Статті в журналах: "Flexible Curves"

1

Wei Chan, Chris Yin, Chee Kidd Chiu, Yun Hui Ng, Saw Huan Goh, Xin Yi Ler, Sherwin Johan Ng, Xue Han Chian, Pheng Hian Tan, and Mun Keong Kwan. "An analysis of preoperative shoulder and neck balance and surgical outcome in 111 adolescent idiopathic scoliosis patients with two subtypes of Lenke 1 curves." Journal of Neurosurgery: Spine 34, no. 1 (January 2021): 37–44. http://dx.doi.org/10.3171/2020.5.spine20397.

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OBJECTIVEThe incidence of postoperative shoulder imbalance following posterior spinal fusion (PSF) is still high in Lenke 1 curves despite following current treatment recommendations for upper instrumented vertebra (UIV) selection. The objective of this retrospective study was to identify differences in preoperative shoulder balance and to report the surgical outcome of two subtypes of Lenke 1 curves (flexible vs stiff) in patients with adolescent idiopathic scoliosis (AIS).METHODSThe authors grouped patients’ curves as Lenke 1–ve (flexible) when their preoperative proximal thoracic side bending (PTSB) Cobb angle was < 15° and as Lenke 1+ve (stiff) when the PTSB Cobb angle was 15°–24.9°. The authors hypothesized that these two subtypes had distinct preoperative and postoperative shoulder and neck balance following PSF using pedicle screw constructs.RESULTSFifty patients had Lenke 1 (flexible) curves and 61 had Lenke 1 (stiff) curves. The mean preoperative T1 tilt for patients with Lenke 1 (flexible) was −4.9° ± 5.3°, and for those with Lenke 1 (stiff) curves it was −1.0° ± 5.3° (p < 0.001). Mean cervical axis (CA) was −0.1° ± 3.2° for Lenke 1 (flexible) curves and 2.3° ± 3.5° for Lenke 1 (stiff) curves (p < 0.001). Preoperative radiographic shoulder height (RSH) and clavicle angle (Cla-A) were similar between the two curve subtypes. Following surgery, there were significant differences between the subtypes in terms of T1 tilt (p < 0.001), RSH (p = 0.014), and Cla-A (p = 0.031). Interestingly, 41.0% of patients with a Lenke 1 (stiff) curve had +ve T1 tilt compared to 2.0% in Lenke 1 (flexible) group. Moreover, 26.2% of patients with the Lenke 1 (stiff) curve had +ve RSH compared to 12.0% of those with Lenke 1 (flexible) curves. And, 24.6% of patients with Lenke 1 (stiff) had +ve Cla-A compared to 10.0% of those with Lenke 1 (flexible) curves.CONCLUSIONSLenke 1 (flexible) and Lenke 1 (stiff) curves had distinct preoperative T1 tilt and CA measurements. Following PSF, the authors noted +ve T1 tilt in 41% of patients with Lenke 1 (stiff) curves versus 2.0% in those with Lenke 1 (flexible) curves. The authors also noted a significant difference in postoperative RSH and Cla-A measurements.

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2

Liu, Zhen-yu, Shi-en Zhou, Jin Cheng, Chan Qiu, and Jian-rong Tan. "Assembly variation analysis of flexible curved surfaces based on Bézier curves." Frontiers of Information Technology & Electronic Engineering 19, no. 6 (June 2018): 796–808. http://dx.doi.org/10.1631/fitee.1601619.

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3

Bu, Fan Hua, Yue Ming Zhang, and Zhao Miao Liu. "Residual Vibration of Flexible Exponential Cam Curves." Applied Mechanics and Materials 635-637 (September 2014): 197–200. http://dx.doi.org/10.4028/www.scientific.net/amm.635-637.197.

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The residual vibration of cam curves is analyzed. The displacement of residual vibration is computed by Duhamel method. The comparison of the residual displacement between the flexible exponential cam curves, the modified constant velocity curves, the modified trapezoidal curves, and the modified sine curves is done. The residual vibration of the flexible exponential curves is smallest.

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4

Tian, Qiuyong, Yichang Zhou, Thilo Hanisch, and Markus Hecht. "Study on railway curve squeal using a rigid-flexible coupling model of vehicle and track." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 1 (February 1, 2023): 6230–37. http://dx.doi.org/10.3397/in_2022_0927.

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Squeal noise occurring in narrow curves is one of the most annoying noise issues for people living by the railway track. When vehicles pass through those curves, squeal noise is mainly generated due to the large, high-frequency, lateral sliding friction force. To investigate generation mechanism of curve squeal, a three-dimensional (3D) vehicle-track interaction model with a flexible wheelset and a flexible curved track is built in a multi-body simulation tool in this paper. Compared to conventional rigid models, this model allows to obtain the high frequency friction force between wheel and rail. This calculated friction force in the frequency domain is analyzed to identify the major modes. Those modes are compared with the modal properties of the wheelsets and rails in order to determine which of their modes have the main contribution to the friction force and the squeal noise. In addition, a parametric study is performed to study the influence of vehicle speed, curve radius, wheel/rail friction coefficient and further parameters on the dominant modes of friction forces.

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Cui, Yunchao, Lingkai Zhang, Chong Shi, and Runhan Zhang. "Research on the Characteristic State of Rockfill Materials and the Evolution Mechanism at the Microscopic Scale." Applied Sciences 14, no. 11 (May 21, 2024): 4353. http://dx.doi.org/10.3390/app14114353.

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In this study, the real particle morphology of rockfill materials is obtained through three-dimensional scanning technology, and flexible boundary conditions are established by coupling the discrete element method and the finite element method. Then, a large-scale three-axis numerical simulation test is carried out on the rockfill materials to study the macroscopic mechanical properties and the change rule of the microscopic view of the rockfill materials in different characteristic states. The macroscopic results show that the stress–strain curves of the rockfill materials can be divided into softening and hardening curves. The phase transition, peak, and critical states of the softening-type curves show different mechanical properties, but no clear distinction between the characteristic state changes can be seen in the hardening-type curves. The microscopic results show that the displacement of the upper and lower parts of the flexible boundary of the softening curve increases with loading, and there is no obvious displacement in the middle part, but the middle particles undergo rotational deformation. An “X” shear band appears, and the strength of the force chain and the coordination number tend to increase first and then decrease. The flexible boundary displacements of the hardening-type curves are similar to those of the softening-type curves, but the central particles show a large number of cleavages instead of shear zones, and the force chain strength and coordination number levels show a continuous upward trend.

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6

Ge, Rong Yu, and P. Q. Guo. "Flexible Cam Profile Synthesis Method Using NURBS and its Optimization Based on Genetic Algorithm." Advanced Materials Research 426 (January 2012): 69–72. http://dx.doi.org/10.4028/www.scientific.net/amr.426.69.

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This paper describes a synthesis method of designing flexible cam profiles by using quintic non-uniform rational B spline (NURBS) curves. The cam profile curve can be optimized by adjusting knot vector, control points and weight factors of NURBS curve. The multiobjective optimization for a cam curve was described to satisfy both kinematic and dynamic requirements. To solve the optimization model for NURBS cam curve, an improved genetic algorithm (GA) called INSGA in the paper was proposed. Application examples on the kinematical and dynamical optimization of cam curves are presented together with detailed discussions. These examples, especial the dynamic optimization to control the residual vibration for a cam curve used in an indexing cam mechanism, sufficiently illustrate the effectiveness of the proposed approach.

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7

İPEK, Egemen, and Haydar AKYAZI. "Turkish Households Consumption Behavior and Flexible Engel Curves." Doğuş Üniversitesi Dergisi 2, no. 18 (July 27, 2017): 35–50. http://dx.doi.org/10.31671/dogus.2018.30.

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8

Belkhatir, Bachir, and Ahmed Zidna. "Construction of flexible blending parametric surfaces via curves." Mathematics and Computers in Simulation 79, no. 12 (August 2009): 3599–608. http://dx.doi.org/10.1016/j.matcom.2009.04.015.

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9

Yamada, Yohei, and Hiroyuki Sasahara. "Free-form curves cutting using flexible circular saw." Precision Engineering 38, no. 3 (July 2014): 611–16. http://dx.doi.org/10.1016/j.precisioneng.2014.02.011.

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10

Winter, Michael, Alexander Luttkau, and Hermann Lödding. "Produktionskennlinien mit Kapazitätsflexibilität/Logistic Operating Curves with Capacity Flexibility." wt Werkstattstechnik online 111, no. 04 (2021): 190–94. http://dx.doi.org/10.37544/1436-4980-2021-04-12.

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Die Kapazitätsflexibilität ist von zentraler Bedeutung für das Produktionsmanagement. Sie ermöglicht es Unternehmen, auf Nachfrageschwankungen zu reagieren. Weniger bekannt ist ihre Bedeutung für die erreichbaren Bestände und Durchlaufzeiten der Produktion. Unternehmen können den erforderlichen Pufferbestand mit flexiblen Kapazitäten reduzieren. Dieser Effekt wird mithilfe von Produktionskennlinien modelliert und dargestellt.   Capacity flexibility is of central importance for production management. It enables companies to respond to fluctuations in demand. Less well known is its significance for the necessary WIP buffers and throughput times in production. Based on flexible capacities, companies can reduce the required level of work-in-process buffer. This effect is modelled and visualized with production operating curves.

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11

Miura, Kenjiro T., and R. U. Gobithaasan. "Aesthetic Curves and Surfaces in Computer Aided Geometric Design." International Journal of Automation Technology 8, no. 3 (May 5, 2014): 304–16. http://dx.doi.org/10.20965/ijat.2014.p0304.

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Aesthetic shapes are usually actualized as 3D objects represented by free-form surfaces. The main components used to achieve aesthetic surfaces are 2D and 3D curves, which are the elements most basic for determining the shapes and silhouettes of industrial products. Bézier, B-Spline and NURBS are types of flexible curves developed for various design intents. These curves, however produce complex curvature functions that may undermine the formulation of shape aesthetics. A viable solution to this problem is to formulate aesthetic curves and surfaces from well-defined curvatures to improve aesthetic design quality. This paper advocates formalizing aesthetic curve and surface theories to fill the gapmentioned above, which has existed since the 1970s. This paper begins by reviewing on fair curves and surfaces. It then extensively discusses on the technicalities of Log-Aesthetic (LA) curves and surfaces and touches on industrial design applications. These emerging LA curves have a high potential for being used as standards to generate, evaluate and reshape aesthetic curves and surfaces, thus revolutionizing efficiency in developing curve and shape aesthetics.

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12

Smith, James A., and Matthew D. Taylor. "A peaked logistic-based selection curve." Canadian Journal of Fisheries and Aquatic Sciences 71, no. 3 (March 2014): 351–55. http://dx.doi.org/10.1139/cjfas-2013-0401.

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Length-based selection curves define the relative catchability of fish to specific types of fishing gear, with catchability often highest at intermediate fish lengths. Distributions such as the normal, lognormal, or gamma are often used to define “peaked” selection curves, but these have limited capabilities to describe strongly asymmetric selection relationships, such as those sometimes observed for hooks or gillnets. Another, more flexible, peaked selection curve is proposed, which is derived by combining multiple logistic distributions. While the logistic distribution is frequently used to describe monotonic selection curves, incorporating multiple logistic equations (that describe either the increasing or decreasing catchability) can define a large range of asymmetric peaked selection curves. This “peak-logistic” curve also allows nonzero asymptotic selection for the largest size classes, which may be the selection occurring in some hook-and-line fisheries. We demonstrate examples of selection in hook, haul net, and mixed hook fisheries, for which the peak-logistic curve is more appropriate than comparative lognormal and binormal selection curves. We also promote an alternative to the peak-logistic: the two-sided normal curve.

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13

Maqsood, Sidra, Muhammad Abbas, Gang Hu, Ahmad Lutfi Amri Ramli, and Kenjiro T. Miura. "A Novel Generalization of Trigonometric Bézier Curve and Surface with Shape Parameters and Its Applications." Mathematical Problems in Engineering 2020 (May 25, 2020): 1–25. http://dx.doi.org/10.1155/2020/4036434.

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Adopting a recurrence technique, generalized trigonometric basis (or GT-basis, for short) functions along with two shape parameters are formulated in this paper. These basis functions carry a lot of geometric features of classical Bernstein basis functions and maintain the shape of the curve and surface as well. The generalized trigonometric Bézier (or GT-Bézier, for short) curves and surfaces are defined on these basis functions and also analyze their geometric properties which are analogous to classical Bézier curves and surfaces. This analysis shows that the existence of shape parameters brings a convenience to adjust the shape of the curve and surface by simply modifying their values. These GT-Bézier curves meet the conditions required for parametric continuity (C0, C1, C2, and C3) as well as for geometric continuity (G0, G1, and G2). Furthermore, some curve and surface design applications have been discussed. The demonstrating examples clarify that the new curves and surfaces provide a flexible approach and mathematical sketch of Bézier curves and surfaces which make them a treasured way for the project of curve and surface modeling.

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14

Fiebig, Everton Quadros, Carlos Henrique Maçaneiro, Ricardo Kiyoshi Miyamoto, Rodrigo Fetter Lauffer, and Ricardo André Acácio dos Santos. "Standardization of dynamic RX for preoperative planning in adolescent idiopathic scoliosis." Coluna/Columna 13, no. 3 (September 2014): 199–201. http://dx.doi.org/10.1590/s1808-18512014130300187.

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OBJECTIVE: To compare X-rays usually performed in supine with lateralization with those in lateral decubitus with fulcrum at the apex of the primary curve caused by cushion, in order to monitor the achievement of improvement patterns of correction in preestablished deformities for the preoperative surgical planning. METHODS: Comparison of radiographic studies in the preoperative supine with lateralization and lateral decubitus with cushion performing fulcrum at the apex of the major curve in patients with adolescent idiopathic scoliosis. RESULTS: Curves varied in AP between 76° e 40° and were corrected in supine with lateralization to the average of 21° observing that when carried out with fulcrum with cushion in lateral decubitus the curves were corrected to 15° on average with higher discrepancy in values among the most rigid curves. CONCLUSIONS: It was verified that on flexible curves the cushions did not produce satisfactory corrections in primary curves. In more rigid curves and in collaborative patients, greater effectiveness on the correction of deformity in main curves was obtained with cushions producing local fulcrum for a better preoperative planning on correction of deformities.

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15

Colagrande, Sandro, Danilo Ranalli, and Marco Tallini. "Ground Penetrating Radar Assessment of Flexible Road Pavement Degradation." International Journal of Geophysics 2011 (2011): 1–11. http://dx.doi.org/10.1155/2011/989136.

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GPR investigations were used to study degraded road pavements built in cutting sections. Road integrity was assessed via quantitative analysis of power curves. 1600 MHz and 600 MHz radar sections were collected in 40 damaged and undamaged road pavement sites. The collected data were processed as follows: (i) linearisation with regression analysis of power curves; (ii) assessment of absorption angleα′ which is directly proportional to absorption coefficientα(this was obtained by setting the e.m. propagation velocity to 10 cm/ns); (iii) comparison of absorption coefficients in both damaged and undamaged zones with respect to road pavement degradation. If the absorption coefficients of damaged and undamaged road sections have nearly the same value, then the likely cause of degradation is the fatigue or the thermal shrinkage; if they are not, then road degradation is due to the different compactness of the soil caused by vehicular traffic load. In a considerable number of sites, the statistical comparison of damaged and undamaged zones through the absorption coefficient analysis shows that surface observations of road pavements are quite consistent with power curve analyses.

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16

Ryan, David L., and Terence J. Wales. "Flexible and Semiflexible Consumer Demands with Quadratic Engel Curves." Review of Economics and Statistics 81, no. 2 (May 1999): 277–87. http://dx.doi.org/10.1162/003465399558076.

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17

Cheng, Fuhua, and Wen‐Chiuan Liao. "Flexible subdivision theorems for b‐spline and bézier curves." Journal of the Chinese Institute of Engineers 9, no. 1 (January 1986): 97–103. http://dx.doi.org/10.1080/02533839.1986.9676866.

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18

Nguyen, Vu-Thinh, and Do-Joong Kim. "Flexible cam profile synthesis method using smoothing spline curves." Mechanism and Machine Theory 42, no. 7 (July 2007): 825–38. http://dx.doi.org/10.1016/j.mechmachtheory.2006.07.005.

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19

Kim, Jin Gyo, Ulrich Menzefricke, and Fred M. Feinberg. "Capturing Flexible Heterogeneous Utility Curves: A Bayesian Spline Approach." Management Science 53, no. 2 (February 2007): 340–54. http://dx.doi.org/10.1287/mnsc.1060.0616.

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20

Kruppa, Kinga, Roland Kunkli, and Miklós Hoffmann. "Possibilities and Advantages of Rational Envelope and Minkowski Pythagorean Hodograph Curves for Circle Skinning." Mathematics 9, no. 8 (April 13, 2021): 843. http://dx.doi.org/10.3390/math9080843.

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Minkowski Pythagorean hodograph curves are widely studied in computer-aided geometric design, and several methods exist which construct Minkowski Pythagorean hodograph (MPH) curves by interpolating Hermite data in the R2,1 Minkowski space. Extending the class of MPH curves, a new class of Rational Envelope (RE) curve has been introduced. These are special curves in R2,1 that define rational boundaries for the corresponding domain. A method to use RE and MPH curves for skinning purposes, i.e., for circle-based modeling, has been developed recently. In this paper, we continue this study by proposing a new, more flexible way how these curves can be used for skinning a discrete set of circles. We give a thorough overview of our algorithm, and we show a significant advantage of using RE and MPH curves for skinning purposes: as opposed to traditional skinning methods, unintended intersections can be detected and eliminated efficiently.

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21

Bouafia, Ali, and Ahmed Bouguerra. "Modélisation en centrifugeuse du comportement d'un pieu flexible chargé horizontalement à proximité d'un talus." Canadian Geotechnical Journal 32, no. 2 (April 1, 1995): 324–35. http://dx.doi.org/10.1139/t95-033.

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This paper presents the results of a static lateral loading test, carried out in a centrifuge, on the reduced model of a single pile, instrumented with strain gauges, installed near a dense sandy slope. The effect of the proximity of the slope on the behaviour of the pile is studied. P–Y lateral reaction curves are constructed, and the variations of the horizontal subgrade modulus are analyzed. A practical method, based on the correction of the horizontal soil P–Y curves, is proposed to study the behaviour of piles near a slope. Key words : horizontal loading, pile, centrifuge, slope, sand, P–Y curve.

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22

BiBi, Samia, Muhammad Abbas, Kenjiro T. Miura, and Md Yushalify Misro. "Geometric Modeling of Novel Generalized Hybrid Trigonometric Bézier-Like Curve with Shape Parameters and Its Applications." Mathematics 8, no. 6 (June 12, 2020): 967. http://dx.doi.org/10.3390/math8060967.

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The main objective of this paper is to construct the various shapes and font designing of curves and to describe the curvature by using parametric and geometric continuity constraints of generalized hybrid trigonometric Bézier (GHT-Bézier) curves. The GHT-Bernstein basis functions and Bézier curve with shape parameters are presented. The parametric and geometric continuity constraints for GHT-Bézier curves are constructed. The curvature continuity provides a guarantee of smoothness geometrically between curve segments. Furthermore, we present the curvature junction of complex figures and also compare it with the curvature of the classical Bézier curve and some other applications by using the proposed GHT-Bézier curves. This approach is one of the pivotal parts of construction, which is basically due to the existence of continuity conditions and different shape parameters that permit the curve to change easily and be more flexible without altering its control points. Therefore, by adjusting the values of shape parameters, the curve still preserve its characteristics and geometrical configuration. These modeling examples illustrate that our method can be easily performed, and it can also provide us an alternative strong strategy for the modeling of complex figures.

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23

Simian, Dana, Oana Adriana Ticleanu, and Nicolae Constantinescu. "Characterization of a cubic interpolation scheme dependent on two parameters and applications." Annals of the University of Craiova - Mathematics and Computer Science Series 49, no. 2 (December 24, 2022): 445–60. http://dx.doi.org/10.52846/ami.v49i2.1703.

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"The aim of this paper is to provide a characterization diagram for a family of B\'{e}zier flexible interpolation curves as well as to present an application of our results in cryptography. In our interpolation scheme, two parameters, $t_1,\ t_2\in (0,1)$ determine the position of the interpolation points on the B\'{e}zier curve. Consequently we obtain a family of B\'{e}zier interpolation curves depending on two parameters. Altering the values of the parameters we modify the intermediary control points and implicitly the shape of the interpolation curve. In order to control the shape of the interpolation curves from this family, we provide a partition of the domain $T=(0,1)\times (0,1)$ where the parameters lie according to the geometric characterization of these curves: with zero, one or two inflexion points; with loop; with cusp and degenerated in quadratic curves. The characterization diagram can be used as a tool for the choice of parameters, with possible applications in different fields. We present one of its application in cryptography, for finding certain subspaces over which particular elliptic sub-curves are defined. Computation, implementation and graphics are made using MATLAB."

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Meng, Wei, Caiyun Li, and Qianqian Liu. "Geometric Modeling of C-Bézier Curve and Surface with Shape Parameters." Mathematics 9, no. 21 (October 20, 2021): 2651. http://dx.doi.org/10.3390/math9212651.

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In order to solve the problem of geometric design and architectural design of complex engineering surface, we introduce the parametric and geometric continuity constraints of generalized C-Bézier curves and surfaces with shape parameters. Firstly, based on C-Bézier basis with parameters, we study the constraints of the control points of the curves needed to be satisfied when connecting them. Moreover, we study the continuity conditions between two adjacent C-Bézier surfaces with parameters. By the continuity conditions and different shape parameters, the curve and surface can be changed easily and be more flexible without altering its control points. Therefore, by adjusting the values of shape parameters, the curve and surface still preserve its characteristics and geometrical configuration. Some graphical examples ensure that the proposed method greatly improves the ability to design complex curves and surfaces and easy to implement.

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Zhang, Xiaolei, and Jinming Wu. "Approximate Implicitization of Parametric Curves Using Cubic Algebraic Splines." Mathematical Problems in Engineering 2009 (2009): 1–12. http://dx.doi.org/10.1155/2009/327457.

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This paper presents an algorithm to solve the approximate implicitization of planar parametric curves using cubic algebraic splines. It applies piecewise cubic algebraic curves to give a globalG2continuity approximation to planar parametric curves. Approximation error on approximate implicitization of rational curves is given. Several examples are provided to prove that the proposed method is flexible and efficient.

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Semenova, Elizaveta, Maria Luisa Guerriero, Bairu Zhang, Andreas Hock, Philip Hopcroft, Ganesh Kadamur, Avid M. Afzal, and Stanley E. Lazic. "Flexible Fitting of PROTAC Concentration–Response Curves with Changepoint Gaussian Processes." SLAS DISCOVERY: Advancing the Science of Drug Discovery 26, no. 9 (September 20, 2021): 1212–24. http://dx.doi.org/10.1177/24725552211028142.

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A proteolysis-targeting chimera (PROTAC) is a new technology that marks proteins for degradation in a highly specific manner. During screening, PROTAC compounds are tested in concentration–response (CR) assays to determine their potency, and parameters such as the half-maximal degradation concentration (DC50) are estimated from the fitted CR curves. These parameters are used to rank compounds, with lower DC50 values indicating greater potency. However, PROTAC data often exhibit biphasic and polyphasic relationships, making standard sigmoidal CR models inappropriate. A common solution includes manual omitting of points (the so-called masking step), allowing standard models to be used on the reduced data sets. Due to its manual and subjective nature, masking becomes a costly and nonreproducible procedure. We therefore used a Bayesian changepoint Gaussian processes model that can flexibly fit both nonsigmoidal and sigmoidal CR curves without user input. Parameters such as the DC50, maximum effect Dmax, and point of departure (PoD) are estimated from the fitted curves. We then rank compounds based on one or more parameters and propagate the parameter uncertainty into the rankings, enabling us to confidently state if one compound is better than another. Hence, we used a flexible and automated procedure for PROTAC screening experiments. By minimizing subjective decisions, our approach reduces time and cost and ensures reproducibility of the compound-ranking procedure. The code and data are provided on GitHub ( https://github.com/elizavetasemenova/gp_concentration_response ).

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Zhu, Zhi, Miaomiao Wang, Zuoxia Xing, Yang Liu, and Shihong Chen. "Optimal Configuration of Power/Thermal Energy Storage for a Park-Integrated Energy System Considering Flexible Load." Energies 16, no. 18 (September 5, 2023): 6424. http://dx.doi.org/10.3390/en16186424.

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The park-integrated energy system can achieve the optimal allocation, dispatch, and management of energy by integrating various energy resources and intelligent control and monitoring. Flexible load participation in scheduling can reduce peak and valley load, optimize load curves, further improve energy utilization efficiency, and reduce system costs. Based on this, firstly, a flexible power-load model is established considering the translatable load, transferable load, and reducible load; and a thermal flexible load model is established based on the fuzziness of user perception of temperature in this study; then, the mixed integer linear programming method is adopted, and the sum of the carbon transaction cost, operation and maintenance cost, compensation cost, power purchase cost, gas purchase cost, wind and light abandonment penalty cost and investment cost of the system is minimized as the objective function, and the configuration of the integrated energy system is optimized, and the optimal capacity of each equipment and the output of each period are obtained. Finally, taking an industrial park in Liaoning Province of China as an example, the analysis is carried out. The example results show that by scheduling the flexible electrical load and flexibly adjusting the indoor temperature, renewable energy consumption can be promoted, and electricity load and heat-load curves can be optimized to increase the installed capacity of wind turbines, reduce the capacity of gas turbines, batteries, and heat-storage tanks, improve system economy, and improve the penetration rate of renewable energy.

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Brustad, Tanita Fossli, and Rune Dalmo. "Exploring Benefits of Using Blending Splines as Transition Curves." Applied Sciences 10, no. 12 (June 19, 2020): 4226. http://dx.doi.org/10.3390/app10124226.

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Track geometry is a fundamental subject in railway construction. With the demand for increased capacity in terms of load and speed, the need for suitable transitions between consecutive track sections is highly relevant. Properly constructed transition curves lead to improved travel comfort, increased safety, and reduced wear. The well known clothoid curve is widely used as a transition curve; however, the linear curvature is not sufficiently smooth to meet the requirements for railways carrying high speed trains or heavy hauls. Blending spline curves are flexible spline constructions possessing favourable smoothness properties at the end points, which makes them considerable for use as transition curves. This paper demonstrates some selected blending splines applied as transition curves between two existing circular arc segments selected from the Ofotbanen railway. The main results in this paper are related to the smoothness at the end points and the behaviour of the curvature of the curves, where the new transition curves were shown to be smoother than the original clothoid. Another new result is the observation that the proposed method allows for the improvement of existing railways without forcing extensive changes to the original track. Some representative examples are included to highlight the flexibility of this first instance of blending splines as transition curves.

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Elston, D. A., C. A. Glasbey, and D. R. Neilson. "Non-parametric lactation curves." Animal Science 48, no. 2 (April 1989): 331–39. http://dx.doi.org/10.1017/s0003356100040320.

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ABSTRACTLactation curves are fitted to data as a preliminary to estimating summary statistics. Two widely quoted curves are atbe-ct (Wood, 1967) and a(1 - e-bt) - ct (Cobby and Le Du, 1978), each of which has three parameters. Restriction to either of these curves imposes limitations on the fit to the data and can result in biased estimation of summary statistics. Alternatively, lactation curves can be generated by the use of a non-parametric method which requires only weak assumptions about the signs of derivatives of the curves. Because the non-parametric curves are more flexible, estimates of summary statistics are less likely to be biased than those based on parametric models. Use of the non-parametric curves is particularly advantageous around the time of peak yield, where the curves of Wood and Cobby and Le Du are known to fit data poorly.

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Fauer, Felix S., Jana Ulrich, Oscar E. Jurado, and Henning W. Rust. "Flexible and consistent quantile estimation for intensity–duration–frequency curves." Hydrology and Earth System Sciences 25, no. 12 (December 20, 2021): 6479–94. http://dx.doi.org/10.5194/hess-25-6479-2021.

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Abstract. Assessing the relationship between the intensity, duration, and frequency (IDF) of extreme precipitation is required for the design of water management systems. However, when modeling sub-daily precipitation extremes, there are commonly only short observation time series available. This problem can be overcome by applying the duration-dependent formulation of the generalized extreme value (GEV) distribution which fits an IDF model with a range of durations simultaneously. The originally proposed duration-dependent GEV model exhibits a power-law-like behavior of the quantiles and takes care of a deviation from this scaling relation (curvature) for sub-hourly durations (Koutsoyiannis et al., 1998). We suggest that a more flexible model might be required to model a wide range of durations (1 min to 5 d). Therefore, we extend the model with the following two features: (i) different slopes for different quantiles (multiscaling) and (ii) the deviation from the power law for large durations (flattening), which is newly introduced in this study. Based on the quantile skill score, we investigate the performance of the resulting flexible model with respect to the benefit of the individual features (curvature, multiscaling, and flattening) with simulated and empirical data. We provide detailed information on the duration and probability ranges for which specific features or a systematic combination of features leads to improvements for stations in a case study area in the Wupper catchment (Germany). Our results show that allowing curvature or multiscaling improves the model only for very short or long durations, respectively, but leads to disadvantages in modeling the other duration ranges. In contrast, allowing flattening on average leads to an improvement for medium durations between 1 h and 1 d, without affecting other duration regimes. Overall, the new parametric form offers a flexible and enhanced performance model for consistently describing IDF relations over a wide range of durations, which has not been done before as most existing studies focus on durations longer than 1 h or day and do not address the deviation from the power law for very long durations (2–5 d).

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Oswald, Stephen A., Ian C. T. Nisbet, Andre Chiaradia, and Jennifer M. Arnold. "FlexParamCurve: R package for flexible fitting of nonlinear parametric curves." Methods in Ecology and Evolution 3, no. 6 (August 10, 2012): 1073–77. http://dx.doi.org/10.1111/j.2041-210x.2012.00231.x.

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32

Laslett, Geoff M., J. Paige Eveson, and Tom Polacheck. "A flexible maximum likelihood approach for fitting growth curves to tagrecapture data." Canadian Journal of Fisheries and Aquatic Sciences 59, no. 6 (June 1, 2002): 976–86. http://dx.doi.org/10.1139/f02-069.

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We describe a novel maximum likelihood method for fitting general growth curves to tagrecapture data. The growth model allows for the asymptotic length and the time to tagging to vary from individual to individual, with other parameters being fixed. Unlike the Fabens approach, we do not take differences to fit the parameters, but instead model the joint density of the release and recapture lengths. We simulate data to examine the bias and precision of the estimated parameters obtained using our fitting method. We include simulations for which the time to tagging model is incorrect, but find that the growth curve is usually still fitted with small bias. Furthermore, we introduce a new growth curve that allows for different growth rates for juveniles and adults. The new growth curve needs sufficient data coverage before and after the transition from juvenile to adult for all parameters to be estimated precisely. We illustrate the method on real data by fitting this new growth curve to southern bluefin tuna tagrecapture data.

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Su, Jing Bo, Yi Huan Zhu, and Feng Wu. "Nonlinear Finite Element Analysis of Flexible Berthing Pier Based on P-Y Curves." Applied Mechanics and Materials 256-259 (December 2012): 1923–27. http://dx.doi.org/10.4028/www.scientific.net/amm.256-259.1923.

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Flexible Berthing Pier is a port structure that absorbs, partly or totally depending on self- deformation, the ship berthing energy and the ship rolling energy caused by the wave. Flexible berthing pier mainly sustains the horizontal load. Present methods to calculate the horizontal bearing capacity of pile foundation consist of P-Y curve method, NL method and m method. P-y curves method is one kind of nonlinear subgrade-reaction methods; it considers the nonlinear character, layer character, different kinds, and load kinds of ground soil. Starting from the concept of spring joint in Newmark method, the contact non-linear finite element model is founded for the pile-soil system. By the formula of P-Y curves of compound foundation reaction method, the formulas of elastic coefficients of non-linear springs are deduced. The corresponding programs are organized based on Marc. By the numerical example, the rationality and the feasibility of the presented method is validated.

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Cao, Guo Qiang, and Yi Yu Sun. "Finite Element Analysis of Deformation of the Multipoint Flexible Clamped Thin-Wall Component during Machining." Advanced Materials Research 542-543 (June 2012): 519–22. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.519.

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A study on deformation of multipoint flexible clamped thin-wall components during numerical control drilling in vertical direction downward is presented. The finite element model of multipoint flexible clamped thin-wall component during machining is established with program ANSYS, and a static analysis of deformation of the model is conducted. The laws of maximum deformation under different skin thickness, under different cutting force and on the 3 special machining paths in the cut area are obtained. The results show that the maximum deformation is linear with cutting force and exponential with skin thickness, and the function curves of the maximum deformation on the 3 special machining paths are all different, the function curve 2 is the composite superposition of the function curve 1 and the function curve 3.

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Yue, Qiu Qin, and Hua Yu. "Development and Application of CNC Turning Macro-Program Based on Non-Circular Curve." Applied Mechanics and Materials 105-107 (September 2011): 2271–74. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.2271.

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Owing to the deficiency of machining non-circular curve by manual programming in CNC system, the universal macro-program of machining non-circular curve based on the ellipse curve in CNC turning of the FANUC system is developed by adopting analytical and inductive approach. The real application of machining ellipse and parabola curves are also proposed in this paper, which showed that the universal macro-program is flexible and convenient. The programming efficiency and quality is increased effectively while machining any other non-circular curve works.

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Daniel, Laurent, and Farid Belahcene. "Flexible Head, Designed for Measuring Residual Stress along Variable Curves Using Ultra-Sonic Tranducers." Advanced Materials Research 996 (August 2014): 398–403. http://dx.doi.org/10.4028/www.scientific.net/amr.996.398.

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Ultra-sonic measure of residual stress has been along for a while. One main drawback of this technique is the need for a measuring head adapted to each new surface shape. We introduce a new measurement head designed to adapt to changing curves. This device will open the possibility of curved surfaces residual stress cartography. We focus on the device geometric design, its possibilities and limitations.

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37

Zaretsky, E., and G. Ben-Dor. "Compressive Stress-Strain Relations and Shock Hugoniot Curves of Flexible Foams." Journal of Engineering Materials and Technology 117, no. 3 (July 1, 1995): 278–84. http://dx.doi.org/10.1115/1.2804540.

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Based on the general shape of the curves describing experimental compressive stress-strain relations of flexible porous materials (e.g., flexible foams) which are known to depend on their relative density, a general mathematical functional dependence of the stress on the strain is proposed. The general function includes two constants. Using experimental and empirical information the values of these constants are determined, so that a final compressive stress-strain relation, in which the relative density is a parameter, is obtained. Good agreement is found when the presently developed empirical stress-strain relations are compared to experimental ones for a wide range of relative densities. The proposed compressive stress-strain relations are then used to derive shock Hugoniot relations for flexible porous materials. With the aid of these relations one can investigate the dynamic behavior of foams struck head-on by shock waves. The finally obtained empirical shock Hugoniot relations are found to be similar to experimental relations which are proposed in the literature. In addition, a mathematical investigation of the asymptotic behavior of the shock Hugoniot relations is conducted. The results of this investigation are found to agree excellently with actual experimental data.

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38

Lindberg, Christina Willecke, Daniela Huppenkothen, R. Lynne Jones, Bryce T. Bolin, Mario Jurić, V. Zach Golkhou, Eric C. Bellm, et al. "Characterizing Sparse Asteroid Light Curves with Gaussian Processes." Astronomical Journal 163, no. 1 (December 21, 2021): 29. http://dx.doi.org/10.3847/1538-3881/ac3079.

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Abstract In the era of wide-field surveys like the Zwicky Transient Facility and the Rubin Observatory’s Legacy Survey of Space and Time, sparse photometric measurements constitute an increasing percentage of asteroid observations, particularly for asteroids newly discovered in these large surveys. Follow-up observations to supplement these sparse data may be prohibitively expensive in many cases, so to overcome these sampling limitations, we introduce a flexible model based on Gaussian processes to enable Bayesian parameter inference of asteroid time-series data. This model is designed to be flexible and extensible, and can model multiple asteroid properties such as the rotation period, light-curve amplitude, changing pulse profile, and magnitude changes due to the phase-angle evolution at the same time. Here, we focus on the inference of rotation periods. Based on both simulated light curves and real observations from the Zwicky Transient Facility, we show that the new model reliably infers rotational periods from sparsely sampled light curves and generally provides well-constrained posterior probability densities for the model parameters. We propose this framework as an intermediate method between fast but very limited-period detection algorithms and much more comprehensive but computationally expensive shape-modeling based on ray-tracing codes.

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39

Chao, Cheng-Kang Ted, Jason Klein, Jianchao Tan, Jose Echevarria, and Yotam Gingold. "ColorfulCurves: Palette-Aware Lightness Control and Color Editing via Sparse Optimization." ACM Transactions on Graphics 42, no. 4 (July 26, 2023): 1–12. http://dx.doi.org/10.1145/3592405.

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Color editing in images often consists of two main tasks: changing hue and saturation, and editing lightness or tone curves. State-of-the-art palette-based recoloring approaches entangle these two tasks. A user's only lightness control is changing the lightness of individual palette colors. This is inferior to state-of-the-art commercial software, where lightness editing is based on flexible tone curves that remap lightness. However, tone curves are only provided globally or per color channel (e.g., RGB). They are unrelated to the image content. Neither tone curves nor palette-based approaches support direct image-space edits---changing a specific pixel to a desired hue, saturation, and lightness. ColorfulCurves solves both of these problems by uniting palette-based and tone curve editing. In ColorfulCurves , users directly edit palette colors' hue and saturation, per-palette tone curves, or image pixels (hue, saturation, and lightness). ColorfulCurves solves an L 2,1 optimization problem in real-time to find a sparse edit that satisfies all user constraints. Our expert study found overwhelming support for ColorfulCurves over experts' preferred tools.

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Lower, Sidney, Desika Narayanan, Joel Leja, Benjamin D. Johnson, Charlie Conroy, and Romeel Davé. "How Well Can We Measure Galaxy Dust Attenuation Curves? The Impact of the Assumed Star-dust Geometry Model in Spectral Energy Distribution Fitting." Astrophysical Journal 931, no. 1 (May 1, 2022): 14. http://dx.doi.org/10.3847/1538-4357/ac6959.

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Abstract One of the most common methods for inferring galaxy attenuation curves is via spectral energy distribution (SED) modeling, where the dust attenuation properties are modeled simultaneously with other galaxy physical properties. In this paper, we assess the ability of SED modeling to infer these dust attenuation curves from broadband photometry, and suggest a new flexible model that greatly improves the accuracy of attenuation curve derivations. To do this, we fit mock SEDs generated from the simba cosmological simulation with the prospector SED fitting code. We consider the impact of the commonly assumed uniform screen model and introduce a new nonuniform screen model parameterized by the fraction of unobscured stellar light. This nonuniform screen model allows for a nonzero fraction of stellar light to remain unattenuated, resulting in a more flexible attenuation curve shape by decoupling the shape of the UV attenuation curve from the optical attenuation curve. The ability to constrain the dust attenuation curve is significantly improved with the use of a nonuniform screen model, with the median offset in UV attenuation decreasing from −0.30 dex with a uniform screen model to −0.17 dex with the nonuniform screen model. With this increase in dust attenuation modeling accuracy, we also improve the star formation rates (SFRs) inferred with the nonuniform screen model, decreasing the SFR offset on average by 0.12 dex. We discuss the efficacy of this new model, focusing on caveats with modeling star-dust geometries and the constraining power of available SED observations.

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41

Scheffer, Christian. "More Flexible Curve Matching via the Partial Fréchet Similarity." International Journal of Computational Geometry & Applications 26, no. 01 (March 2016): 33–52. http://dx.doi.org/10.1142/s0218195916500023.

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We study a modified version of the partial Fréchet similarity that is motivated by real world applications, e.g. the analysis of spectroscopic data in the context of astroinformatics and the analysis of birds’ migration trajectories. In those practical applications of curve matching it is often necessary to ignore outliers while dissimilarities regarding individual directions should be weighted by individual costs. We enable both by computing the partial Fréchet similarity between polygonal curves w.r.t. a non-uniform metric. In particular, we measure distances by a function [Formula: see text] that is induced by a set of weighted vectors. We discuss the approximation quality of [Formula: see text] regarding any [Formula: see text] metric and present a polynomial time algorithm for computing an exact solution of the resulting modified partial Fréchet similarity.

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KIM, JINMYONG, and HAKMYONG MUN. "NONLINEAR RECURRENT HIDDEN VARIABLE FRACTAL INTERPOLATION CURVES WITH FUNCTION VERTICAL SCALING FACTORS." Fractals 28, no. 06 (September 2020): 2050096. http://dx.doi.org/10.1142/s0218348x20500966.

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In this paper, we present a construction of new nonlinear recurrent hidden variable fractal interpolation curves. In order to get new fractal curves, we use Rakotch’s fixed point theorem. We construct recurrent hidden variable iterated function systems with function vertical scaling factors to generate more flexible fractal interpolation curves. We also give an illustrative example to demonstrate the effectiveness of our results.

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Späth, H., and J. Meier. "Flexible smoothing with periodic cubic splines and fitting with closed curves." Computing 40, no. 4 (December 1988): 293–300. http://dx.doi.org/10.1007/bf02276913.

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44

Orevkov, S. Yu. "Classification of flexible M -curves of degree 8 up to isotopy." Geometric And Functional Analysis 12, no. 4 (October 1, 2002): 723–55. http://dx.doi.org/10.1007/s00039-002-8264-6.

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45

Cadarso-Suárez, Carmen, Luís Meira-Machado, Thomas Kneib, and Francisco Gude. "Flexible hazard ratio curves for continuous predictors in multi-state models." Statistical Modelling: An International Journal 10, no. 3 (September 28, 2010): 291–314. http://dx.doi.org/10.1177/1471082x0801000303.

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46

Wang, Aizeng, Gang Zhao, and Chuan He. "Unified Representation of Curves and Surfaces." Mathematics 9, no. 9 (April 30, 2021): 1019. http://dx.doi.org/10.3390/math9091019.

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In conventional modeling, shared control points can be employed to realize a unified representation for an object consisting of only curves or only surfaces touching one another. However, this method fails in treating the following two cases: (a) a system consisting of detached curves or surfaces; (b) a system having both curves and surfaces. The purpose of the present paper is to develop a new theoretical tool to solve such problems. By introducing the definitions of naked knot and I-mesh, the concept of I-spline is put forth, which is, in essence, an expanded B-spline or T-spline. It is verified by examples that the naked knots make I-splines flexible and effective in transforming different surfaces and/or curves into a unified one, especially in the above two cases.

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Jónás, Tamás, Gábor Árva, and Zsuzsanna Eszter Tóth. "Forecasting Failure Rates of Electronic Goods by Using Decomposition and Fuzzy Clustering of Empirical Failure Rate Curves." Periodica Polytechnica Social and Management Sciences 26, no. 1 (July 3, 2017): 10. http://dx.doi.org/10.3311/ppso.9026.

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In this paper a novel methodology founded on the joint application of analytic decomposition of empirical failure rate time series and soft computational techniques is introduced in order to predict bathtub-shaped failure rate curves of consumer electronic goods. Empirical failure rate time series are modeled by a flexible function the parameters of which have geometric interpretations, and so the model parameters grab the characteristics of bathtub-shaped failure rate curves. The so-called typical standardized failure rate curve models, which are derived from the model functions through standardization and fuzzy clustering processes, are applied to predict failure rate curves of consumer electronics in a method that combines analytic curve fitting and soft computing techniques. The forecasting capability of the introduced method was tested on real-life data. Based on the empirical results from practical applications, the introduced method can be considered as a new, alternative reliability prediction technique the application of which can support the electronic repair service providers to plan their resources in the long run.

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48

Collalti, Dino, Nekeisha Spencer, and Eric Strobl. "Flash flood detection via copula-based intensity–duration–frequency curves: evidence from Jamaica." Natural Hazards and Earth System Sciences 24, no. 3 (March 14, 2024): 873–90. http://dx.doi.org/10.5194/nhess-24-873-2024.

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Abstract. Extreme rainfall events frequently cause hazardous floods in many parts of the world. With growing human exposure to floods, studying conditions that trigger floods is imperative. Flash floods, in particular, require well-defined models for the timely warning of the population at risk. Intensity–duration–frequency (IDF) curves are a common way to characterize rainfall and flood events. Here, the copula method is employed to model the dependence between the intensity and duration of rainfall events flexibly and separately from their respective marginal distribution. Information about the localization of 93 flash floods in Jamaica was gathered and linked to remote-sensing rainfall data, and additional data on location-specific yearly maximum rainfall events were constructed. The estimated normal copula has Weibull and generalized extreme value (GEV) marginals for duration and intensity, respectively. Due to the two samples, it is possible to pin down above which line in the intensity duration space a rainfall event likely triggers a flash flood. The parametric IDF curve with an associated return period of 216 years is determined as the optimal threshold for flash flood event classification. This methodology delivers a flexible approach to generating rainfall IDF curves that can directly be used to assess flash flood risk.

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Luo, Liqin, Chenxuan Zhu, Chaowei Wang, and Yanhua Long. "Analysis of Power Load Characteristics Based on Adaptive Ensemble Clustering Algorithm." Journal of Physics: Conference Series 2378, no. 1 (December 1, 2022): 012094. http://dx.doi.org/10.1088/1742-6596/2378/1/012094.

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Abstract With the growing number of power users and more flexible power consumption, how to cluster the power load curves efficiently becomes particularly important. In order to improve the accuracy, effectiveness and rapidity of load clustering, an adaptive integrated fuzzy clustering algorithm was proposed in this paper. Firstly, the initial clustering centroids were obtained by the improved DPC algorithm; then, under the dual guarantee of Euclidean distance and membership, FCM algorithm was used to cluster load curves; finally, the optimal number of clusters was obtained by the improved adaptive method in the iterative process; thus, the autonomous and accurate clustering of power load curve was realized. The proposed algorithm, DPC algorithm and FCM algorithm were applied to the load clustering experiment of power system respectively. The comparative analysis shows that this algorithm is effective and superior for load curve clustering.

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Kazakevič, Michael I., and Victoria E. Volkova. "THE INDUCED OSCILLATIONS OF FLEXIBLE PRESTRESSED ELEMENTS OF STRUCTURES (SYMMETRICAL SYSTEM)." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 6, no. 1 (February 28, 2000): 55–59. http://dx.doi.org/10.3846/13921525.2000.10531564.

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The results of the investigations of dynamic behaviour of the flexible prestressed structure elements are presented in the paper. The given physical model can be applied to the flexible structures like sloping arches, shells, bending plates, elements of the large space antenna fields (LSAF). The dynamic behaviour of the investigated systems is described by the equations where ϵ is damping coefficient, α,β are coefficients determining the character of non-linear restoring force are parameters of outer effect. The analysis of the “skeleton” curves disclosed the double qualities of system (1). Thus, “large” oscillations possess the peculiarities of the rigid system behaviour, and “small” oscillations possess the qualities of soft systems. The character of the oscillation amplitude changing with the increase or decrease of the excitation frequencies is followed in Fig 1. The establishment of the forced oscillation regimes from one branch to another is accompanied not only by the transition from “large” oscillations to “small”, or vice versa, but also by the development of the combination tones (2ω, 3ω 5ω, …, ω/2, ω/3). The analytical solutions for “large” and “small” forced oscillations are given by harmonic balance method. The solution was found in the form φ = Acosωt for “large” oscillation, and for “small” oscillation, where . The for curves disclosed unstable branches of amplitude-frequency curves and critical value amplitude of “large” oscillations were obtained. The methods and results of the computing experiment are presented in the paper. For working out the software necessary for the given task, the method of numerical integration (Runge-Kutta method of the fourth order), spectral analysis (Hertzel algorithm), computer graphics, etc were used. The results of the numerical integration are well-coordinated with the analytical solution for the “framework” curves and for the amplitude-frequency curves of forced oscillations.

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