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Journal articles on the topic 'Splines'

Author: Grafiati

Published: 4 June 2021

Last updated: 26 July 2025

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1

Morozov, Alexander, Gennady Fedotov, Lilia Fedorova, Damir Musharapov, and Lilia Khabieva. "The providing durability of the movable square-sided spline joints by electromechanical treatment of the working surfaces." MATEC Web of Conferences 298 (2019): 00117. http://dx.doi.org/10.1051/matecconf/201929800117.

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The article deals with the operating conditions and causes of loss of performance of movable involute splines joints. In order to ensure the durability of the movable involute splines joints, an effective method of hardening the working surfaces of the splined hub by electromechanical treatment is proposed. The influence of the current on the change of microstructure and microhardness in the electromechanical processing of the working surfaces of the spline bushing was determined. The obtained results of the comparative wear testing of samples involute splines joints depending on the time of t

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2

Jena, Hrushikesh. "A Constructive Approach to Bivariate Hyperbolic Box Spline Functions." Armenian Journal of Mathematics 17, no. 1 (2025): 1–18. https://doi.org/10.52737/18291163-2025.17.1-1-18.

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This article is based on the construction procedure of bivariate hyperbolic box spline functions. Generally, box splines are considered as the multivariate generalizations of univariate B-splines. Both B-splines and box splines are refinable functions. Two different kinds of box splines like the polynomial box splines and the trigonometric box splines along with their usefulness are well studied in literature. However, another variant of box splines named as the class of hyperbolic box spline functions, has not gained much attention. This article focuses on the construction of bivariate hyperb

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3

Zhao, Guang, Xiangyang Zhao, Liting Qian, Yunbo Yuan, Song Ma, and Mei Guo. "A Review of Aviation Spline Research." Lubricants 11, no. 1 (2022): 6. http://dx.doi.org/10.3390/lubricants11010006.

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Splines are irreplaceable in high-speed aviation fields due to their simplicity, reliability, and high specific power. Aviation splines are not only subjected to severe operating mechanical loads, but also sometimes operate under grease-lubricated and non-lubricated environments. All of this results in aviation splines suffering widespread failures. Since the 1960s, many researchers have carried out much research on aviation splines. The wide range of research topics demonstrates the technical challenges of understanding aviation spline. This paper reviews the research of aviation spline from

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Speleers, Hendrik. "Algorithm 1020: Computation of Multi-Degree Tchebycheffian B-Splines." ACM Transactions on Mathematical Software 48, no. 1 (2022): 1–31. http://dx.doi.org/10.1145/3478686.

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Multi-degree Tchebycheffian splines are splines with pieces drawn from extended (complete) Tchebycheff spaces, which may differ from interval to interval, and possibly of different dimensions. These are a natural extension of multi-degree polynomial splines. Under quite mild assumptions, they can be represented in terms of a so-called multi-degree Tchebycheffian B-spline (MDTB-spline) basis; such basis possesses all the characterizing properties of the classical polynomial B-spline basis. We present a practical framework to compute MDTB-splines, and provide an object-oriented implementation in

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Sun, Fangli, and Zhanchuan Cai. "Generalized Cardinal Polishing Splines Signal Reconstruction." Mathematics 13, no. 6 (2025): 983. https://doi.org/10.3390/math13060983.

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Sampling and reconstruction are indispensable processes in signal processing, and appropriate foundations are crucial for spline reconstruction models. Generalized cardinal polishing splines (GCP-splines) are a class of high-precision explicit splines with pretty properties. We propose the theory of GCP-splines for signal reconstruction and differential signaling to improve signal reconstruction accuracy. First, the elementary theory of the GCP-splines signal processing is proposed, and it mainly includes Fourier transformation and Z-transformation of the GCP-splines. Then, a GCP-splines filte

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6

Barka, Noureddine, Sasan Sattarpanah Karganroudi, Rachid Fakir, Patrick Thibeault, and Vincent Blériot Feujofack Kemda. "Effects of Laser Hardening Process Parameters on Hardness Profile of 4340 Steel Spline—An Experimental Approach." Coatings 10, no. 4 (2020): 342. http://dx.doi.org/10.3390/coatings10040342.

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This study displays the effect of laser surface hardening parameters on the hardness profile (case depth) of a splined shaft made of AISI 4340 steel. The approach is mainly based on experimental tests wherein the hardness profile of laser hardened splines is acquired using micro-hardness measurements. These results are then evaluated with statistical analysis (ANOVA) to determine the principal effect and the contributions of each parameter in the laser hardening process. Using empirical correlations, the case depth of splined shaft at tip and root of spline’s teeth is also estimated and verifi

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7

Ezhov, Nikolaj, Frank Neitzel, and Svetozar Petrovic. "Spline approximation, Part 1: Basic methodology." Journal of Applied Geodesy 12, no. 2 (2018): 139–55. http://dx.doi.org/10.1515/jag-2017-0029.

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Abstract In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of “irregularly” distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Man

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8

Hong, J., D. Talbot, and A. Kahraman. "A generalized semi-analytical load distribution model for clearance-fit, major-fit, minor-fit, and mismatched splines." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230, no. 7-8 (2015): 1126–38. http://dx.doi.org/10.1177/0954406215603741.

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A generalized semi-analytical load distribution model for all common types of involute spline joints is proposed. It is formulated to model clearance-fit (side-fit) involute splines with contacts happening only at the drive flanks of the spline teeth, major or minor-diameter fit splines where additional contact occurs along the top land and the root land of the external spline teeth, respectively, as well as mismatched splines where an intentional lead mismatch is introduced to initiate contact along both drive and back (coast) flanks. Using this model, load distribution and tooth-to-tooth loa

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9

Mijiddorj, Renchin-Ochir, and Tugal Zhanlav. "Algorithm to construct integro splines." ANZIAM Journal 63 (November 16, 2021): 359–75. http://dx.doi.org/10.21914/anziamj.v63.15855.

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We study some properties of integro splines. Using these properties, we design an algorithm to construct splines \(S_{m+1}(x)\) of neighbouring degrees to the given spline \(S_{m}(x)\) with degree \(m\). A local integro-sextic spline is constructed with the proposed algorithm. The local integro splines work efficiently, that is, they have low computational complexity, and they are effective for use in real time. The construction of nonlocal integro splines usually leads to solving a system of linear equations with band matrices, which yields high computational costs. doi:10.1017/S1446181121000

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10

Xue, Xiangzhen, Wei Yu, Kuan Lin, Ning Zhang, Li Xiao, and Yiqiang Jiang. "Design Method and Teeth Contact Simulation of PEEK Involute Spline Couplings." Materials 17, no. 1 (2023): 60. http://dx.doi.org/10.3390/ma17010060.

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In order to design an involute spline made of PEEK (polyetheretherketone)-based material with better performance and improve the design rules of involute splines, initially, an involute splines design theory for PEEK (polyetheretherketone)-based materials is presented, which combines international standards (ISO 4156, 1. 2. 3, 2005), American standards (ANSI B92.2M. 1989), and traditional empirical formulas. Second, using the involute splines calibration method in international standards as a guide, we developed the involute splines calibration method for PEEK-based materials by estimating the

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11

Kačala, Viliam, and Csaba Török. "Optimal Approximation of Biquartic Polynomials by Bicubic Splines." EPJ Web of Conferences 173 (2018): 03012. http://dx.doi.org/10.1051/epjconf/201817303012.

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Recently an unexpected approximation property between polynomials of degree three and four was revealed within the framework of two-part approximation models in 2-norm, Chebyshev norm and Holladay seminorm. Namely, it was proved that if a two-component cubic Hermite spline’s first derivative at the shared knot is computed from the first derivative of a quartic polynomial, then the spline is a clamped spline of classC2and also the best approximant to the polynomial.Although it was known that a 2 × 2 component uniform bicubic Hermite spline is a clamped spline of classC2if the derivatives at the

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12

Wang, Zhihua, Falai Chen, and Jiansong Deng. "Evaluation Algorithm of PHT-Spline Surfaces." Numerical Mathematics: Theory, Methods and Applications 10, no. 4 (2017): 760–74. http://dx.doi.org/10.4208/nmtma.2017.0003.

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AbstractPHT-splines are a type of polynomial splines over hierarchical T-meshes which posses perfect local refinement property. This property makes PHT-splines useful in geometric modeling and iso-geometric analysis. Current implementation of PHT-splines stores the basis functions in Bézier forms, which saves some computational costs but consumes a lot of memories. In this paper, we propose a de Boor like algorithm to evaluate PHT-splines provided that only the information about the control coefficients and the hierarchical mesh structure is given. The basic idea is to represent a PHT-spline l

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13

Istiqomatul Fajriyah Yuliati and Pardomuan Sihombing. "Pemodelan Fertilitas Di Indonesia Tahun 2017 Menggunakan Pendekatan Regresi Nonparametrik Kernel dan Spline." Jurnal Statistika dan Aplikasinya 4, no. 1 (2020): 48–60. http://dx.doi.org/10.21009/jsa.04105.

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Tujuan dari penelitian ini adalah untuk menganalisis pola hubungan Total Fertility Rate (TFR) dengan Contraceptive Prevalence Rate (CPR). Analisis yang sering digunakan untuk pemodelan adalah analisis regresi. Analisis regresi menurut pendekatannya dapat dibedakan menjadi dua, parametrik dan nonparametrik. Metode regresi nonparametrik yang sering digunakan adalah regresi kernel dan spline. Pada penelitian ini untuk regresi kernel yang digunakan adalah regresi kernel dengan metode penaksir Nadaraya-Watson (NWE) dan penaksir polinomial lokal (LPE), sedangkan untuk regresi spline yang digunakan a

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14

Ustuner, K. F., and L. A. Ferrari. "Discrete splines and spline filters." IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 39, no. 7 (1992): 417–22. http://dx.doi.org/10.1109/82.160167.

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15

Zhao, Yanchun, Mengzhu Zhang, Qian Ni, and Xuhui Wang. "Adaptive Nonparametric Density Estimation with B-Spline Bases." Mathematics 11, no. 2 (2023): 291. http://dx.doi.org/10.3390/math11020291.

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Learning density estimation is important in probabilistic modeling and reasoning with uncertainty. Since B-spline basis functions are piecewise polynomials with local support, density estimation with B-splines shows its advantages when intensive numerical computations are involved in the subsequent applications. To obtain an optimal local density estimation with B-splines, we need to select the bandwidth (i.e., the distance of two adjacent knots) for uniform B-splines. However, the selection of bandwidth is challenging, and the computation is costly. On the other hand, nonuniform B-splines can

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16

WULANDARY, SEPTIE, and DRAJAT INDRA PURNAMA. "PERBANDINGAN REGRESI NONPARAMETRIK KERNEL DAN B-SPLINES PADA PEMODELAN RATA-RATA LAMA SEKOLAH DAN PENGELUARAN PERKAPITA DI INDONESIA." Jambura Journal of Probability and Statistics 1, no. 2 (2020): 89–97. http://dx.doi.org/10.34312/jjps.v1i2.7501.

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Analisis regresi merupakan salah satu alat statistik yang banyak digunakan untuk mengetahui hubungan antara dua variabel acak atau lebih. Metode penaksiran model regresi terbagi atas regresi parametrik dan nonparametrik. Penelitian ini bertujuan menganalisis pola hubungan pengeluaran perkapita terhadap rata-rata lama sekolah di Indonesia tahun 2018 melalui perbandingan regresi nonparametrik, yaitu regresi kernel dan spline. Regresi kernel yang digunakan adalah regresi kernel dengan metode penaksir Nadaraya-Watson (NWE), sedangkan regresi spline yang digunakan adalah B-Splines. Berdasarkan nila

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17

A., Srinivasulu, Sarojamma B., and Anil kumar K. "Splines for annual temperature Data in India." RESEARCH REVIEW International Journal of Multidisciplinary 03, no. 06 (2018): 328–33. https://doi.org/10.5281/zenodo.1288683.

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Spline algorithms are the way to fit data points with a set of connecting curves (each one is called a Spline), such that the values between data points can be computed. They are various types/order of equations that can be used to specify the splines including Linear, Quadratic, Cubic, etc. Here annual temperature data is taken for 30 years from 1987 to 2016. In this data the highest temperature is in the year 1995, has structural break. So from 1987 to 1995 (9 years) we consider as before, and from 1996 to 2016 (21 years) consider as after. We applied four models such as Quadratic splines, H

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18

Burova, I. G., and G. O. Alcybeev. "The Application of Splines of the Seventh Order Approximation to the Solution of Integral Fredholm Equations." WSEAS TRANSACTIONS ON MATHEMATICS 22 (May 25, 2023): 409–18. http://dx.doi.org/10.37394/23206.2023.22.48.

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There are various numerical methods for solving integral equations. Among the new numerical methods, methods based on splines and spline wavelets should be noted. Local interpolation splines of a low order of approximation have proved themselves well in solving differential and integral equations. In this paper, we consider the construction of a numerical solution to the Fredholm integral equation of the second kind using spline approximations of the seventh order of approximation. The support of the basis spline of the seventh order of approximation occupies seven grid intervals. We apply var

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19

Rahayu, Putri Indi, and Pardomuan Robinson Sihombing. "PENERAPAN REGRESI NONPARAMETRIK KERNEL DAN SPLINE DALAM MEMODELKAN RETURN ON ASSET (ROA) BANK SYARIAH DI INDONESIA." JURNAL MATEMATIKA MURNI DAN TERAPAN EPSILON 14, no. 2 (2021): 115. http://dx.doi.org/10.20527/epsilon.v14i2.2968.

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Sharia Bank Return On Assets (ROA) modeling in Indonesia in 2018 aims to analyze the relationship pattern of Retturn On Assets (ROA) with interest rates. The analysis that is often used for modeling is regression analysis. Regression analysis is divided into two, namely parametric and nonparametric. The most commonly used nonparametric regression methods are kernel and spline regression. In this study, the nonparametric regression used was kernel regression with the Nadaraya-Watson (NWE) estimator and Local Polynomial (LPE) estimator, while the spline regression was smoothing spline and B-spli

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20

Chen, Wenyu, Yusha Li, Jianjiang Pan, Jianmin Zheng, and Yiyu Cai. "Effective T-spline representation for VRML." International Journal of Virtual Reality 11, no. 1 (2012): 15–24. http://dx.doi.org/10.20870/ijvr.2012.11.1.2833.

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Less control points are needed to represent a shape in T-Splines compared to NURBS and subsequently less time is spent in modeling. While getting more and more accepted by commercial software, T-splines, however, are yet part of VRML/X3D. The T-spline VRML is proposed in this work. An effective data structure is designed for T-splines to support online visualization. Compared to the NURBS and the polygonal representations, the proposed T-spline data structure representation can significantly reduce the VRML file size which is a central concern in online applications. As such, complex objects m

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Sivak, Roman. "DEFINITION OF KINEMATICS OF DEFORMATION BASED ON SPLINE-APPROXIMATIONS." Vibrations in engineering and technology, no. 2(97) (August 27, 2020): 101–7. http://dx.doi.org/10.37128/2306-8744-2020-2-11.

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It is suggested to use smoothing cubic spline functions to approximate the current functions. The structure of the selected functional provides the minimum curvature of the spline and the smallest deviation of the spline from the function smoothed at the nodes. The necessary correlation between these requirements is provided by the choice of weights. The algorithm for approximating the current function is implemented by moving from a grid created by current lines and auxiliary lines to a rectangular grid. To reduce the effect of random errors of experimental information on the current line, a

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Sarfraz, Muhammad, Munaza Ishaq, and Malik Zawwar Hussain. "Shape Designing of Engineering Images Using Rational Spline Interpolation." Advances in Materials Science and Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/260587.

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In modern days, engineers encounter a remarkable range of different engineering problems like study of structure, structure properties, and designing of different engineering images, for example, automotive images, aerospace industrial images, architectural designs, shipbuilding, and so forth. This paper purposes an interactive curve scheme for designing engineering images. The purposed scheme furnishes object designing not just in the area of engineering, but it is equally useful for other areas including image processing (IP), Computer Graphics (CG), Computer-Aided Engineering (CAE), Compute

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Wang, Shenying, Zhichao Hu, Fengwei Gu, et al. "A Rapid Manufacturing Method for Rectangular Splines Based on Laser Cutting and Welding." Transactions of the ASABE 64, no. 1 (2021): 117–26. http://dx.doi.org/10.13031/trans.14216.

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HighlightsA rapid manufacturing method for internal and external rectangular spline shafts for use in agricultural machinery was developed using a combination of laser cutting and welding.The shear strength of the internal spline welds, extrusion strength of the spline tooth surfaces, and extrusion and shear strength of the external spline pins were tested.Threshold values were obtained for the average diameter of the internal and external splines.Two case studies (light load and heavy load) were performed to verify the feasibility and reliability of the method.Abstract. In recent years, speci

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Budakçı, Gülter, and Halil Oruç. "Further Properties of Quantum Spline Spaces." Mathematics 8, no. 10 (2020): 1770. http://dx.doi.org/10.3390/math8101770.

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We construct q-B-splines using a new form of truncated power functions. We give basic properties to show that q-B-splines form a basis for quantum spline spaces. On the other hand, we derive algorithmic formulas for 1/q-integration and 1/q-differentiation for q-spline functions. Moreover, we show a way to find the polynomial pieces on each interval of a q-spline function.

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Xie, Jin, and Xiaoyan Liu. "The EH Interpolation Spline and Its Approximation." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/745765.

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A new interpolation spline with two parameters, called EH interpolation spline, is presented in this paper, which is the extension of the standard cubic Hermite interpolation spline, and inherits the same properties of the standard cubic Hermite interpolation spline. Given the fixed interpolation conditions, the shape of the proposed splines can be adjusted by changing the values of the parameters. Also, the introduced spline could approximate to the interpolated function better than the standard cubic Hermite interpolation spline and the quartic Hermite interpolation splines with single param

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MacCarthy, B. L., and N. D. Burns. "An Evaluation of Spline Functions for use in Cam Design." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 199, no. 3 (1985): 239–48. http://dx.doi.org/10.1243/pime_proc_1985_199_118_02.

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This paper shows how spline functions can be employed for kinematic motion specification in cam design. The polynomial spline is introduced as a special case of a continuous piecewise function. Cubic and quintic splines are derived and their properties are discussed in the cam design context. It is shown how standard cam laws can be approximated extremely accurately with a small number of points and appropriate boundary conditions. The modified sinusoidal acceleration cam law is used as an example. The application of quintic splines to non-standard and special motions is discussed. The algebra

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Sihombing, Pardomuan Robinson, and Ade Famalika. "Penerapan Analisis Regresi Nonparametrik dengan Pendekatan Regresi Kernel dan Spline." Jurnal Ekonomi Dan Statistik Indonesia 2, no. 2 (2022): 172–81. http://dx.doi.org/10.11594/jesi.02.02.05.

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Penelitian ini bertujuan untuk menerapkan regresi nonparametrik menggunakan regresi kernel dan spline. Regresi kernel menggunakan metode penaksir Nadaraya-Watson (NWE) dan penaksir Polinomial Lokal (LPE), sedangkan untuk regresi spline adalah smoothing spline dan b-splines. Metode ini diterapkan dalam menganalisis pola hubungan Pertumbuhan Produksi Industri (PPI) dan Tingkat Pajak Perusahaan (TPP). Hasil pengepasan kurva (fitting curve) menunjukkan bahwa model regresi nonparametrik terbaik adalah model regresi b-splines dengan degree 2 dan jumlah knot 5. Hal ini dikarenakan model regresi b-spl

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Akhmedov, Yunus, and Kakhramon Sharipov. "Smoothness assurance of the restorable surface of the cones of drill bits by cubic splines." E3S Web of Conferences 486 (2024): 03016. http://dx.doi.org/10.1051/e3sconf/202448603016.

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The article covers the issues of the application of the spline functions in engineering practice, in particular, in the design of cone drill bits. The polynomial splines, which most commonly used in computational methods are also described. It is also expedient to indicate three important advantages of the spline function for describing the design of cone drill bits. Obtaining a unified mathematical equation for the technical surface of the cones of drill bits is a routine work. The construction of a cubic spline causes difficulties due to the determination of the parameters of the spline, whi

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Zhao, Zemin, Shuangshuang Zhou, Qiang Liu, Long Zhang, Bin Shen, and Jiaming Han. "Simulation and Experimental Study of Ultrasonic Vibratory Grinding of Internal Splines." Machines 12, no. 10 (2024): 732. http://dx.doi.org/10.3390/machines12100732.

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As an important component of mechanical transmission systems, internal splines are widely used in aerospace, industrial equipment, and other fields. However, internal splines are prone to deformation and shrinkage after heat treatment. At present, most internal splines with a pitch circle diameter greater than φ60 mm can be processed and shaped by ordinary corundum grinding wheels, but there is no effective processing method for the shaping of small- and medium-sized internal splines. This paper establishes a single abrasive material removal model; uses Abaqus to simulate three-body free grind

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Guo, Mayi, Wei Wang, Gang Zhao, Xiaoxiao Du, Ran Zhang, and Jiaming Yang. "T-Splines for Isogeometric Analysis of the Large Deformation of Elastoplastic Kirchhoff–Love Shells." Applied Sciences 13, no. 3 (2023): 1709. http://dx.doi.org/10.3390/app13031709.

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In this paper, we develop a T-spline-based isogeometric method for the large deformation of Kirchhoff–Love shells considering highly nonlinear elastoplastic materials. The adaptive refinement is implemented, and some relatively complex models are considered by utilizing the superiorities of T-splines. A classical finite strain plastic model combining von Mises yield criteria and the principle of maximum plastic dissipation is carefully explored in the derivation of discrete isogeometric formulations under the total Lagrangian framework. The Bézier extraction scheme is embedded into a unified f

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Liu, Chaoyang, and Xiaoping Zhou. "Spline Surfaces over Arbitrary Topological Meshes: Theoretical Analysis and Application." Numerical Mathematics: Theory, Methods and Applications 9, no. 3 (2016): 383–415. http://dx.doi.org/10.4208/nmtma.2016.y14020.

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AbstractBased on polyhedral splines, some multivariate splines of different orders with given supports over arbitrary topological meshes are developed. Schemes for choosing suitable families of multivariate splines based on pre-given meshes are discussed. Those multivariate splines with inner knots and boundary knots from the related meshes are used to generate rational spline shapes with related control points. Steps for up to C2-surfaces over the meshes are designed. The relationship among the meshes and their knots, the splines and control points is analyzed. To avoid any unexpected discont

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Sablonniére, Paul. "Positive spline operators and orthogonal splines." Journal of Approximation Theory 52, no. 1 (1988): 28–42. http://dx.doi.org/10.1016/0021-9045(88)90035-4.

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Yaseen, Muhammad, Qamar Un Nisa Arif, Reny George, and Sana Khan. "Comparative Numerical Study of Spline-Based Numerical Techniques for Time Fractional Cattaneo Equation in the Sense of Caputo–Fabrizio." Fractal and Fractional 6, no. 2 (2022): 50. http://dx.doi.org/10.3390/fractalfract6020050.

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This study focuses on numerically addressing the time fractional Cattaneo equation involving Caputo–Fabrizio derivative using spline-based numerical techniques. The splines used are the cubic B-splines, trigonometric cubic B-splines and extended cubic B-splines. The space derivative is approximated using B-splines basis functions, Caputo–Fabrizio derivative is discretized, using a finite difference approach. The techniques are also put through a stability analysis to verify that the errors do not pile up. The proposed scheme’s convergence analysis is also explored. The key advantage of the sch

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Sana, Madiha, and Muhammad Mustahsan. "Finite Element Approximation of Optimal Control Problem with Weighted Extended B-Splines." Mathematics 7, no. 5 (2019): 452. http://dx.doi.org/10.3390/math7050452.

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In this research article, an optimal control problem (OCP) with boundary observations is approximated using finite element method (FEM) with weighted extended B-splines (WEB-splines) as basis functions. This type of OCP has a distinct aspect that the boundary observations are outward normal derivatives of state variables, which decrease the regularity of solution. A meshless FEM is proposed using WEB-splines, defined on the usual grid over the domain, R 2 . The weighted extended B-spline method (WEB method) absorbs the regularity problem as the degree of the B-splines is increased. Convergence

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He, Min, Wenbo Du, Hongbo Gao, et al. "Research on precise measurement method of full parameters of spline interlocks." Journal of Physics: Conference Series 2174, no. 1 (2022): 012009. http://dx.doi.org/10.1088/1742-6596/2174/1/012009.

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Abstract This paper mainly introduces the types, characteristics and applications of spline, studies the high-precision measurement technology of different types of spline. Based on gear measuring instrument, optical coordinate measuring machine and coordinate measuring machine, the high-precision full-parameter measurement methods of spline. Developed countries in Europe have spline standards in the 1950s. At present, China has formed a relatively complete system of key and spline linkage standards, but the overall level is still far from developed countries. With the revision of national sta

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MASSON, ROLAND. "BIORTHOGONAL SPLINE WAVELETS ON THE INTERVAL FOR THE RESOLUTION OF BOUNDARY PROBLEMS." Mathematical Models and Methods in Applied Sciences 06, no. 06 (1996): 749–91. http://dx.doi.org/10.1142/s0218202596000328.

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We construct biorthogonal spline wavelets on the interval for different spline orders. We then discuss the accuracy of the construction and test the wavelet transform. Building the corresponding wavelet basis for [Formula: see text] boundary conditions we use it for the resolution of elliptic boundary problems both with pure Galerkin and Petrov-Galerkin schemes. The results are compared from stability and convergence points of view. The main conclusion is that using the biorthogonal counterpart of spline functions as trial spaces for low order splines provides much more advantages than using s

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Hayotov, A. R., F. A. Nuraliev, and G. Sh Abdullaeva. "The Coeffisients of the Spline Minimizing Semi Norm in K2(P3)." International Journal of Analysis and Applications 23 (January 2, 2025): 7. https://doi.org/10.28924/2291-8639-23-2025-7.

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Our goal is to construct an approximation of the unknown function f by Sobolev’s method, we construct an approximation form of unknown function by interpolation splines minimizing the semi norm in K2(P3) Hilbert space. Explicit formulas for coefficients of the interpolation splines are obtained. The resulting interpolation spline is exact for the hyperbolic functions and constant. In the last section, we obtain several absolute errors graph in interpolating functions with the sixth order algebraic-hyperbolic spline, and we compare absolute errors of cubic spline and algebraic-hyperbolic in int

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Pepin, A., S. S. Beauchemin, S. Léger, and N. Beaudoin. "A New Method for High-Degree Spline Interpolation: Proof of Continuity for Piecewise Polynomials." Canadian Mathematical Bulletin 63, no. 3 (2019): 655–69. http://dx.doi.org/10.4153/s0008439519000742.

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AbstractEffective and accurate high-degree spline interpolation is still a challenging task in today’s applications. Higher degree spline interpolation is not so commonly used, because it requires the knowledge of higher order derivatives at the nodes of a function on a given mesh.In this article, our goal is to demonstrate the continuity of the piecewise polynomials and their derivatives at the connecting points, obtained with a method initially developed by Beaudoin (1998, 2003) and Beauchemin (2003). This new method, involving the discrete Fourier transform (DFT/FFT), leads to higher degree

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Burova, I. G. "Fredholm Integral Equation and Splines of the Fifth Order of Approximation." WSEAS TRANSACTIONS ON MATHEMATICS 21 (May 20, 2022): 260–70. http://dx.doi.org/10.37394/23206.2022.21.31.

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This paper considers the numerical solution of the Fredholm integral equation of the second kind using local polynomial splines of the fifth order of approximation and the fourth order of approximation (cubic splines). The basis splines in these cases occupy five and four adjacent grid intervals respectively. Different local spline approximations of the fifth (or fourth) order of approximation are used at the beginning of the integration interval, in the middle of the integration interval, and at the end of the integration interval. The construction of the calculation schemes for solving the F

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Burova, I. G., G. O. Alcybeev, and S. A. Schiptcova. "Splines of the Second and Seventh Order Approximation and the Stability of the Solution of the Fredholm Integral Equations of the Second Kind." WSEAS TRANSACTIONS ON MATHEMATICS 23 (November 16, 2023): 1–15. http://dx.doi.org/10.37394/23206.2024.23.1.

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This work is a continuation of a series of works on the use of continuous local polynomial splines for solving interpolation problems and for solving the Fredholm integral equation of the second kind. Here the construction of a numerical solution to the Fredholm integral equation of the second kind using local spline approximations of the second order and the seventh order of approximation is considered. This paper is devoted to the investigation of the stability of the solution of the integral equation using these local splines. Approximation constants are given in the theorem about the error

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K.S. Krishnamohan. "Splines and Special Functions to Solve Boundary Value Problems in Differential Equations." Journal of Information Systems Engineering and Management 10, no. 3 (2025): 1912–26. https://doi.org/10.52783/jisem.v10i3.8859.

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Professional applications in engineering and physics and applied sciences require Boundary value problems (BVPs) for their mathematical modeling. The traditional solution methods struggle to handle nonlinear BVPs because stability issues and accuracy limits prevent them from obtaining satisfactory results. The research explores spline-based numerical methods that use special function approximations to achieve efficient solutions of nonlinear BVPs. The combination of B-splines and high-degree splines with spectral special functions allows for building accurate smooth approximations that preserv

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Burova, I. G. "The Local Nonpolynomial Splines and Solution of Integro-Differential Equations." WSEAS TRANSACTIONS ON MATHEMATICS 21 (October 24, 2022): 718–30. http://dx.doi.org/10.37394/23206.2022.21.84.

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The application of the local polynomial splines to the solution of integro-differential equations was regarded in the author’s previous papers. In a recent paper, we introduced the application of the local nonpolynomial splines to the solution of integro-differential equations. These splines allow us to approximate functions with a presribed order of approximation. In this paper, we apply the splines to the solution of the integro-differential equations with a smooth kernel. Applying the trigonometric or exponential spline approximations of the fifth order of approximation, we obtain an approx

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Journal, Baghdad Science. "B-splines Algorithms for Solving Fredholm Linear Integro-Differential Equations." Baghdad Science Journal 1, no. 2 (2004): 340–46. http://dx.doi.org/10.21123/bsj.1.2.340-346.

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Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

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Strelkovskaya, Irina, Irina Solovskaya, and Juliya Strelkovska. "Application of real and complex splines in infocommunication problems." Problemi telekomunìkacìj, no. 1(28) (December 22, 2021): 3–19. http://dx.doi.org/10.30837/pt.2021.1.01.

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The work offers the solution to problems of analysis and synthesis of infocommunication systems with the help of real and complex spline functions. The use of the spline approximation method for solving problems of recovery of random signals and self-similar traffic, management of network objects and network as a whole, and procedures of infocommunication objects and networks functioning is offered. To solve the problems of forecasting, in particular, forecasting the characteristics of network traffic and maintaining the QoS characteristics in its service and formation of requirements for netw

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Zaharov, A., and Y. Zakharova. "Content of the “Geometric Modeling” Course for the “Mathematics and Computer Science” Training Program." Geometry & Graphics 9, no. 4 (2022): 35–45. http://dx.doi.org/10.12737/2308-4898-2022-9-4-35-45.

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In this paper has been considered the main content and distinctive features of the “Geometric Modeling” training course for the “Mathematics and Computer Science” training program 02.03.01 (“Mathematical and Computer Modeling” specialization). The goal of the “Geometric Modeling” course study is the assimilation of mathematical methods for construction of geometric objects with complex curved shapes, and techniques for their computer visualization by using polygons of curves and surfaces. Methods for construction of structures’ curved shapes using spline representations, as well as techn

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Osborne, M. R., and Tania Prvan. "Smoothness and conditioning in generalised smoothing spline calculations." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 30, no. 1 (1988): 43–56. http://dx.doi.org/10.1017/s0334270000006020.

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AbstractWe consider a generalisation of the stochastic formulation of smoothing splines, and discuss the smoothness properties of the resulting conditional expectation (generalised smoothing spline), and the sensitivity of the numerical algorithms. One application is to the calculation of smoothing splines with less than the usual order of continuity at the data points.

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Kushpel, Alexander, and Kenan Tas. "ON THE PROBLEM OF SCHOENBERG ON R n." Journal of Mathematical Analysis 15, no. 6 (2024): 71–81. https://doi.org/10.54379/jma-2024-6-6.

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In 1946 Schoenberg introduced splines on R, which play now one of the central roles in Numerical Analysis, and posed the problem on spline interpolation. The main aim of this article is to establish explicit representations of fundamental splines on Rn and give a positive solution of the problem of Schoenberg on Rn

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Marinov, Svetlin, Ognyan Alipiev, and Toni Uzunov. "Interference of the profiles when meshing internal straight splines with gear shapers." MATEC Web of Conferences 287 (2019): 01015. http://dx.doi.org/10.1051/matecconf/201928701015.

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The possibilities for cutting internal straight splines with gear shapers by internal meshing, without interference between meshed profiles, are shown in this article. The interference is an undesirable occurrence whereby the straight profile of the splines and the instrumental contour intersect with each other beyond the meshing line. As a result, the shaper teeth cut off a part of the splines’ straight profile and they are made with some defects. The research shows that the undesirable interference depends directly on the parameters of the splined opening and the number of shaper teeth. Also

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Vasiliev, N. P., and M. R. Vagizov. "Using B-splines for alignment of satellite geolocation elevation data." Geodesy and Cartography 1014, no. 12 (2025): 54–59. https://doi.org/10.22389/0016-7126-2024-1014-12-54-59.

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The possibility of constructing analytical models of terrain elevation is studied with mathematical apparatus of B-splines based on satellite geolocation data. For constructing regression models the main nodes of splines are chosen independently of measurements. An algorithmic approach is discussed to avoid degenerate cases, which may arise from this selection. B-splines can be used to create more accurate digital elevation models; their applications in practical field are land-use planning, disaster risk management and mapping, operational visualization of more accurate geofield data. The pre

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Burova, I. G., and G. O. Alcybeev. "Application of Splines of the Fifth Order Approximation for Solving Integral Equations of the Second Kind with a Weak Singularity." WSEAS TRANSACTIONS ON SYSTEMS 24 (March 26, 2025): 66–74. https://doi.org/10.37394/23202.2025.24.8.

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Previously, the authors showed that local splines of the different order of approximation give good results on both uniform and non-uniform grids. In this paper, we investigate the stability of the numerical method based on the splines of the fifth order of approximation and the use of these splines for solving weak singular Fredholm and Volterra integral equations of the second kind. The solution method consists of replacing the unknown function under the integral sign with a spline approximation. We compare the errors of the solutions of integral equations obtained using splines of the secon

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