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Artykuły w czasopismach na temat „Dual curve”

Autor: Grafiati

Data publikacji: 3 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

Balkı Okullu, Pınar, and Hasan Hüseyin Uğurlu. "Characterization of Dual Spacelike Curves on Dual Lightlike Cone Q~2 Utilizing the Structure Function." Symmetry 16, no. 12 (2024): 1574. http://dx.doi.org/10.3390/sym16121574.

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This study is about the dual spacelike curves lying on the dual lightlike cone, which can be either symmetric or asymmetric. We first establish the dual associated curve, which is related to the reference curve. Using these curves and the derivative of the reference curve, we derive the dual asymptotic orthonormal frame. Next, we define the dual structure function, curvature function, and Frenet formulae, and express the curvature function in terms of the dual structure function. This leads to a differential equation that characterizes the dual cone curve in relation to its curvature function.

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2

Nurkan, Semra Kaya, and İlkay Arslan Güven. "Construction of vectorial moments via direction curves." AIMS Mathematics 8, no. 6 (2023): 12857–71. http://dx.doi.org/10.3934/math.2023648.

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<abstract><p>In a recent paper Tunçer <sup>[<xref ref-type="bibr" rid="b14">14</xref>]</sup> described and examined the moment vectors (T -dual, N-dual, B-dual curve) of the curve with respect to the origin of the vector by using T(s), N(s), B(s) and the position vector of the curve. With the inspiration this paper provided, we define some new associated curves called dual-direction curves as integral curves of a vector field in this study. They are generated with the help of vectorial moments of a space curve in three-dimensional Euclidean space. We attain

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3

Kahraman, Tanju, Mehmet Onder, and H. Huseyin Ugurlu. "Dual Smarandache Curves Of A Curve Lying On Dual Unit Hyperbolic Sphere." Journal of Mathematics and Computer Science 14, no. 04 (2015): 326–44. http://dx.doi.org/10.22436/jmcs.014.04.07.

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4

Tunçer, Yılmaz. "Vectorial moments of curves in Euclidean 3-space." International Journal of Geometric Methods in Modern Physics 14, no. 02 (2017): 1750020. http://dx.doi.org/10.1142/s0219887817500207.

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In this study, we introduced the vectorial moments as a new curves as [Formula: see text]-dual curve, where [Formula: see text], constructed by the Frenet vectors of a regular curve in Euclidean 3-space and we gave the Frenet apparatus of [Formula: see text]-dual curves and also we applied to helices and curve pairs of constant breadth.

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5

Karaca, Emel. "Slant ruled surfaces generated by the striction curves of the hyper-dual curves." Filomat 38, no. 27 (2024): 9463–74. https://doi.org/10.2298/fil2427463k.

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In this paper, exploiting some considerable properties of hyper-dual curves and the concept of unit hyper-dual sphere, it is shown that each striction curve of the hyper-dual curve denotes two slant ruled surfaces in R3. Moreover, these slant ruled surfaces have a common striction curve. Then, it is proved that the normal vectors of these slant ruled surfaces are orthogonal along the common base curve. Consequently, an example is given to verify the obtained results.

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6

Chi, Baotao, Shengmin Bai, Qianjian Guo, Yaoming Zhang, Wei Yuan, and Can Li. "A New Definition of the Dual Interpolation Curve for CAD Modeling and Geometry Defeaturing." Mathematics 11, no. 16 (2023): 3473. http://dx.doi.org/10.3390/math11163473.

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The present paper provides a new definition of the dual interpolation curve in a geometric-intuitive way based on adaptive curve refinement techniques. The dual interpolation curve is an implementation of the interpolatory subdivision scheme for curve modeling, which comprises polynomial segments of different degrees. Dual interpolation curves maintain various desirable properties of conventional curve modeling methods, such as local adaptive subdivision, high interpolation accuracy and convergence, and continuous and discontinuous boundary representation. In addition, the dual interpolation c

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7

KAHRAMAN, Tanju, and Hasan Hüseyin UĞURLU. "Dual Smarandache Curves of a Timelike Curve lying on Unit dual Lorentzian Sphere." Mathematical Sciences and Applications E-Notes 4, no. 2 (2016): 1–13. http://dx.doi.org/10.36753/mathenot.421439.

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8

Qian, Jinhua, Xueqian Tian, and Young Ho Kim. "Normal Partner Curves of a Pseudo Null Curve on Dual Space Forms." Mathematics 8, no. 6 (2020): 919. http://dx.doi.org/10.3390/math8060919.

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In this work, a kind of normal partner curves of a pseudo null curve on dual space forms is defined and studied. The Frenet frames and curvatures of a pseudo null curve and its associate normal curve on de-Sitter space, its associate normal curve on hyperbolic space, are related by some particular function and the angles between their tangent vector fields, respectively. Meanwhile, the relationships between the normal partner curves of a pseudo null curve are revealed. Last but not least, some examples are given and their graphs are plotted by the aid of a software programme.

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9

Abdel-Baky, Rashad A., and Fatemah Mofarreh. "On an Explicit Characterization of Spherical Curves in Dual Lorentzian 3-Space D 1 3." Mathematical Problems in Engineering 2022 (June 25, 2022): 1–9. http://dx.doi.org/10.1155/2022/3044305.

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In this study, we developed a mathematical framework for studying spherical and null curves in dual Lorentzian 3-space D 1 3 . Considering the causal character of the dual curve, sufficient and necessary conditions for spacelike curves to be dual Lorentzian spherical were given. Also, new sufficient and necessary conditions for non-null curves to be hyperbolic dual spherical were presented. Then, an insight on curves with null-principal normal is reported.

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10

ABALI, Bahar, and Ahmet YÜCESAN. "Associated curves of a Frenet curve in the dual Lorentzian space." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 1 (2022): 285–304. http://dx.doi.org/10.31801/cfsuasmas.877170.

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11

Purwar, Anurag, and Qiaode Jeffrey Ge. "On the Effect of Dual Weights in Computer Aided Design of Rational Motions." Journal of Mechanical Design 127, no. 5 (2005): 967–72. http://dx.doi.org/10.1115/1.1906263.

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In recent years, it has become well known that rational Bézier and B-spline curves in the space of dual quaternions correspond to rational Bézier and B-spline motions. However, the influence of weights of these dual quaternion curves on the resulting rational motions has been largely unexplored. In this paper, we present a thorough mathematical exposition on the influence of dual-number weights associated with dual quaternions for rational motion design. By deriving the explicit equations for the point trajectories of the resulting motion, we show that the effect of real weights on the resulti

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12

Fukasawa, Satoru, and Kei Miura. "Galois points for a plane curve and its dual curve." Rendiconti del Seminario Matematico della Università di Padova 132 (2014): 61–74. http://dx.doi.org/10.4171/rsmup/132-5.

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13

Çı̇mdı̇ker Aslan, Muradı̇ye, and Gülşah Aydın Şekerci̇. "Dual curves associated with the Bonnet ruled surfaces." International Journal of Geometric Methods in Modern Physics 17, no. 13 (2020): 2050204. http://dx.doi.org/10.1142/s0219887820502047.

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An interest problem arises to determine the surfaces in the Euclidean three space, which admit at least one nontrivial isometry that preserves the principal curvatures. This leads to a class of surface known as a Bonnet surface. The intention of this study is to examine a Bonnet ruled surface in dual space and to calculate the dual geodesic trihedron of the dual curve associated with the Bonnet ruled surface and derivative equations of this trihedron by the dual geodesic curvature. Also, we find that the dual curvature, the dual torsion for the dual curves associated with the Bonnet ruled surf

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14

Fukasawa, Satoru, and Kei Miura. "Galois points for a plane curve and its dual curve, II." Journal of Pure and Applied Algebra 220, no. 5 (2016): 2038–48. http://dx.doi.org/10.1016/j.jpaa.2015.10.015.

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15

Al-ossmi, Laith H. M., and Imad Ibrahim Dawood. "Cohen's kappa curves, new geometrical forms of dual curves." Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika 5, no. 2 (2023): 226–46. http://dx.doi.org/10.35316/alifmatika.2023.v5i2.226-246.

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In this article, we introduce the concepts of taxicab and uniform products in the context of dual curves associated with Cohen's kappa, primarily defined by a set of inflection curvatures of an ellipse and a circle using parallel asymptotes. The novel curve under scrutiny, denominated as the "Like-Bulb Filament" (LBF) curve, is delineated as the locus of dual vertices originating from a couple of conic curvatures. The emergence of LBF transpires through the orchestrated arrangement of line segments emanating from a predetermined central focal point upon an elliptical form concomitant with a ci

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16

Li, Yanlin, Yushu Zhu, and Qing-You Sun. "Singularities and dualities of pedal curves in pseudo-hyperbolic and de Sitter space." International Journal of Geometric Methods in Modern Physics 18, no. 01 (2020): 2150008. http://dx.doi.org/10.1142/s0219887821500080.

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For the spherical unit speed nonlightlike curve in pseudo-hyperbolic space and de Sitter space [Formula: see text] and a given point P, we can define naturally the pedal curve of [Formula: see text] relative to the pedal point P. When the pseudo-sphere dual curve germs are nonsingular, singularity types of such pedal curves depend only on locations of pedal points. In this paper, we give a complete list of normal forms for singularities and locations of pedal points when the pseudo-sphere dual curve germs are nonsingular. Furthermore, we obtain the extension results in dualities, which has wid

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17

Nakwattanaset, A., S. Panich, and S. Suranuntchai. "Formability prediction of high‐strength steel sheet using experimental, analytical and theoretical analysis based on strain and stress forming limit curves and its application to automotive forming parts." Materialwissenschaft und Werkstofftechnik 54, no. 9 (2023): 1122–37. http://dx.doi.org/10.1002/mawe.202200323.

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AbstractIn this work, the high‐strength steel (HSS) sheet dual‐phase 440 (DP440) were conducted to establish the forming limit curve (FLC) and analytical forming limit stress curve (FLSC) obtained from experimental forming limit curve. First, the Nakajima stretch forming examination was carried out to obtain forming limit curve of investigated sheet. Afterwards, the theoretical Marciniak–Kuczinsky (M–K) model was developed and calculated to evaluate localized necking limits both in strain and stress spaces combination with anisotropic yield criteria. Then, the analytical forming limit stress c

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18

Çöken, A. Ceylan, and Ali Görgülü. "ON THE DUAL DARBOUX ROTATION AXIS OF THE DUAL SPACE CURVE." Demonstratio Mathematica 35, no. 2 (2002): 385–90. http://dx.doi.org/10.1515/dema-2002-0219.

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19

Yau, Stephen S. T., Qiwei Zhu, and Huaiqing Zuo. "Classification of weighted dual graphs consisting of $-2$-curves and exactly one $-3$-curve." Izvestiya: Mathematics 87, no. 5 (2023): 1078–116. http://dx.doi.org/10.4213/im9337e.

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Let $(V, p)$ be a normal surface singularity. Let $\pi\colon (M, A)\to (V, p)$ be a minimal good resolution of $V$. The weighted dual graphs $\Gamma$ associated with $A$ completely describes the topology and differentiable structure of the embedding of $A$ in $M$. In this paper, we classify all the weighted dual graphs of $A=\bigcup_{i=1}^n A_i$ such that one of the curves $A_i$ is a $-3$-curve, and all the remaining ones are $-2$-curves. This is a natural generalization of Artin's classification of rational triple points. Moreover, we compute the fundamental cycles of maximal graphs (see § 5)

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20

Zhou, Qingxin, Jingbo Xu, and Zhigang Wang. "Hyperbolic worldsheets and worldlines of null Cartan curves in de Sitter 3-space." International Journal of Modern Physics A 36, no. 04 (2021): 2150026. http://dx.doi.org/10.1142/s0217751x21500263.

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The hyperbolic worldsheets and the hyperbolic worldline generated by null Cartan curves are defined and their geometric properties are investigated. As applications of singularity theory, the singularities of the hyperbolic worldsheets and the hyperbolic worldline are classified by using the approach of the unfolding theory in singularity theory. It is shown that under appropriate conditions, the hyperbolic worldsheet is diffeomorphic to cuspidal edge or swallowtail type of singularity and the hyperbolic worldline is diffeomorphic to cusp. An important geometric invariant which has a close rel

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21

Yau, Stephen S. T., Qiwei Zhu, and Huaiqing Zuo. "Classification of weighted dual graphs consisting of $-2$-curves and exactly one $-3$-curve." Известия Российской академии наук. Серия математическая 87, no. 5 (2023): 232–70. http://dx.doi.org/10.4213/im9337.

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Let $(V, p)$ be a normal surface singularity. Let $\pi\colon (M, A)\to (V, p)$ be a minimal good resolution of $V$. The weighted dual graphs $\Gamma$ associated to $A$ completely describes the topology and differentiable structure of the embedding of $A$ in $M$. In this paper, we classify all the weighted dual graphs of $A=\bigcup_{i=1}^n A_i$ such that one of the curves $A_i$ is $-3$-curve, and the rest are all $-2$-curves. This is a natural generalization of Artin's classification of rational triple points. Moreover, we compute the fundamental cycles of maximal graphs (see Section 5) which c

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22

Limaiem, A., and H. A. ElMaraghy. "Curve and Surface Modeling with Uncertainties Using Dual Kriging." Journal of Mechanical Design 121, no. 2 (1999): 249–55. http://dx.doi.org/10.1115/1.2829451.

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This paper presents a new technique based on dual Kriging interpolation for modeling curves and surfaces in the presence of uncertainties in data points. Uncertainties result from measurement errors; therefore, a direct application of this method is found in curve/surface modeling using discrete sets of digitized points. It focuses on a common problem in geometric modeling, the trade-off between curve/surface smoothness and the approximation errors. The Kriging model filters the noise in the data while controlling the deviation locally at each point. However, the classical least-squares techni

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23

Bruce, J. W., and P. J. Giblin. "Generic isotopies of space curves." Glasgow Mathematical Journal 29, no. 1 (1987): 41–63. http://dx.doi.org/10.1017/s0017089500006650.

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For a single space curve (that is, a smooth curve embedded in ℝ3) much geometrical information is contained in the dual and the focal set of the curve. These are both (singular) surfaces in ℝ3, the dual being a model of the set of all tangent planes to the curve, and the focal set being the locus of centres of spheres having at least 3-point contact with the curve. The local structures of the dual and the focal set are (for a generic curve) determined by viewing them as (respectively) the discriminant of a family derived from the height functions on the curve, and the bifurcation set of the fa

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24

Burger, Craig A., and Charles D. Shackelford. "Evaluating dual porosity of pelletized diatomaceous earth using bimodal soil-water characteristic curve functions." Canadian Geotechnical Journal 38, no. 1 (2001): 53–66. http://dx.doi.org/10.1139/t00-084.

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Soil-water characteristic curve data for specimens containing either ~1 mm or ~2 mm diameter pellets of processed diatomaceous earth are measured using a variety of methods (Tempe cell, pressure plate, filter paper, and chilled-mirror psychrometer). The measured soil-water characteristic curve data are bimodal, reflecting both the microscopic porosity region within the individual pellets, or intrapellet porosity, and the macroscopic porosity region between the pellets, or interpellet porosity. The bimodal distributions are consistent with scanning electron micrographs that show the existence o

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25

Hayashi, Hiroyuki, and Hisao Yoshihara. "Galois Group at Each Point for Some Self-Dual Curves." Geometry 2013 (January 30, 2013): 1–6. http://dx.doi.org/10.1155/2013/369420.

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We study the Galois group defined by a point projection for plane curve. First, we present a sufficient condition that the group is primitive and then determine the structure at each point for some self-dual curves.

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26

Peralta-Torres, Jorge Alonso, Yuliana Izquierdo-Camacho, Nadia Florencia Ojeda-Robertos, Víctor Hugo Severino-Lendechy, Jesús Enrique Ek-Mex, and José Candelario Segura-Correa. "Lactation curves of Holstein x Gyr dual-purpose cows under humid tropical conditions." Revista de Investigaciones Veterinarias del Perú 33, no. 6 (2022): e22510. http://dx.doi.org/10.15381/rivep.v33i6.22510.

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The aim of this study was to identify the foremost model that depict the lactation curve of dual-purpose crossbred cows under a humid tropical environment. Six models were compared to describe the lactation curves of three breed groups using 1231 milk records of 160 cows. The breed groups were 0-25%, F1 (50%) and 62.5-75% Holstein x Gyr crosses. Parameters of the models and curves were estimated using non-linear procedures. The best model was determined by the Akaike information criterion. Wood, Sikka and Wilmink models provided a good fit to the lactation curves for the breed groups; however,

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27

Garanzha, Vladimir A., Liudmila N. Kudryavtseva, and Dmitry A. Makarov. "Discrete curvatures for planar curves based on Archimedes’ duality principle." Russian Journal of Numerical Analysis and Mathematical Modelling 37, no. 2 (2022): 85–98. http://dx.doi.org/10.1515/rnam-2022-0007.

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Abstract We introduce discrete curvatures for planar curves based on the construction of sequences of pairs of mutually dual polylines. For piecewise-regular curves consisting of a finite number of fragments of regular generalized spirals with definite (positive or negative) curvatures our discrete curvatures approximate the exact averaged curvature from below and from above. In order to derive these estimates one should provide a distance function allowing to compute the closest point on the curve for an arbitrary point on the plane.With refinement of the polylines, the averaged curvature ove

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28

Kulikov, Victor Stepanovich. "On the local fundamental group of the complement of a curve in a normal surface." Izvestiya: Mathematics 87, no. 3 (2023): 562–85. http://dx.doi.org/10.4213/im9357e.

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We give a presentation of the fundamental group of the complement of a curve $C$ in its "tubular" neighbourhood in a normal surface $S$. The presentation is given in terms of the double weighted dual graph of the resolution of singularities of $C$ (and $S$). This result generalizes the presentation of the fundamental group of the complement of a normal singularity in its neighbourhood given by Mumford in the case, where the dual graph of the resolution is a tree and all exceptional curves of the resolution are rational curves.

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Satoh, A., and K. Takano. "A scalable dual-field elliptic curve cryptographic processor." IEEE Transactions on Computers 52, no. 4 (2003): 449–60. http://dx.doi.org/10.1109/tc.2003.1190586.

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Brinjikji, Waleed, Gregory Michalak, Ramanathan Kadirvel, et al. "Utility of single-energy and dual-energy computed tomography in clot characterization: An in-vitro study." Interventional Neuroradiology 23, no. 3 (2017): 279–84. http://dx.doi.org/10.1177/1591019917694479.

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Background and purpose Because computed tomography (CT) is the most commonly used imaging modality for the evaluation of acute ischemic stroke patients, developing CT-based techniques for improving clot characterization could prove useful. The purpose of this in-vitro study was to determine which single-energy or dual-energy CT techniques provided optimum discrimination between red blood cell (RBC) and fibrin-rich clots. Materials and methods Seven clot types with varying fibrin and RBC densities were made (90% RBC, 99% RBC, 63% RBC, 36% RBC, 18% RBC and 0% RBC with high and low fibrin density

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31

Ismael, Sarwar S., and Faris R. Ahmed. "Seismic Fragility Curves for Reinforced Concrete Dual System Buildings." ARO-THE SCIENTIFIC JOURNAL OF KOYA UNIVERSITY 11, no. 1 (2023): 149–56. http://dx.doi.org/10.14500/aro.11172.

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A seismic fragility curve is a visual representation that illustrates the likelihood of a structure surpassing a particular damage or performance limit state caused by an earthquake with a specific intensity or ground motion level. This curve is typically generated using probabilistic seismic hazard analysis and structural reliability analysis methods. It is based on statistical models that rely on past earthquake data and simulations of future earthquake scenarios to predict the structure or system’s behavior under seismic forces. In this study, the seismic performance of 30 stories of 95 m h

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Karadag, Muge, and Ali Sivridag. "Some Characterizations for a Quaternion-Valued and Dual Variable Curve." Symmetry 11, no. 2 (2019): 125. http://dx.doi.org/10.3390/sym11020125.

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Quaternions, which are found in many fields, have been studied for a long time. The interest in dual quaternions has also increased after real quaternions. Nagaraj and Bharathi developed the basic theories of these studies. The Serret–Frenet Formulae for dual quaternion-valued functions of one real variable are derived. In this paper, by making use of the results of some previous studies, helixes and harmonic curvature concepts in Q D 3 and Q D 4 are considered and a characterization for a dual harmonic curve to be a helix is given.

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Ko, Tse-Pang, Yu-Pin Chang, and Jyh-Wen Chai. "Assessment of solitary pulmonary nodules using dual-layer spectral detector computed tomography." Medicine 103, no. 41 (2024): e40014. http://dx.doi.org/10.1097/md.0000000000040014.

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We aim to quantitatively investigate the difference between benign and malignant solid pulmonary nodules that appeared on dual-energy spectral computed tomography, and assess the diagnostic accuracy of several parameters derived from computed tomography in differentiating malignant from benign pulmonary nodules. Between September 2021 and December 2022, spectral images of 71 patients (male:female = 44:27, mean age = 71.0 years) confirmed by pathology were retrospectively analyzed in the venous phase. Patients were classified into the malignant group and the benign group. The iodine concentrati

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LANGE, H., and E. SERNESI. "SEVERI VARIETIES AND BRANCH CURVES OF ABELIAN SURFACES OF TYPE (1, 3)." International Journal of Mathematics 13, no. 03 (2002): 227–44. http://dx.doi.org/10.1142/s0129167x02001381.

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A polarized abelian surface (A, L) of type (1, 3) induces a 6:1 covering of A onto the projective plane with branch curve, a plane curve B of degree 18. The main result of the paper is that for a general abelian surface of type (1, 3), the curve B is irreducible and reduced and admits 72 cusps, 36 nodes or tacnodes, each tacnode counting as 2 nodes, 72 flexes and 36 bitangents. The main idea of the proof is that for a general (A, L) the discriminant curve in the linear system |L| coincides with the closure of the Severi variety of curves in |L| admitting a node and is dual to the curve B in th

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Magaña-Sevilla, H., and CA Sandoval-Castro. "An analysis of the dual purpose cattle (B. taurus x B. indicus) lactation curve." Proceedings of the British Society of Animal Science 2002 (2002): 191. http://dx.doi.org/10.1017/s1752756200008474.

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The shape of the lactation curve (description of milk production through lactation) which is relevant in order to predict past, current and future lactations. Curves type I show fast increment during early lactation, followed by a slow decline. However, continuous decreasing curves, named type II (Landete-Castillejos and Gallego, 2000) are frequent in tropical diary cattle, maybe due to low nutritional status (Contreras and Rincon, 1979). Curves type II could not be accurately described by Wood (1967) model. In addition, Wood’s model do not describe the inner processes in the udder. Recently,

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Liu, Siyao, and Zhigang Wang. "Singularities of worldsheets associated with null Cartan curves in Lorentz–Minkowski space–time." International Journal of Modern Physics A 33, no. 33 (2018): 1850192. http://dx.doi.org/10.1142/s0217751x18501920.

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In this paper, as applications of singularity theory, we study the singularities of several worldsheets generated by null Cartan curves in Lorentz–Minkowski space–time. Using the approach of the unfolding theory in singularity theory, we establish the relationships between these worldsheets and invariants such that the cuspidal edge type of singularity and the swallowtail type of singularity can be characterized by these invariants, respectively. Meanwhile, the contact of the tangent curve of a null Cartan curve with some model surfaces are discussed in detail. In addition, we also describe th

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Gao, Yun Kai, Hai Xing Feng, and Xiao Yan Zhou. "Design of the Dual-Curvature Door Glass Guide System." Applied Mechanics and Materials 198-199 (September 2012): 112–16. http://dx.doi.org/10.4028/www.scientific.net/amm.198-199.112.

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The drum surface method was proposed to fit the dual-curvature glass. Based on the drum line principle, the proportional function method is used to obtain the guide channel curve and the guide rail curve. According to the analysis of motion deviation, the max position deviation is less than 0.5mm and the results satisfied the engineering deviation requirements. It is proved that the fitting method of the door glass surfaces, the design of the guide channel curve and the guide rail curve are reasonable.

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McCarthy, J. M. "The Instantaneous Kinematics of Line Trajectories in Terms of a Kinematic Mapping of Spatial Rigid Motion." Journal of Mechanisms, Transmissions, and Automation in Design 109, no. 1 (1987): 95–100. http://dx.doi.org/10.1115/1.3258792.

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The dual Euler parameters of a rigid spatial motion are used to define a curve on a dual unit hypersphere. The dual velocity, curvature, and torsion of this curve form a set of instantaneous parameters related to the instantaneous invariants of the motion. In this paper these new parameters are used to reformulate the kinematic theory of line trajectories. The distribution parameter, Disteli formulas, and the inflection congruence are examined in detail.

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39

Hathout, F., M. Bekar, and Y. Yayli. "Ruled surfaces and tangent bundle of unit 2-sphere." International Journal of Geometric Methods in Modern Physics 14, no. 10 (2017): 1750145. http://dx.doi.org/10.1142/s0219887817501456.

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In this paper, a one-to-one correspondence is given between the tangent bundle of unit 2-sphere, [Formula: see text], and the unit dual sphere, [Formula: see text]. According to Study’s map, to each curve on [Formula: see text] corresponds a ruled surface in Euclidean 3-space, [Formula: see text]. Through this correspondence, we have corresponded to each curve on [Formula: see text] a unique ruled surface in [Formula: see text]. Moreover, the relationships between the developability conditions of these ruled surfaces and their striction curves are analyzed. It is shown that the ruled surfaces

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40

Taş, Ferhat, and Kazım İlarslan. "A new approach to design the ruled surface." International Journal of Geometric Methods in Modern Physics 16, no. 06 (2019): 1950093. http://dx.doi.org/10.1142/s0219887819500932.

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This paper considers a kind of design of a ruled surface. The design interconnects some concepts from the fields of computer-aided geometric design (CAGD) and kinematics. Dual unit spherical Bézier-like curves on the dual unit sphere (DUS) are obtained by a novel method with respect to the control points. A dual unit spherical Bézier-like curve corresponds to a ruled surface by using Study’s transference principle and closed ruled surfaces are determined via control points and also, integral invariants of these surfaces are investigated. Finally, the results are illustrated by several examples

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41

Zhou, Chuan, Suying Gui, Yan Liu, Junpeng Ma, and Hao Wang. "Fault Location of Distribution Network Based on Back Propagation Neural Network Optimization Algorithm." Processes 11, no. 7 (2023): 1947. http://dx.doi.org/10.3390/pr11071947.

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Research on fault diagnosis and positioning of the distribution network (DN) has always been an important research direction related to power supply safety performance. The back propagation neural network (BPNN) is a commonly used intelligent algorithm for fault location research in the DN. To improve the accuracy of dual fault diagnosis in the DN, this study optimizes BPNN by combining the genetic algorithm (GA) and cloud theory. The two types of BPNN before and after optimization are used for single fault and dual fault diagnosis of the DN, respectively. The experimental results show that th

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42

Sheng, Xianjun, Jingjing Fan, Ning Liu, and Chunbo Zhang. "A dual-band fractal FSS with SZ curve elements." IEICE Electronics Express 14, no. 13 (2017): 20170518. http://dx.doi.org/10.1587/elex.14.20170518.

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Baviera, Roberto, and Alessandro Cassaro. "A Note on Dual-Curve Construction: Mr. Crab’s Bootstrap." Applied Mathematical Finance 22, no. 2 (2014): 105–32. http://dx.doi.org/10.1080/1350486x.2014.959665.

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Noor, A., and Z. Hu. "Metamaterial dual polarised resistive Hilbert curve array radar absorber." IET Microwaves, Antennas & Propagation 4, no. 6 (2010): 667. http://dx.doi.org/10.1049/iet-map.2009.0047.

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45

Piontkowski, Jens. "Self-dual modules over local rings of curve singularities." Journal of Pure and Applied Algebra 207, no. 2 (2006): 327–39. http://dx.doi.org/10.1016/j.jpaa.2005.10.001.

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46

Bouziane, Driss, and Mhammed El Kahoui. "Computation of the Dual of a Plane Projective Curve." Journal of Symbolic Computation 34, no. 2 (2002): 105–17. http://dx.doi.org/10.1006/jsco.2002.0544.

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47

Gailienė, Inesa, Martynas Gedaminskas, and Alfredas Laurinavičius. "APPROACH TO RATIONAL CALCULATION OF SUPERELEVATION IN DUAL GAUGE TRACK." Transport 33, no. 3 (2018): 699–706. http://dx.doi.org/10.3846/transport.2018.1577.

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One of the technical possibilities to solve a gauge crossing is to install a dual gauge. This solution has several advantages and disadvantages discussed in this paper. Lack of experience of maintenance and lack of standards for the design of dual track are among the most important disadvantages. The wheel and rail interface on track curves is more difficult than in straight sections. Therefore, the subject of the present article is a geometrical parameter of dual gauge track, i.e., the rail superelevation, which has an impact on the wheel–rail interaction at curves and influences the value of

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48

Giblin, Peter, and Farid Tari. "Perpendicular bisectors, duality and local symmetry of plane curves." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 1 (1995): 181–94. http://dx.doi.org/10.1017/s0308210500030821.

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For a smooth, simple closed curve α in the plane, the perpendicular bisector map P associates to each pair of distinct points (p, q) on α the perpendicular bisector of the chord joining p and q. To a pair (p, p), the map P associates the normal to α at p. The set of critical values of this map is the union of the dual of the symmetry set of α and the dual of the evolute. (The symmetry set is the locus of the centres of circles bitangent to α.) We study the mapP and use it to give a complete list of the transitions which take place on the dual of the symmetry set and the dual of the evolute, as

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Yan, H. S., and W. H. Hsieh. "ON THE COUPLER CURVE OF 3R2C LINKAGES." Transactions of the Canadian Society for Mechanical Engineering 22, no. 3 (1998): 251–67. http://dx.doi.org/10.1139/tcsme-1998-0014.

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The purpose of this paper is to investigate the properties of the coupler curves generated by all 3R2C linkages. First, the 3x3 matrix with dual elements is used to derive the loop closure equation, the displacement equations are derived, and all joints variables are expressed in terms of input and output variables. Then, the parametric equations of the coupler curve are found by the D-H matrix. Finally, homogeneous coordinate is introduced to those displacement equations, and the order and some critical properties of the coupler curve are investigated based on the theories of algebraic curve

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Jia-Jia, Hao, Li Chunling, Yuan Runsen, Khansa Pervaiz, Muhammad Asif Khan, and Sun Xiaoran. "Dual Innovation Performance through Knowledge-Based Network Structure: Evidence from Electronic Information Industry." Engineering Economics 33, no. 1 (2022): 47–58. http://dx.doi.org/10.5755/j01.ee.33.1.25899.

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This study analyzes how knowledge-based network affects the dual innovation performance. Dual innovation includes exploratory and exploitative innovation, and knowledge-based network represents the relationships among knowledge-based elements. We take 269 enterprises having gone public in Shanghai and Shenzhen stock markets of the electronic information industry of China as samples and get the patent data for 5 years from 2014 to 2018. We consider building the knowledge-based network structure based on social network analysis method, and measure three features of the knowledge-based network, t

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