan April sampai Oktober 2021, bertempat di Laboratorium Perbengkelan Alat dan Mesin Pertanian Program Studi Teknik Pertanian Fakultas Pertanian Universitas Syiah Kuala Darussalam Banda Aceh. Metode yang dilakukan pada penelitian ini adalah mendesain pengering Efek Rumah Kaca (ERK) atap parabolik menggunakan software SolidWorks 2017. Selanjutnya, rancang bangun pembuatan pengering ERK atap parabolik dan melakukan pengujian fungsional alat tanpa bahan dan menggunakan bahan kacang tanah untuk mengetahui performansi pengering ini sudah berfungsi dengan baik atau belum. Parameter penelitian pada penelitian ini adalah kadar air, kapasitas pengering, dan analisis energi panas.Hasil dari penelitian ini adalah prinsip kerja pengering ERK Atap Parabolik dengan mensirkulasikan udara panas yang terperangkap di dalam ruang pengering. Lalu, mengeluarkan udara menggunakan kipas outlet. Uji kinerja rancang bangun pengering ERK Atap Parabolik dapat berfungsi dengan baik dalam melakukan pengeringan, karena terlihat adanya fluktuasi suhu dalam ruang pengering selama 8 jam pengeringan. Rata-rata pengeringan menggunakan kacang tanah adalah 36,15℃, dan rata-rata suhu lingkungan adalah 29,4℃ . Kadar air akhir kacang tanah pada rak 1, 2, dan 3 sebesar 19,55%, 11,90%, dan 8,06%. Kadar air kacang tanah pada rak 3 memenuhi SNI mutu II, sedangkan kadar air kacang pada rak 1 dan 2 belum memenuhi SNI. Kapasitas kerja pengeringan input (KKPI) adalah 1,875 kg/jam dan kapasitas kerja pengeringan output (KKPO) adalah 1,532 kg/jam. Energi panas yang dibutuhkan untuk pengeringan kacang tanah (Qd) adalah sebesar 803.128,61 Joule atau setara dengan 223,091 Wh. Sedangkan energi listrik yaitu dibutuhkan yaitu 427,68 Wh.Modification Of Greenhouse Effect Dryer (Erk) Parabolic Roof For Peanut (Arachis Hypogaeai L.)The purpose of this study was to design and construct and perform functional testing of the Roof parabolic Greenhouse Effect (ERK) dryer for peanuts (Arachis hypogaeai L.). This research was conducted from April to October 2021, at the Agricultural Equipment and Machinery Workshop Laboratory, Agricultural Engineering Study Program, Faculty of Agriculture, Syiah Kuala Darussalam University, Banda Aceh. The method used in this research is to design a parabolic roof greenhouse effect (ERK) dryer using the SolidWorks 2017 software. Next, design the manufacture of a parabolic roof ERK dryer and perform functional testing of the tool without materials and using peanuts to determine the performance of this dryer already working. well or not. The research parameters in this study were moisture content, drying capacity, and heat energy analysis.The result of this research is the working principle of Parabolic Roof ERK dryer by circulating hot air trapped in the drying chamber. Then, remove the used air using the outlet fan. The performance test of the Parabolic Roof ERK dryer design can function properly in drying, because it can be seen that there are temperature fluctuations in the drying chamber for 8 hours of drying. The average drying using peanuts is 36.15℃, and the average environmental temperature is 29.4℃. It can be seen that the temperature of using peanuts is higher than that of the environment. The final moisture content of peanuts on shelves 1, 2, and 3 was 19.55%, 11.90%, and 8.06%. The moisture content of peanuts on rack 3 meets SNI quality II, while the moisture content of peanuts on racks 1 and 2 does not meet SNI. The input drying working capacity (KKPI) is 1.875 kg/hour. Meanwhile, the output drying working capacity (KKPO) is 1,532 kg/hour. The heat energy required for drying peanuts (Qd) is 803.128.61 Joules or equivalent to 223.091 Wh. Meanwhile, the electrical energy required is 427.68 Wh.
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Sun, Qiyao. "Research on Shape Adjustment of Large Aperture Reflector Based on Differential Equation." Highlights in Science, Engineering and Technology 38 (March 16, 2023): 76–81. http://dx.doi.org/10.54097/hset.v38i.5736.
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The FAST active reflector can transform the reference state's spherical surface into the working condition's parabolic surface by adjusting the system so that the radio telescope has high sensitivity. This paper mainly studies the structure of the ideal paraboloid in the working state and the influence of various factors of the adjustment system on signal reception. The primary cable node distribution model is established based on the paraboloid equation and coordinate rotation. The optimization model, the difference method and the stochastic simulation are used to solve the problem. Firstly, the ideal paraboloid focus selection range is determined as an interval near the feed cabin according to the properties of the focused parallel rays of the paraboloid and the receiving area as the central disk. At the same time, considering the adjustment factors of the reflective panel, the ideal paraboloid endpoint is given. With the constraint interval, an optimization model can be established for the two variables, the distance d from the focal point to the feed cabin and the z-coordinate b of the vertex of the ideal parabola, with the perfect paraboloid and the reference sphere as close as possible as the objective function. It is formed by rotating around the central axis. Therefore, to simplify the operation, the plane because is selected to analyze the ideal parabola, and finally, the optimal solution is obtained by using the two-dimensional grid search algorithm as , , The resulting ideal paraboloid equation is . The FAST active reflector can transform the reference state's spherical surface into the working condition's parabolic surface by adjusting the system so that the radio telescope has high sensitivity. This paper mainly studies the structure of the ideal paraboloid in the working state and the influence of various factors of the adjustment system on signal reception. The primary cable node distribution model is established based on the paraboloid equation and coordinate rotation. The optimization model, the difference method and the stochastic simulation are used to solve the problem.The average vector of each reflective panel can be obtained according to Cramer's law. Then according to the reflection properties of the wave, the direction vector of the reflected electromagnetic wave can be obtained from the incident electromagnetic wave and the average vector. The end of the panel is projected to the feed along the direction of the reflected electromagnetic wave. The cabin's plane can obtain the area reflected from each panel to the plane of the feed cabin. To simplify the calculation and improve efficiency, the Monte Carlo stochastic simulation algorithm is used to obtain the reflected signal receiving ratio of the working paraboloid. The receiving ratio is that the signal receiving the effect of the working paraboloid is much better than that of the reference reflective spherical surface.
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Ahmadi, Mohammad Taghi, Zaharah Johari, N. Aziziah Amin, Amir Hossein Fallahpour, and Razali Ismail. "Graphene Nanoribbon Conductance Model in Parabolic Band Structure." Journal of Nanomaterials 2010 (2010): 1–4. http://dx.doi.org/10.1155/2010/753738.
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Many experimental measurements have been done on GNR conductance. In this paper, analytical model of GNR conductance is presented. Moreover, comparison with published data which illustrates good agreement between them is studied. Conductance of GNR as a one-dimensional device channel with parabolic band structures near the charge neutrality point is improved. Based on quantum confinement effect, the conductance of GNR in parabolic part of the band structure, also the temperature-dependent conductance which displays minimum conductance near the charge neutrality point are calculated. Graphene nanoribbon (GNR) with parabolic band structure near the minimum band energy terminates Fermi-Dirac integral base method on band structure study. While band structure is parabola, semiconducting GNRs conductance is a function of Fermi-Dirac integral which is based on Maxwell approximation in nondegenerate limit especially for a long channel.
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Azzahra, Camelia, Entin Halimah Subekti, and Bayu Setiaji. "FISIKA DALAM PERMAINAN BOLA VOLI: PENGARUH BESAR SUDUT TERHADAP SERVIS BAWAH DITINJAU DARI GERAK PARABOLA." JURNAL PEMBELAJARAN FISIKA 12, no. 1 (April 1, 2023): 23. http://dx.doi.org/10.19184/jpf.v12i1.37959.
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Parabolic motion is the curved motion of an object whose trajectory is a
parabola. In objects that experience parabolic motion, objects will experience the
farthest distance and the highest point. The farthest distance traveled by an object in
motion with a parabolic trajectory is influenced by the elevation angle formed, this is
because the velocity in the direction of the x-axis and the velocity in the direction of
the y-axis are affected by the magnitude of the angle of elevation formed. The purpose
of this study is to analyze the motion of the parabola on the volleyball serve with a
variety of different angles so that volleyball players can find out the ideal angle for
the under serve so that the ball can fall on target and over the net. This research is
using experimental method. The results of a good and ideal angle when serving under
a volleyball so that the ball falls on target and crosses the net using an initial angle of
600, a falling angle of 250, and with a speed of 11.2 m/s which is analyzed using a
tracker.
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Dzhydzhora, Yevhen. "THE PARABOLIC STRUCTURE OF GOSPEL PARABLES." Odessa National University Herald. Series: Philology 27, no. 1(25) (April 23, 2023): 19–27. http://dx.doi.org/10.18524/2307-8332.2022.1(25).283133.
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The article is devoted to the analysis of the special parabolic structure of the evangelical parables. It is not only about the actual literary understanding of the parabola as a stylistic device, with the help of which foreign language expression is carried out, but also about a mathematical graph – a curved curve, divided at the point of intersection into two symmetrical branches. In the structure of the evangelical parable, these branches can be represented as real-factographic and symbolic interpretive plans, between which there is a direct semantic dependence. All narrative situations that make up the real plan of the parable and are represented by the right branch of the parabola must be interpreted in the same sequence to build a symmetrical left branch. In the article, the parabolic structure of two symmetrical plans is demonstrated on the example of two gospel parables well-known in culture: The Parable of the Prodigal Son [Luk. 15, 11 32] and Proverbs about ten virgins [Matt. 15, 1–11]. Obviously, a similar way of interpretive reading of the Gospel parables can be qualified as a fullfledged hermeneutic technique of analysis of other biblical works.
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Pletser, Vladimir. "Are aircraft parabolic flights really parabolic?" Acta Astronautica 89 (August 2013): 226–28. http://dx.doi.org/10.1016/j.actaastro.2013.04.019.
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Tarya, Ayi, Harish H. Maulamulki, Ivonne M. Radjawane, and Hanif S. Sutiyoso. "Pengaruh Pasang Surut Terhadap Profil Kecepatan Arus Melintang Di Sungai Berau, Kalimantan Timur." Buletin Oseanografi Marina 12, no. 1 (September 29, 2022): 65–77. http://dx.doi.org/10.14710/buloma.v12i1.45438.
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Profil kecepatan arus melintang pada aliran sungai merupakan parameter penting yang diperoleh dalam pengukuran debit sungai dengan instrumen Horizontal Acoustic Doppler Current Profiler (H‐ADCP). Dinamika sirkulasi arus di aliran sungai dibangkitkan oleh interaksi antara debit sungai, topografi dan pasang surut. Sungai Berau di Kalimantan Timur merupakan salah satu aliran sungai yang dominan dipengaruhi oleh pasang surut. Penelitian ini bertujuan untuk mengetahui pengaruh pasang surut terhadap variasi profil kecepatan arus melintang sungai dan identifikasi tingkat kecocokan antara profil data kecepatan arus dengan persamaan parabolik. Metode penelitian yang digunakan yaitu dekomposisi kecepatan arus dengan band pass filter (BPF) dan low pass filter (LPF), dan pencocokan kurva (curve fitting) profil kecepatan arus sungai hasil pengukuran H-ADCP dengan persamaan parabolik. Hasil studi menunjukkan pasang surut berperan dalam menentukan arah kecepatan arus, dimana arus bergerak ke arah hulu saat kondisi pasang dan bergerak menuju ke hilir saat kondisi surut, dengan magnitudo kecepatan arus saat purnama mencapai 1,2 m/s dan saat perbani sekitar 0,5 m/s. Pasang surut mempunyai pengaruh yang signifikan terhadap kontribusi kecepatan arus, berdasarkan hasil BPF diperoleh 85% dari kecepatan arus total adalah arus yang dibangkitkan oleh pasang surut, sedangkan arus non-pasang surut berkontribusi hanya 15%. Hasil pencocokan kurva antara profil kecepatan arus dan persamaan parabolik diperoleh bahwa kondisi pasang surut purnama merupakan periode yang paling optimal, hal ini ditunjukkan dengan tingkat kecocokan mencapai 94%, nilai korelasi rata-rata ( ) adalah 0,95 dan panjang rata-rata profil kecepatan arus yang dapat didekati persamaan parabolik mencapai 125 m. The cross-sectional velocity profile in river flow is an important parameter which obtained in measuring river discharge with the Horizontal Acoustic Doppler Current Profiler (H‐ADCP) instrument. Circulation dynamic of river flow is generated by the interaction between river discharge, topography and tides. The Berau River in East Kalimantan is one of the river which has dominant influenced by tides. This study aims to determine the effect of tides on variations in the river cross-sectional velocity profile and to identify the degree of agreement between the flow velocity data profile and the parabolic equation. The research method is used the band pass filter (BPF) and low pass filter (LPF) for velocity data decomposition, and curve fitting of the velocity profile as measured by H-ADCP with parabolic equation. Parameter of the quality of curve fitting parabolic equation is determined by the degree of agreement, correlation coefficient (R), and the length of the velocity profile that can be approximated by the parabolic equation. The results of the study show the tides have a significant influence on the flow velocity in the Berau River. Tides play a role in determining the direction of flow velocity, the current moves upstream during high tide and flow moves downstream during low tide, with the magnitude of the velocity at spring tide reaching 1.2 m/s and around 0.5 m/s at neap tide. Tides have a significant influence on the contribution of current velocity, based on BPF result is obtained that 85% of the total current velocity is generated by tides, while non-tidal current contributes only 15%. The results of the curve fitting between the velocity profile and the parabolic equation show the spring tide condition as the most optimal period, this is indicated by the agreement level reaching 94%, the mean correlation is 0.95 and the average length of the velocity profile which can be approached with the parabolic equation is 125 m.
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Mijajlovic, Z., N. Pejovic, G. Damljanovic, and D. Ciric. "Envelopes of cometary orbits." Serbian Astronomical Journal, no. 177 (2008): 101–7. http://dx.doi.org/10.2298/saj0877101m.
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We discuss cometary orbits from the standpoint of Nonstandard (Leibnitz) analysis, a relatively new branch of mathematics. In particular, we consider parabolic cometary paths. It appears that, in a sense, every parabola is an ellipse.
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Zhang, Z. Y., Y. Liang, Y. P. Hou, and Q. Wang. "Designing a warehouse internal layout using a parabolic aisles based method." Advances in Production Engineering & Management 16, no. 2 (June 25, 2021): 223–39. http://dx.doi.org/10.14743/apem2021.2.396.
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Refined layout is a basis of warehousing efficiency. Straight aisle is a typical feature of current warehouse internal layouts. The purpose of this paper is to explore the possibility of using curve aisles for warehouse layout. By Choosing typical non-traditional layouts and transforming their inclined cross-aisle trajectory into parabola, two parabolic aisle layouts, parabolic Flying-V and parabolic Fishbone, are constructed. For unit-load warehouses, based on the morphological characteristic analysis and the parabolic types selection, the picking distance model and the cross-aisle length formula are presented. Interval Numerical Simulation Method (INSM) and Genetic Algorithms (GA) are adopted to solve the model respectively in order to verify the results. This research breaks through the realistic situation of straight aisle leading warehouse layout, and enriches the relevant layout theory. The calculation results of 100 warehouses with different sizes show that the picking distance of parabolic Flying-V could be reduced by 0.22-0.62 % compared with the straight layout, and the theoretical possible improvement space has been compressed by 2.42-12.26 %. Its length of cross-aisle is shortened by -0.03-3.10 %. The picking distance of parabolic Fishbone could be only reduced by 0.02-0.04 %. The theoretical possible improvement space has been compressed by 1.27-1.83 %. But its length of cross-aisle will increase by 4.63-19.50 % significantly. We believe that the layout of non-rectangular complex special-shaped warehouses based on curve trajectory aisles would become an important research topic. In addition, after some necessary modifications to the objectives and constraints, the proposed method in this paper may also be used for the arrangement of machines and devices in a workshop in principle.
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Zhang, Z. Y., Y. Liang, Y. P. Hou, and Q. Wang. "Designing a warehouse internal layout using a parabolic aisles based method." Advances in Production Engineering & Management 16, no. 2 (June 25, 2021): 223–39. http://dx.doi.org/10.14743/apem2021.2.396.
Full textAbstract:
Refined layout is a basis of warehousing efficiency. Straight aisle is a typical feature of current warehouse internal layouts. The purpose of this paper is to explore the possibility of using curve aisles for warehouse layout. By Choosing typical non-traditional layouts and transforming their inclined cross-aisle trajectory into parabola, two parabolic aisle layouts, parabolic Flying-V and parabolic Fishbone, are constructed. For unit-load warehouses, based on the morphological characteristic analysis and the parabolic types selection, the picking distance model and the cross-aisle length formula are presented. Interval Numerical Simulation Method (INSM) and Genetic Algorithms (GA) are adopted to solve the model respectively in order to verify the results. This research breaks through the realistic situation of straight aisle leading warehouse layout, and enriches the relevant layout theory. The calculation results of 100 warehouses with different sizes show that the picking distance of parabolic Flying-V could be reduced by 0.22-0.62 % compared with the straight layout, and the theoretical possible improvement space has been compressed by 2.42-12.26 %. Its length of cross-aisle is shortened by -0.03-3.10 %. The picking distance of parabolic Fishbone could be only reduced by 0.02-0.04 %. The theoretical possible improvement space has been compressed by 1.27-1.83 %. But its length of cross-aisle will increase by 4.63-19.50 % significantly. We believe that the layout of non-rectangular complex special-shaped warehouses based on curve trajectory aisles would become an important research topic. In addition, after some necessary modifications to the objectives and constraints, the proposed method in this paper may also be used for the arrangement of machines and devices in a workshop in principle.
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Żyto, Kamila. "„Chyba w ten sposób toczy się ta ludzka komedia przez całe pokolenia drogą na Zachód i przez pustynie”. Paraboliczność w kinie braci Coen." Załącznik Kulturoznawczy, no. 9 (2022): 685–718. http://dx.doi.org/10.21697/zk.2022.9.35.
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The Coen brothers stylized films, full of quotations and borrowings, are for many scholars the quintessence of a postmodern game with remnants, interpretive openness, and ambiguity. This fact does not incline to look in these films for the rules governing the world or human existence what is typical of parabolic thinking. The article is an attempt to demonstrate that the makers of the Oscar-winning Fargo (Fargo, 1996) often use in their work elements, tricks, or strategies typical of a traditional parabola, though their films may often be read as its contemporary invariants. Numerous Coens’ films bear the hallmarks of parabolic texts, even if in this case one cannot speak of a parabola as a genre. The messages they contain are never unambiguous and are not intended to educate. However, owing to their enigmatic nature, they encourage viewers to search for extra meanings.
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Hidayati, Destia Wahyu, and Arie Wahyuni. "Analisis kemampuan pembuktian matematis parabola menggunakan guided learning berdasarkan tingkat resiliensi." Jurnal Inovasi Pendidikan Matematika (JIPM) 2, no. 2 (November 28, 2020): 121–30. http://dx.doi.org/10.37729/jipm.v2i2.6713.
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One of the geometry materials at the high school level is a parabolic. The ability to prove parabolic formulas is needed by students majoring in Mathematics Education who will become mathematics teachers after graduating. Having an understanding of proof of the formula will make learning more meaningful. The purpose of this research is to find out a description of the proof of parabolic formula based on high, medium, and low resilience levels, so that various obstacles can be overcome early. This research is qualitative research. Data collection techniques used resilience questionnaires, test questions to prove the parabola formula, and interviews. The data analysis technique used data triangulation. The results showed that (1) there are three indicators in mathematical proof of parabolic mastered by students at high, medium, and low resilience levels, namely drawing the vertex, fixed point, and directrix line, determining the length of the two points, determining the results of the equation squared, (2) determining the coordinates of the vertex, fixed point, and the equations of the directrix mastered by students with a high level of resilience, but not yet mastered by students at moderate and low resilience levels, (3) determining two lines of the same length in the image according to the definition parabolic and determining the results of the multiplication distribution on addition and subtraction have been mastered by students at high and medium resilience levels, but not yet mastered by students at low resilience levels,
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NEMENKO, A. V., and M. M. NIKITIN. "APPLICATION OF ELASTIC DEFORMATIONS TO PARABOLOIDAL SURFACE MAKING." Fundamental and Applied Problems of Engineering and Technology 3 (2020): 11–19. http://dx.doi.org/10.33979/2073-7408-2020-341-3-11-19.
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The transformation of a spherical concave mirror into a parabolic one with the help of elastic bending deformations is considered. The magnitude and direction of the load, which creates the necessary bend for transforming the mirror with the given parameters, are determined. Uneven material removal during machining is replaced by the bend of an optically accurate spherical surface already obtained. The application of the results to the creation of an active control system for the shaping of the surface of a paraboloid of rotation is considered. The proposed finishing technology is aimed at solving the problem of guaranteed obtaining optically accurate surface of a parabolic mirror.
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Вышнепольский, Владимир, Vladimir Vyshnepol'skiy, К. Киршанов, K. Kirshanov, К. Егиазарян, and K. Egiazaryan. "Loci of Points Equally Spaced From Two Given Geometrical Figures. Part 3." Geometry & Graphics 6, no. 4 (January 29, 2019): 3–19. http://dx.doi.org/10.12737/article_5c21f207bfd6e4.78537377.
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The loci (L) equally spaced from a sphere and a straight line, and from a conic surface and a plane, are considered. The following options have been considered. The straight line passes through the center of the sphere (a = 0), at the same time completely at spheres’ positive radiuses a surface of rotation is obtained, forming which the parabola is, and a rotation axis – this straight line. The parabola’s top forms the biggest parallel on the site points of intersection of the parabola’s forming with the rotation axis. Let's call such paraboloid a perpendicular paraboloid of rotation. The straight line crosses the sphere, but does not pass through the center (0 < a < R/2) – a perpendicular paraboloid, at that the surface is also completely obtained at radiuses’ positive values. The straight line is tangent to the sphere (a = R/2) – a surface which projections are parabolas, lemniscates and circles, and a piece from a tangency point to the sphere center – at radiuses positive values; a beam from the sphere center, perpendicular to this straight line – at radiuses negative values, at that the beam and the piece belong to one straight line. The straight line lies out of the sphere (α > R/2) – two different surfaces, having the general properties with a hyperbolic paraboloid, are obtained, one of which is obtained at radius positive values, and another one – at radius negative values. It has been noticed that loci, equally spaced from a sphere and a straight line, and from a cylinder and a point, coincide at equal radiuses and distances from axes to points and straight lines if to take into account the surfaces obtained both at positive, and negative values of radiuses. Locus, equally spaced from the conic surface of rotation and the plane, are two elliptic conic surfaces which in case 7.4.1 degenerate in the conic surfaces of rotation. In cases 7.4.3 and 7.4.4 one elliptic conic surface degenerates in a plane and a parabolic cylinder respectively.
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Lyachek, Yuliy. "An Efficient Method for Forming Parabolic Curves and Surfaces." Mathematics 8, no. 4 (April 15, 2020): 592. http://dx.doi.org/10.3390/math8040592.
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A new method for the formation of parabolic curves and surfaces is proposed. It does not impose restrictions on the relative positions in space of the sequence of reference points relative to each other, meaning it compares favorably with other prototypes. The disadvantages of the Overhauser and Brever–Anderson methods are noted. The method allows one to effectively form and edit curves and surfaces when changing the coordinates of any given point. This positive effect is achieved due to the appropriate choice of local coordinate systems for the mathematical description of each parabola, which together define a composite interpolation curve or surface. The paper provides a detailed mathematical description of the method of parabolic interpolation of curves and surfaces based on the use of matrix calculations. Analytical descriptions of a composite parabolic curve and its first and second derivatives are given, and continuity analysis of these factors is carried out. For the matrix of points of the defining polyhedron, expressions are presented that describe the corresponding surfaces, as well as the unit normal at any point. The comparative table of the required number of pseudo-codes for calculating the coordinates of one point for constructing a parabolic curve for the three methods is given.
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Atifah, Nailul, Sunny Ineza Putri, Sa'adah Meilufi, and Adlinsyah Hakim Syawaluddin. "Analisis Transien Pada Parabolic Trough Reflector Solar Water Heater." Jurnal Inovasi Ilmu Pengetahuan dan Teknologi 5, no. 1 (October 31, 2023): 22. http://dx.doi.org/10.32493/jiptek.v5i1.35239.
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Salah satu sumber energi terbarukan yang melimpah adalah energi matahari. Hal ini dikarenakan Indonesia terletak pada garis khatulistiwa. Intensitas rata-rata radiasi matahari untuk wilayah Jabodetabek adalah sekitar 4,98334 sampai dengan 5,02111 kWh/m2/hari. Pemanfaatan energi matahari dengan sistem termal bekerja dengan mengonversi radiasi matahari menjadi energi panas. Panas matahari dapat dimanfaatkan dengan teknologi solar kolektor. Salah satu tipe solar collector adalah reflector yang berbentuk parabolic trough. Tipe ini memantulkan radiasi matahari menuju ke titik fokus yang tersusun membentuk garis imajiner sepanjang collector. Kinerja dari sistem pemanas air tipe concentrated parabolic reflector tergantung pada parameter dimensi reflektor, absorber penampung air, dan fluida kerja serta sifat termal dan optik dari komponen-komponen tersebut yang meliputi reflektansi parabola, emisivitas absorber, serta isolasi termal pada absorber penampung airnya. Parameter- parameter tersebut sangat berpengaruh terhadap kinerja sistem ini yang meliputi peningkatan kecepatan pemanasan, temperatur air, daya output termal dan efisiensi termalnya. Penelitian ini bertujuan untuk investigasi hasil ekperimen reflector yang berbentuk parabolic trough dan hasil simulasinya dengan Software Ansys Fluent. Hasil simulasi menunjukkan bahwa temperatur air maksimal adalah 106,65°C, temperatur air rata-rata 62,54°C, energi output 107,05 kJ, dan efisiensi termal 61,5%. Berdasarkan hasil tersebut, sistem pemanas air parabolic through collector dapat diandalkan.
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Tibebu, Solomon, and Arkbom Hailu. "Design, Construction, and Evaluation of the Performance of Dual-Axis Sun Trucker Parabolic Solar Cooker and Comparison of Cooker." Journal of Renewable Energy 2021 (September 6, 2021): 1–10. http://dx.doi.org/10.1155/2021/8944722.
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Energy demand is increasing due to population increment and industrialization. To meet this energy demand, technologies that use renewable energy such as solar energy are being developed. A parabolic solar cooker is one of the main solar cookers, which can cook food and boil water at a high temperature within a short period. This study aimed to design, construct, and evaluate the performance of the constructed parabolic solar cookers. Moreover, this study aimed to compare the constructed cooker with firewood, charcoal, kerosene, and electricity in terms of cooking time and energy cost. The cooker was constructed using different materials such as old satellite dishes, tyres, steel, and aluminum foil. The aperture diameter, aperture area, receiver diameter, receiver area, depth of the parabola, focal length, rim angle, circumference of the circle, surface area, length of the circumference, and concentration of the cooker were 1.8 m, 2.54 m2, 0.16 m, 0.02 m2, 0.3 m, 0.67 m, 67.38°, 5.76 m, 2.81 m2, 5.76 m, and 123.46, respectively. The cooker can track the sun from north to south and from east to west. The performance of the cooker was evaluated by calculating the efficiency and power. The output energy, input energy, and average upcoming solar radiation of the constructed parabolic solar cooker were 0.182 kW/m2, 1.691 kW/m2, and 0.665 kW/m2, respectively. The efficiency and power of the cooker were 10.75% and 0.3 kW/hr, respectively. The constructed parabolic solar cooker relatively showed better performance in cooking different foods. A family, which has five members, was considered to compare the constructed cooker with other fuels in terms of energy cost of cooking. Since the parabolic solar cooker does not have any energy cost, it can save the energy cost of cooking foods. Therefore, parabolic solar cookers have a great advantage for developing countries including Ethiopia.
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Chiyo, Yutaro. "Large time behavior in a quasilinear parabolic-parabolic-elliptic attraction-repulsion chemotaxis system." Archivum Mathematicum, no. 2 (2023): 163–71. http://dx.doi.org/10.5817/am2023-2-163.
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Persson, Jeanette, Per-Olov Käll, and Mats Nygren. "Parabolic-non-parabolic oxidation kinetics of Si3N4." Journal of the European Ceramic Society 12, no. 3 (January 1993): 177–84. http://dx.doi.org/10.1016/0955-2219(93)90119-c.
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Čap, Andreas, and Tomáš Salač. "Parabolic conformally symplectic structures II: parabolic contactification." Annali di Matematica Pura ed Applicata (1923 -) 197, no. 4 (December 5, 2017): 1175–99. http://dx.doi.org/10.1007/s10231-017-0719-3.
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Suter, C., S. Tembhurne, I. Holmes-Gentle, and S. Haussener. "Optical characterization of a solar concentrating dish system." Journal of Physics: Conference Series 2766, no. 1 (May 1, 2024): 012094. http://dx.doi.org/10.1088/1742-6596/2766/1/012094.
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Abstract Solar dishes concentrate the quasi-collimated sun light towards a focal point. Typically, the optical characterization consists of experimental flux map measurements and Monte-Carlo ray-tracing (MCRT) simulations, which are fitted based on experimental data and serve for the prediction of the distribution of the irradiation in receivers or reactors. However, the MCRT simulations usually rely on idealized mirror geometries (i.e. parabolic mirrors), neglecting the actual dish geometry resulting from its construction method (such as petals, facets or segments). Thus, the parameter fitting might yield unrealistic parameters and local radiative flux peaks (“hot spots”), which are often experimentally detected behind the focal plane, cannot be predicted. Here, we characterized the 7m diameter solar dish at EPFL comprising 27 petals with a nominal focal length of 3.8 m and a rim angle of 50.3°. The measured peak concentration was 1781 suns and the received integrated solar power was 20.0 kW over an 18 cm diameter spot. We proposed an advanced geometry approach for the MCRT model considering the curvature of the dish, i.e. geometries mathematically described by a parabola with an exponent not equal, but close to 2. The advanced geometry approach was then applied for predicting experimentally measured flux distribution in focal and off-focus planes. The fitted reflectivities were 70% and 86% for the idealized and advanced geometry approach, respectively. The idealized geometry approach found an unrealistically low value whereas the advanced geometry approach’s value was within 1% of the manufacturer’s specification. The advanced geometry approach predicted a parabola exponent of 1.94, which emphasizes that the best geometry to describe the solar dish deviates from a perfect paraboloid. We conclude that MCRT models should consider non-perfect parabolic geometries for solar dishes in order to obtain more realistic values for the fitted parameters.
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García-Moreno, F., S. T. Tobin, M. Mukherjee, C. Jiménez, E. Solórzano, G. S. Vinod Kumar, S. Hutzler, and J. Banhart. "Analysis of liquid metal foams through X-ray radioscopy and microgravity experiments." Soft Matter 10, no. 36 (2014): 6955–62. http://dx.doi.org/10.1039/c4sm00467a.
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The foaming process of a thixocast AlSi6Cu4 precursor material followed in situ by X-ray radioscopy shown for different experimental stages with and without drainage during the plane parabolic trajectory and the corresponding temperature T(t) (red line) and gravity g(t) profiles (blue line) during the parabolas.
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A. B, BANDE, GARBA M. M, ALIYU S, HAMZA B.S, and SHEHU A. "PERFORMANCE EVALUATION OF PARABOLIC CONCENTRATOR WITH THERMAL STORAGE SYSTEM FOR DOMESTIC APPLICATIONS." BIMA JOURNAL OF SCIENCE AND TECHNOLOGY (2536-6041) 6, no. 01 (April 30, 2022): 29–40. http://dx.doi.org/10.56892/bimajst.v6i01.311.
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Solar energy is a free natural resource but its harvesting requires a high capital investment whichprohibits its maximum exploitation. A Parabolic Dish Solar Collector (PDSC) with a thermalstorage system was been constructed and developed to harness solar beam radiation. The thermalstorage system and PDSC were constructed using locally and less cost materials such asgalvanized metal sheet and steel rods curved to obey the equation of a parabola then weldedtogether with circular support rings which was then lined with stainless steel reflector pasted forthe construction of PDSC. The receiver was made of blackened aluminium material incorporatedwith coiled copper tube carrying water as the heat transfer fluid. A parabolic dish which acts of aheat collector is used to track and reflects solar radiation at a single point (focus) on a receiverabsorber. Heat transfer from the solar collector to the storage tank was done by usingthermosyphonic principle to circulate the water (heat transfer fluid) between storage tank andheating system (receiver). The evaluation of thermal storage and analyzing the efficiency oftracking and non-tracking parabolic dish solar collector was carried out during month of June,2020 for the composite climate of Sokoto. According to the finding, the efficiency of trackingPDSC with thermal storage system and non- tracking PDSC with thermal storage tank weredetermined and obtained to be 52.9% and 50% respectively.Keywords: thermal efficiency, parabolic dish collector, solar radiation, storage system andstainless steel reflector.
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Greco, Francesco, Luigi Boccia, Emilio Arnieri, and Giandomenico Amendola. "A Ka-Band Cylindrical Paneled Reflectarray Antenna." Electronics 8, no. 6 (June 10, 2019): 654. http://dx.doi.org/10.3390/electronics8060654.
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Cylindrical parabolic reflectors have been widely used in those applications requiring high gain antennas. Their design is dictated by the geometric relation of the parabola, which relate the feed location, f, to the radiating aperture, D. In this work, the use of reflectarrays is proposed to increase D without changing the feed location. In the proposed approach, the reflecting surface is loaded with dielectric panels where the phase of the reflected field is controlled using continuous metal strips of variable widths. This solution is enabled by the cylindrical symmetry and, with respect to rectangular patches or to other discrete antennas, it provides increased gain. The proposed concept has been evaluated by designing a Ka-band antenna operating in the Rx SatCom band (19–21 GHz). A prototype has been designed and the results compared with the ones of a parabolic cylindrical reflector using the same feed architecture. Simulated results have shown how this type of antenna can provide higher gain in comparison to the parabolic counterpart, reaching a radiation efficiency of 65%.
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NUGROHO, YOSAN AGENG, and WALUYO WALUYO. "Investigasi Sagging Metoda Parabola pada Saluran Transmisi Terhadap Parameter Temperatur pada Saluran 150 Kv pada Gardu Induk Cigereleng." MIND Journal 6, no. 1 (August 1, 2021): 46–56. http://dx.doi.org/10.26760/mindjournal.v6i1.46-56.
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AbstrakAndongan adalah bentangan kawat konduktor dari dua ujung titik terendah ditarik garis lurus konduktor tersebut sehingga terbentuk lengkungan kebawah, kekuatan tarik pada andongan berfungsi untuk menahan dari kedua ujung kawat konduktor yang dibentangkan. Besar suatu nilai andongan dapat dilihat dari temperature pada sekeliling saluran transmisi, sehingga siang hari panjang kawat konduktor akan sedikit memanjang diakibatkan sinar matahari, dan sebaliknya malam hari. Untuk mempermudah perhitungan dan analisis andongan dengan menggunakan metoda parabola pada saluran transmisi 150 Kv, dengan hasil perhitungan secara manual. Andongan dengan metoda parabola pada parameter temperature, temperatur 20oC besar andongan 0,0898%, pada temperature 70oC tinggi andongan 0,01186% turun ketika temperature 175oC andongan 0,1544%.Kata kunci: Andongan, temperatur, metoda parabola, gardu induk, saluran transmisi 150 Kv AbstractSagging is main the stretch of conductor wire from the two ends of the lowest point drawn by a straight line of the conductor so that a downward curve is formed, the tensile strength of sagging serves to hold from both ends of the stretched conductor wire the magnitude of a sagging value can be seen from the temperature around the transmission line, so that during the day the length of the conductor wire will be slightly elongated due to sunlight, and vice versa at night. The facilitate for calculation and analysis of the sagging used the parabolic method on a 150 Kv transmission line, with the results of calculations manually. Sagging with parabolic method at temperature parameters, temperature 20 oC large sagging of 0.0898%, at a temperature of 70 oC, the sagging height of 0.01186% decreases when the temperature is 175 oC sagging 0.1544%.Keywords: sagging, temperature, parabolic method, substation, 150 Kv transmission line
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Salam, Badru, and Sri Latifah. "Pengembangan Projectile Launcher Sebagai Alat Praktikum Sederhana Fisika pada Materi Gerak Parabola." Indonesian Journal of Science and Mathematics Education 2, no. 2 (June 22, 2019): 177–83. http://dx.doi.org/10.24042/ijsme.v2i2.4323.
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Abstract:This research is a development research that aims to produce media product projectile launcher as a simple practical tool of physics on parabolic motion material and to know the feasibility of media projectile launcher as a simple practical tool of physics on parabolic motion material. Problems in this research, among others, is how to develop projectile launcher as a simple practical tool of physics on parabolic motion material and how is the response of learners to media projectile launcher as a simple physics practicum tool on parabolic motion material. . Subjects in this study are class IX SMA N 1 Way Tenong and SMA N 2 Way Tenong. This research is a development research using Research and Development (R & D) research method that adopt the development of Borg & Gall that has been modified by sugionoProducts are categorized very feasible based on the validation of material experts with 100% percentage and based on the validation of media experts with a percentage of 100% , as well as Projectile Launcher media are very interesting to be used as teaching materials based on teacher's assessment to get 100% score percentage and student's response in limited group trial to get 95% percentage score for SMA N 1 Way Tenong and 92% for SMA N 2 Way Tenong.Abstrak:Penelitian ini merupakan penelitian pengembangan yang bertujuan untuk menghasilkan produk media projectile launcher sebagai alat praktikum sederhana fisika pada materi gerak parabola dan untuk mengetahui kelayakan dari media projectile launcher sebagai alat praktikum sederhana fisika pada materi gerak parabola. Masalah dalam penelitian ini antara lain bagaimanakah mengembangkan projectile launcher sebagai alat praktikum sederhana fisika pada materi gerak parabola dan bagaimanakah respon peserta didik terhadap media projectile launcher sebagai alat praktikum sederhana fisika pada materi gerak parabola. . Subjek dalam penelitian ini adalah kelas IX SMA N 1 Way Tenong dan SMA N 2 Way Tenong. Penelitian ini merupakan penelitian pengembangan menggunakan metode penelitian Research and Development (R&D) yang mengadopsi pengembangan dari Borg & Gall yang telah dimodifikasi oleh sugionoProduk yang dihasilkan berkategori sangat layak berdasarkan validasi dari ahli materi dengan presentase 100% dan berdasarkan validasi dari ahli media dengan presentase 100%, serta mediaProjectile Launchersangatmenarikuntukdijadikanbahanajarberdasarkanpenilaiangurumemperolehpresentaseskor100% dan respon peserta didik pada uji coba kelompok terbatas memperoleh skor presentase 95% untuk SMA N 1 Way Tenong dan 92% untuk SMA N 2 Way Tenong
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Parthasarathi, R., and P. Gargi. "The Euler Characteristic of Parabolic Sheaves." Indian Journal Of Science And Technology 17, no. 16 (April 19, 2024): 1695–701. http://dx.doi.org/10.17485/ijst/v17i16.493.
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Objectives: The primary aim of this study is to explicitly determine the Euler characteristic of the parabolic sheaves with rank 2 on a smooth projective algebraic surface defined over complex numbers with the smooth irreducible parabolic divisor . Methods: The computation of the parabolic Hilbert polynomial involves the use of -filtered sheaves on a smooth projective surface , with weights corresponding to the points where the filtration jumps. The Riemann-Roch theorem and Chern class computation have also been used. Findings: The study provides explicit computations of the parabolic Hilbert polynomial as well as the parabolic Chern classes for parabolic rank 2 bundles. Novelty: This work contributes to the understanding of parabolic sheaves on smooth projective surfaces, bridging the gap between different constructions of stable bundles. The explicit computation of the parabolic Hilbert polynomial for rank 2 bundles adds valuable insights to the study of moduli spaces of parabolic bundles. Keywords: Euler characteristic, Hilbert polynomial, Chern class, Parabolic sheaves, Smooth projective algebraic surface
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Yang, Zhuo, Wuquan He, Yubao Wang, Zongke Lou, and Pinzhang Duan. "Research on the Comprehensive Optimization of the Hydraulic Performance and Frost-Heaving Resistance of a Parabolic Channel." Water 12, no. 9 (September 15, 2020): 2574. http://dx.doi.org/10.3390/w12092574.
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Hydraulic performance and frost-heaving resistance should be considered simultaneously in the channel design of seasonally frozen soil areas. Quadratic parabolic channels have good water and sand transport capacities and high frost-heaving resistances. The width–depth ratio of a parabola determines its section structural form, which in turn determines the hydraulic performance and frost-heaving resistance. In this research, based on the current lack of a comprehensive optimization method that accounts for the hydraulic performance and frost-heaving resistance of the cross-section structures of parabolic channels, a multi-objective optimization model was established with the goal of achieving a minimum cross-sectional flow area and a uniform channel section force. Taking the flow velocity, the width–depth ratio and the crack resistance of concrete lining plate as constraints, the α method of the linear weighted sum method was used to optimize the calculation, and the comprehensive optimal quadratic parabolic channel section was obtained. The comprehensive optimal section of an actual parabolic channel in the Shijin Irrigation District was determined using this method, and the comprehensive optimal section was analyzed and compared to the original design section and two typical parabolic channel sections. The comprehensive optimal section was compared with the original design section in the Shijin Irrigation District. The force uniformity of the optimal section was 23.2% better, the hydraulic performance was 1.96% better, and the land use was 12.35% less. Compared with the values for the hydraulic optimal section, the maximum positive and negative bending moments of the comprehensive optimal section decreased by 5.6% and 11.89%, respectively, and the force uniformity increased by 7.62%. Additionally, compared with the values for the practical economic section, the force uniformity and the hydraulic performance of the comprehensive optimal section increased by 1.79% and 0.2%, respectively, and the land use decreased by 4.49%. Thus, the comprehensive optimal section met the engineering requirements and it could provide a reference for the design and selection of parabolic channels in seasonally frozen soil areas.
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Huda, Muhammad Fatihul Huda. "Alat Penggerak Parabola Otomatis pada Satelit Ku-band Berbasis Mikrokontroler." Jurnal JEETech 1, no. 2 (October 21, 2020): 85–89. http://dx.doi.org/10.48056/jeetech.v1i2.10.
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ABSTRAK
Penelitian ini bertujuan merancang sebuah alat pengendali parabola yang dapat mencari sinyal satelit ku-band secara otomatis yang dikendalikan oleh mikrokontroler Atmega328, menggunakan 2 motor servo sebagai penggerak untuk menggerakkan parabola kearah barat dan ketimur dan juga menggerakkan kearah utara keselatan, progam pada mikrokontroler memberikan perintah untuk menggerakkan 2 motor servo dan menghentikanya jika terdapat sinyal audio yang terdeteksi oleh komparator yang dikirimkan ke mikrokontroler.
Hasil dari penelitian ini adalah perancangan dan pembuatan alat pengendali parabola bergerak mencari sinyal pada satelit ku-band. Reflektor yang digunakan berbahan plat baja berdiameter 45 cm dengan tinggi tiang fokus 39 cm. Desain dari pengendali parabola ini terdiri dari 5 komponen utama, dimana komponen pertama sebagai tiang penopang dari reflektor yang terbuat dari besi, komponen kedua Reflektor berdiameter 45 cm yang terbuat dari plat besi, komponen yang ketiga LNB sebagai penerima dari sinyal yang di pantulkan oleh reflektor, komponen keempat rangkaian komparator dengan IC LM324 dan komponen yang kelima mikrokontroler sebagai pengontrol dari pergerakan parabola.
Kata Kunci : Mikrokontroler, Komparator, Parabola, Satelit Ku-band, Sinyal audio
ABSTRACT
The aim of this study is to design a parabolic controller that can seek for Ku-band satellite signals automatically which controlled by the Atmega328 microcontroller, by using two servo motor as activator to stirring the parabola toward west to east and also stirring toward north to south. The program on the microcontroller gives the command to move 2 motor serves and stop it if there is an audio signal detected by the comparator which sent to the microcontroller.
The results of this study are design and generation of parabola control tool which move to looking for signals on ku-band. The reflector that used is made by steel plate on a diameter of 45 cm with a height of 39 cm focus pole. The design of this parabolic controller consists of 5 main components where the first component is a supporting post of a reflector made by iron, the second component is reflector with diameter of 45 centimeter that made by iron, the third component is LNB as receiver of the signal reflected by the reflector, the fourth component is network comparator with IC LM324 and the fifth is microcontroller as a controller movement of a parabola.
Keywords : Microcontroller, Comparator, Parabolic, Ku-Band Satellite, Audio Signal
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Qiao, Xiaoying, Chunyan Yang, Qian Zhang, Shengke Yang, Yangyang Chen, Dan Zhang, Xiaoyu Yuan, Wenke Wang, and Yaqian Zhao. "Preparation of Parabolic Superhydrophobic Material for Oil-Water Separation." Materials 11, no. 10 (October 9, 2018): 1914. http://dx.doi.org/10.3390/ma11101914.
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In order to prepare parabolic superhydrophobic materials, copper meshes were used as the substrate and ultrasonic etching and oxidative corrosion were carried out with FeCl3 solution and H2O2 solution, respectively, and then the surface was modified with stearic acid (SA). The topological structure and surface wettability of the prepared mesh were characterized by fluorescence microscope, scanning electron microscopy and contact angle measurement. Finally, the as-prepared copper meshes were applied to oil-water separation. The results showed that the micro-nano-mastoid structure on the surface of the copper mesh was flaky bulges, forming a rough structure similar to a paraboloid. When the oxidative corrosion time of H2O2 was 1 min, it is more beneficial to increase the hydrophobicity of the surface of the copper mesh and increase the contact angle of water droplets on the surface of the membrane. Additionally, based on superhydrophobic materials of the parabolic copper mesh, the static contact angles of the water droplets, engine oil and carbon tetrachloride with the surface were approximately 153.6°, 5° and 0.1°, respectively and the sliding angle of the water droplets with the surface were approximately 4.9°. The parabolic membrane was applied to discuss the separation efficiency of different oils with deionized water and the separation efficiency was obtained as benzene > carbon tetrachloride > oil > machine oil. Therefore, based on the research, the parabolic superhydrophobic material has good efficiency of oil-water separation.
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French, Doug. "Parabolic Reflectors." Mathematical Gazette 83, no. 497 (July 1999): 237. http://dx.doi.org/10.2307/3619046.
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Kilner, Steven J., and David L. Farnsworth. "Parabolic coordinates." Mathematical Gazette 105, no. 563 (June 21, 2021): 226–36. http://dx.doi.org/10.1017/mag.2021.51.
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An important first step in understanding or solving a problem can be the selection of coordinates. Insight can be gained from finding invariants within a class of coordinate systems. For example, an important feature of rectangular coordinates is that the Euclidean distance between two points is an invariant of a change to another rectangular system by a rigid motion, which consists of translations, rotations and reflections. Indeed, the form of the distance function is an invariant. In calculus courses, students learn about polar coordinates, so that useful curves can be simply expressed and more easily studied.