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Journal articles on the topic 'R-curve'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Ghadirdokht, A., and M. Heidari-Rarani. "Delamination R-curve behavior of curved composite laminates." Composites Part B: Engineering 175 (October 2019): 107139. http://dx.doi.org/10.1016/j.compositesb.2019.107139.

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2

Short, J. S., and D. W. Hoeppner. "R-curve thermodynamics revisited." International Journal of Fracture 45, no. 2 (1990): 145–57. http://dx.doi.org/10.1007/bf00037172.

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3

KAHRAMAN AKSOYAK, Ferdağ. "Quaternionic Bertrand curves according to type 2-quaternionic frame in $\mathbb{R}^{4}$." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 2 (2022): 395–406. http://dx.doi.org/10.31801/cfsuasmas.991631.

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In this paper, we give some characterization of quaternionic Bertrand curves whose the torsion is non-zero but bitorsion is zero in $\mathbb{R}^{4}$ according to Type 2-Quaternionic Frame. One of the most important points in working on quaternionic curves is that given a curve in $\mathbb{R}^{4}$, the curve in $\mathbb{R}^{3}$ associated with this curve is determined individually. So, we obtain some relationships between quaternionic Bertrand curve $\alpha^{(4)}$ in $\mathbb{R}^{4}$ and its associated spatial quaternionic curve $\alpha$ in $\mathbb{R}^{3}$. Also, we support some theorems in th

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4

Farnsworth, David L. "Axes for symmetric convex curves." Mathematical Gazette 102, no. 553 (2018): 23–30. http://dx.doi.org/10.1017/mag.2018.4.

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Curves are given in polar coordinates (r, θ)by equations of the form r = f (θ), where for f (θ) > 0 all θ. Consider curves which are symmetric about the origin O, so that, f(θ + π) = f (θ) for all θ. For such a curve, its interior is the set {(r, θ) : 0 ≤ r ≤ f (θ)}. Further, assume that the curve is convex. Recall that a closed curve is convex if a line segment between any two of its points has no points exterior to the curve [1], [2, pp. 198-203]. We call these curves M-curves, because the curves are fundamental objects in Minkowski geometry, where they are called Minkowski circles or sim

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5

Sarkar, Debasish, Bikramjit Basu, Min Cheol Chu, and Seong Jai Cho. "R-curve behavior of Ti3SiC2." Ceramics International 33, no. 5 (2007): 789–93. http://dx.doi.org/10.1016/j.ceramint.2006.01.002.

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6

Echabbi, Nidal, and Amina Ouazzani Chahdi. "Direction Curves Associated with Darboux Vectors Fields and Their Characterizations." International Journal of Mathematics and Mathematical Sciences 2021 (November 22, 2021): 1–11. http://dx.doi.org/10.1155/2021/3814032.

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In this paper, we consider the Darboux frame of a curve α lying on an arbitrary regular surface and we use its unit osculator Darboux vector D ¯ o , unit rectifying Darboux vector D ¯ r , and unit normal Darboux vector D ¯ n to define some direction curves such as D ¯ o -direction curve, D ¯ r -direction curve, and D ¯ n -direction curve, respectively. We prove some relationships between α and these associated curves. Especially, the necessary and sufficient conditions for each direction curve to be a general helix, a spherical curve, and a curve with constant torsion are found. In addition to

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7

Gajdoš, Ľubomír, Martin Šperl, Jan Korouš, and Jiří Kuželka. "Evaluating the Suitability of the Gurson—Tvergaard—Needleman Plasticity Model for Crack Resistance Curve Analysis." Applied Sciences 14, no. 13 (2024): 5882. http://dx.doi.org/10.3390/app14135882.

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The operational safety of oil and gas storage units is crucial, as any potential imperfections or cracks in a container wall could result in fracture. The key parameter in ensuring the integrity of oil and gas storage units is their fracture toughness. For its determination, compact tension (CT) and single-edge notched bend (SENB) specimens are commonly used. However, these specimens may lead to unnecessary conservatism in safety assessments. Single-edge notched tension (SENT) specimens, on the other hand, could be a more acceptable substitute, as they are shown to lead to less conservatism. T

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8

Crasmareanu, Mircea. "A new generalization of Tzitzeica curves in arbitrary dimension." Annals of the Alexandru Ioan Cuza University - Mathematics 70, no. 1 (2024): 89–99. http://dx.doi.org/10.47743/anstim.2024.00007.

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We generalize the notion of a Tzitzeica curve r in the nth dimension by using the constant ratio of the αth power of the Wronskians W(r′) of the derivative curve r′ and the βth power of the Wronskian W(r) of the original curve. In this context, the powers α and β may be seen as control parameters whose interplay determine special classes of (α, β)-Tzitzeica curves. Our paper is intended to be example–oriented and, therefore, several intriguing, new families of generalized Tzitzeica curves in the nth dimension, such as the power and exponential curves, are introduced and discussed in detail. In

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9

Jiang, Zhengwen, Shui Wan, Thomas Keller, Zhi Fang, and Anastasios P. Vassilopoulos. "Influence of curved delamination front on R-curve of DCB specimen." Composite Structures 227 (November 2019): 111311. http://dx.doi.org/10.1016/j.compstruct.2019.111311.

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10

Wolfenden, A., HS Pearson, and DE McCabe. "R-Curve Round-Robin Program for ASTM Recommended Practice for R-Curve Determination (E 561)." Journal of Testing and Evaluation 14, no. 4 (1986): 191. http://dx.doi.org/10.1520/jte11261j.

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11

Bujalance, E., G. Gromadzki, and M. Izquierdo. "On real forms of a complex algebraic curve." Journal of the Australian Mathematical Society 70, no. 1 (2001): 134–42. http://dx.doi.org/10.1017/s1446788700002329.

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AbstractTwo projective nonsingular complex algebraic curves X and Y defined over the field R of real numbers can be isomorphic while their sets X(R) and Y(R) of R-rational points could be even non homeomorphic. This leads to the count of the number of real forms of a complex algebraic curve X, that is, those nonisomorphic real algebraic curves whose complexifications are isomorphic to X. In this paper we compute, as a function of genus, the maximum number of such real forms that a complex algebraic curve admits.

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12

Sharf Aldeen, Asame, Ali Abdi Kordani, Afshin Fallah, and Seyed Mohsen Hosseinian. "Safety Comparison of Simple and Spiral Horizontal Curves Based on Side Friction Factor Dynamic Modeling." Journal of Advanced Transportation 2023 (February 10, 2023): 1–23. http://dx.doi.org/10.1155/2023/7954346.

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A horizontal curve’s geometric design is considered an important factor in highway accidents, and simple and spiral curves are regarded as the most common types of horizontal curves. Various factors affect the safety of horizontal curves, one of the most important of which is the side friction factor in the horizontal curves. Therefore, in this study, the safety of simple and spiral horizontal curves was investigated for the E-class sedan, E-class SUV, and two-axle conventional truck based on the side friction factor. In this regard, CarSim and TruckSim vehicle dynamic simulation software were

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13

Akatsu, Takashi, Minoru Suzuki, Yasuhiro Tanabe, and Eiichi Yasuda. "Effects of whisker content and dimensions on the R-curve behavior of an alumina matrix composite reinforced with silicon carbide whiskers." Journal of Materials Research 16, no. 7 (2001): 1919–27. http://dx.doi.org/10.1557/jmr.2001.0263.

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A study was made of the effects of whisker content and dimensions on the R-curve behavior of an alumina matrix composite reinforced with silicon carbide whiskers. Experiments showed that the rising R-curve behavior is strongly enhanced by the increase in the volume fraction and the size of whiskers. Simulation based on a model of crack face whisker bridgings was made to elucidate the effects on the R-curve of the composite. The validity of the simulation was confirmed by good agreement between the experimental and the calculated R-curves. In addition to the R-curve, the distribution of crack c

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14

Amanullah, Amir A., Taemin Oh, Brandon J. Toll, et al. "Risk Factors for Progression of Cervical Congenital Scoliosis and Associated Compensatory Curve Behavior." Journal of Clinical Medicine 13, no. 11 (2024): 3039. http://dx.doi.org/10.3390/jcm13113039.

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Background: This study investigated risk factors for progression of deformity in pediatric congenital cervical scoliosis (CCS) and evaluated the correlation between congenital cervical curves and compensatory thoracic and lumbar curves. Methods: Medical records were retrospectively reviewed for 38 pediatric patients with CCS with a minimum 2-year follow-up. Curve progression was defined as >10° increase in cervical coronal curve angle between presentation and last follow-up. Results: A total of 38 patients (16 girls, 22 boys) with a mean age at presentation of 5.6 ± 4.1 years met the inclus

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15

Srinivasan, S., and R. O. Scattergood. "R-curve measurements in PSZ ceramics." Journal of Materials Research 5, no. 7 (1990): 1490–95. http://dx.doi.org/10.1557/jmr.1990.1490.

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An indentation-bend failure-stress method was used for measurement of R-curves in a series of PSZ ceramics with varying peak toughness. Dilatational transformation-stress constraints are included in the residual-stress driving force contribution to the applied stress intensity factor. A power-law fit to the form of the R-curve simplifies the analysis. While the resulting curves show the expected form, measured toughness values are high relative to the expected peak toughness. Limitations and the range of applicability of the indentation-bend technique are discussed.

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16

Rödiger, Stefan, Alexander Böhm, and Ingolf Schimke. "Surface Melting Curve Analysis with R." R Journal 5, no. 2 (2013): 37. http://dx.doi.org/10.32614/rj-2013-024.

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17

Rosa, V., K. A. Fukushima, M. Borba, H. N. Yoshimura, and P. F. Cesar. "R-curve behavior of dental porcelains." Dental Materials 27 (January 2011): e72. http://dx.doi.org/10.1016/j.dental.2011.08.568.

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18

Vekinis, G., M. F. Ashby, and P. W. R. Beaumont. "R-curve behaviour of Al2O3 ceramics." Acta Metallurgica et Materialia 38, no. 6 (1990): 1151–62. http://dx.doi.org/10.1016/0956-7151(90)90188-m.

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19

ÇAYIR, HAŞİM, and SÜLEYMAN ŞENYURT. "THE TRANSFORMATION OF THE EVOLUTE CURVES USING LIFTS ON R^3 TO TANGENT SPACE TR^3." Journal of Science and Arts 24, no. 1 (2024): 145–54. http://dx.doi.org/10.46939/j.sci.arts-24.1-a13.

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In this paper, firstly, we define the evolute curve of any curve concerning the vertical, complete, and horizontal lifts on space R^3 to its tangent space TR^3=R^6. Secondly, we examine the Frenet-Serret apparatus {T^* (s),N^* (s),B^* (s),κ^*,τ^* } and the Darboux vector W^* of the evolute curve α^* according to the vertical, complete and horizontal lifts on TR^3 by depend on the lifting of Frenet-Serret aparatus {T(s),N(s),B(s),κ,τ} of the first curve α on space R^3. In addition, we include all special cases the curvature κ^* (s) and torsion τ^* (s) of the Frenet-Serret aparatus {T^* (s),N^*

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20

Knutsen, Andreas Leopold, Margherita Lelli-Chiesa, and Giovanni Mongardi. "Severi varieties and Brill–Noether theory of curves on abelian surfaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 749 (2019): 161–200. http://dx.doi.org/10.1515/crelle-2016-0029.

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Abstract Severi varieties and Brill–Noether theory of curves on K3 surfaces are well understood. Yet, quite little is known for curves on abelian surfaces. Given a general abelian surface S with polarization L of type {(1,n)} , we prove nonemptiness and regularity of the Severi variety parametrizing δ-nodal curves in the linear system {|L|} for {0\leq\delta\leq n-1=p-2} (here p is the arithmetic genus of any curve in {|L|} ). We also show that a general genus g curve having as nodal model a hyperplane section of some {(1,n)} -polarized abelian surface admits only finitely many such models up t

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21

Zhu, Xian-Kui, and Brian N. Leis. "Application of Constraint Corrected J-R Curves to Fracture Analysis of Pipelines." Journal of Pressure Vessel Technology 128, no. 4 (2005): 581–89. http://dx.doi.org/10.1115/1.2349571.

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Fracture properties of an API X80 pipeline steel have been developed using a set of single edge notched bend (SENB) and single edge notched tension (SENT) specimens with shallow and deep cracks to generate different crack-tip constraint levels. The test data show that the J-R curves for the X80 pipeline steel are strongly constraint dependent. To facilitate transfer of the experimental J-R curves to those for actual cracked components, like flawed pipeline, constraint corrected J-R curves are developed. The two-parameter J-A2 formulation is adopted to quantify constraint effect on the crack-ti

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22

Ding, Xu, ZhiMing Song, ChuanJun Wang, and KaiFan Ji. "Detection of Contact Binary Candidates Observed By TESS Using the Autoencoder Neural Network." Astronomical Journal 167, no. 5 (2024): 192. http://dx.doi.org/10.3847/1538-3881/ad3048.

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Abstract A contact binary may be the progenitor of a red nova that eventually produces a merger event and have a cut-off period of around 0.2 days. Therefore, a large number of contact binaries is needed to search for the progenitor of red novae and to study the characteristics of short-period contact binaries. In this paper, we employ the Phoebe program to generate a large number of light curves based on the fundamental parameters of contact binaries. Using these light curves as samples, an autoencoder model is trained, which can reconstruct the light curves of contact binaries very well. Whe

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23

Ghafari, Sepehr, Fereidoon Moghadas Nejad, and Hadi Kazemi. "Developing a Single-Specimen Technique for Low-Temperature R-Curve Determination of Asphalt Concrete Using a Modified Unloading Compliance Method." Key Engineering Materials 951 (August 7, 2023): 141–46. http://dx.doi.org/10.4028/p-z0h762.

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Fracture resistance curves (R-curves) have served as a robust tool in characterizing the entire fracture process of engineering materials. However, obtaining such curves for asphalt concrete (AC) mixtures is cumbersome due to the non-linear inelastic behavior of the mixtures. In this research, a single-specimen technique is developed based on the unloading compliance method which is used for metals. AC mixtures with limestone aggregate and PG58-22 binder were prepared. Beam specimens were fabricated and single-edge notched beam (SE(B)) fracture testing was conducted at low temperatures. A load

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24

Jones, Rhys, Andrew S. M. Ang та Daren Peng. "Simple Scaling as a Tool to Help Assess the Closure-Free da/dN Versus ΔKeff Curve in a Range of Materials". Materials 17, № 22 (2024): 5423. http://dx.doi.org/10.3390/ma17225423.

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Recent studies have proposed a simple formula, which is based on Elber’s original approach to account for R-ratio effects, for determining the crack closure-free ΔKeff versus da/dN curve from the measured R-ratio-dependent ΔK versus da/dN curves. This approach, which is termed “Simple Scaling,” has been shown to collapse the various R-ratio-dependent curves onto a single curve. Indeed, this approach has been verified for a number of tests on metals, polymers, and a medium-entropy alloy. However, it has not yet been used to help assess/determine the closure-free ΔKeff versus da/dN curve. The cu

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25

Szutkowska, Magdalena, and Marek Boniecki. "Crack Growth Resistance of Carbide Reinforced Composite Ceramics Based on Alumina." Key Engineering Materials 409 (March 2009): 231–36. http://dx.doi.org/10.4028/www.scientific.net/kem.409.231.

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The relationship of KR versus crack length c (R curve) for Al2O3-30wt.% Ti(C,N).and for comparison alumina ceramics has been examined. The R-curve has been evaluated using pronounced long-crack formed during the three point bending (3PB) of the double edge notched beam. A combination of in situ microscopic crack growth observation and mechanical testing enabled measurement of crack growth resistance curves. The special device consisting of light microscope coupled with CCD camera, was fitted to Zwick 1446 testing machine. These observations reveal the existence of flat R-curve for Al2O3-30wt.%

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26

Raimondo, Antonio. "Numerical Investigation of the R-Curve Effect in Delamination of Composite Materials Using Cohesive Elements." Applied Sciences 14, no. 6 (2024): 2535. http://dx.doi.org/10.3390/app14062535.

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This paper presents a numerical investigation of the R-curve effect in delamination propagation in composite materials. The R-curve effect refers to the phenomenon whereby resistance to crack propagation increases with the advancement of the delamination, due to toughening mechanisms, such as fiber bridging. Numerical models often neglect this effect assuming a constant value of the fracture toughness. A numerical approach based on cohesive elements and on the superposition of two bilinear traction-separation laws is adopted here to accurately predict the R-curve effect in skin-doubler composi

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27

Bernardo, Nicholas D., and Gretchen A. Macht. "Learning ‘Learning Curves’ with R Shiny." Proceedings of the Human Factors and Ergonomics Society Annual Meeting 65, no. 1 (2021): 1567–71. http://dx.doi.org/10.1177/1071181321651119.

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Learning curves are fundamental in understanding individual task performance, with ubiquitous implementation in task assignments, worker scheduling, team formulation, etc., in domains bridging from manufacturing to healthcare. With a broad range of applicability, it is critical that students conceptualize, visualize, and build learning curves to activate that knowledge for effective decision-making. This paper describes a hands-on experiential approach for teaching learning curves that utilizes building LEGO® sets with mathematical formulation and data visualization in an open-source R Shiny a

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28

Yoon, Young Sik, Sang Woong Na, Jaehyung Lee, Myeong-Woo Cho, Eun-Sang Lee, and Won-Seung Cho. "R-Curve Behavior of Si3N4-BN Composites." Journal of the American Ceramic Society 87, no. 7 (2004): 1374–77. http://dx.doi.org/10.1111/j.1151-2916.2004.tb07740.x.

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29

Fischer, H., W. Rentzsch, and R. Marx. "R-Curve Behavior of Dental Ceramic Materials." Journal of Dental Research 81, no. 8 (2002): 547–51. http://dx.doi.org/10.1177/154405910208100809.

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30

Olsson, Marten, and Antonios E. Giannakopoulos. "R-CURVE MODEL OF CERTAIN CERAMIC COMPOSITES." Fatigue & Fracture of Engineering Materials & Structures 16, no. 5 (1993): 539–54. http://dx.doi.org/10.1111/j.1460-2695.1993.tb00765.x.

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31

Sumpter, J. D. G. "An alternative view of R curve testing." Engineering Fracture Mechanics 64, no. 2 (1999): 161–76. http://dx.doi.org/10.1016/s0013-7944(99)00074-0.

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32

Kim, Y. W., M. Mitomo, and N. Hirosaki. "R-curve behaviour of sintered silicon nitride." Journal of Materials Science 30, no. 16 (1995): 4043–48. http://dx.doi.org/10.1007/bf00360707.

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33

Yu, Hang-Hai, Shou-Ren Wang, and Li-Ying Yang. "R-Curve Behavior of Si3N4/BNNT Composites." Applied Composite Materials 20, no. 5 (2013): 947–60. http://dx.doi.org/10.1007/s10443-013-9311-1.

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34

Mekky, Waleed, and Patrick S. Nicholson. "R-curve modeling for Ni/Al2O3 laminates." Composites Part B: Engineering 38, no. 1 (2007): 35–43. http://dx.doi.org/10.1016/j.compositesb.2006.05.001.

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35

Fett, T., and D. Munz. "Evaluation of R-curve effects in ceramics." Journal of Materials Science 28, no. 3 (1993): 742–52. http://dx.doi.org/10.1007/bf01151251.

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36

Lutz, Ekkehard H., and Mototsugu Sakai. "R-Curve and Compliance Change upon Renotching." Journal of the American Ceramic Society 76, no. 12 (1993): 3113–22. http://dx.doi.org/10.1111/j.1151-2916.1993.tb06616.x.

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37

Henning, W., M. Calvo, and F. Osterstock. "R-curve behaviour of metallic glass ribbons." Journal of Materials Science 20, no. 5 (1985): 1889–900. http://dx.doi.org/10.1007/bf00555298.

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38

Suo, Z., G. Bao, and B. Fan. "Delamination R-curve phenomena due to damage." Journal of the Mechanics and Physics of Solids 40, no. 1 (1992): 1–16. http://dx.doi.org/10.1016/0022-5096(92)90198-b.

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39

Petersen, Jonas, and Mads T. Frandsen. "A method for discriminating between dark matter models and MOND modified inertia via galactic rotation curves." Monthly Notices of the Royal Astronomical Society 496, no. 2 (2020): 1077–91. http://dx.doi.org/10.1093/mnras/staa1541.

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ABSTRACT Dark matter (DM) and modified Newtonian dynamics (MOND) models of rotationally supported galaxies lead to curves with different geometries in (gN, gtot)-space (g2-space). Here, gtot is the total acceleration and gN is the acceleration as obtained from the baryonic matter via Newtonian dynamics. In MOND modified inertia (MI) models, the curves in g2-space are closed with zero area and so curve segments at radii r ≥ rN (large radii) and r &lt; rN (small radii) coincide, where rN is the radius where gN is greatest. In DM models with cored density profiles where gtot is also zero at t

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40

Fall, Moussa. "Morphisms and Algebraic Points on the Quotients of the Fermat Quintic." Indonesian Journal of Mathematics and Applications 2, no. 2 (2024): 96–104. http://dx.doi.org/10.21776/ub.ijma.2024.002.02.4.

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The purpose of this paper is to determine morphisms and algebraic points of low degree on the quotients of the Fermat quintic. An algebraic point of degree at most $3$ is called an algebraic point of low degree. The quotients of the Fermat quintic is a family curves $\mathcal{C}_{rs}(5) : v^5 =u^r(u-1)^s$ where $r$ and $s$ are integers such that: $1< r, s, r+s< 5$. We determine explicitly the morphisms between the curves $\mathcal{C}_{rs}(5)$. By applying Abel Jacobi's theorem and using Riemann-Roch spaces, we give a parametrization of algebraic points of low degree on the special curve

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41

Martynenko, L. V. "Ensuring the safety of rolling stock movement when entering transition curves." E3S Web of Conferences 402 (2023): 06010. http://dx.doi.org/10.1051/e3sconf/202340206010.

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The main factor in the issue of the safety of the rolling stock movement in the rail track is the change in the magnitude of the lateral forces arising from the interaction of the wheel with the rail. The dynamics of changes in lateral forces directly depends on the increase in rolling stock speeds in curves and, especially, in transition curves. To prevent the sudden appearance of centrifugal force, the outer rail is elevated, the track is broadened when moving from a straight line to a circular curve and a transition curve of variable curvature r = l / p, where p is the variable radius of th

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42

Fett, T., D. Munz, and G. Thun. "Fracture Toughness Testing on Bars Under Opposite Cylinder Loading." Journal of Engineering for Gas Turbines and Power 126, no. 1 (2004): 50–54. http://dx.doi.org/10.1115/1.1639003.

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Bars loaded by opposite concentrated forces via rollers are appropriate test specimens for the determination of the fracture toughness, KIc, and the crack resistance curve (R-curve) of ceramic materials. In this paper stress solutions for the proposed test specimens are provided, as well as the stress intensity factor and the T-stress solutions. As practical applications, R-curves are determined for a soft PZT ceramic and several alumina ceramics.

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43

Zhao, J., J. Tang, and H. C. Wu. "A Reliability Assessment Method in Strain-Based Fatigue Life Analysis." Journal of Pressure Vessel Technology 120, no. 1 (1998): 99–104. http://dx.doi.org/10.1115/1.2841893.

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For the purpose of fatigue reliability assessment based on strain-life analysis, a family of reliability-defined ε-Nf curves, called R-ε-Nf curves, is constructed by considering the interference model of fatigue strain capacity and applied strain history. The main effort of this work is to define reliability factors which are used to modify the conventional ε-Nf curve into a family of R-ε-Nf curves. A major contribution of this paper is to define two “unique” reliability factors, one for elastic-strain-life relation and the other for plastic-strain-life relation, for a certain reliability by u

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44

Ferrandino, Francis J. "Relating the Progeny Production Curve to the Speed of an Epidemic." Phytopathology® 103, no. 3 (2013): 204–15. http://dx.doi.org/10.1094/phyto-04-12-0093-r.

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The dependence of the initial infection rate, r, on the basic reproductive number, R0, and the temporal moments of the progeny production curve are examined. A solution to the linearized Kermack-McKendrick equation is presented and used to analyze a variety of theoretical models of pathogen reproduction. The solution yields a relation between r and the basic reproductive number, R0; the mean time between pathogen generations, μ; and the standard deviation about this mean, σ. A transformation using the dimensionless variables rμ and rσ is introduced, which maps the solution onto a one-dimension

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45

Ciampa, Donato, and Saverio Olita. "The Use of Bloss Curve in The Exit Lanes of Road Intersections." Baltic Journal of Road and Bridge Engineering 15, no. 1 (2020): 76–102. http://dx.doi.org/10.7250/bjrbe.2020-15.462.

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The paper proposes the use of the Bloss curve (also known as biparametric or bi-hyperclothoid) as a braking curve in the exit lanes of road intersections. The main international standards continue using the clohoid as the principal transitional geometric element, even though the limits of its use in driving regimes with non-uniform speeds are known. The proposal to use the Bloss curve is aimed at overcoming these limitations and opening a debate on the possible need to codify, even in the international standards, the use of more suitable alternative braking curves. In this context, a kinematic

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Cheng, Yingxin, Yanlin Li, Pushpinder Badyal, Kuljeet Singh, and Sandeep Sharma. "Conformal Interactions of Osculating Curves on Regular Surfaces in Euclidean 3-Space." Mathematics 13, no. 5 (2025): 881. https://doi.org/10.3390/math13050881.

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Conformal maps preserve angles and maintain the local shape of geometric structures. The osculating curve plays an important role in analyzing the variations in curvature, providing a detailed understanding of the local geometric properties and the impact of conformal transformations on curves and surfaces. In this paper, we study osculating curves on regular surfaces under conformal transformations. We obtained the conditions required for osculating curves on regular surfaces R and R˜ to remain invariant when subjected to a conformal transformation ψ:R→R˜. The results presented in this paper

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47

Bakker, Benjamin. "A CLASSIFICATION OF LAGRANGIAN PLANES IN HOLOMORPHIC SYMPLECTIC VARIETIES." Journal of the Institute of Mathematics of Jussieu 16, no. 4 (2015): 859–77. http://dx.doi.org/10.1017/s1474748015000328.

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Classically, an indecomposable class $R$ in the cone of effective curves on a K3 surface $X$ is representable by a smooth rational curve if and only if $R^{2}=-2$. We prove a higher-dimensional generalization conjectured by Hassett and Tschinkel: for a holomorphic symplectic variety $M$ deformation equivalent to a Hilbert scheme of $n$ points on a K3 surface, an extremal curve class $R\in H_{2}(M,\mathbb{Z})$ in the Mori cone is the line in a Lagrangian $n$-plane $\mathbb{P}^{n}\subset M$ if and only if certain intersection-theoretic criteria are met. In particular, any such class satisfies $(

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48

Güler, Fatma. "The ruled surface obtained by the natural mate curve." Boletim da Sociedade Paranaense de Matemática 41 (December 23, 2022): 1–5. http://dx.doi.org/10.5269/bspm.51670.

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The natural mate curve r1 of r is deﬁned the integral of principal normal vector with any parameter s, of a curve r. We investigate the ruled surface generated by the natural mate curve of any Frenet curve r = r(s) in the Euclidean 3-space. We obtained some necessary and suﬃcient conditions for this surface to be developable and minimal ruled surface. We research related to be the asymptotic curve and the geodesic curve of the base curve on the ruled surface. Example of our main results are also presented.

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KAVATHEKAR, PARITOSH A., BRUCE A. CRAIG, ALAN M. FRIEDMAN, CHRIS BAILEY-KELLOGG, and DEVIN J. BALKCOM. "CHARACTERIZING THE SPACE OF INTERATOMIC DISTANCE DISTRIBUTION FUNCTIONS CONSISTENT WITH SOLUTION SCATTERING DATA." Journal of Bioinformatics and Computational Biology 08, no. 02 (2010): 315–35. http://dx.doi.org/10.1142/s0219720010004781.

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Scattering of neutrons and X-rays from molecules in solution offers alternative approaches to the study of a wide range of macromolecular structures in their solution state without crystallization. We study one part of the problem of elucidating three-dimensional structure from solution scattering data, determining the distribution of interatomic distances, P(r), where r is the distance between two atoms in the protein molecule. This problem is known to be ill-conditioned: for a single observed diffraction pattern, there may be many consistent distance distribution functions, and there is a ri

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Karimi, F., A. Ranjbaran, and P. Amirian. "Effect of R, µ and T on the Fragility Curves for Two Spans Reinforced Concrete Highway Bridges." Journal of Applied Engineering Sciences 9, no. 2 (2019): 145–54. http://dx.doi.org/10.2478/jaes-2019-0020.

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Abstract Fragility curves are useful tools for evaluating the probability of structural damage due to earthquakes as a function of ground motion indices. The force reduction factor (R) is one of the seismic design parameters that determine the nonlinear performance of building structures during strong earthquakes. R factor itself is mostly a function of displacement ductility (µ), natural period of a structure, and soil conditions. A statistical method (Path Analysis) is proposed for the first time to determine the effect of R, µ and T on the column fragility curve parameters of typical box gi

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