Arc Of Circle Research Articles

Angular measures and Birkhoff orthogonality in Minkowski planes

Let x and y be two unit vectors in a normed plane mathbb {R}^2. We say that x is Birkhoff orthogonal to y if the line through x in the direction y supports the unit disc. A B-measure (Fankhänel in Beitr Algebra Geom 52(2):335–342, 2011) is an angular measure mu on the unit circle for which mu (C)=pi /2 whenever C is a shorter arc of the unit circle connecting two Birkhoff orthogonal points. We present a characterization of the normed planes that admit a B-measure.

The Fourier extension method and discrete orthogonal polynomials on an arc of the circle

The Fourier extension method, also known as the Fourier continuation method, is a method for approximating non-periodic functions on an interval using truncated Fourier series with period larger than the interval on which the function is defined. When the function being approximated is known at only finitely many points, the approximation is constructed as a projection based on this discrete set of points. In this paper we address the issue of estimating the absolute error in the approximation. The error can be expressed in terms of a system of discrete orthogonal polynomials on an arc of the unit circle, and these polynomials are then evaluated asymptotically using Riemann–Hilbert methods.

Machine Learning design of Volume of Fluid schemes for compressible flows

Our aim is to establish the feasibility of Machine-Learning-designed Volume of Fluid algorithms for compressible flows. We detail the incremental steps of the construction of a new family of Volume of Fluid-Machine Learning (VOF-ML) schemes adapted to bi-material compressible Euler calculations on Cartesian grids. An additivity principle is formulated for the Machine Learning datasets. We explain a key feature of this approach which is how to adapt the compressible solver to the preservation of natural symmetries. The VOF-ML schemes show good accuracy for advection of a variety of interfaces, including regular interfaces (straight lines and arcs of circle), Lipschitz interfaces (corners) and non Lipschitz triple point (the Trifolium test problem). Basic comparisons with a SLIC/Downwind scheme are presented together with elementary bi-material calculations with shocks.

Understanding Thoracic Spine Morphology, Shape, and Proportionality.

Retrospective review. The aim of this study was to describe thoracic kyphosis (TK) in a normal asymptomatic population and to evaluate the association between TK magnitude and its shape. Understanding spinal anatomy requires a three-dimensional appreciation of the spine's shape, morphology, and proportions. The customary definition of TK is the angle between T4 and T12. However, little is known on the actual shape of TK in adults. Asymptomatic volunteers were recruited; demographic data along with full-body standing radiographs were recorded. Radiographic data such as T1-12 and T4-12 angles were collected. Maximum TK and vertebral orientation/tilt were also collected, in addition to cumulative TK and Centered Kyphosis at T7. The cohort was stratified by T1-12 value (<40°, 40°-60°, and>60°) and comparisons and regressions were performed afterward. One hundred nineteen subjects were included (average age 50.8 yrs, 81 female). Mean T1-12 kyphosis was 49.5°, mean T4-12 kyphosis 41.5°, and mean maximum TK was 52.6°. T1 was the most anteriorly tilted vertebra, L1 the most posteriorly tilted; T7 was horizontal, independently of T1-12 value or age. Cumulative kyphosis analysis revealed that the apex of kyphosis was located at T6-T7. Regression analysis predicting the value and the percentage of T1-7 both yielded T1-12 as a predictor (Adj. r = 0.32, Adj. r = 0.13). Changes in kyphosis distribution in an asymptomatic population suggest that TK is not a simple circle arc: with low TK, 2/3 of the kyphosis is located in the upper part and when TK increases, the distribution of kyphosis will be symmetric around T7. It is possible to predict the amount of kyphosis in the upper part using total kyphosis value. This could help estimate preoperative compensation and predict reciprocal change. 3.

Geometric modeling of a flat contour using a circle

In geometric modeling of contours, in most cases it is convenient to use the equations of curves written in a parametric form. In this case, when modeling flat contours of the first order of smoothness, can be used circular arcs. The article proposes a method for determining the parametric equation of a circle (arc of a circle) for two ways: defining a circle over three points, as well as defining a circle over two points and a tangent in one of them. The definition of the parametric equations of circles in both cases was carried out using a projective coordinate system. In the first case, the conditions for the membership of three given points of this curve were imposed on the classical parametric equation of a second-order curve in the projective coordinate system to determine the unknown coefficients of the equation, and the given points were taken as three basis points of the projective system. Passing the obtained second-order curve through cyclic points made it possible to determine all unknown coefficients of the equation and, thus, determine the desired parametric equation of the circle in the projective coordinate system.In the second case, for simplicity, a local system of affine coordinates was chosen in which two given points were located on the Ox axis symmetrically with respect to the Oy axis, and the point on the tangent was located on the Oy axis. These 3 points were taken as 3 basis points of the projective coordinate system, and the fourth point of the projective coordinate system — the unit point — was defined in the affine system as a point belonging to this circle. The classical equation of a second-order curve in a projective coordinate system that passes through 3 basis points of the projective system and touches the coordinate lines in two of them, provided that the unit point belongs to the circle, is the desired equation of circle.After determining both of the desired equations in the projective coordinate system, using the transfer formulas from the projective system to the affine, the desired parametric equations of the circles in the affine system are determined.

3D Smith Chart Constant Quality Factor Semi-Circles Contours for Positive and Negative Resistance Circuits

The article proves first that the constant quality factor (Q) contours for passive circuits, while represented on a 2D Smith chart, form circle arcs on a coaxal circle family. Furthermore, these circle arcs represent semi-circles families in the north hemisphere while represented on a 3D Smith chart. On the contrary we show that the constant Q contours for active circuits with negative resistance form complementary circle arcs on the same family of coaxal circles in the exterior of the 2D Smith chart. Also, we find out that these constant Q contours represent complementary semi-circles in the south hemisphere while represented on the 3D Smith chart for negative resistance circuits. The constant Q - computer aided design (CAD) implementation of the Q semi-circles on the 3D Smith chart is then successfully used to evaluate the quality factor variations of newly fabricated Vanadium dioxide inductors first, directly from their reflection coefficient, as the temperature is increased from room temperature to 50 degrees Celsius ({\deg}C). Thus, a direct multi-parameter frequency dependent analysis is proposed including Q, inductance and reflection coefficient for inductors. Then, quality factor direct analysis is used for two tunnel diode small signal equivalent circuits analysis, allowing for the first time the Q and input impedance direct analysis on Smith chart representation of a circuit, including negative resistance

Regular linear surfaces in architecture and construction

Linear surfaces are widely used in engineering, architecture and construction, which is explained by their simplicity and adaptability. The linear surface is formed by the movement of a straight line sliding along curvilinear guides. The shape of the guides is determined by the architect-designer and depends on the geometric boundary conditions. At the same time, the surface must meet certain aesthetic criteria. As a result, the shape of the curved guides may be overly complex, and the designed surface becomes irregular, that is, it does not have an exact analytical description. For visualization of the irregular surface, two-dimensional spline approximation methods (Koons surface, Bezier, NURBS surfaces) are used. The technology for making such a surface is, as a rule, extremely complicated. The article proposes a simplified graphical algorithm for constructing a regular linear surface, given by flat guides of arbitrary shape. The algorithm is based on approximation of the guide lines by arcs of curves of the second order. To build a linear surface that passes through given guides, the method of dividing the chords into proportional parts is used. In the general case, a proportional or projective correspondence is established between the points of the chords. The points of division are transferred to curvilinear guides by the method of central or parallel projection, after which the corresponding points are connected by segments of straight lines. In addition to general surfaces, the article considers oblique transition surfaces and wedge-shaped surfaces. The surface of an oblique transition rests on arcs of circles of the same radius. The wedge-shaped surface contains one or two rectilinear guides. The use of such surfaces in the practice of architectural and construction design allows to create a variety of forms while ensuring good technological conditions for the manufacture of the supporting framework of the designed surface.

Splitting of a gap in the bulk of the spectrum of random matrices

We consider the probability of having two intervals (gaps) without eigenvalues in the bulk scaling limit of the Gaussian Unitary Ensemble of random matrices. We describe uniform asymptotics for the transition between a single large gap and two large gaps. For the initial stage of the transition, we explicitly determine all the asymptotic terms (up to the decreasing ones) of the logarithm of the probability. We obtain our results by analyzing double-scaling asymptotics of a Toeplitz determinant whose symbol is supported on two arcs of the unit circle.

Cytoplasmic RNA Sensor Pathways and Nitazoxanide Broadly Inhibit Intracellular Mycobacterium tuberculosis Growth.

SummaryTo establish stable infection, Mycobacterium tuberculosis (MTb) must overcome host innate immune mechanisms, including those that sense pathogen-derived nucleic acids. Here, we show that the host cytosolic RNA sensing molecules RIG-I-like receptor (RLR) signaling proteins RIG-I and MDA5, their common adaptor protein MAVS, and the RNA-dependent kinase PKR each independently inhibit MTb growth in human cells. Furthermore, we show that MTb broadly stimulates RIG-I, MDA5, MAVS, and PKR gene expression and their biological activities. We also show that the oral FDA-approved drug nitazoxanide (NTZ) significantly inhibits intracellular MTb growth and amplifies MTb-stimulated RNA sensor gene expression and activity. This study establishes prototypic cytoplasmic RNA sensors as innate restriction factors for MTb growth in human cells and it shows that targeting this pathway is a potential host-directed approach to treat tuberculosis disease.

The algorithm for generation of structured grids in deformed volumes of revolution

For the volume of revolution deformed by another volume of revolution, a grid generation algorithm is suggested. The algorithm is designed for multimaterial hydrodynamic simulation and for solving other physical and engineering problems. The algorithm represents the non-stationary procedure generating three-dimensional structured grids in domains with moving boundaries. The algorithm is developed within the variational approach for constructing optimal curvilinear grids. The volume of revolution is obtained by the rotation about the axis through 180° of a plane generatrix curve consisting of straight line segments and arcs of circles. The non-stationary algorithm is the iterative process at each stage of which the deformation of a grid and then its optimization are carried out. The deformation of a grid is implemented within the geometrical approach, and the optimization of a grid within the variational approach. Iterations are continued until the necessary deformation is reached. The algorithm is realized in the computer code written in C++.

Geometrical Analysis of Connecting Beam Mandala: A Planar Deployable Mechanism

Abstract Connecting beam (CB) mandala is a kind of planar deployable mechanism with the ability of scaling up and down like a mandala flower. It is constructed by many-component connecting beams, which are identical circle arcs with specific arc angle and three revolving joints (one middle joint and two end joints) located symmetrically. In this paper, a detailed geometrical analysis of CB mandala is reported. Some basic concepts and parameters are proposed to describe CB mandala's geometry. Based on them, the scaling motion of CB mandala is analyzed, and its five morphologies and their unique features are presented. CB mandala's application is also discussed and illustrated with a simple case.

Tool Path and Sheet Thickness Distribution of Axisymmetric Cup in Single Point Incremental Forming

This study involved planning different tool paths for an axisymmetric cup to explore the forming characteristics of the single point incremental forming (SPIF) process. In addition, this study developed a gradient theory to compute the inclined angle between the tangential and horizontal directions of the cup formed using single point incremental forming. The sheet thickness distribution of the cup was also calculated. To verify the theory, circle arc cups were formed by CNC machining using different tool paths. It was found that the cup formed using the spiral evolutional snail-line tool path produced a better surface than that formed using the equal height evolutional tool path. The sheet thicknesses of circle arc cups obtained by the experiment and using the cosine law were compared. A larger deviation was noted in the initial portion of the cup, whereas a smaller deviation was found in the other portion. This study also adopted a dual-conical cup to investigate the relationship between thickness and the initial inclined angle at the initial portion. It was found that a larger initial inclined angle led to good coincidence between the experimental and theoretical sheet thicknesses.

Equating Method for Prevent Discrimination in Classroom

This study aims to determine effectivenes Simplified Cirlce Arc method used at the school level to prevent discrimination against student grades. This study National Examination data on mathematics subjects from of the Center for Educational Assessment in DKI Jakarta and Tangerang regions. Using the Rasch Model analysis, data obtained for 2135 in the DKI Jakarta (X) and 2271 in the Tangerang area (Y). The data was obtained after conducting Rasch analysis with Mean Square Outfit (MNSQ) of 0.5 &lt;MNSQ &lt;1.5. Replication is done 50 times for each form data distribution from each region. Results of replication then RMSE value is calculated. The results showed that equal form with normal data distribution, statistically the average RMSE with the Simplified Circle Arc method smaller than the average RMSE result of equalization with the Nominal Weight Mean method which indicates that the Simplified Circle Arc method more accurate than Nominal Weight Mean method. Likewise, with equal equations with positive skeweness and negative skewness data distribution, the average RMSE with the Simplified Circle Arc Method is smaller than average RMSE resulting in equalization of the score with Nominal Weight Mean method. A small RMSE value indicates a fairly accurate result of equalization.

Millimeter-level ultra-long period multiple Earth-circling surface waves retrieved from dense high-rate GPS network

High-rate GPS networks have proven to be capable of continuously recording strong ground motion, which is valuable for studying earthquake rupture processes and seismic hazard mitigation. Previous studies of high-rate GPS usually resolved dynamic ground displacements of some major seismic phases stronger than a few millimeters. In this study, we explore the feasibility of retrieving much weaker ground motions (sub-millimeter) in long duration records by stacking high-rate GPS network. We processed data of the 2011 Tohoku-Oki earthquake recorded by more than 600 high-rate GPS stations of the Plate Boundary Observatory (PBO) and analyzed kinematic displacement results with seismic array methods. From these high-rate GPS seismograms, we identified abundant seismic phases, not only including clear body waves such as multiple S waves (S, SS, SSS, SSSS traveling along minor/major great circle arc, and SSSSSS beyond 360 degrees), but also the R1–R5 Rayleigh waves and G1–G6 Love waves, some of which travel around the Earth multiple times. Many of these seismic phases have not been reported by previous high-rate GPS studies. The group velocity dispersion curves extracted from multiple earth-circling Love waves of high-rate GPS are consistent with those of broadband seismic records in the period from 150 to 600 s, which can sample the mantle structure down to top of the lower mantle, thus important for understanding interaction between upper mantle and lower mantle. So the dense high-rate GPS networks should be useful for deep mantle research as an additional valuable dataset. With the development of multi-system GNSS and the more precise modeling of error sources, high-rate GNSS data should have great potential for accurately detecting more geodynamic processes with much wider bandwidth in geoscience studies.

Additive manufacturing and mechanical properties of lattice-curved structures

Purpose The purpose of this paper is to study the feasibility of the fabrication of circle arc curved-layered structures via conventional fused deposition modeling (FDM) with three-axis machines and to identify the main structural parameters that have an influence on their mechanical properties. Design/methodology/approach Customized G-codes were generated via a script developed in MATLAB. The G-codes contain nozzle trajectories with displacements in the three axes simultaneously. Using these, the samples were fabricated with different porosities, and their influence on the mechanical responses evaluated via tensile testing. The load-displacement curves were analyzed to understand the structure-property relationship. Findings Circled arc curved-layered structures were successfully fabricated with conventional three-axis FDM machines. The response of these curved lattice structures under tensile loads was mapped to three main stages and deformation mechanisms, namely, straightening, stretching and fracture. The micro-structure formed by the transverse filaments affect the first stage significantly and the other two minimally. The main parameters that affect the structural response were found to be the transverse filaments, as these could behave as hinges, allowing the slide/rotation of adjacent layers and making the structure more shear sensitive. Research limitations/implications This paper was restricted to arc-curved samples fabricated with conventional three-axis FDM machines. Originality/value The FDM fabrication of curved-structures with controlled porosity and their relation to the resulting mechanical properties is presented here for the first time. The study of curved-lattice structures is of great relevance in various areas, such as biomedical, architecture and aerospace.

A Note on Robust Biarc Computation

A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical configurations. The proposed algorithm uses an algebraic construction which is reduced to the solution of a single $2$ by $2$ linear system. Singular angles configurations are treated smoothly by using the pseudoinverse matrix when solving the linear system. The proposed algorithm is compared with the Matlab's routine \texttt{rscvn} that solves geometrically the same problem. Numerical experiments show that Matlab's routine sometimes fails near singular configurations and does not select the correct solution for large angles, whereas the proposed algorithm always returns the correct solution. The proposed solution smoothly depends on the geometrical parameters so that it can be easily included in more complex algorithms like splines of biarcs or least squares data fitting.

Simultaneous Chain-Forming and Generalization of Road Networks

Streets are essential entities of urban terrain and their automatic extraction from airborne sensor data is cumbersome because of a complex interplay of geometric, topological, and semantic aspects. Given a binary image representing the road class, centerlines of road segments are extracted by means of skeletonization. The focus of this paper lies in a well-reasoned representation of these segments by means of geometric primitives, such as straight line segments as well as circle and ellipse arcs. Thereby, we aim at a fusion of raw segments to longer chains which better match to the intuitive perception of what a street is. We propose a two-step approach for simultaneous chain-forming and generalization. First, we obtain an over-segmentation of the raw polylines. Then, a model selection approach is applied to decide whether two neighboring segments should be fused to a new geometric entity. For this purpose, we propose an iterative greedy optimization procedure in order to find a strong minimum of a cost function based on a Bayesian information criterion. Starting at the given initial raw segments, we thus can obtain a set of chains describing long alleys and important roundabouts. Within the procedure, topological attributes, such as junctions and neighborhood structures, are consistently updated, in a way that for the greedy optimization procedure, accuracy, model complexity, and topology are considered simultaneously. The results on two challenging datasets indicate the benefits of the proposed procedure and provide ideas for future work.

Small Arcs of Larger Circles: Framing through Other Patterns, Nora Bateson (2016)

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Uranometría Argentina and the constellation boundaries

AbstractThe astronomical community accepts the division of the celestial sphere into 88 constellations, according to what was established by the IAU. In the first Assembly of 1922 the use of Latin names for constellations and their abbreviations was resolved. The pending issue of the limits of the constellations was discussed in the next meeting and Eugène Delporte had the responsibility for the complete theoretical demarcation. For his work, Delporte took into account what was done half a century earlier in the famous work Uranometría Argentina, published in 1877 and 1879, under the supervition of Benjamin Gould. In ths presentation we discusse the situation at the moment when the constellation boundaries were proposed using arcs of RA circles and parallels of declination, choosing them in such a way that they did not deviate too much from those used in the most important celestial atlas of the time, and minimizing the changes of which constellations stars would belong to.

Sur la détermination du périmètre de l'ovale à huit centres

This note aims to present the history of the main researches carried out to represent an ellipse by means of an eight-centered oval and to complete them by giving a geometrical demonstration of the formulas expressing the coordinates of the centers, the radii and the central angles of these arcs of circles making up this oval. These formulas will make it possible to determine its perimeter and thus to approximate the value of that of the ellipse. This result could be useful for archaeologists, who will test the hypothesis according to which some Roman amphitheatres, such as the Coliseum, were built from eight-centered ovals.