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Journal articles on the topic 'Gauss points'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Gautschi, Walter, and Shikang Li. "Gauss—Radau and Gauss—Lobatto quadratures with double end points." Journal of Computational and Applied Mathematics 34, no. 3 (1991): 343–60. http://dx.doi.org/10.1016/0377-0427(91)90094-z.

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2

Mai, Heng. "Convergence for the optimal control problems using collocation at Legendre-Gauss points." Transactions of the Institute of Measurement and Control 44, no. 6 (2021): 1263–74. http://dx.doi.org/10.1177/01423312211043335.

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The convergence of the novel Legendre-Gauss method is established for solving a continuous optimal control problem using collocation at Legendre-Gauss points. The method allows for changes in the number of Legendre-Gauss points to meet the error tolerance. The continuous optimal control problem is first discretized into a nonlinear programming problem at Gauss collocations by the Legendre-Gauss method. Subsequently, we prove the convergence of the Legendre-Gauss algorithm under the assumption that the continuous optimal control problem has a smooth solution. Compared with those of the shooting

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3

Peng, Lijun, Xiaojun Duan, and Jubo Zhu. "A New Sparse Gauss-Hermite Cubature Rule Based on Relative-Weight-Ratios for Bearing-Ranging Target Tracking." Modelling and Simulation in Engineering 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/2783781.

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A new sparse Gauss-Hermite cubature rule is designed to avoid dimension explosion caused by the traditional full tensor-product based Gauss-Hermite cubature rule. Although Smolyak’s quadrature rule can successfully generate sparse cubature points for high dimensional integral, it has a potential drawback that some cubature points generated by Smolyak’s rule have negative weights, which may result in instability for the computation. A relative-weight-ratio criterion based sparse Gauss-Hermite rule is presented in this paper, in which cubature points are kept symmetric in the input space and cor

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4

Kwon, Young-Doo, Soon-Bum Kwon, Bo-Kyung Shim, and Hyun-Wook Kwon. "Comprehensive Interpretation of a Three-Point Gauss Quadrature with Variable Sampling Points and Its Application to Integration for Discrete Data." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/471731.

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This study examined the characteristics of a variable three-point Gauss quadrature using a variable set of weighting factors and corresponding optimal sampling points. The major findings were as follows. The one-point, two-point, and three-point Gauss quadratures that adopt the Legendre sampling points and the well-known Simpson’s 1/3 rule were found to be special cases of the variable three-point Gauss quadrature. In addition, the three-point Gauss quadrature may have out-of-domain sampling points beyond the domain end points. By applying the quadratically extrapolated integrals and nonlinear

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5

Li, Mingwu, Haijun Peng, and Zhigang Wu. "Symplectic Irregular Interpolation Algorithms for Optimal Control Problems." International Journal of Computational Methods 12, no. 06 (2015): 1550040. http://dx.doi.org/10.1142/s0219876215500401.

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Symplectic numerical methods for optimal control problems with irregular interpolation schemes are developed and the comparisons between irregular interpolation schemes and equidistant scheme are made in this paper. The irregular interpolation points, which are the collocation points usually adopted by pseudospectral (PS) methods, such as Legendre–Gauss, Legendre–Gauss–Radau, Legendre–Gauss–Lobatto and Chebyshev–Gauss–Lobatto points, are taken into consideration in this study. The symplectic numerical method with irregular points is proposed firstly. Then, several examples with different compl

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6

Bos, L., M. A. Taylor, and B. A. Wingate. "Tensor product Gauss-Lobatto points are Fekete points for the cube." Mathematics of Computation 70, no. 236 (2000): 1543–48. http://dx.doi.org/10.1090/s0025-5718-00-01262-x.

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7

Liu, Xi Wen, and Chao Ying Liu. "An Optional Gauss Filter Image Denoising Method Based on Difference Image Fast Fuzzy Clustering." Applied Mechanics and Materials 411-414 (September 2013): 1348–52. http://dx.doi.org/10.4028/www.scientific.net/amm.411-414.1348.

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Gaussian filtering algorithm has the defect that it will cause a blur at the image edges, therefore, an optional Gauss filter denoising method based on difference image fast fuzzy clustering is proposed. In this method, Gauss filtered image is firstly calculated, the difference image between the original image and the Gauss filtered image is acquired hereafter; and then fast FCM clustering of the Gauss filter image is carried out, the image histogram frequencies are taken as weighting coefficients of objective function when clustering, therefore the noise points of the original image are gotte

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8

Yi, Shi-Chao, Fu-jun Chen, and Lin-Quan Yao. "Radial Basis Point Interpolation Method with Reordering Gauss Domains for 2D Plane Problems." Journal of Applied Mathematics 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/219538.

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We present novel Gauss integration schemes with radial basis point interpolation method (RPIM). These techniques define new Gauss integration scheme, researching Gauss points (RGD), and reconstructing Gauss domain (RGD), respectively. The developments lead to a curtailment of the elapsed CPU time without loss of the accuracy. Numerical results show that the schemes reduce the computational time to 25% or less in general.

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9

Demirci Akarsu, Emek. "Short incomplete Gauss sums and rational points on metaplectic horocycles." International Journal of Number Theory 10, no. 06 (2014): 1553–76. http://dx.doi.org/10.1142/s1793042114500444.

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In this paper, we investigate the limiting behavior of short incomplete Gauss sums at random argument as the number of terms goes to infinity. We prove that the limit distribution is given by the distribution of theta sums and differs from the limit law for long Gauss sums studied by the author and Marklof. The key ingredient in the proof is an equidistribution theorem for rational points on horocycles in the metaplectic cover of SL(2, ℝ).

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10

Mihic, Ljubica, Aleksandar Pejcev, and Miodrag Spalevic. "Error bounds for Gauss-Lobatto quadrature formula with multiple end points with Chebyshev weight function of the third and the fourth kind." Filomat 30, no. 1 (2016): 231–39. http://dx.doi.org/10.2298/fil1601231m.

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For analytic functions the remainder terms of quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points -+1, for Gauss-Lobatto quadrature formula with multiple end points with Chebyshev weight function of the third and the fourth kind. Starting from the explicit expression of the corresponding kernel, derived by Gautschi and Li, we determine the locations on the ellipses where maximum modulus of the kernel is attained. The obtained values confirm the corresponding conjectured values given by Gautschi an

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11

Prathap, G. "Barlow points and Gauss points and the aliasing and best fit paradigms." Computers & Structures 58, no. 2 (1996): 321–25. http://dx.doi.org/10.1016/0045-7949(95)00133-2.

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12

Ali, Liyaqat, N. A. Rather, and Suhail Gulzar. "Gauss Lucas theorem and Bernstein-type inequalities for polynomials." Acta Universitatis Sapientiae, Mathematica 14, no. 2 (2022): 211–19. http://dx.doi.org/10.2478/ausm-2022-0013.

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Abstract According to Gauss-Lucas theorem, every convex set containing all the zeros of a polynomial also contains all its critical points. This result is of central importance in the geometry of critical points in the analytic theory of polynomials. In this paper, an extension of Gauss-Lucas theorem is obtained and as an application some generalizations of Bernstein-type polynomial inequalities are also established.

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13

HAFEZ, R. M., and Y. H. YOUSSRI. "Shifted Gegenbauer-Gauss Collocation Method for Solving Fractional Neutral Functional-Differential Equations with Proportional Delays." Kragujevac Journal of Mathematics 46, no. 6 (2022): 981–96. http://dx.doi.org/10.46793/kgjmat2206.981h.

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In this paper, the shifted Gegenbauer-Gauss collocation (SGGC) method is applied to fractional neutral functional-diﬀerential equations with proportional delays. The technique we have used is based on shifted Gegenbauer polynomials and Gauss quadrature integration. The shifted Gegenbauer-Gauss method reduces solving the generalized fractional pantograph equation fractional neutral functional-diﬀerential equations to a system of algebraic equations. Reasonable numerical results are obtained by selecting few shifted Gegenbauer-Gauss collocation points. Numerical results demonstrate its accuracy,

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14

Borbély, Albert. "On the self-intersections of an immersed sphere." Bulletin of the Australian Mathematical Society 75, no. 3 (2007): 453–58. http://dx.doi.org/10.1017/s000497270003937x.

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A closed curve f: S1 → ℝ2 in general position gives rise to a word whose letters are the self-intersection points, each of them appearing exactly twice. Such a word is called a Gauss code. The problem of determining whether a given Gauss code is realisable or not was first proposed by Gauss and it has been settled a long time ago. The analogous question for immersions f: S2 → ℝ3 in general position is settled only in a special case when the immersion has no triple points. We give a necessary condition for a system of curves to be realisable by a general immersion f: S2 → ℝ3.

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15

Pejcev, Aleksandar, and Ljubica Mihic. "Errors of Gauss-Radau and Gauss-Lobatto quadratures with double end point." Applicable Analysis and Discrete Mathematics 13, no. 2 (2019): 463–77. http://dx.doi.org/10.2298/aadm180408011p.

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Starting from the explicit expression of the corresponding kernels, derived by Gautschi and Li (W. Gautschi, S. Li: The remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadrature rules with multiple end points, J. Comput. Appl. Math. 33 (1990) 315{329), we determine the exact dimensions of the minimal ellipses on which the modulus of the kernel starts to behave in the described way. The effective error bounds for Gauss- Radau and Gauss-Lobatto quadrature formulas with double end point(s) are derived. The comparisons are made with the actual errors.

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16

CASTEL, N., G. COHEN, and M. DURUFLÉ. "APPLICATION OF DISCONTINUOUS GALERKIN SPECTRAL METHOD ON HEXAHEDRAL ELEMENTS FOR AEROACOUSTIC." Journal of Computational Acoustics 17, no. 02 (2009): 175–96. http://dx.doi.org/10.1142/s0218396x09003914.

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A discontinuous Galerkin method is developed for linear hyperbolic systems on general hexahedral meshes. The use of hexahedral elements and tensorized quadrature formulas to evaluate the integrals leads to an efficient matrix–vector product. It is shown that for high order approximations, the reduction in computational time can be very important, compared to tetrahedral elements. Two choices of quadrature points are considered, the Gauss points or Gauss–Lobatto points. The method is applied to the aeroacoustic system ("simplified" Linearized Euler Equations). Some 3D numerical experiments show

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17

Cao, Ting, Huo-tao Gao, Chun-feng Sun, Yun Ling, and Guo-bao Ru. "Application of Improved Simplex Quadrature Cubature Kalman Filter in Nonlinear Dynamic System." Mathematical Problems in Engineering 2020 (May 14, 2020): 1–13. http://dx.doi.org/10.1155/2020/1072824.

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A novel spherical simplex Gauss–Laguerre quadrature cubature Kalman filter is proposed to improve the estimation accuracy of nonlinear dynamic system. The nonlinear Gaussian weighted integral has been approximately evaluated using the spherical simplex rule and the arbitrary order Gauss–Laguerre quadrature rule. Thus, a spherical simplex Gauss–Laguerre cubature quadrature rule is developed, from which the general computing method of the simplex cubature quadrature points and the corresponding weights are obtained. Then, under the nonlinear Kalman filtering framework, the spherical simplex Gaus

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18

Yamashita, Shinji. "Local minima of the Gauss curvature of a minimal surface." Bulletin of the Australian Mathematical Society 44, no. 3 (1991): 397–404. http://dx.doi.org/10.1017/s0004972700029907.

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Let D be a domain in the complex ω-plane and let x: D → R3 be a regular minimal surface. Let M(K) be the set of points ω0 ∈ D where the Gauss curvature K attains local minima: K(ω0) ≤ K(ω) for |ω – ω0| < δ(ω0), δ(ω0) < 0. The components of M(K) are of three types: isolated points; simple analytic arcs terminating nowhere in D; analytic Jordan curves in D. Components of the third type are related to the Gauss map.

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19

Biryukov, Oleg N. "Parity conditions for realizability of Gauss diagrams." Journal of Knot Theory and Its Ramifications 28, no. 01 (2019): 1950015. http://dx.doi.org/10.1142/s0218216519500159.

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We consider a problem of realizability of Gauss diagrams by closed plane curves where the plane curves have only double points of transversal self-intersection. We formulate the necessary and sufficient conditions for realizability. These conditions are based only on the parity of double and triple intersections of the chords in the Gauss diagram.

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20

Zhedanov, A. S. "Gauss Sums and Orthogonal Polynomials." International Journal of Modern Physics A 12, no. 01 (1997): 289–94. http://dx.doi.org/10.1142/s0217751x97000438.

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It is shown that q-Hermite polynomials for q a root of unity are orthogonal on finite numbers of points of the real axes. The (complex) weight function coincides with a special type of the Gauss sums in number theory. The same Gauss sum plays the role of the weight function for the Stiltjes–Wigert and Rogers–Szegö polynomials leading to the orthogonality on the regular N-gons.

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21

Liu, Ran, Zhen-Guo Yan, Huajun Zhu, Feiran Jia, and Xinlong Feng. "Energy Stability Property of the CPR Method Based on Subcell Second-Order CNNW Limiting in Solving Conservation Laws." Entropy 25, no. 5 (2023): 729. http://dx.doi.org/10.3390/e25050729.

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This paper studies the energy stability property of the correction procedure via reconstruction (CPR) method with staggered flux points based on second-order subcell limiting. The CPR method with staggered flux points uses the Gauss point as the solution point, dividing flux points based on Gauss weights, with the flux points being one more point than the solution points. For subcell limiting, a shock indicator is used to detect troubled cells where discontinuities may exist. Troubled cells are calculated by the second-order subcell compact nonuniform nonlinear weighted (CNNW2) scheme, which h

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22

Bhrawy, Ali H., Abdulrahim AlZahrani, Dumitru Baleanu, and Yahia Alhamed. "A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line." Abstract and Applied Analysis 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/692193.

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The modified generalized Laguerre-Gauss collocation (MGLC) method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss coll

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23

Al-Fadhel, Tariq A. "LUCAS POLYNOMIALS AND THE FIXED POINTS OF THE GAUSS MAP." Far East Journal of Applied Mathematics 101, no. 2 (2019): 113–21. http://dx.doi.org/10.17654/am101020113.

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24

Swarztrauber, Paul N. "On Computing the Points and Weights for Gauss--Legendre Quadrature." SIAM Journal on Scientific Computing 24, no. 3 (2003): 945–54. http://dx.doi.org/10.1137/s1064827500379690.

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25

An, Congpei, and Hao-Ning Wu. "Tikhonov regularization for polynomial approximation problems in Gauss quadrature points." Inverse Problems 37, no. 1 (2020): 015008. http://dx.doi.org/10.1088/1361-6420/abcd44.

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26

Gulzar, Suhail, N. A. Rather, and F. A. Bhat. "The location of critical points of polynomials." Asian-European Journal of Mathematics 12, no. 07 (2019): 1950087. http://dx.doi.org/10.1142/s1793557119500876.

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Given a set of points in the complex plane, an incomplete polynomial is defined as one which has these points as zeros except one of them. Recently, the classical result known as Gauss–Lucas theorem on the location of zeros of polynomials and their derivatives was extended to the linear combinations of incomplete polynomials. In this paper, a simple proof of this result is given, and some results concerning the critical points of polynomials due to Jensen and others have extended the linear combinations of incomplete polynomials.

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27

Doha, E. H., D. Baleanu, A. H. Bhrawy, and R. M. Hafez. "A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/816473.

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A new Legendre rational pseudospectral scheme is proposed and developed for solving numerically systems of linear and nonlinear multipantograph equations on a semi-infinite interval. A Legendre rational collocation method based on Legendre rational-Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational-Gauss collocation points. The numerical results obtained by this method have been compared with various exact solutions in order to dem

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28

Bhrawy, A. H., and W. M. Abd-Elhameed. "New Algorithm for the Numerical Solutions of Nonlinear Third-Order Differential Equations Using Jacobi-Gauss Collocation Method." Mathematical Problems in Engineering 2011 (2011): 1–14. http://dx.doi.org/10.1155/2011/837218.

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A new algorithm for solving the general nonlinear third-order differential equation is developed by means of a shifted Jacobi-Gauss collocation spectral method. The shifted Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the proposed algorithm, and some comparisons are made with the existing results. The method is easy to implement and yields very accurate results.

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29

Görög, Augustín. "Number of Points for Roundness Measurement - Measured Results Comparison." Research Papers Faculty of Materials Science and Technology Slovak University of Technology 19, no. 30 (2011): 19–24. http://dx.doi.org/10.2478/v10186-010-0035-x.

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Number of Points for Roundness Measurement - Measured Results Comparison Paper deals with filtering roundness. It presents experimental results measured for roundness turning and cylindrical grinding. Roundness was measured using Prismo Navigator 5 coordinate measuring machine. Evaluation was done by four methods: Minimum zone reference circles (MZCI), Least squares reference circle (LSCI), Minimum circumscribed reference circle (MCCI) and Maximum inscribed reference circle (MICI). The filters used were: Gauss, Spline and no filter.

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30

Li, Yanlin, Kemal Eren, Kebire Hilal Ayvacı, and Soley Ersoy. "The developable surfaces with pointwise 1-type Gauss map of Frenet type framed base curves in Euclidean 3-space." AIMS Mathematics 8, no. 1 (2022): 2226–39. http://dx.doi.org/10.3934/math.2023115.

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<abstract><p>In this study, the ruled developable surfaces with pointwise 1-type Gauss map of Frenet-type framed base (Ftfb) curve are introduced in Euclidean 3-space. The tangent developable surfaces, focal developable surfaces, and rectifying developable surfaces with singular points are considered. Then the conditions for the Gauss map of these surfaces to be pointwise 1-type are obtained separately. In order to form a basis for the study, first, the basic concepts related to the Ftfb curve and the Gauss map of a surface are recalled. Later, the necessary and sufficient conditio

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31

Gautschi, Walter, and Shikang Li. "The remainder term for analytic functions of Gauss-Radau and Gauss-Lobatto quadrature rules with multiple end points." Journal of Computational and Applied Mathematics 33, no. 3 (1990): 315–29. http://dx.doi.org/10.1016/s0377-0427(05)80007-x.

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32

GAUTSCHI, W., and S. LI. "The remainder term for analytic functions of Gauss-Radau and Gauss-Lobatto quadrature rules with multiple end points." Journal of Computational and Applied Mathematics 3, no. 3 (1990): 315–29. http://dx.doi.org/10.1016/0377-0427(90)90276-6.

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33

Johnson, Shyjo, and T. Jeyapoovan. "Evaluation of stiffness matrix in finite element analysis using element edge method for the 8-node brick element." International Journal of Computational Materials Science and Engineering 08, no. 04 (2019): 1950018. http://dx.doi.org/10.1142/s2047684119500180.

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An element edge method is developed for the evaluation of stiffness matrix for the 8-node brick element. Handling of large data leads to take more computational time in finite element analysis. The new set of quadrature consist of 13 sampling points and weights out which 12 points are at the edges of the brick element and one point is considered at the center of the element. The new set of sampling points is a mimic of Gauss numerical integration method. Finally, the proposed element edge method is evaluated using the standard benchmarked problems and compared the results with conventional Gau

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34

Zulhendra, Wahyu Srigutomo, and Cahyo Aji Hapsoro. "Implementation of the Gauss-Kronrod Quadrature Method (G7, K15) on 2D Gravity Anomaly Modeling in Basins with a Polynomial Variation of Density Distribution with Depth." Jurnal Penelitian Pendidikan IPA 10, no. 8 (2024): 6252–59. http://dx.doi.org/10.29303/jppipa.v10i8.8493.

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Forward modeling of 2D gravity anomalies, considering density contrasts that vary polynomially with depth, was performed to examine basin structures. This process involved two main stages: deriving analytical formulas and executing numerical integration. The Gauss-Kronrod Quadrature Method, utilizing 7 Gauss points and 15 Kronrod points, was employed to precisely compute these integrals. Initial modeling applied to theoretical basement scenarios with fixed density contrasts showed gravity anomalies that accurately reflected the curvature of the basement. To validate the approach, it was then a

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35

Zhang, Lei. "Vanishing Estimates for Fully Bubbling Solutions of SU (n + 1) Toda Systems at a Singular Source." International Mathematics Research Notices 2020, no. 18 (2018): 5774–95. http://dx.doi.org/10.1093/imrn/rny183.

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AbstractFor Gauss curvature equation (or more general Toda systems) defined on 2D spaces, the vanishing rate of certain curvature functions on blowup points is a key estimate for numerous applications. However, if these equations have singular sources, very few vanishing estimates can be found. In this article we consider a Toda system with singular sources defined on a Riemann surface and we prove a very surprising vanishing estimates and a reflection phenomenon for certain functions involving the Gauss curvature.

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Huang, Jing-Jing, and Huixi Li. "On two lattice points problems about the parabola." International Journal of Number Theory 16, no. 04 (2019): 719–29. http://dx.doi.org/10.1142/s1793042120500360.

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We obtain asymptotic formulae with optimal error terms for the number of lattice points under and near a dilation of the standard parabola, the former improving upon an old result of Popov. These results can be regarded as achieving the square root cancellation in the context of the parabola, whereas its analogues are wide open conjectures for the circle and the hyperbola. We also obtain essentially sharp upper bounds for the latter lattice points problem associated with the parabola. Our proofs utilize techniques in Fourier analysis, quadratic Gauss sums and character sums.

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37

Mehrpouya, Mohammad A. "A modified pseudospectral method for indirect solving a class of switching optimal control problems." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 234, no. 9 (2020): 1531–42. http://dx.doi.org/10.1177/0954410020916303.

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In the present paper, an efficient pseudospectral method for solving the Hamiltonian boundary value problems arising from a class of switching optimal control problems is presented. For this purpose, based on the Pontryagin's minimum principle, the first-order necessary conditions of optimality are derived. Then, by partitioning the time interval related to the problem under study into some subintervals, the states (and costates) and control functions are approximated on each subintervals with piecewise interpolating polynomials based on Legendre–Gauss–Radau points and a piecewise constant fun

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38

Hossain, M. A., and M. S. Islam. "Applications of Composite Numerical Integrations Using Gauss-Radau and Gauss-Lobatto Quadrature Rules." Journal of Scientific Research 2, no. 3 (2010): 465. http://dx.doi.org/10.3329/jsr.v2i3.5123.

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In this paper, numerical integrals over an arbitrary triangular region are evaluated exploiting finite element method. The physical region is transformed into a standard triangular finite element using the basis functions in local space. Then the standard triangle is discretized into 4×n2 right isosceles triangles, in which each of these triangles having area 1/2n2, and thus composite numerical integration is employed. In addition, the affine transformation over each discretized triangle and the use of linearity property of integrals are applied. Finally, each isosceles triangle is transformed

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39

HINOJOSA, PEDRO A., and GILVANEIDE N. SILVA. "The Gauss Map of Complete Minimal Surfaces with Finite Total Curvature." Anais da Academia Brasileira de Ciências 85, no. 4 (2013): 1217–26. http://dx.doi.org/10.1590/0001-3765201376911.

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In this paper we are concerned with the image of the normal Gauss map of a minimal surface immersed in ℝ3 with finite total curvature. We give a different proof of the following theorem of R. Osserman: The normal Gauss map of a minimal surface immersed in ℝ3 with finite total curvature, which is not a plane, omits at most three points of��2 Moreover, under an additional hypothesis on the type of ends, we prove that this number is exactly 2.

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40

MOVASATI, H., and S. REITER. "HYPERGEOMETRIC SERIES AND HODGE CYCLES OF FOUR DIMENSIONAL CUBIC HYPERSURFACES." International Journal of Number Theory 02, no. 03 (2006): 397–416. http://dx.doi.org/10.1142/s1793042106000632.

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In this article we find connections between the values of Gauss hypergeometric functions and the dimension of the vector space of Hodge cycles of four-dimensional cubic hypersurfaces. Since the Hodge conjecture is well-known for those varieties we calculate values of hypergeometric series on certain CM points. Our methods are based on the calculation of the Picard–Fuchs equations in higher dimensions, reducing them to the Gauss equation and then applying the Abelian Subvariety Theorem to the corresponding hypergeometric abelian varieties.

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41

Debnath, Partha Sarathi. "Causal cosmology with braneworld gravity including Gauss Bonnet coupling." Modern Physics Letters A 35, no. 26 (2020): 2050216. http://dx.doi.org/10.1142/s0217732320502168.

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Causal cosmological evolutions in Randall Sundrum type II (RS) braneworld gravity with Gauss Bonnet coupling and dissipative effects are discussed here. Causal theory of dissipative effects are illustrated by Full Israel Stewart theory are implemented. We consider the numerical solutions of evolutions and analytic solutions as a special case for extremely non-linear field equation in Randall Sundrum type II braneworld gravity with Gauss Bonnet coupling. Cosmological models admitting Power law expansion, Exponential expansion and evolution in the vicinity of the stationary solution of the unive

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42

Kim, Young-Ho, Chul-Woo Lee, and Dae-Won Yoon. "ON THE GAUSS MAP OF SURFACES OF REVOLUTION WITHOUT PARABOLIC POINTS." Bulletin of the Korean Mathematical Society 46, no. 6 (2009): 1141–49. http://dx.doi.org/10.4134/bkms.2009.46.6.1141.

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43

Brandolini, L., L. Colzani, A. Iosevich, A. Podkorytov, and G. Travaglini. "Geometry of the gauss map and lattice points in convex domains." Mathematika 48, no. 1-2 (2001): 107–17. http://dx.doi.org/10.1112/s0025579300014376.

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Zhou, Zhen, Xiaofeng Jia, and Xiaodong Qiang. "GPU-accelerated element-free reverse-time migration with Gauss points partition." Journal of Geophysics and Engineering 15, no. 3 (2018): 718–28. http://dx.doi.org/10.1088/1742-2140/aaa0a9.

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45

Liu, Yang, Huajun Zhu, Zhen-Guo Yan, Feiran Jia, and Xinlong Feng. "Entropy Stable DGSEM Schemes of Gauss Points Based on Subcell Limiting." Entropy 25, no. 6 (2023): 911. http://dx.doi.org/10.3390/e25060911.

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The discontinuous Galerkin spectral element method (DGSEM) is a compact and high-order method applicable to complex meshes. However, the aliasing errors in simulating under-resolved vortex flows and non-physical oscillations in simulating shock waves may lead to instability of the DGSEM. In this paper, an entropy-stable DGSEM (ESDGSEM) based on subcell limiting is proposed to improve the non-linear stability of the method. First, we discuss the stability and resolution of the entropy-stable DGSEM based on different solution points. Second, a provably entropy-stable DGSEM based on subcell limit

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Arbieto†, Alexander, and Carlos Matheus‡. "Immersions with fractal set of points of zero Gauss-Kronecker curvature." Bulletin Brazilian Mathematical Society 35, no. 3 (2004): 363–76. http://dx.doi.org/10.1007/s00574-004-0019-6.

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Teukolsky, Saul A. "Short note on the mass matrix for Gauss–Lobatto grid points." Journal of Computational Physics 283 (February 2015): 408–13. http://dx.doi.org/10.1016/j.jcp.2014.12.012.

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Ortleb, Sigrun. "A Kinetic Energy Preserving DG Scheme Based on Gauss–Legendre Points." Journal of Scientific Computing 71, no. 3 (2016): 1135–68. http://dx.doi.org/10.1007/s10915-016-0334-2.

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Darvishi, M. T. "Spectral collocation method and Darvishi's preconditionings for Tchebychev-Gauss-Lobatto points." International Mathematical Forum 2 (2007): 263–72. http://dx.doi.org/10.12988/imf.2007.07025.

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Farajzadeh, A., M. H. Rahmani Doust, F. Haghighifar, and D. Baleanu. "The Stability of Gauss Model Having One-Prey and Two-Predators." Abstract and Applied Analysis 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/219640.

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The study of the dynamics of predator-prey interactions can be recognized as a major issue in mathematical biology. In the present paper, some Gauss predator-prey models in which three ecologically interacting species have been considered and the behavior of their solutions in the stability aspect have been investigated. The main aim of this paper is to consider the local and global stability properties of the equilibrium points for represented systems. Finally, stability of some examples of Gauss model with one prey and two predators is discussed.

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