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Journal articles on the topic 'Integral Basis'

Author: Grafiati

Published: 3 June 2025

Last updated: 19 July 2025

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1

Hu, Jin-Xiu, Hai-Feng Peng, and Xiao-Wei Gao. "Numerical Evaluation of Arbitrary Singular Domain Integrals Using Third-Degree B-Spline Basis Functions." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/284106.

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A new approach is presented for the numerical evaluation of arbitrary singular domain integrals. In this method, singular domain integrals are transformed into a boundary integral and a radial integral which contains singularities by using the radial integration method. The analytical elimination of singularities condensed in the radial integral formulas can be accomplished by expressing the nonsingular part of the integration kernels as a series of cubic B-spline basis functions of the distancerand using the intrinsic features of the radial integral. In the proposed method, singularities invo

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2

Mukha, V. S., and N. F. Kako. "Integrals and integral transformations related to the vector Gaussian distribution." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 4 (2020): 457–66. http://dx.doi.org/10.29235/1561-2430-2019-55-4-457-466.

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This paper is dedicated to the integrals and integral transformations related to the probability density function of the vector Gaussian distribution and arising in probability applications. Herein, we present three integrals that permit to calculate the moments of the multivariate Gaussian distribution. Moreover, the total probability formula and Bayes formula for the vector Gaussian distribution are given. The obtained results are proven. The deduction of the integrals is performed on the basis of the Gauss elimination method. The total probability formula and Bayes formula are obtained on t

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3

Haghighi, Mohmood. "Relative integral basis for algebraic number fields." International Journal of Mathematics and Mathematical Sciences 9, no. 1 (1986): 97–104. http://dx.doi.org/10.1155/s0161171286000121.

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At first conditions are given for existence of a relative integral basis forOK≅Okn−1⊕Iwith[K;k]=n. Then the constrtiction of the idealIinOK≅Okn−1⊕Iis given for proof of existence of a relative integral basis forOK4(m1,m2)/Ok(m3). Finally existence and construction of the relative integral basis forOK6(n3,−3)/Ok3(n3),OK6(n3,−3)/Ok2(−3)for some values ofnare given.

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4

Jakhar, Anuj, Sudesh K. Khanduja, and Neeraj Sangwan. "ON INTEGRAL BASIS OF PURE NUMBER FIELDS." Mathematika 67, no. 1 (2020): 187–95. http://dx.doi.org/10.1112/mtk.12067.

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5

Cao, T. "Hierarchical basis methods for hypersingular integral equations." IMA Journal of Numerical Analysis 17, no. 4 (1997): 603–19. http://dx.doi.org/10.1093/imanum/17.4.603.

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6

Haus, Utz-Uwe, Matthias Köppe, and Robert Weismantel. "The integral basis method for integer programming." Mathematical Methods of Operations Research (ZOR) 53, no. 3 (2001): 353–61. http://dx.doi.org/10.1007/s001860100124.

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7

Dorri, B., and V. Kadambi. "Boundary integral analysis with orthogonal basis functions." Communications in Applied Numerical Methods 4, no. 5 (1988): 623–30. http://dx.doi.org/10.1002/cnm.1630040505.

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8

عبد الله, أمل علي محمد. "تطبيقات نظرية البواقي لحساب بعض أنواع من التكاملات الحقيقية المعتلة". International Science and Technology Journal 35, № 1 (2024): 1–24. https://doi.org/10.62341/ampt203.

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A complex variable is a quantity that contains both a real part and an imaginary part. Complex analysis is an application of mathematics that analyses the features of functions of complex variables. Physics, engineering, and computer science are just a few of the scientific disciplines that benefit from complex analysis. In order to tackle issues that are challenging or impossible to resolve using only real variables, complex analysis is crucial. ( Chanyu Xie، 2024) This research provides a definition of the most important theories in complex analysis, which is called the residue theory، which

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9

Carbó, Ramon, and Emili Besalú. "AO integral evaluation using Cartesian exponential type orbitals (CETOs)." Canadian Journal of Chemistry 70, no. 2 (1992): 353–61. http://dx.doi.org/10.1139/v92-050.

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CETO functions and their properties are defined and described, to provide a means of obtaining general expressions for many-center many-electron integral formulae. Compact integral expressions are written by means of nested summation symbols, a new concept developed in this paper. Integrals over CETO functions are computed by means of a set of several auxiliary integral forms. No transformations other than frame rotations are needed to compute the usual integral terms. The formulae obtained are immediately programmable in any high level language and the parallelizable terms are obtained with a

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10

Tran, Thanh, Ernst p. Stephan, and Patrick Mund. "Hierarchical basis preconditioners for first kind integral equations." Applicable Analysis 65, no. 3-4 (1997): 353–72. http://dx.doi.org/10.1080/00036819708840566.

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11

Giese, Timothy J., and Darrin M. York. "Contracted auxiliary Gaussian basis integral and derivative evaluation." Journal of Chemical Physics 128, no. 6 (2008): 064104. http://dx.doi.org/10.1063/1.2821745.

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12

Chang, Ruinan, and Vitaliy Lomakin. "Quadrilateral Barycentric Basis Functions for Surface Integral Equations." IEEE Transactions on Antennas and Propagation 61, no. 12 (2013): 6039–50. http://dx.doi.org/10.1109/tap.2013.2280472.

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13

Peterson, Andrew F. "Mapped Vector Basis Functions for Electromagnetic Integral Equations." Synthesis Lectures on Computational Electromagnetics 1, no. 1 (2006): 1–124. http://dx.doi.org/10.2200/s00008ed1v01y200508cem001.

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14

Jakhar, Anuj, and Neeraj Sangwan. "Integral basis of pure prime degree number fields." Indian Journal of Pure and Applied Mathematics 50, no. 2 (2019): 309–14. http://dx.doi.org/10.1007/s13226-019-0326-7.

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15

Hu, Anguang, and Brett I. Dunlap. "Three-center molecular integrals and derivatives using solid harmonic Gaussian orbital and Kohn–Sham potential basis sets." Canadian Journal of Chemistry 91, no. 9 (2013): 907–15. http://dx.doi.org/10.1139/cjc-2012-0485.

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Three-center integrals over Gaussian orbital and Kohn–Sham (KS) basis sets are reviewed. An orbital basis function carries angular momentum about its atomic center. That angular momentum is created by solid harmonic differentiation with respect to the center of an s-type basis function. That differentiation can be brought outside any purely s-type integral, even nonlocal pseudopotential integrals. Thus the angular factors associated with angular momentum and differentiation with respect to atom position can be pulled outside loops over orbital and KS Gaussian exponents.

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16

Rababah, Abedallah. "Integration of Jacobi and Weighted Bernstein Polynomials Using Bases Transformations." Computational Methods in Applied Mathematics 7, no. 3 (2007): 221–26. http://dx.doi.org/10.2478/cmam-2007-0013.

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AbstractThis paper presents methods to compute integrals of the Jacobi polynomials by the representation in terms of the Bernstein — B´ezier basis. We do this because the integration of the Bernstein — B´ezier form simply corresponds to applying the de Casteljau algorithm in an easy way. Formulas for the definite integral of the weighted Bernstein polynomials are also presented. Bases transformations are used. In this paper, the methods of integration enable us to gain from the properties of the Jacobi and Bernstein bases.

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17

Qu, Jia Le, Yun Xue, and Xi Ying Qian. "Conserved Quantities of Lagrange Equation of a Growing Elastic Rod Dynamics." Applied Mechanics and Materials 684 (October 2014): 94–99. http://dx.doi.org/10.4028/www.scientific.net/amm.684.94.

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Conservedquantities of a growing elastic roddynamics are studied on the basis of Lagrange equation. Several of conserved quantities and their condition of existencearederived, which expanded the concept of conversation from the time to the space, i.e. arc coordinate.Lagrange equation is applied to analyzed energy integral and cyclic integral. First integrals are of practical significance in both theoretical and numerical analysis for a growing elastic rod dynamics.

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18

Assari, Pouria. "The numerical solution of Fredholm-Hammerstein integral equations by combining the collocation method and radial basis functions." Filomat 33, no. 3 (2019): 667–82. http://dx.doi.org/10.2298/fil1903667a.

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Hammerstein integral equations have been arisen from mathematical models in various branches of applied sciences and engineering. This article investigates an approximate scheme to solve Fredholm-Hammerstein integral equations of the second kind. The new method uses the discrete collocation method together with radial basis functions (RBFs) constructed on scattered points as a basis. The discrete collocation method results from the numerical integration of all integrals appeared in the approach. We employ the composite Gauss-Legendre integration rule to estimate the integrals appeared in the m

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19

Du, Jie, and Qiang Fu. "The Integral Quantum Loop Algebra of $\mathfrak {gl}_{n}$." International Mathematics Research Notices 2019, no. 20 (2018): 6179–215. http://dx.doi.org/10.1093/imrn/rnx300.

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Abstract We will construct the Lusztig form for the quantum loop algebra of $\mathfrak {gl}_{n}$ by proving the conjecture [4, 3.8.6] and establish partially the Schur–Weyl duality at the integral level in this case. We will also investigate the integral form of the modified quantum affine $\mathfrak {gl}_{n}$ by introducing an affine stabilisation property and will lift the canonical bases from affine quantum Schur algebras to a canonical basis for this integral form. As an application of our theory, we will also discuss the integral form of the modified extended quantum affine $\mathfrak {sl

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20

Ichimura, Humio, and Fuminori Kawamoto. "Normal integral basis and ray class group modulo 4." Proceedings of the Japan Academy, Series A, Mathematical Sciences 79, no. 9 (2003): 139–41. http://dx.doi.org/10.3792/pjaa.79.139.

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21

Adams, R. J., A. Zhu, and F. X. Canning. "Efficient Solution of Integral Equations in a Localizing Basis." Journal of Electromagnetic Waves and Applications 19, no. 12 (2005): 1583–94. http://dx.doi.org/10.1163/156939305775537438.

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22

Belyaev, A. A., A. V. Kurachenkov, Yu K. Panov, and O. B. Samoilov. "Nuclear energy sources on the basis of integral reactors." Nuclear Engineering and Design 173, no. 1-3 (1997): 131–41. http://dx.doi.org/10.1016/s0029-5493(97)00089-7.

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23

Primova, H. A., D. M. Sotvoldiyev, R. T. Raximov, and X. Bobabekova. "COMPUTING FUZZY INTEGRAL OF THE BASIS OF FUZZY MESURE." Journal of Physics: Conference Series 1441 (January 2020): 012161. http://dx.doi.org/10.1088/1742-6596/1441/1/012161.

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24

Abelman, S., and D. Eyre. "A rational basis for second-kind Abel integral equations." Journal of Computational and Applied Mathematics 34, no. 3 (1991): 281–90. http://dx.doi.org/10.1016/0377-0427(91)90089-3.

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25

Pethő, Attila, and Volker Ziegler. "On biquadratic fields that admit unit power integral basis." Acta Mathematica Hungarica 133, no. 3 (2011): 221–41. http://dx.doi.org/10.1007/s10474-011-0103-5.

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26

Matsuhara, Masanori, and Tuptim Angkaew. "Vector basis functions in mixed-potential integral equation method." Electronics and Communications in Japan (Part II: Electronics) 79, no. 10 (1996): 49–55. http://dx.doi.org/10.1002/ecjb.4420791006.

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27

Adams, R. J., F. X. Canning, and A. Zhu. "Sparse representations of integral equations in a localizing basis." Microwave and Optical Technology Letters 47, no. 3 (2005): 236–40. http://dx.doi.org/10.1002/mop.21135.

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28

Hanninen, Ilari, Matti Taskinen, and Jukka Sarvas. "SINGULARITY SUBTRACTION INTEGRAL FORMULAE FOR SURFACE INTEGRAL EQUATIONS WITH RWG, ROOFTOP AND HYBRID BASIS FUNCTIONS." Progress In Electromagnetics Research 63 (2006): 243–78. http://dx.doi.org/10.2528/pier06051901.

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29

Burova, I. G., and G. O. Alcybeev. "Application of Splines of the Seventh Order Approximation to the Solution of the Fredholm Integral Equations with Weekly Singularity." WSEAS TRANSACTIONS ON MATHEMATICS 22 (June 28, 2023): 475–82. http://dx.doi.org/10.37394/23206.2023.22.53.

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We consider the construction of a numerical solution to the Fredholm integral equation of the second kind with weekly singularity using polynomial spline approximations of the seventh order of approximation. The support of the basis spline of the seventh order of approximation occupies seven grid intervals. In the beginning, in the middle, and at the end of the integration interval, we apply various modifications of the basis splines of the seventh order of approximation. We use the Gaussian-type quadrature formulas to calculate the integrals with a weakly singularity. It is assumed that the s

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30

Bernard, Matthew, Vladislav A. Guskov, Mikhail G. Ivanov, Alexey E. Kalugin, and Stanislav L. Ogarkov. "Nonlocal Scalar Quantum Field Theory—Functional Integration, Basis Functions Representation and Strong Coupling Expansion." Particles 2, no. 3 (2019): 385–410. http://dx.doi.org/10.3390/particles2030024.

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Nonlocal quantum field theory (QFT) of one-component scalar field φ in D-dimensional Euclidean spacetime is considered. The generating functional (GF) of complete Green functions Z as a functional of external source j, coupling constant g and spatial measure d μ is studied. An expression for GF Z in terms of the abstract integral over the primary field φ is given. An expression for GF Z in terms of integrals over the primary field and separable Hilbert space (HS) is obtained by means of a separable expansion of the free theory inverse propagator L ^ over the separable HS basis. The classificat

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31

Makogin, Vitalii, and Yuliya Mishura. "Fractional integrals, derivatives and integral equations with weighted Takagi–Landsberg functions." Nonlinear Analysis: Modelling and Control 25, no. 6 (2020): 1079–106. http://dx.doi.org/10.15388/namc.2020.25.20566.

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In this paper, we find fractional Riemann–Liouville derivatives for the Takagi–Landsberg functions. Moreover, we introduce their generalizations called weighted Takagi–Landsberg functions, which have arbitrary bounded coefficients in the expansion under Schauder basis. The class of weighted Takagi–Landsberg functions of order H > 0 on [0; 1] coincides with the class of H-Hölder continuous functions on [0; 1]. Based on computed fractional integrals and derivatives of the Haar and Schauder functions, we get a new series representation of the fractional derivatives of a Hölder continuous funct

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32

Sautbekov, Seil, Merey Sautbekova, Kuralay Baisalova, and Mustakhim Pshikov. "Calculation of Sommerfeld Integrals in Dipole Radiation Problems." Mathematics 12, no. 2 (2024): 298. http://dx.doi.org/10.3390/math12020298.

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This article proposes asymptotic methods for calculating Sommerfeld integrals, which enable us to calculate the integral using the expansion of a function into an infinite power series at the saddle point, where the role of a rapidly oscillating function under the integral can be fulfilled either by an exponential or by its product by the Hankel function. The proposed types of Sommerfeld integrals are generalized on the basis of integral representations of the Hertz radiator fields in the form of the inverse Hankel transform with the subsequent replacement of the Bessel function by the Hankel

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33

Wen, Pi Hua, and M. H. Aliabadi. "Meshless Local Integral Equation Method with Analytical Formulation and its Application to Computational Fracture Mechanics." Key Engineering Materials 488-489 (September 2011): 791–94. http://dx.doi.org/10.4028/www.scientific.net/kem.488-489.791.

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In this paper, the exact forms of integrals in the meshless local boundary integral equation method are presented and applications were demonstrated for fracture mechanics. A weak form for a set of governing equations with a unit test function or polynomial test functions is transformed into local integral equations. Each node has its own support domain and is surrounded by a local integral domain with different shapes of boundaries. The meshless approximation based on the Radial Basis Function (RBF) is employed for the implementation of displacements. For cracked plate, opening displacement o

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34

Farhadzadeh, E. M., A. Z. Muradaliyev, and U. K. Ashurova. "Methodological basis of comparative analysis of unique facilities of electric power systems." Safety and Reliability of Power Industry 14, no. 1 (2021): 20–26. http://dx.doi.org/10.24223/1999-5555-2021-14-1-20-26.

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One of the basic problems of electric power systems is the absence of normative documents regulating the operation, maintenance and repair of the capital equipment, the service life of which exceeds the normative value. We shall name them «old equipment» (OE). The essence of the difficulties to be overcome is reduced to the absence of methodologies for quantitative estimation of operational reliability and safety of OE, with the subsequent comparative analysis of OE. Considering the science intensity, cumbersomeness and labour intensity of solving this problem, the necessity of development of

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35

Remete, László. "Integral bases of pure fields with square-free parameter." Studia Scientiarum Mathematicarum Hungarica 57, no. 1 (2020): 91–115. http://dx.doi.org/10.1556/012.2020.57.1.1450.

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Abstract Let m ≠ 0, ±1 and n ≥ 2 be integers. The ring of algebraic integers of the pure fields of type is explicitly known for n = 2, 3,4. It is well known that for n = 2, an integral basis of the pure quadratic fields can be given parametrically, by using the remainder of the square-free part of m modulo 4. Such characterisation of an integral basis also exists for cubic and quartic pure fields, but for higher degree pure fields there are only results for special cases. In this paper we explicitly give an integral basis of the field , where m ≠ ±1 is square-free. Furthermore, we show that si

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36

T. Shivaram, K., and S. Kiran. "A simple and efficient wavelet approach for evaluating surface integral over curved domain." International Journal of Engineering & Technology 7, no. 4.5 (2018): 511. http://dx.doi.org/10.14419/ijet.v7i4.5.21145.

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This paper presents, a simple and efficient wavelet approach for computing the surface integrals over irregular or curved dom ain, the limit of the integrals are nonlinear function are transformed to standard two square by using finite element basis function, Haar wavelet based integration technique is applied to evaluation of surface integral over curved domain, the computational efficiency of the method is illustrated with several numerical examples.

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37

Li, Haibin, Yangtian Li, and Shangjie Li. "Dual Neural Network Method for Solving Multiple Definite Integrals." Neural Computation 31, no. 1 (2019): 208–32. http://dx.doi.org/10.1162/neco_a_01145.

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This study, which examines a calculation method on the basis of a dual neural network for solving multiple definite integrals, addresses the problems of inefficiency, inaccuracy, and difficulty in finding solutions. First, the method offers a dual neural network method to construct a primitive function of the integral problem; it can approximate the primitive function of any given integrand with any precision. On this basis, a neural network calculation method that can solve multiple definite integrals whose upper and lower bounds are arbitrarily given is obtained with repeated applications of

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38

YALÇIN, Numan, and Sinem KAYMAK. "On Bigeometric Laplace Integral Transform." Journal of the Institute of Science and Technology 13, no. 3 (2023): 2042–56. http://dx.doi.org/10.21597/jist.1283580.

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The purpose of this study is to mention the Laplace integral transform in bigeometric analysis, which is one of the non-Newtonian analysis by using the fundamental definitions and theorems of the Laplace integral transform, which is one of the integral transform methods of classical analysis. First of all, the concept of exponential arithmetic, which forms the basis of non Newtonian analysis, is given. As in classical analysis, definitions of the concepts of bigeometric limit, bigeometric continuity, bigeometric derivative and bigeometric integral are given in bigeometric analysis. Here, the d

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39

EFTANG, JENS L., and EINAR M. RØNQUIST. "EVALUATION OF FLUX INTEGRAL OUTPUTS FOR THE REDUCED BASIS METHOD." Mathematical Models and Methods in Applied Sciences 20, no. 03 (2010): 351–74. http://dx.doi.org/10.1142/s021820251000426x.

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In this paper, we consider the evaluation of flux integral outputs from reduced basis solutions to second-order PDEs. In order to evaluate such outputs, a lifting function v⋆ must be chosen. In the standard finite element context, this choice is not relevant, whereas in the reduced basis context, as we show, it greatly affects the output error. We propose two "good" choices for v⋆ and illustrate their effect on the output error by examining a numerical example. We also make clear the role of v⋆ in a more general primal-dual reduced basis approximation framework.

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40

Dzoba, Oleh, and Nataliia Stavnycha. "Methodical basis of social security measurement of the state." Environmental Economics and Sustainable Development, no. 7(26) (2020): 56–62. http://dx.doi.org/10.37100/2616-7689/2020/7(26)/7.

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Summary the article has analyzed the existing scientific and methodological approaches to assessing the level of social security of the state. It was revealed that they differ because: scientists include various components that form social security; they use various indicators and calculation methods; have various aspects of both generalization and practical direction. It was revealed that most often the components of social security include: safety of life, health, social protection and aspects of social and labor relations. The methods that are most often used in calculating the level of soc

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41

Firouzdor, Reza, Shukooh Sadat Asari, and Majid Amirfakhrian. "Application of radial basis function to approximate functional integral equations." Journal of Interpolation and Approximation in Scientific Computing 2016, no. 2 (2016): 77–86. http://dx.doi.org/10.5899/2016/jiasc-00089.

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42

Levan, A., and J. Royer. "Theoretical basis of regularized integral equations for elastostatic crack problems." International Journal of Fracture 44, no. 3 (1990): 155–66. http://dx.doi.org/10.1007/bf00035513.

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43

Mouley, Jyotirmoy, M. M. Panja, and B. N. Mandal. "Approximate solution of Abel integral equation in Daubechies wavelet basis." Cubo (Temuco) 23, no. 2 (2021): 245–64. http://dx.doi.org/10.4067/s0719-06462021000200245.

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44

Meinershagen. "D ^# Derivation Basis and the Lebesgue-Stieltjes Integral." Real Analysis Exchange 12, no. 1 (1986): 265. http://dx.doi.org/10.2307/44151794.

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45

DAI, Baodong. "LOCAL BOUNDARY INTEGRAL EQUATION METHOD BASED ON RADIAL BASIS FUNCTIONS." Chinese Journal of Mechanical Engineering 42, no. 11 (2006): 150. http://dx.doi.org/10.3901/jme.2006.11.150.

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46

Hesthaven, J. S., B. Stamm, and S. Zhang. "Certified Reduced Basis Method for the Electric Field Integral Equation." SIAM Journal on Scientific Computing 34, no. 3 (2012): A1777—A1799. http://dx.doi.org/10.1137/110848268.

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47

Mei Song Tong, Weng Cho Chew, B. J. Rubin, J. D. Morsey, and Lijun Jiang. "On the Dual Basis for Solving Electromagnetic Surface Integral Equations." IEEE Transactions on Antennas and Propagation 57, no. 10 (2009): 3136–46. http://dx.doi.org/10.1109/tap.2009.2028622.

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48

王, 斌斌. "Nonlinear Integral Equation Solution Based on Radial Basis Function Interpolation." Advances in Applied Mathematics 08, no. 11 (2019): 1795–801. http://dx.doi.org/10.12677/aam.2019.811209.

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49

Aquilante, Francesco, Roland Lindh, and Thomas Bondo Pedersen. "Unbiased auxiliary basis sets for accurate two-electron integral approximations." Journal of Chemical Physics 127, no. 11 (2007): 114107. http://dx.doi.org/10.1063/1.2777146.

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50

Wen, Dingbang, Zaiping Nie, Yiling Wang, and Lu Liu. "Hierarchical loop‐flower basis for solving electric field integral equation." IET Microwaves, Antennas & Propagation 12, no. 6 (2018): 925–30. http://dx.doi.org/10.1049/iet-map.2017.0693.

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