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In this paper, exact hydrostatic particulars equations for the centre of buoyancy curve and metacentric locus curve are given for rectangular cross section using quadratic functions. Those equations have not been given for the hyperbola range of the heel angles so far, and here it is done by using basic quadratic functions and their horizontally symmetric immersion shapes, with two new methods defined: 1. Rotation of basic cross section shapes, and 2. Hydrostatic cross section area complement method that uses homothety or scaling properties of emerged and immersed areas of the rectangular cross section. Observed metacentric curve for rectangle consists of semi-cubic parabolas and Lamé curve with 2/3 exponent and negative sign, resulting in the cusp discontinuities in the symmetry of those functions definition. In order to achieve above, two theorems are given: the theorem about scaling using hydrostatic cross section area complement and the theorem about parallelism of centre of buoyancy tangents with waterlines. After non-dimensional bounds are given for the existence of the swallowtail discontinuity of metacentric curve for rectangular cross section in the Part 1 of this paper, the proof of its position in the symmetry of rectangle vertex angle is given in this Part 2 of the paper, thus confirming its position from theory. [ABSTRACT FROM AUTHOR]

At the beginning of the naval architecture theory, in the 18th century, Bouguer and Euler set the foundations of naval architecture with the centre of buoyancy and metacentric curve definition. After that, in 20th century, it is determined from bifurcation and catastrophe theory developed by Thom, and its application for ships in works of Zeeman, Stewart and others, that the centre of buoyancy curve for the rectangular cross section consists of parabola and hyperbola equations, but no exact equations are given for the hyperbola segment of that curve. Therefore, the hyperbola segment of the centre of the buoyancy curve is re-examined in this paper with emphasis on belonging metacentric locus curve as the evolute of the centre of the buoyancy curve. The observed metacentric curve consists of semi-cubic parabolas and Lamé curves with 2/3 exponent and negative sign, resulting in the cusp discontinuities in the symmetry of functions definition. Belonging swallowtail discontinuity in the hyperbola range between two heel angles of the rectangular cross section deck immersion/bottom emersion angles is examined, depending on existence of extremes of belonging hyperbola curve. After that, the single condition for hyperbola extreme the existence is given with the belonging new lower and upper non-dimensional bounds of rectangle cross section dimensions. [ABSTRACT FROM AUTHOR]

The cellular-counterfort retaining structure, which combines cellular retaining wall with counterfort retaining wall, can effectively increase the height of backfilled retaining walls, and boast a broad prospect in earthwork projects. In the presence of the rib plates of counterfort retaining wall, the soil pressure on the vertical plate of the cellular-counterfort retaining structure is not uniformly distributed in the horizontal direction. The distribution model and size of the pressure directly affects the structural calculation. Through mathematical analysis, the fill between rib plates was divided into horizontal layers. Considering the friction between the fill counterfort in the counterfort section and the soil stripes, the authors derived the soil pressure formulas on the vertical and bottom plates of the cellular-counterfort retaining structure. Through centrifuge model test, the authors discussed the distribution law of soil pressure on the vertical plate of the cellular-counterfort retaining structure, and the influence of counterfort interval on soil pressure. The results show that: The soil pressure at the midspan of the vertical plate between counterforts increased linearly with the depth, and the soil pressure near the counterforts increased from the top to middle and then gradually decreased from the middle to the bottom of the wall. On the side of vertical plate, the soil pressure obeyed the parabola distribution in the wall length direction, i.e., the pressure was smaller on the two ends than in the middle; the soil pressure on the bottom plate decreased with the distance to the vertical plate. The counterfort had an obvious frictional reduction effect on the soil pressure from the fill to the vertical plate, and the effect became increasingly obvious with the growing depth; the effect was weakened when the counterfort spacing increased. The centrifugal model test verified the reasonability of the proposed formulas for the soil pressures in the cellular-counterfort retaining structure. [ABSTRACT FROM AUTHOR]

The second part of the article is based on the starting points in the decision-making problem (DPR) indicated at the first stage of research [1, point 2]. Here, the comparison of alternative autoclaved and non-autoclaved technologies for the production of carbon-plastic aircraft structures (AC) of the highly loaded type is continued wing caisson stringer panels of B787, A350, MC-21, CSeries mainline aircraft. The main provisions of decision-making theory and a system-process approach with the involvement of practice results are taken as the methodological basis. From the beginning, the following are presented: a scheme for assessing the relative quality of technological process objects; a block-type conceptual model of the subject area of decision-making and its basis; composition of selection criteria and indicators. Based on the above and with the involvement of autonomous dynamic systems (ADS) with discrete time, as well as the theory of the parabola (quadratic function), a formalized model of systemically grouped processes in the evaluation of alternatives is given. On this basis, the study of the essential differences of the alternatives with the interpretation of the ideas of topology (homology groups) was continued to support the adoption of a reasoned final decision in the future, as the goal of modeling this separate side of the functioning of the technical system. [ABSTRACT FROM AUTHOR]

In the fifth-generation (5G) mobile system, new millimeter-wave technologies such as small cell size and multibeam operation are introduced at the base station. Currently, the hybrid beam forming array antennas are developed for beam steering operations. However, the array antenna configuration has drawback of increased feed circuit loss and antenna gain reduction. Moreover, many modulation/demodulation circuits increase the antenna price. The reflector antenna is another option for multi beam operations that has high gain and small feeder loss. The problem of the reflector antenna is how to achieve good multi beam radiation patterns. Previously, reflector shaping method of the dual reflector antenna was proposed. However, previous method can't apply for good multi beam designing. In this paper, modification to the reflector shaping method using equivalent parabola reflector and equivalent circle reflector method is proposed to achieve a good multi beam radiation patterns. First, the equivalent parabola and circle equation is implemented in the reflector shaping algorithms. Second, a Matrix Laboratory (MATLAB) program is developed in order to obtain the main and sub reflector shapes. The accuracy of MATLAB program is ensured from the obtained ray path results, aperture distribution and radiation pattern. In the final step, multi beam performance is validated using an electromagnetic simulator, FEKO. Through comparison of the equivalent parabola with the equivalent circle reflectors, an antenna efficiency of 67.6% is obtained and better multi beam radiation patterns are demonstrated using the equivalent circle reflector. Therefore, the usefulness of the newly developed shaping method employing equivalent circle reflector is ensured. [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]

Chingiz Aitmatov's The Day Lasts Longer than a Hundred Years (I dol'she veka dlitsia den'), published in 1980, has long been read in terms of its affiliations with socialist realism as well as its radical departures into the realms of science fiction and folklore, resulting in a range of debates about the genre of the novel and the political allegories encoded in its various storylines. This essay returns to the fantastic elements that contaminate Aitmatov's late-Soviet text not as a historiography of the author's present, as Fredric Jameson would put it, but as an experiment in composing parabolas of the Anthropocene. Both as a geometric figure and as a fugitive cosmopolitics, parabolas inscribe a novel spacetime in which deep histories of colonial violence and dislocation intersect with futuristic arcs of planetary devastation, rewriting the Russian and Soviet empire's Central Asian periphery into a generative epicenter of ecological storytelling. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin Institute of Technology. Social Sciences Edition / Haerbin Gongye Daxue Xuebao. Shehui Kexue Ban is the property of Harbin Institute of Technology 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.)

This investigation deals with some exact analytical solutions of the incompressible second grade fluid by using the method based on the separation of variables. In many cases, this method can derive exact analytical solutions easier than other methods. A family of solutions is derived in this paper, which governs scientific and engineering experimentations. The derived solutions represent the flows having streamlines as a family of ellipses, parabolas, concentric circles, and rectangular hyperbolas. From practical point of view, these flows have applications in many manufacturing processes in industry. Some physical features of the derived solutions are also illustrated by their contour plots. [ABSTRACT FROM AUTHOR]

This article contributes a numerical scheme for finding approximate solutions of one-dimensional parabolic partial differential equations (PDEs) under non-classical boundary conditions. This scheme is based on the direct Chebyshev collocation method that has been frequently used for problems of ordinary differential equations (ODEs). In fact, the approximate solution of the problem in the truncated Chebyshev series form is obtained by this method. By substituting Chebyshev series solution into the considered problems and by using the matrix operations and the collocation points, the suggested scheme reduces the problems into the associated linear algebraic systems. By solving this system of equations, the unknown Chebyshev coefficients can be determined. To show the accuracy and the efficiency of the method, two numerical examples are implemented and the comparisons are given by a new collocation method. [ABSTRACT FROM AUTHOR]

We propose a numerical method for solving singularly perturbed one-dimensional non-linear parabolic problems. The equation converted to the nonlinear ordinary differential equation by discretization first in time then subsequently in each time level we use the Sinc collocation method on the ordinary differential equation. The convergence analysis of proposed technique is discussed, and it is shown that the approximate solution converges to the exact solution at an exponential rate as well. We know that the conventional methods for these types of problems suffer due to decreasing of perturbation parameter, but the Sinc method handles such difficulty. For efficiency and accuracy of the method, we validate the proposed method by several examples. The numerical results confirm the theoretical behavior of the rates of convergence. [ABSTRACT FROM AUTHOR]

In this paper, we derive some exact solutions of the equations governing the steady plane motions of an incompressible second grade fluid. For this purpose, the vorticity and stream functions both are expressed in terms o f complex variables and complex functions. The derived solutions represent the flows having streamlines as a family of ellipses, parabolas, concentric circles, and rectangular hyperbolas. Some physical features of the derived solutions are also illustrated by their contour plots. [ABSTRACT FROM AUTHOR]

In this work we study the problem with the nonlocal integral condition of the first type for the multidimensional heat equation. Applying the connection between nonlocal and inverse problems we investigate the associated inverse problem. The existence and uniqueness of the generalized solution are shown using Galerkin method. [ABSTRACT FROM AUTHOR]

Due to the fact that the image sensors have a fixed resolution and pixel size -- a lot of image processing algorithms are limited with pixel resolution. One of those image processing algorithms is related to 3D laser scanners and in particularly to the laser line detection from images. This pixel quantization resolution, however, in many cases is not sufficient and greatly limits the laser scanner precision. In particularly the problem is highlighted in the linearly growing or declining surfaces, but also in strait lines where the actual laser line centre position is between two pixels. In this paper two laser line centre position detection methods with sub-pixel accuracy have been proposed and investigated. The methods have been tested on real images and as seen from the results at the end of the paper, the methods greatly improve the laser line detection accuracy and resolution. [ABSTRACT FROM AUTHOR]

In the projecting calculations, it is necessary to consider the fact that the deforming force generally has a void value when the parameter and it increases according to a parabolic variation. [ABSTRACT FROM AUTHOR]

Copyright of Hacettepe University Journal of Education is the property of Hacettepe University Journal of Education 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.)

This paper presents an algorithm for the evaluation of stresses in reinforced concrete sections under service loads. The algorithm is applicable to any section defined by polygonal contours and is based on an analytical integration of the stresses: The nonlinear behaviour of concrete is represented by the parabola-rectangle law used in the Eurocode-2 for the ultimate concrete design. An integrated definition of the strains in concrete and steel is possible by the use of Heaviside functions, similarly to what is done for ultimate section design in Barros et al. (2004). Other constitutive equations for the definition of the stresses in the concrete or steel can be easily incorporated into the code. The examples presented consist in the evaluation of resulting axial load and bending moment in an irregular section and in a section in L shape. The results, for service stresses, can also be plotted in terms of design abacus; a rectangular doubly reinforced section is presented as example. [ABSTRACT FROM AUTHOR]

Processes described with parabola-hyperbolic differential equations are crucial in the theory of mathematical physics. The article deals with the heterogeneous parabola-hyperbolic equation with nonlocal boundary conditions. To further investigate this class of problems, we need to find its classical solution. We show the system of eigenfunctions and associated functions of the boundary value problem. Using these biorthogonal systems forming the basis Riesz, we build the desired classical solution that presents an infinite number whose elements are defined as solutions of the corresponding Cauchy problem. We prove the lemma for evaluating the elements of the problem solution. Using calculations for homogeneous parabola-hyperbolic equations and statements required auxiliary lemmas on assessing the elements solution; we derive the conditions for existence and uniqueness of the problem solution, which is formulated as a theorem. The results can be used to study optimal control problems for parabola-hyperbolic equations. [ABSTRACT FROM AUTHOR]

The article presents a Mirage Illusion laboratory activity showcasing concrete applications of parabolic concepts. It discusses fundamental formula derivation, the parabolic reflection principle and the likeness of parabola in the context of ellipses. According to the author, the activity aims to allow students to develop a geometric equation from the illusion.

This paper performs loaded tooth contact analysis of modified double helical gears by proposing a method that combines the mathematical programming method with finite element method. Firstly, based on reducing vibration and noise and raising working efficiency, the method of three segment modifications for pinion profile is presented. Cutter surface equation is deduced by changing the shape of cutter-edge, substituting three segment parabolas for the line. Secondly, according to the condition of compatibility of deformation, force equilibrium and the non-embedment, the model of loaded tooth contact of double helical gears is obtained. LTCA program is developed successfully in a personal computer. By using this program, tooth load distributions and loaded transmission error are obtained in a meshing period. Finally, the comparison experiment of loaded transmission error both before modification and after modification is carried out. The results indicate that the LTCA method of modified double helical gears is reliable. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the effect of time-dependent deformations (such as shrinkage and creep) on the interfacial stresses between an RC beam and FRP plate is presented. For this end, a closed-form solution for such stresses in externally FRP plated RC beams including creep and shrinkage effects is presented. The developed model is formulated to predict the interfacial stresses at time ‘t’, in which the RC beams have been already subjected to creep and shrinkage effects. The adherend shear deformations have been included in the present theoretical analysis by assuming a parabolic shear stress through the thickness of the RC beam and the FRP panel. Contrary to some existing studies, the assumption that both RC beam and FRP panel have the same curvature is not used in the present investigation. This research is helpful for the understanding on mechanical behavior of the interface and design of the FRP-RC hybrid structures. [Copyright &y& Elsevier]

Copyright of Pamukkale University Journal of Education is the property of Pamukkale University Journal of Education 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 Teocomunicação is the property of EDIPUCRS - Editora Universitaria da PUCRS 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.)

The article describes a deduced precise catenary of stay cables in cable-stayed bridges. An approximate configuration of parabola for simplifying the calculation is presented, which is said to have higher precision compared with former studies. The precise and simplified solutions that have been derived for sag and cable parameters solutions indicate that cable tension decreases monotonously along the cable from the top end to the low one.

The article investigates the Quadrature of the Parabola by following the path of Archimedes and provides rigorous analytical proofs of the propositions and claims. The Quadrature examines the ratio between the area of the parabolic section bounded by a parabola and a chord. Meanwhile, a parabola is the locus of points equidistant from a fixed point, called the focus, and a fixed line called the directrix. The Quadrature is an example of what a brilliant mind can achieve by using mathematical principles. Archimedes' work can be used by instructors to introduce students to some concepts in calculus.

This article presents a new eyelid localization algorithm based on a parabolic curve fitting. To deal with eyelashes, low contrast or false detection due to iris texture, we propose a two steps algorithm. First, possible edge candidates are selected by applying edge detection on a restricted area inside the iris. Then, a gradient maximization is applied along every parabola, on a larger area, to refine parameters and select the best one. Experiments have been conducted on a database of 151 iris that have been manually segmented. The performance evaluation is carried out by comparing the segmented images obtained by the proposed method with the manual segmentation. The results are satisfactory in more than 90% of the cases. [ABSTRACT FROM AUTHOR]

The article reports on the cubic equation's number of real roots. To illustrate, it mentions about the number of normals to the parabola by a given point in the plane. It states that to find the number of real roots, Cardan's cubic formula is useful, but not easily in general. To tell the real root's number without firts solving the equation, discrimination is suggested. It presents how the discriminant defines a boundary in the plane. These ideas are showed from a first calculus course: critical point, derivative, and graphing in an intuitive way.

Archimedes is generally regarded as the greatest mathematician of antiquity and along side Isaac Newton and C F Gauss as the top three of all times. He was also an excellent theoretician-cum-engineer who identified mathematical problems in his work on mechanics, got hints on their solution through engineering techniques and then solved those mathematical problems, many a time discovering fundamental results in mathematics, for instance, the concepts of limits and integration. In his own words, "… which I first discovered by means of mechanics and then exhibited by means of geometry". In this article we briefly described some his main contributions to mathematics. [ABSTRACT FROM AUTHOR]

In this paper we present a new method for lane detection in video frames of a camera. The main idea is to find the features of the lane in consecutive frames which match a geometric model. The geometric model is a parabola, an approximation of a circular curve. By mapping of this model in image space and calculation of Edginess for each pixel in R, G, B channels and maximizing a fitness function using a Genetic Algorithm (GA), the parameters of the lane can be obtained. The proposed algorithm is tested on different road images taken by a video camera from Ghazvin-Rasht road in Iran. The results show good performance of the algorithm in different weather and lighting conditions. [ABSTRACT FROM AUTHOR]

In this paper, we present a semi-automatic road extraction method based on a piecewise parabola model with 0-order continuity. The piecewise parabola model is constructed by seed points coarsely placed by a human operator. In this case, road extraction actually becomes a physical problem of solving of each piece of parabola with only two or three unknown parameters by using image constraints. We have used a least square template matching to solve the parabola parameters. The template is deformable developed based on the automatic detection of dual road edges. In addition, a method of flexible observation weight evaluation has also been developed in this matching method. Extensive testing experiments on various image sets demonstrate that the method is able to extract road centerlines reliably. It offers much higher efficiency in contrast to manual digitizing process. We also discuss some issues about semiautomatic road extraction and future work for improving the reliability and extending the availability of our method. [ABSTRACT FROM AUTHOR]

The article provides information on the most famous classical construction problems, known as the Problem of Appollonius, which calls for "constructing a circle tangent to three given circles. Substantive and historical problems can provide an effective classroom strategy for mathematically motivating students. It stated that the Problem of Apollonius was offered to one of the authors during his high school geometry class, and his teacher promised an "A" in the course for any student who could find a solution. Moreover, a mathematician proposed the problem to Adrianus Romanus, who solved it by finding that the centers of the tangent circle is the intersection of two parabolas.

This article focuses on the Greek astronomer Apollonius of Perga, a contemporary of Greek mathematicians Archimedes and Eudemus and King Attalus I. Topics discussed include Apollonius' study at Alexandria, Egypt, under the successors of Greek mathematician Euclid and his works, including the eight-volume "Conics" which gained for him the name "the great geometer." Mentioned also is Book 1 Proposition 11 of "Conics" which contains Apollonius' insightful approach to the parabola.

The article focuses on the graphical representation of complex solutions of the quadratic equation in the xy plane. The imaginary portion of the complex solution can be represented on the xy-plane by drawing a line tangent to the parabola at a point and passing through a point on the x-axis directly above/below the vertex of the parabola. The conjugate of the complex solution can found by drawing the line from tangent to the parabola a the point on the parabola.

Abstract: Mathematics is the application of algebra and arithmetic to describe physical situations. In anaesthesia this may be an arithmetic calculation using a standard algebraic equation to calculate a drug dose or the development of an algebraic equation to model the uptake and clearance of a drug. Applications of mathematical concepts that can seem foreboding to some are described in a way that makes their use easier. The general use of indices is described and this is expanded into the specific area of the use of exponentials. Logarithms are described, including their use to solve the problem of calculating indices, and their use in supporting the description of data that span very small to very large values. The sinusoidal function is described with examples of its use in modelling real situations. The parabola is described to identify its special features and demonstrate some specific applications. [Copyright &y& Elsevier]

The article offers information on the ellipse in Glassboro, New Jersey. The entity is commonly used by astronomers and workers in celestial mechanics but is not usually tackled in undergraduate textbooks on mathematics. It is usually called the angle E or the eccentric anomaly by astronomers, which means irregularity. They used anomaly instead of angle in referring to angles that describe planetary locations because the term originates from the predicted location of a planet which showed small deviations from the observed data.

The article reflects on a demonstration of projectile motion in a physics class. It is not easy for physics teachers to achieve success with a first throw of coin along the parabola. Moreover, two approaches are discussed to provide the initial velocity and necessary acceleration needed for the projectile motion.

An introduction to the publication MathAMATYC Educator is presented in which the editor cites reports within the issue including one by Vicki Sealey on the concept of Riemann sums, one by Sid Kolpas and Tom Voden on reflective parabolas, and one by Barbara Illowsky on free learning resources open for student use.