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Funicular structures can resist a given load with pure axial forces and therefore tend to use material very efficiently. One main challenge in their design is form finding, which often requires advanced numerical methods. In this article, we show analytically that a very common family of curves, conics, is funicular for a particular load case: a uniform radial load emanating from a focus. The result is a generalization of the well-known funicularity of parabolas and arcs of circles, respectively, under uniform vertical load and constant normal pressure. It can be used to design self-stressed structures by hand without the need for calculations. Portions of conics can be combined to obtain original shapes. [ABSTRACT FROM AUTHOR]

Sensing of vortex shedding in unsteady airfoil flows can be beneficial in controlling and positively harnessing their effects for increased aerodynamic performance. The time variation of the leading-edge suction parameter (LESP), which is a non-dimensional measure of the leading-edge suction force, is shown to be useful in deducing the various events related to vortex shedding from unsteady airfoils. The recently developed leading-edge flow sensing (LEFS) technique, which uses a few pressures in the airfoil leading-edge region for deducing the aerodynamic state of an airfoil, is adapted to deduce the variation of LESP during an unsteady motion in incompressible flow. For this purpose, the flow over the airfoil is divided into an outer-region flow over the chord, modeled using thin airfoil theory, and an inner-region flow over the leading edge, modeled as a flow past a parabola. By matching these two flows, relations are derived for calculating the LESP from a few pressures at the leading edge. By studying the variations of the LEFS outputs and the calculated LESP for various unsteady motions, guidelines are presented for detecting events related to vortex shedding: initiation, pinch-off, and termination. Computational and experimental results for additional unsteady motions confirm the effectiveness of the LEFS as a sensing technique for events associated with vortex shedding on unsteady airfoils. [ABSTRACT FROM AUTHOR]

Conics typically include ellipses, hyperbolas, and parabolas with equal eccentricities that intersect infinite line at absolute points. According to the imaging characteristics of conics under a pinhole camera, a dual image of the absolute points can be obtained. By analysing the representative coefficient matrix of the dual image, the algebraic relationship between the image of the centre of the conic and its projection matrix can be obtained; thus, the vanishing line can be determined by the pole-polar relationship of the dual image of the absolute points. A group of orthogonal vanishing points can be obtained to determine the camera intrinsic parameters by two conics with aligned principal axes. The feasibility and robustness of the algorithm are verified by simulation data and real experiments. [ABSTRACT FROM AUTHOR]

The binary quadratic Diophantine equation represented by the negative pellian y² = 10x² - 54 is analysed for its non-zero distinct solutions. A few interesting relations among the solutions are given. Further, employing the solutions of the above hyperbola, we have obtained some second order Ramanujan numbers and solutions of other choices of hyperbolas, parabolas. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of obtaining non-zero distinct integer solutions to the nonhomogeneous binary quadratic equation represented by the Pell-like equation 11x2 - 10y2 = 11. Different sets of integer solutions are presented. Employing the solutions of the above equation, integer solutions for other choices of hyperbolas, parabolas and straight lines are obtained. A special Pythagorean triangle is also determined. The formation of Diophantine 3 - tuples with suitable property is illustrated. [ABSTRACT FROM AUTHOR]

Copyright of Przegląd Elektrotechniczny is the property of Przeglad Elektrotechniczny and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Good mathematics stands the test of time. As culture changes, we often ask different questions, bringing new perspectives, but modern mathematics stands on ancient discoveries. Isaac Newton’s discovery of calculus (along with Leibniz) may seem old but is predated by Archimedes’ findings. Current mathematics students should be familiar with parabolas and simple curves; in our introductory calculus courses, we teach them to compute the areas under such curves. Our modern approach derives its roots from Newton’s work; however, we have filled in many of the gaps in the pursuit of mathematical rigor. What many students may not know is that Archimedes solved the area problem for parabolas long before the use of algebraic expressions became mainstream. Archimedes used the geometry of the ancient Greeks, which gave him a vastly different perspective. In this paper, we provide both Archimedes’ and Newton’s proofs involving the quadrature of the parabola, trying to remain true to their original texts as much as feasible. [ABSTRACT FROM AUTHOR]

This article investigates the 'conflict parabola' of the negotiations between EU member states during the COVID-19 pandemic. The crisis reopened the foundational controversy over cross-national solidarity under economic adversities. After a peak of conflict in March–April 2020, the political climate gradually shifted from antagonism to appeasement, creating the conditions necessary for the adoption of the Next Generation EU plan. Building on the negative experiences of past crises, some EU leaders engaged in a strategy of 'polity maintenance', i.e. keeping the EU polity together, regardless of interest-based divisions. This strategy mainly rested on public communication. The article documents both conflict and appeasement by analysing a corpus of leaders' quotes drawn from the press (covering eight countries) and a corpus of speeches by Angela Merkel. The Chancellor made a high political investment in EU polity maintenance, presenting European cohesion as part and parcel of Germany's national interest. [ABSTRACT FROM AUTHOR]

The article discusses the problem of introducing and constructing mathematical concepts using a computer. The Wolfram Mathematica 12 symbolic calculation system is used at each stage of the complex spiral process to form the notion of conic section and the related concepts of focus, directrix and eccentricity. The nature of these notions implies the use of appropriate animations, 3D graphics and symbolic calculations. Our vision of the process of formation of mathematical concepts is presented. The notions ellipse, parabola and hyperbola are defined as the intersection of a conical surface with a plane not containing the vertex of the conical surface. The conical section is represented as a geometric location of points on the plane for which the ratio of the distance to the focus to the distance to the directrix is a constant value. The lines of hyperbola and ellipse are determined by their foci. The equivalence of different definitions for conical sections is commented. [ABSTRACT FROM AUTHOR]

The article aims to understand the meaning of Jesus' praise of the administrator in the Parable of the Astute Administrator, recorded in Lk 16:1-8, as well as to propose theological and hermeneutical developments, aiming at Christian performance. The interpretation of this parable is marked by exegetical and theological discussions, by the discussions regarding the delimitation of the parable, the relationship with the sayings of vv. 9-13, and the theological complication of Jesus telling a story highlighting a dishonest action. In order to contribute to the discussion, the article develops from the analysis of the literary context, delimitation, form, structure, and setting, to then address its contents considering the narrative dynamics proper to the parable. By exploring the sense of the parable's praise of the administrator's urgent and intelligent action in a context of threat, and considering the eschatological context of Jesus' application of the parable, we trace a look at the theology of action. It takes up the eschatological context and language of the parable and proposes that in challenging, eschatological times, biblically called the "present age," the action of Christians must be urgent and intelligent. As a basis for the discussions, authors with important contributions to the understanding of the parable are revisited. [ABSTRACT FROM AUTHOR]

The article approaches the parable as a literary, pedagogical and thought resource, based on two short stories by Brazilian writers of Jewish origin, born in Eastern Europe: "Parábola do filho" [Parable of the son], by Samuel Rawet, and "Os desastres de Sofia" [Sofia's disasters], by Clarice Lispector. [ABSTRACT FROM AUTHOR]

Foot posture and function is important in diabetes, particularly as neuropathy in diabetes may present with motor in addition to sensory neural deficits. Examination of the anatomical architecture of the foot can inform on its load-bearing and balancing function. An examination that does not feature in guidelines on assessment of the diabetic foot is that of assessing whether a metatarsal parabola is present or malformed. The metatarsal 'parabola' (in the transverse plane) is so called because the cascade of the differing lengths of the metatarsals form a parabola, defined as the intersection of an arc with a flat (plantar) surface. The parabola serves a function in the rollover motion or forefoot rocker of the foot before heel rise to provide stability and balance in static stance. A further function ensures that the lever-action at the first metatarsophalangeal joint takes place with dorsiflexion of the hallux. This narrative review summarises the literature regarding methods of measuring the metatarsal parabola, dysfunction of the foot due to a dysmorphic metatarsal parabola, clinical relevance, examination and management in diabetes care. It documents the short first metatarsal (SFM) as a risk factor for diabetic foot ulceration. Examination for identification and management of dysmorphic metatarsal parabolae is recommended for foot examinations in diabetes care. [ABSTRACT FROM AUTHOR]

We have constructed the empirical formula for fusion barrier height (V B), fusion barrier position (R B), and inverted parabola (ħω) of light nuclei with atomic number in the range 2 ≤ Z C ≤ 10. This formula is obtained by studying the fusion barrier characteristics of 333 projectile target combinations. The values produced by the present formula are also compared with experiments. The present semi-empirical formula produces fusion barrier characteristics of light nuclei with the simple inputs of mass number (A) and atomic number (Z) of projectile targets. This semi-empirical formula can be utilized to calculate and interpret fusion barrier characteristics in light nuclear systems. [ABSTRACT FROM AUTHOR]

This paper introduces a novel class of fair and interpolatory planar curves called pκ -curves. These curves are comprised of smoothly stitched Bézier curve segments, where the curvature distribution of each segment is made to closely resemble a parabola, resulting in an aesthetically pleasing shape. Moreover, each segment passes through an interpolated point at a parameter where the parabola has an extremum, encouraging the alignment of interpolated points with curvature extrema. To achieve these properties, we tailor an energy functional that guides the optimization process to obtain the desired curve characteristics. Additionally, we develop an efficient algorithm and an initialization method, enabling interactive modeling of the pκ -curves without the need for global optimization. We provide various examples and comparisons with existing state-of-the-art methods to demonstrate the curve modeling capabilities and visually pleasing appearance of pκ -curves. • Introduce fair and interpolatory pκ -curves with parabolic-like curvature distribution. • Customize energy functionals to guide pκ -curve construction. • Develop an efficient and practical algorithm to solve the tailored optimization problem. [ABSTRACT FROM AUTHOR]

Summary: The main thesis of this article is inspired by Lessing's "Nathan the Wise": the monotheistic religions – regardless of what else they might be – are social systems. Though as such they cannot be true or false, they do include propositions and coherent religious worldviews, each of them claiming to be true. Yet, there is no possibility to verify those claims. As human beings, we can only search for truth and hope that God may guide us into all truth. Therefore, we have to reflect upon the relationship of religion and truth by models of participation and approximation – whereas the models of dogmatism, scepticism, pluralism, indifferentism and „egalitarianism" concerning truth must be rejected. [ABSTRACT FROM AUTHOR]

The present scientific article intends to detail the Christian ethics present in the parable of the good Samaritan given by Jesus Christ to the doctor of the Jewish law in the Gospel of Luke 10.25-37. Faced with so many contemporary ethical alternatives present today, it is worth observing Jesus' dialogue with the scholar of the law and from the position in the story told of the Priest, Levite and Samaritan, extracting Christian ethical principles to be applied in social life of the present time. To develop this research, it will be necessary to start from the Holy Scriptures with an emphasis on the exegesis of the mentioned text, with the support of biblical commentators of the New Testament. It will also require the support of New Testament theologians, contemporary theology and especially theorists in the area of Christian ethics. The methodology used will be descriptive research with the aim of generating reflection and applicability to relationships in contemporary society. The concluding proposal of this article, then, intends to show what must be a priority in the choice of Christian principles that must guide both simple and complex choices and decisions that life can provide to human beings. [ABSTRACT FROM AUTHOR]

Various real-time applications such as Human–Computer Interactions, Psychometric analysis, etc. use facial expressions as one of the important parameters. The researchers have used Action Units (AU) of the face as feature points and its deformation is compared with the reference points on the face to estimate the facial expressions. Among many parts of the face, features from the mouth contribute largely to all the well-known emotions. In this paper, the parabola theory is used to identify and mark various points on the lips. These points are considered as feature points to construct feature vectors. The Latus Rectum, Focal Point, Directrix, Vertex, etc. are also considered to identify the feature points of the lower lips and upper lips. The proposed approach is evaluated on benchmark datasets such as JAFFEE and Cohn–Kanade dataset and it is found that the performance is encouraging in understanding the facial expressions. The results are compared with contemporary methods and found that the proposed approach has given good classification accuracy in recognizing facial expressions. [ABSTRACT FROM AUTHOR]

Among the quasi-Newton algorithms, the BFGS method is often discussed by related scholars. However, in the case of inexact Wolfe line searches or even exact line search, the global convergence of the BFGS method for nonconvex functions is not still proven. Based on the aforementioned issues, we propose a new quasi-Newton algorithm to obtain a better convergence property; it is designed according to the following essentials: (1) a modified BFGS formula is designed to guarantee that B k + 1 inherits the positive definiteness of B k ; (2) a modified weak Wolfe–Powell line search is recommended; (3) a parabola, which is considered as the projection plane to avoid using the invalid direction, is proposed, and the next point x k + 1 is designed by a projection technique; (4) to obtain the global convergence of the proposed algorithm more easily, the projection point is used at all the next iteration points instead of the current modified BFGS update formula; and (5) the global convergence of the given algorithm is established under suitable conditions. Numerical results show that the proposed algorithm is efficient. [ABSTRACT FROM AUTHOR]

El presente artículo se deriva de una investigación a nivel doctoral en el campo de la educación matemática. Objetivo: Caracterizar los niveles de razonamiento del modelo de Van Hiele asociados a la comprensión del concepto de parábola como lugar geométrico por parte de estudiantes de décimo grado, haciendo uso del software de geometría dinámica GeoGebra. Método: En una primera etapa de la investigación y a partir del análisis del modelo y de la literatura que aborda la enseñanza de las cónicas como lugar geométrico con el uso de GeoGebra, se formulan descriptores preliminares para los niveles de pensamiento del modelo de Van Hiele, posteriormente se diseña una estrategia orientada por la entrevista socrática mediante la cual se refinan los descriptores para cada nivel. Resultados: En el presente artículo se presentan los descriptores que se detectaron en la etapa final de refinamiento de la entrevista socrática. Discusión y Conclusiones: Esta investigación valida el modelo de Van Hiele para la comprensión del concepto de parábola como lugar geométrico, mediado por el software de geometría dinámica

The problem of the rectification of curves and the calculation (for which we shall adopt the more geometric term “flattening”) of the surface of a rotating solid generated by a curve, once the rotation axis has been fixed, were treated by John Wallis in two short inter-related tracts on cycloids and cissoids in 1659. In this work, we focus on the problem of the rectification of the parabola, an ancient problem reproposed in the 17th century, and on the solution obtained by Wallis using particular series that reflect the mechanical method of Archimedes, even if this is not immediately apparent to the reader. In presenting Wallis’s speech, we use the language closest to us and make explicit all the calculations not performed by the author, favoring an understanding of the part of his writing dedicated to the rectification of the parabola.

In a 2-alternative forced-choice protocol, observers judged the duration of ball motions shown on an immersive virtual-reality display as approaching in the sagittal plane along parabolic trajectories compatible with Earth gravity effects. In different trials, the ball shifted along the parabolas with one of three different laws of motion: constant tangential velocity, constant vertical velocity, or gravitational acceleration. Only the latter motion was fully consistent with Newton's laws in the Earth gravitational field, whereas the motions with constant velocity profiles obeyed the spatio-temporal constraint of parabolic paths dictated by gravity but violated the kinematic constraints. We found that the discrimination of duration was accurate and precise for all types of motions, but the discrimination for the trajectories at constant tangential velocity was slightly but significantly more precise than that for the trajectories at gravitational acceleration or constant vertical velocity. The results are compatible with a heuristic internal representation of gravity effects that can be engaged when viewing projectiles shifting along parabolic paths compatible with Earth gravity, irrespective of the specific kinematics. Opportunistic use of a moving frame attached to the target may favour visual tracking of targets with constant tangential velocity, accounting for the slightly superior duration discrimination. [ABSTRACT FROM AUTHOR]

Classical theoretical approaches to evaluate CPTU-based hydraulic conductivity gave the expression of a bilinear relation defined by K D - B q Q t , for undrained and drained soils. In fact, a dividing line may be selected with a certain degree of subjectivity, and several undrained/drained points occur in opposite sites, which may make us doubt the necessity of two intersecting lines to distinguish the undrained and drained soils. And a uniform and relatively simple curve including an arc, parabola, or ellipse correlation may be more suitable and accessible from a practical point of view. A database in the Yangtze Delta region has been collated to assess the three curves compared with the bilinear line. With the graphical and statistical analyses, the results indicate that the arc, parabola, and ellipse simplified curves could give better performance than the bilinear line. Through the statistical analyses and the number of variables, the overall best curve was the ellipse with only two variables, which is expected to improve the application scope and simplicity of hydraulic conductivity. [ABSTRACT FROM AUTHOR]

It has been known for more than a decade that, if a self-similar arc can be shifted along itself by similarity maps that are arbitrarily close to identity, then is a straight line segment. We extend this statement to the class of self-affine arcs and prove that each self-affine arc admitting affine shifts that may be arbitrarily close to identity is a segment of a parabola or a straight line. [ABSTRACT FROM AUTHOR]

Recently, endoscopic transsphenoidal transclival approaches have been developed and their role is widely accepted for extradural pathologies. Their application to intradural pathologies is still debated, but is undoubtedly increasing. In the past five decades, different authors have reported various extracranial, anterior transclival approaches for intradural pathologies. The aim of this review is to provide a historical overview of transclival approaches applied to intradural pathologies. PubMed was searched in October 2018 using the terms transcliv*, cliv* intradural, transsphenoidal transcliv*, transoral transcliv*, transcervical transcliv*, transsphenoidal brainstem, and transoral brainstem. Exclusion criteria included not reporting reconstruction technique, anatomical studies, reviews without new data, and transcranial approaches. Ninety-one studies were included in the systematic review. Since 1966, transcervical, transoral, transsphenoidal microsurgical, and, recently, endoscopic routes have been used as a corridor for transclival approaches to treat intradural pathologies. Each approach presents a curve that follows Scott's parabola, with evident phases of enthusiasm that quickly faded, possibly due to high post-operative CSF leak rates and other complications. It is evident that the introduction of the endoscope has led to a significant increase in reports of transclival approaches for intradural pathologies. Various reconstruction techniques and materials have been used, although rates of CSF leak remain relatively high. Transclival approaches for intradural pathologies have a long history. We are now in a new era of interest, but achieving effective dural and skull base reconstruction must still be definitively addressed, possibly with the use of newly available technologies. [ABSTRACT FROM AUTHOR]

In the spaceborne inverse synthetic aperture radar (ISAR) imagery for space targets, the noise environment can be worse than traditional imaging scenarios because of the signal decay caused by the long radial range. Parametric translational motion compensation (TMC) method based on the image quality optimization has been proved to be useful in the low signal-to-noise ratio environments. However, a proper estimation of the initial values is indispensable to avoid local optimum solutions and improve computational efficiency. In this letter, a TMC method based on the parabolic curve detection and the entropy minimization is proposed. An initial compensation result is firstly obtained with the range shifts estimated by the parabolic curve detection using the Hough transform. Further, the minimum entropy-based method is employed to improve compensation accuracy. The imaging results of the real data are provided and compared with other methods to demonstrate the effectiveness and the high accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

• We investigated whether dynamic visual cues modifies the perceived visual vertical. • Parabolic motions implying Gravity vector orientations affected the perceived visual vertical. • The ability to estimate time-to-contact in an interception task was influenced by motion orientation. • These effect changed with the body tilt of the participant. Observers typically present a strong bias in estimating the orientation of a visual bar when their body is tilted > 60 ° in the roll plane and in the absence of visual background information. Known as the A-effect , this phenomenon likely results from the under-compensation of body tilt. Static visual cues can reduce such bias in the perceived vertical. Yet, it is unknown whether dynamic visual cues would be also effective. Here we presented projectile motions of a visual target along parabolic trajectories with different orientations relative to physical gravity. The aim of the experiment was twofold: First, we assessed whether the projectile motions could bias the estimation of the perceived orientation of a visual bar, measured with a classical subjective visual vertical (SVV) task. Second, we evaluated whether the ability to estimate time-to-contact of the visual target in an interception task was influenced by the orientation of these parabolic trajectories. Two groups of participants performed the experiment, either with their head and body tilted 90 ° along the roll plane or in an upright position. We found that the perceived orientation of the visual bar in the SVV task was affected by the orientation of the parabolic trajectories. This result was present in the tilted but not in the upright participants. In the interception task, the timing error increased linearly as a function of the orientation of the parabola. These results support the hypothesis that a gravity vector estimated from dynamic visual stimuli contributes to the subjective visual vertical. [ABSTRACT FROM AUTHOR]

Drawing on the Semiotic-cultural approach and the Anthropological theory of the didactic, this paper discusses how exploration of historically framed conceptualizations of mathematical objects can establish bridges between different mathematical areas such as calculus and Euclidean geometry. A classroom intervention study in two secondary mathematics classrooms involving dynamic geometry software tools to support the construction of a parabola and its tangent and aiming at the development of representational flexibility between algebraic/ functional and geometrical approaches, illustrates how students may benefit from participation in such explorations. [ABSTRACT FROM AUTHOR]

This paper explores Archimedes' works in conoids, which are three dimensional versions of conic sections, and will discuss ideas that came up in Archimedes' book On Conoids and Spheroids. In particular, paraboloids, or three dimensional parabolas, will be the primary focus, and a proof of one of the propositions is provided for a clearer understanding of how Archimedes proved many of his propositions. His main method is called method of exhaustion, with results justified by double contradiction. This paper will compare the ideas and problems brought up in On Conoids and Spheroids and how they relate to modern day calculus. This paper will also look into some basic details on the method of exhaustion and how it allowed the ancient Greek mathematicians to prove propositions without any knowledge of calculus. In addition, this paper will discuss some mathematical contributions made by Arabic mathematicians such as Ibn al-Haytham and how his work connects to mathematics in the seventeenth Century regarding sums of powers of whole numbers and the Basel Problem. Complicated forms of conoids such as hyperbolic paraboloids and other shapes that came after Archimedes will not be covered. [ABSTRACT FROM AUTHOR]

This paper deals in exhibiting a property for which type (R) of an integral function of an integral function represented by Dirichlet series for a finite order (R) is finite. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and study the class of conics provided by the symmetric matrices of the 3 × 3 magic squares. This class depends on three real parameters and various relationships between these parameters give special subclasses of conics. Although there are no magic circles we find an ellipse, a parabola and two hyperbolas of magic type. A search of integer points and a complex approach are also included. We study also a pair of complementary ellipses, called Pythagorean. [ABSTRACT FROM AUTHOR]

Eduardo J. Couture is considered one of the great jurists of the 20th century and, especially, recognized for his contributions in the area of procedural law. However, it may not be, to the same extent, because of his literary work. In the present his conceptions about justice, freedom, order and tolerance are addressed in the Parable of the Four Princes, from a more aesthetic point of view, but, not for that reason, less profound. This study also allows us to warn about the relevance of the possible relationships between Law and literature. [ABSTRACT FROM AUTHOR]

For two classical Cepheids, CEa Cas and CEb Cas, members of the open cluster NGC 7790, we have constructed diagrams spanning a time interval of 125 years. The diagrams have the shape of parabolas, which has allowed us for the first time to determine the quadratic light elements and to calculate the rates of evolutionary changes in their periods: s yr for CEa Cas and s yr for CEb Cas, in agreement with the theoretical calculations for the second and third crossings of the instability strip, respectively. The pulsation stability test proposed by Lombard and Koen has confirmed that the changes in the periods are real. [ABSTRACT FROM AUTHOR]

We present an easy and at the same time effective computational algorithm for tracing the interferograms of phase objects. The approach to preprocessing of interference patterns, which includes image denoising and removal of distortions, is given. We provide a detailed description of the parabola method involved in the algorithm for searching candidates for extreme points and consider the criteria for their selection and drawing lines connecting such points, i.e., the traces of the interference fringes. The advantages and disadvantages of the method, when applied to the study of complex-structured phase objects such as spark channels, which are formed during electrical discharges in ambient air, are discussed. [ABSTRACT FROM AUTHOR]

All previous studies reporting the application time-of-day effect for herbicides have been conducted with a single-orifice, flat fan nozzle. Whether an increased number of flat fans in the nozzle could affect the application time-of-day effect is unknown. A replicated outdoor pot experiment was conducted to determine the best application time for trifloxysulfuron from 05:00 (before sunrise), 07:00 (after sunrise), 09:00, 11:00, 13:00, 15:00, 17:00, 19:00 (before sunset), and 21:00 (after sunset) against velvetleaf when sprayed with a single-, dual-, or tripletorifice flat fan nozzles. Trifloxysulfuron sprayed with the single-orifice flat fan nozzle at 05:00 was the least effective treatment reducing velvetleaf fresh weight by 51%. When the single-orifice flat fan nozzle was used, velvetleaf fresh weight, expressed as a quadratic polynomial function with a parabola opening upward, decreased as the application time changed from 05:00 to 11:00 (70% control); thereafter, it increased until 21:00. When the dual- and triplet-orifice flat fan nozzles were used, velvetleaf fresh weight, expressed as a quadratic polynomial function with a parabola opening downward, increased from 05:00 to 07:00; thereafter, it increased as the application time changed until 19:00 (the best application time, reducing velvetleaf fresh weight by 82%). Foliar nyctinasty in velvetleaf is responsible for decreased efficacy of trifloxysulfuron sprayed with the single-orifice flat fan nozzle before sunset. This obstacle can be overcome using the dual- or triplet-orifice flat fan nozzles. [ABSTRACT FROM AUTHOR]

Copyright of Studia Norwidiana is the property of Towarzystwo Naukowe Katolickiego Uniwersytetu Lubelskiego Jana Pawla II and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Science & Studies of Accounting & Finance: Problems & Perspectives / Apskaitos ir Finansu Mokslas ir Studijos: Problemos ir Perspectyvos is the property of Vytautas Magnus University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Human eye disease classification adapted by many pieces of research in the last decade due to the importance of (eye) optical organ for humans and the evolution in classification techniques. Seven external eye diseases plus normal eye classified in this paper using back propagation with linear cyclic learning rate-based parabola function. The classification accuracy achieved in this paper is (89.83%). [ABSTRACT FROM AUTHOR]

Copyright of Educación y Humanismo is the property of Universidad Simon Bolivar and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Educación y Humanismo is the property of Universidad Simon Bolivar and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas and two lines. For an integral with respect to an appropriate weight function defined on any quadratic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. Convergence of the Fourier orthogonal expansions is also studied in each case. We discuss applications to the Fourier extension problem, interpolation of functions with singularities or near singularities and the solution of Schrödinger's equation with nondifferentiable or nearly nondifferentiable potentials. [ABSTRACT FROM AUTHOR]

Objetivo: Caracterizar los espacios de trabajo geométricos personales de profesores en formación en el contexto de problemas que involucran la articulación entre la geometría sintética y analítica. Método: Se llevó a cabo de la mano de la teoría de los paradigmas y los espacios de trabajo geométricos desarrollados por Alain Kuzniak y Houdement. El trabajo de investigación se desarrolló con un enfoque cualitativo y fundamentado en una estrategia investigativa clínica, se empleó un análisis a priori y a posteriori como metodología de investigación y una muestra de cuatro docentes de matemáticas en formación de una universidad pública del norte de Colombia. Resultados: Se evidenciaron carencias existentes de técnicas tanto sintéticas como analíticas al momento de desarrollar la situación problema, lo cual condujo a la desarticulación entre las geometrías sintéticas y analíticas. Discusiones y Conclusiones: El problema propuesto promovió la utilización de estrategias en donde se puede abordar de manera eficaz la geometría sintética como vía exploratoria de las definiciones de geometría analítica.

El recurso a otros lenguajes que caracteriza el “giro teológico” implica para Ricoeur y Henry el caso de las parábolas. Para el primero, las parábolas constituyen expresiones límites que remiten a experiencias límites de apertura. Para Henry, significan modos de acceso a las relaciones trascendentales de la Vida, que ponen de manifiesto la insuficiencia de la metáfora. El artículo explora estas significaciones a la luz de los textos evangélicos y de las obras de los filósofos mencionados, en dirección a una fenomenología de la excedencia.

Aerial barrage balls serve for marking high-voltage wires in order to visually warn pilots of civil and military aviation about the presence of overhead lines. The present article deals with the mechanical calculation of flexible overhead wires of overhead lines, in which aerial warning barrage balls are installed. The wire is considered as a homogeneous flexible thread having the outline of a parabola and a chain line. The load from the aerial barrage balls must not be substituted with a distributed one by simple division of the total load into the span length, since it can cause incorrect results. The formulas for determining the sag are given for a different number of aerial barrage balls as a function of their number and the coefficient of concentrated forces. The acceptable accuracy of mechanical calculation is demonstrated when using the model of wire in the form of a parabola adopted in the design practice, provided that the components of concentrated forces are correctly determined. The equation of state is recorded, taking into account the weight and wind loads on the wire, as well as load coefficients in two planes, depending on the number of barrage balls. The performed calculations demonstrate an acceptable accuracy of the determination of the stress at various loadings of the span. For more accurate calculation of mechanical stresses and sag arrows, a vector-parametric method for calculating the flexible wires of overhead lines is suggested, where the calculated model of wires in the form of a flexible elastic thread is put taking into account of the spatial arrangement of all structural elements. The results of mechanical calculation according to the program that had been developed and to the existing methods for a different number of aerial barrier balls moved along the span are presented.

L’articolo presenta l’esperienza di un primo approccio alla peer education, sia per il docente sia per gli studenti, realizzato in una classe di III liceo. La metodologia utilizzata è quella della peer tutoring, caratterizzata dal lavoro in gruppi composti da studenti tutor di livello disciplinare più alto e da studenti tutorandi di livello disciplinare più basso. Le giornate del percorso sono commentate sulla base dell’analisi di registrazioni effettuate durante i lavori; inoltre si analizzano qualitativamente i questionari e la discussione collettiva realizzate a fine percorso, al fine di individuare i punti di forza e di criticità dell’esperienza. Il focus dell’analisi riguarda principalmente aspetti legati alla metodologia applicata, e non al ruolo giocato dal contesto matematico. Si evidenziano da un lato il carattere di criticità che la peer tutoring riveste laddove non siano mai state realizzate attività cooperative, dall’altro la necessità, per un’efficace azione didattica, di una commistione di approcci didattici sia cooperativi (fra alunni) sia orchestrati dall’insegnante, in un’ottica dialogica che non preveda l’utilizzo esclusivo di un metodo piuttosto che un altro.

The objective of mechanical calculation of flexible wires of substations and overhead lines is to determine the sag and tension in different climatic conditions. A wire with a uniformly distributed load is considered as a homogeneous flexible thread having the form of a parabola. Concentrated loads from spacers, barrier balls, stubs, taps to electrical apparatus and other elements are replaced with the one distributed over the span. On behalf of a span without tension springs of insulators the action of concentrated loads on the wire is considered, an error is determined when replacing the concentrated forces with the one uniformly distributed along the span by the load. The sag for the equivalent wire is determined with the aid of the ratio of the increase of the sag, due to the presence of concentrated forces. An equation of state has been drawn up which makes it possible to determine the tension after changing the number of concentrated loads, e.g., after installing spacers, hanging the barrier balls, fixing the taps. The dependence of the maximum sag on the number of concentrated forces is given. The definition of the coefficient of concentrated forces as the ratio of the sum of the concentrated loads to the weight of the wire in the span is presented. A relationship between the load factors, the increase of the sag and the coefficient of concentrated forces is established. The formula has been deduced for determining the error in the replacement of concentrated forces by a uniformly distributed load along the span as a function of the number of concentrated forces and the coefficient of concentrated forces. A decrease in the error with an increase in the number of concentrated forces has been demonstrated. A more accurate calculation of mechanical tensions and sag is possible with the use of a vector-parametric method for calculating the flexible busbar of substations and air-line wires, where the design model of wires in the form of a flexible elastic thread is placed, taking into account the spatial disposition of all structural elements.

The COVID-19 epidemic has brought a huge impact to the clothing industry. Because of the inconveniences caused by countermeasures, clothing consumers can't go to physical stores to try on, so it is urgent to develop a virtual clothing trial system. In addition, online fitting and online shopping gradually become the trend of clothing consumption. Based on virtual reality technology, this paper proposes a virtual clothing fitting system, and studies the color saturation in the process. In this paper, a method of parametric drawing of garment characteristic curve is proposed, and the shape of garment is designed by using control vertices. Based on this, this paper presents four forms of sutured parabola space and their control point solving algorithm. According to the principle of scale method, a three-dimensional coordinate transformation model of feature points is established. The model can calculate the coordinates of each characteristic value point of clothing according to the body shape information provided by customers and the empirical formula of different clothing styles, and then reverse calculate the curve control point. Furthermore, Bezier surface generation method is used to fit the control points. After the surface patches are spliced, the 3D rigid clothing model can be obtained. Experiments show that the method of personalized clothing modeling in this paper is efficient and accurate, which can be further extended to the observation system with larger degree of freedom. [ABSTRACT FROM AUTHOR]