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Автор: Grafiati
Опубліковано: 30 травня 2022
Оновлено: 31 травня 2022

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1

Ryabushko, A. P., та T. A. Zhur. "ρ-Libration point in the three body problem". Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 57, № 3 (7 жовтня 2021): 330–46. http://dx.doi.org/10.29235/1561-2430-2021-57-3-330-346.

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Анотація:
Herein, the restricted circular three-body problem in homogeneous and inhomogeneous media is considered. Particular attention is paid to libration points. The conditions of their existence or non-existence in the Newtonian and post-Newtonian approximations of the general theory of relativity are derived. Several regularities, new Newtonian and relativistic effects arising due to the impact of the additional relativistic forces on bodies of gravitational fields of mediums in the differential equations of the motion of bodies are indicated. Using the previously derived equations of the motion of two bodies A1, A2 in the medium, the authors substantiated the following statements. In a homogeneous medium (density of the medium ρ = const) in the Newtonian approximation of the general theory of relativity there are ρ-libration points , 1,...,5, moving along the same circles as the Euler and Lagrangian libration points Li but with an angular velocity 0 , greater than the angular velocity ω0 of libration points Li in a vacuum. Bodies A1, A2 also move along their circles with an angular velocity 0 > w When passing from the Newtonian approximation of the general theory of relativity to the post-Newtonian approximation of the general theory of relativity, the centre of mass of two bodies, resting in a homogeneous medium in the Newtonian approximation of the general theory of relativity, must move along a cycloid. The trajectories of the bodies can not be circles, the libration points Li disappear. In the case of an inhomogeneous medium distributed, for example, spherically symmetrically, the centre of mass of two bodies, already in the Newtonian approximation of the general theory of relativity, must move along the cycloid, despite it was at rest in the void. Therefore, bodies A1, A2 must describe loops that form, figuratively speaking, a «lace», as in the case of a homogeneous medium in the post-Newtonian approximation of the general theory of relativity. The figure illustrating the situation is provided. Due to the existence of the «lace» effect, the libration point Li movements are destroyed. In the special case, when the masses of bodies A1, A2 are equal (m1 = m2), the cycloids disappear and all the ρ-libration points exist in homogeneous and inhomogeneous media in the Newtonian and post-Newtonian approximations of the general theory of relativity. Numerical estimates of the predicted patterns and effects in the Solar and other planetary systems, interstellar and intergalactic mediums are carried out. For example, displacements associated with these effects, such as the displacement of the centre of mass, can reach many billions of kilometres per revolution of the two-body system. The possible role of these regularities and effects in the theories of the evolution of planetary systems, galaxies, and their ensembles is discussed. A brief review of the studies carried out by the Belarusian scientific school on the problem of the motion of bodies in media in the general theory of relativity is given.
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2

Gual-Arnau, Ximo, Maria Victoria Ibáñez Gual, and Juan Monterde. "CURVATURE APPROXIMATION FROM PARABOLIC SECTORS." Image Analysis & Stereology 36, no. 3 (December 18, 2017): 233. http://dx.doi.org/10.5566/ias.1702.

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Анотація:
We propose an invariant three-point curvature approximation for plane curves based on the arc of a parabolic sector, and we analyze how closely this approximation is to the true curvature of the curve. We compare our results with the obtained with other invariant three-point curvature approximations. Finally, an application is discussed.
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3

Salajegheh, E. "Optimum design of plate structures using three-point approximation." Structural Optimization 13, no. 2-3 (April 1997): 142–47. http://dx.doi.org/10.1007/bf01199233.

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4

Mikdam, A., A. Makradi, S. Ahzi, H. Garmestani, D. S. Li, and Y. Remond. "A new approximation for the three-point probability function." International Journal of Solids and Structures 46, no. 21 (October 2009): 3782–87. http://dx.doi.org/10.1016/j.ijsolstr.2009.07.004.

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5

Guo, Xu, Koetsu Yamazaki, and Geng Dong Cheng. "A new three-point approximation approach for design optimization problems." International Journal for Numerical Methods in Engineering 50, no. 4 (2001): 869–84. http://dx.doi.org/10.1002/1097-0207(20010210)50:4<869::aid-nme56>3.0.co;2-c.

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6

Drumm, Eric C., Richard M. Bennett, and Gary J. Oakley. "Probabilistic response of laterally loaded piers by three-point approximation." International Journal for Numerical and Analytical Methods in Geomechanics 14, no. 7 (September 1990): 499–507. http://dx.doi.org/10.1002/nag.1610140704.

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7

Kawecki, Bartosz, Jerzy Podgórski, and Aleksandra Głowacka. "Natural plant stems modelling in a three-point bending test." MATEC Web of Conferences 252 (2019): 07001. http://dx.doi.org/10.1051/matecconf/201925207001.

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Анотація:
The paper presents an approach to natural plant stems numerical modelling in a three-point bending test. Introduced subject was connected with elaborating more efficient systems for harvesting energetic plants. There were modelled, and laboratory tested two types of stems – sida hermaphrodita and miscanthus giganteus. Course of proceedings for obtaining natural cross-sectional dimensions with graphical data processing was described in detail. Basing on dozens of stems slices from random parts of plants, three different cross-section approximations were proposed and computationally implemented – a circular pipe, an elliptical pipe (symmetrical cross-section) and a sine-cosine series pipe (asymmetrical cross-section). Analytical formulas for calculating a cross-sectional area and moments of inertia for each approximation were given. Basic material parameters as an elastic modulus and yielding stress was obtained from simply supported beam theory and laboratory force – the deflexion relation. FEM models were created in Simulia Abaqus software using C3D20R elements. Preliminary approach to modelling damage with perfect plasticity was done basing on several samples bended to failure in laboratory tests. Conclusions for future work with numerical modelling natural plant stems were drawn.
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8

Yao, Jianyao, Weimin Wu, Kun Zhang, Dongyang Sun, Yaolu Liu, Huiming Ning, Ning Hu, and G. R. Liu. "Development of Three-Dimensional GSM-CFD Solver for Compressible Flows." International Journal of Computational Methods 14, no. 04 (April 18, 2017): 1750037. http://dx.doi.org/10.1142/s0219876217500372.

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Анотація:
A three-dimensional (3D) Computational Fluid Dynamics (CFD) solver based on the gradient smoothing method (GSM) is developed for compressible flows based on previous research. The piecewise constant smoothing function with one-point integration scheme is implemented for gradient approximation of field variables and convective fluxes. The matrix-based method for gradient approximations is also developed to improve the numerical efficiency. Numerical examples of gradient approximations of several given functions have shown that the proposed GSM is more accurate and robust to mesh distortion. A transonic ONERA M6 wing is used to demonstrate the effectiveness of the proposed GSM-CFD solver.
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9

Chinh, P. Duc. "Three-point interpolation approximation for the macroscopic properties of isotropic two-component materials." Philosophical Magazine 87, no. 24 (August 21, 2007): 3531–44. http://dx.doi.org/10.1080/14786430701344541.

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10

Devaney, Anthony J. "Generalized Projection-Slice Theorem for Fan Beam Diffraction Tomography." Ultrasonic Imaging 7, no. 3 (July 1985): 264–75. http://dx.doi.org/10.1177/016173468500700306.

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Анотація:
A generalized projection-slice theorem is derived for transmission fan beam diffraction tomography within the Born or Rytov approximations. The development is based on the use of the so-called paraxial approximation which requires that the object being probed subtend a small angle relative to the source point and to the measurement plane. Within this approximation it is shown that the transmitted field measured over a plane surface located on the opposite side of the object from the insonifying point source determines the three-dimensional spatial Fourier transform of the object profile over the surface of an ellipsoid of revolution in Fourier space. In the special case where the point source is in the far field of the object the semiaxes of the ellipsoid become equal and the surface degenerates to a sphere and the result reduces to the usual projection-slice theorem of plane beam diffraction tomography.
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11

Xu, Shibo, and Alexey Stovas. "Estimation of the conversion point position in elastic orthorhombic media." GEOPHYSICS 84, no. 1 (January 1, 2019): C15—C25. http://dx.doi.org/10.1190/geo2018-0375.1.

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Анотація:
Determination of the conversion point position is very important to carry out seismic processing in the common conversion point gather of converted wave data. The anisotropic effect is very obvious for a converted wave when estimating the physical and processing parameters from real data. To estimate the conversion point in an elastic orthorhombic (ORT) medium, we have defined an explicit rational form approximation for the radial coordinate of the conversion point for converted [Formula: see text], [Formula: see text], and [Formula: see text] waves. To obtain the approximation coefficients, the Taylor series approximation in the corresponding vertical slowness for three pure wave modes is applied. The coefficients in our proposed approximation are computed within two vertical symmetry planes. The difference between the acquisition azimuth and the azimuth of the conversion point position is analyzed for different combinations of the wave modes. The accuracy of the conversion point position estimation for three ORT models is illustrated in the numerical examples. One can see from the results that for converted [Formula: see text] and [Formula: see text] waves, our approximation is very accurate in estimating the conversion point position regardless of the tested ORT model. For a converted [Formula: see text] wave, due to the existence of cusps, triplications, and shear singularities, the error in conversion point estimation is relatively larger compared with PS-waves in the vicinity of the singularity point.
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12

Benammar, Mohieddine, Abdulrahman Alassi, Adel Gastli, Lazhar Ben-Brahim, and Farid Touati. "New Fast Arctangent Approximation Algorithm for Generic Real-Time Embedded Applications." Sensors 19, no. 23 (November 25, 2019): 5148. http://dx.doi.org/10.3390/s19235148.

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Анотація:
Fast and accurate arctangent approximations are used in several contemporary applications, including embedded systems, signal processing, radar, and power systems. Three main approximation techniques are well-established in the literature, varying in their accuracy and resource utilization levels. Those are the iterative coordinate rotational digital computer (CORDIC), the lookup tables (LUTs)-based, and the rational formulae techniques. This paper presents a novel technique that combines the advantages of both rational formulae and LUT approximation methods. The new algorithm exploits the pseudo-linear region around the tangent function zero point to estimate a reduced input arctangent through a modified rational approximation before referring this estimate to its original value using miniature LUTs. A new 2nd order rational approximation formula is introduced for the first time in this work and benchmarked against existing alternatives as it improves the new algorithm performance. The eZDSP-F28335 platform has been used for practical implementation and results validation of the proposed technique. The contributions of this work are summarized as follows: (1) introducing a new approximation algorithm with high precision and application-based flexibility; (2) introducing a new rational approximation formula that outperforms literature alternatives with the algorithm at higher accuracy requirement; and (3) presenting a practical evaluation index for rational approximations in the literature.
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13

Phillips, C. G., and S. R. Kaye. "A uniformly asymptotic approximation for the development of shear dispersion." Journal of Fluid Mechanics 329 (December 25, 1996): 413–43. http://dx.doi.org/10.1017/s002211209600897x.

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In this paper we consider the development of shear dispersion following the introduction of a diffusing tracer substance into a tube or duct containing flowing fluid, with emphasis on the characterization of the temporal variation of concentration at a fixed axial position. Asymptotic results are derived by assuming that the distance downstream of the point of tracer introduction, appropriately non-dimensionalized, is large. First, we consider the central moments of the temporal concentration variation, including their dependence on transverse position and on the initial transverse distribution of tracer. The moments for finite Péclet number are expressed in terms of their infinite-Péclet-number counterparts, and the latter are given explicitly for Poiseuille flow. Then, assuming the Péclet number is infinite, we derive an approximate solution for the Green's function expressing tracer concentration following its introduction at an arbitrary point within the tube. The solution is expressed in terms of three numerically evaluated functions of a dimensionless time variable, with parametric dependence on the distance downstream of the point of tracer release. The method is illustrated by calculation of the approximate solution for dispersion in Poiseuille flow. Unlike previous approximations, the present solution is uniformly asymptotic and represents the tails of the concentration distribution as well as the approximately Gaussian central part; in these three regions, simpler analytic forms of the approximation are given. Comparison with previous computational solutions suggests the present approximation remains reasonably accurate even at quite short distances from the point where tracer is released.
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14

Benbouras, Youssef, Mouad Bellahkim, Aziz Maziri, Elhassan Mallil, and Jamal Echaabi. "Nonlinear modeling of the failure of a graphite epoxy under a three-point bending test." Polymers and Polymer Composites 28, no. 2 (August 13, 2019): 119–39. http://dx.doi.org/10.1177/0967391119866597.

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The application of modeling theories and the choice of failure criteria are difficult in part because they are too varied and must be validated by biaxial tests, which are expensive to be performed. This article is devoted to the nonlinear modeling and failure criteria which are employed in the design and analysis of anisotropic materials. Indeed, in this work, a study of the macroscopic and microscopic behavior of a graphite epoxy under a three-point bending test is conducted, and the successive failures are also predicted. Experimentally, the damage progression and the effect of geometrical parameters are followed and identified in detail. The analytical modeling is based on a recently developed approximation for isotropic materials. This approximation is also valid for the studied quasi-isotropic laminated composite. A software program has been elaborated for the application of the most general failure criteria. The results obtained by this analytical modeling show a good correlation with those of the experimental study.
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15

Szász, A. "One Possible Analytical Approximation of the Critical Point of the Three-Dimensional Ising Model." physica status solidi (b) 130, no. 2 (August 1, 1985): K97—K100. http://dx.doi.org/10.1002/pssb.2221300250.

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16

Khan, Rahmat Ali, Juan J. Nieto, and V. Otero-Espinar. "Existence and approximation of solution of three-point boundary value problems on time scales." Journal of Difference Equations and Applications 14, no. 7 (July 2008): 723–36. http://dx.doi.org/10.1080/10236190701840906.

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17

Gabovich, Alexander M., and Alexander I. Voitenko. "Electrostatic Interaction of Point Charges in Three-Layer Structures: The Classical Model." Condensed Matter 4, no. 2 (May 2, 2019): 44. http://dx.doi.org/10.3390/condmat4020044.

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Анотація:
Electrostatic interaction energy W between two point charges in a three-layer plane system was calculated on the basis of the Green’s function method in the classical model of constant dielectric permittivities for all media involved. A regular method for the calculation of W ( Z , Z ′ , R ) , where Z and Z ′ are the charge coordinates normal to the interfaces, and R the lateral (along the interfaces) distance between the charges, was proposed. The method consists in substituting the evaluation of integrals of rapidly oscillating functions over the semi-infinite interval by constructing an analytical series of inverse radical functions to a required accuracy. Simple finite-term analytical approximations of the dependence W ( Z , Z ′ , R ) were proposed. Two especially important particular cases of charge configurations were analyzed in more detail: (i) both charges are in the same medium and Z = Z ′ ; and (ii) the charges are located at different interfaces across the slab. It was demonstrated that the W dependence on the charge–charge distance S = R 2 + Z − Z ′ 2 differs from the classical Coulombic one W ∼ S − 1 . This phenomenon occurs due to the appearance of polarization charges at both interfaces, which ascribes a many-body character to the problem from the outset. The results obtained testify, in particular, that the electron–hole interaction in heterostructures leading to the exciton formation is different in the intra-slab and across-slab charge configurations, which is usually overlooked in specific calculations related to the subject concerned. Our consideration clearly demonstrates the origin, the character, and the consequences of the actual difference. The often used Rytova–Keldysh approximation was analyzed. The cause of its relative success was explained, and the applicability limits were determined.
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18

Ru, Zhong Liang, Hong Bo Zhao, and Chuan Rui Zhu. "Crack Propagation Analysis of Concrete Beam Subjected to Three-Point Bending Using XFEM." Applied Mechanics and Materials 94-96 (September 2011): 1655–58. http://dx.doi.org/10.4028/www.scientific.net/amm.94-96.1655.

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Анотація:
Extended finite element method (XFEM) has been applied to the crack propagation problems. A standard displacement-base approximation is enriched near a crack by incorporating both a discontinuous field and the near crack front asymptotic fields through a partition of unity method. This technique allows the entire crack to be represented independently of the mesh, so remeshing is not necessary to model crack growth. Applications of the proposed technique to beam subjected to three-point bending have been presented, results shown the location of the crack imposes important effect on the crack propagation direction.
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19

Matus, P. P., and Hoang Thi Kieu Anh. "Compact Difference Schemes on a Three-Point Stencil for Second-Order Hyperbolic Equations." Differential Equations 57, no. 7 (July 2021): 934–46. http://dx.doi.org/10.1134/s0012266121070090.

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Abstract We consider compact difference schemes of approximation order $$4+2 $$ on a three-point spatial stencil for the Klein–Gordon equations with constant and variable coefficients. New compact schemes are proposed for one type of second-order quasilinear hyperbolic equations. In the case of constant coefficients, we prove the strong stability of the difference solution under small perturbations of the initial conditions, the right-hand side, and the coefficients of the equation. A priori estimates are obtained for the stability and convergence of the difference solution in strong mesh norms.
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20

Salthouse, D. G., G. Indelicato, P. Cermelli, T. Keef, and R. Twarock. "Approximation of virus structure by icosahedral tilings." Acta Crystallographica Section A Foundations and Advances 71, no. 4 (May 29, 2015): 410–22. http://dx.doi.org/10.1107/s2053273315006701.

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Анотація:
Viruses are remarkable examples of order at the nanoscale, exhibiting protein containers that in the vast majority of cases are organized with icosahedral symmetry. Janner used lattice theory to provide blueprints for the organization of material in viruses. An alternative approach is provided here in terms of icosahedral tilings, motivated by the fact that icosahedral symmetry is non-crystallographic in three dimensions. In particular, a numerical procedure is developed to approximate the capsid of icosahedral viruses by icosahedral tilesviaprojection of high-dimensional tiles based on the cut-and-project scheme for the construction of three-dimensional quasicrystals. The goodness of fit of our approximation is assessed using techniques related to the theory of polygonal approximation of curves. The approach is applied to a number of viral capsids and it is shown that detailed features of the capsid surface can indeed be satisfactorily described by icosahedral tilings. This work complements previous studies in which the geometry of the capsid is described by point sets generated as orbits of extensions of the icosahedral group, as such point sets are by construction related to the vertex sets of icosahedral tilings. The approximations of virus geometry derived here can serve as coarse-grained models of viral capsids as a basis for the study of virus assembly and structural transitions of viral capsids, and also provide a new perspective on the design of protein containers for nanotechnology applications.
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21

RONTO, A., and M. RONTO. "Existence results for three-point boundary value problems for systems of linear functional differential equations." Carpathian Journal of Mathematics 28, no. 1 (2012): 163–82. http://dx.doi.org/10.37193/cjm.2012.01.01.

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Анотація:
Conditions guaranteeing the solvability of certain three-point boundary value problems for a system of linear functional differential equations are obtained by using a special successive approximation scheme. We also establish some conditions necessary for a certain set belonging to the domain of the space variables to contain a point determining the initial value of the solution. An algorithm for selecting such points is also indicated.
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22

Džunić, Jovana, and Miodrag S. Petković. "A Family of Three-Point Methods of Ostrowski's Type for Solving Nonlinear Equations." Journal of Applied Mathematics 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/425867.

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Анотація:
A class of three-point methods for solving nonlinear equations of eighth order is constructed. These methods are developed by combining two-point Ostrowski's fourth-order methods and a modified Newton's method in the third step, obtained by a suitable approximation of the first derivative using the product of three weight functions. The proposed three-step methods have order eight costing only four function evaluations, which supports the Kung-Traub conjecture on the optimal order of convergence. Two numerical examples for various weight functions are given to demonstrate very fast convergence and high computational efficiency of the proposed multipoint methods.
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23

Barbour, A. D., and Aihua Xia. "Normal approximation for random sums." Advances in Applied Probability 38, no. 03 (September 2006): 693–728. http://dx.doi.org/10.1017/s0001867800001233.

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Анотація:
In this paper, we adapt the very effective Berry-Esseen theorems of Chen and Shao (2004), which apply to sums of locally dependent random variables, for use with randomly indexed sums. Our particular interest is in random variables resulting from integrating a random field with respect to a point process. We illustrate the use of our theorems in three examples: in a rather general model of the insurance collective; in problems in geometrical probability involving stabilizing functionals; and in counting the maximal points in a two-dimensional region.
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24

Barbour, A. D., and Aihua Xia. "Normal approximation for random sums." Advances in Applied Probability 38, no. 3 (September 2006): 693–728. http://dx.doi.org/10.1239/aap/1158684998.

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Анотація:
In this paper, we adapt the very effective Berry-Esseen theorems of Chen and Shao (2004), which apply to sums of locally dependent random variables, for use with randomly indexed sums. Our particular interest is in random variables resulting from integrating a random field with respect to a point process. We illustrate the use of our theorems in three examples: in a rather general model of the insurance collective; in problems in geometrical probability involving stabilizing functionals; and in counting the maximal points in a two-dimensional region.
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25

Salajegheh, E. "Optimum design of steel space frames with frequency constraints using three point Rayleigh quotient approximation." Journal of Constructional Steel Research 54, no. 2 (May 2000): 305–13. http://dx.doi.org/10.1016/s0143-974x(99)00060-7.

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26

Khan, Rahmat. "Existence and approximation of solutions to three-point boundary value problems for fractional differential equations." Electronic Journal of Qualitative Theory of Differential Equations, no. 58 (2011): 1–8. http://dx.doi.org/10.14232/ejqtde.2011.1.58.

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27

Tobias, S. M., and J. B. Marston. "Three-dimensional rotating Couette flow via the generalised quasilinear approximation." Journal of Fluid Mechanics 810 (November 28, 2016): 412–28. http://dx.doi.org/10.1017/jfm.2016.727.

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Анотація:
We examine the effectiveness of the generalised quasilinear (GQL) approximation introduced by Marston et al. (Phys. Rev. Lett., vol. 116 (21), 2016, 214501). This approximation splits the variables into large and small scales in directions where there is a translational symmetry and removes nonlinear interactions involving only small scales. We utilise as a paradigm problem three-dimensional, turbulent, rotating Couette flow. We compare the results obtained from direct numerical solution of the equations with those from quasilinear (QL) and GQL calculations. In this three-dimensional setting, there is a choice of cutoff wavenumber for the GQL approximation both in the streamwise and in the spanwise directions. We demonstrate that the GQL approximation significantly improves the accuracy of mean flows, spectra and two-point correlation functions over models that are quasilinear in any of the translationally invariant directions, even if only a few streamwise and spanwise modes are included. We argue that this provides significant support for a programme of direct statistical simulation utilising the GQL approximation.
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28

Zhang, Dun Fu, Wei Shen Zhu, and Shu Cai Li. "Research of 3D EFG of Limiting Nodal Point Number and Applied for Three-Dimensional Elastic Problem." Key Engineering Materials 306-308 (March 2006): 721–26. http://dx.doi.org/10.4028/www.scientific.net/kem.306-308.721.

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Анотація:
The formulation and implementation of three-dimensional element free Galerkin method (3D EFG) are developed. A simple and efficient scheme for a variable domain of influence stipulates that a constant number of nodal points are visible from each integration location is proposed. This method significantly increases the efficiency of the variable domain of influence by limiting the size of the least-square problem that is solved when computing approximate functions. The 3D EFG methods based on moving least square method use only nodal points to built local and global approximation. Discrete model of the 3D EFG for three-dimensional elastic problems is derived by least potential energy principle. Reference to the 2D EFG, in the 3D EFG, it is enforced to meet displacements boundary conditions by use of limiting nodal point number method and penalty method. The stress concentration of a small column-shaped cavity in a cube subjected to uniaxial uniform tension at two opposing faces in far field. Compared the approximation solutions with theory ones, the results indicate that the 3D EFG is validity in solving three-dimensional elastic problems and the limiting nodal point number method is validity.
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29

JIN, GYO TAEK, and SEOJUNG PARK. "QUADRISECANT APPROXIMATION OF HEXAGONAL TREFOIL KNOT." Journal of Knot Theory and Its Ramifications 20, no. 12 (December 2011): 1685–93. http://dx.doi.org/10.1142/s0218216511009467.

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Анотація:
It is known that every nontrivial knot has at least two quadrisecants. Given a knot, we mark each intersection point of each of its quadrisecants. Replacing each subarc between two nearby marked points with a straight line segment joining them, we obtain a polygonal closed curve which we will call the quadrisecant approximation of the given knot. We show that for any hexagonal trefoil knot, there are only three quadrisecants, and the resulting quadrisecant approximation has the same knot type.
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30

Wu, Zuqing, Jialun Ping, and Hongshi Zong. "Effects of Fierz transformation on gap equation and CEP at finite chemical potential and finite temperature in Hartree–Fock approximation." Modern Physics Letters A 32, no. 40 (December 28, 2017): 1750222. http://dx.doi.org/10.1142/s0217732317502224.

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Анотація:
Three representations of Nambu–Jona-Lasinio interaction Lagrangians are constructed by Fierz transformation, and gap equation and critical end point in these three representations at finite temperature and finite chemical potential are studied. We find that the values of the quark mass and the critical end point are different in these three representations because of the consideration of Hartree–Fock approximation in our calculation.
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31

Qin, Bo-Wei, Kwok-Wai Chung, Antonio Algaba, and Alejandro J. Rodríguez-Luis. "High-Order Analysis of Global Bifurcations in a Codimension-Three Takens–Bogdanov Singularity in Reversible Systems." International Journal of Bifurcation and Chaos 30, no. 01 (January 2020): 2050017. http://dx.doi.org/10.1142/s0218127420500170.

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Анотація:
A codimension-three Takens–Bogdanov bifurcation in reversible systems has been very recently analyzed in the literature. In this paper, we study with the help of the nonlinear time transformation method, the codimension-one and -two homoclinic and heteroclinic connections present in the corresponding unfolding. The algorithm developed allows to obtain high-order approximations for the global connections, in such a way that it supplies in a very efficient manner the coefficients that would be obtained with high-order Melnikov functions. As we show, all our analytical predictions have excellent agreement with the numerical results. In particular we remark that, for the two different codimension-two points, the theoretical approximation coincides in six decimal digits with the numerical continuation, even being quite far from the codimension-three point. The better approximations we provide in this work will help in the study of reversible systems that exhibit this codimension-three Takens–Bogdanov bifurcation.
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32

Beggs, E. J., and J. V. Tucker. "Experimental computation of real numbers by Newtonian machines." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2082 (March 27, 2007): 1541–61. http://dx.doi.org/10.1098/rspa.2007.1835.

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Following a methodology we have proposed for analysing the nature of experimental computation, we prove that there is a three-dimensional Newtonian machine which given any point x ∈[0, 1] can generate an infinite sequence [ p n , q n ], for n =1, 2, …, of rational number interval approximations, that converges to x as n →∞. The machine is a system for scattering and collecting particles. The theorem implies that every point x∈[0, 1] is computable by a simple Newtonian kinematic system that is bounded in space and mass and for which the calculation of the nth approximation of x takes place in O ( n ) time with O ( n ) energy. We describe variants of the scatter machine which explain why our machine is non-deterministic.
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33

Druskin, Vladimir, and Shari Moskow. "Three-point finite-difference schemes, Padé and the spectral Galerkin method. I. One-sided impedance approximation." Mathematics of Computation 71, no. 239 (November 19, 2001): 995–1019. http://dx.doi.org/10.1090/s0025-5718-01-01349-7.

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34

Ezhov, Nikolaj, Frank Neitzel, and Svetozar Petrovic. "Spline approximation, Part 1: Basic methodology." Journal of Applied Geodesy 12, no. 2 (April 25, 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. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.
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35

SONG, H. Q., M. BALDO, A. FIASCONARO, G. GIANSIRACUSA, and U. LOMBARDO. "THREE NUCLEON CORRELATIONS IN NUCLEAR MEDIUM." Modern Physics Letters A 18, no. 02n06 (February 28, 2003): 317–21. http://dx.doi.org/10.1142/s0217732303010429.

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Анотація:
The equation of state(EOS) of nuclear matter is studied up to the three-hole-line level of approximation in the Behte-Brueckner-Goldstone expansion. The results indicate a good convergence of the theory. The fact that the resulting EOS does not reproduce the empirical saturation point suggests that the three-body forces are most likely the main term missing in the nuclear Hamiltonian.
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36

Zhang, X. F., Y. E. Zhao, Y. M. Zhang, X. Z. Huang, and H. Li. "A points estimation and series approximation method for uncertainty analysis." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223, no. 9 (April 16, 2009): 1997–2007. http://dx.doi.org/10.1243/09544062jmes1229.

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Анотація:
The objective of this article is to present an algorithm for moment evaluation and probability density function approximation of performance function for structural reliability analysis. In doing so, a point estimation method for probability moment of performance function is discussed at first. Based on the coherent relationship between the orthogonal polynomial and probability density function, formulas for point estimation are derived. Vector operators are defined to alleviate computational burden for computer programming. Then, by utilizing C-type Gram—Charlier series expansion method, a procedure for probability density function approximation of the performance function is studied. At last, the accuracy of the proposed method is demonstrated using three numerical examples.
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37

Aminov, Rufat, Alexander Shmyrov, and Vasily Shmyrov. "Impulse control flight to the invariant manifold near collinear libration point." Cybernetics and Physics, Volume 8, 2019, Number 2 (September 30, 2019): 51–57. http://dx.doi.org/10.35470/2226-4116-2019-8-2-51-57.

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Анотація:
We consider the special problem of flight from near-Earth orbit to a neighborhood of first collinear libration point of the Sun-Earth system. For such flight the numerical experiments substantiate the adequacy of the model of Hill’s equations, which is the nonlinear approximation of equations of circular limited three-body problem. Otherwise, we would be obliged to use the model of limited three-body problem (or its approximation) in conjunction with the model of two-body problem for modeling of motion. During of approach to the neighborhood of libration point (in space of positions), the series of impulse controls are implemented. Controls are built on the basis of equations in variations. The purpose of implementing presented controls is hitting the manifold, where a spacecraft will be as long as possible in the linear case. This manifold is achieved when the special functions of phase variables is equal to zero. All the presented studies are illustrated in detail.
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38

Bashir, Robina, and Ghulam Mustafa. "A Family of 6-Point n-Ary Interpolating Subdivision Schemes." October 2018 37, no. 4 (October 1, 2018): 481–90. http://dx.doi.org/10.22581/muet1982.1804.03.

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Анотація:
We derive three-step algorithm based on divided difference to generate a class of 6-point n-ary interpolating sub-division schemes. In this technique second order divided differences have been calculated at specific position and used to insert new vertices. Interpolating sub-division schemes are more attractive than approximating schemes in computer aided geometric designs because of their interpolation property. Polynomial generation and polynomial reproduction are attractive properties of sub-division schemes. Shape preserving properties are also significant tool in sub-division schemes. Further, some significant properties of ternary and quaternary sub-division schemes have been elaborated such as continuity, degree of polynomial generation, polynomial reproduction and approximation order. Furthermore, shape preserving property that is monotonicity is also derived. Moreover, the visual performance of proposed schemes has also been demonstrated through several examples.
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39

Ahmed, Raheel, Michael G. Edwards, Sadok Lamine, Bastiaan A. H. Huisman, and Mayur Pal. "Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model." Journal of Computational Physics 303 (December 2015): 470–97. http://dx.doi.org/10.1016/j.jcp.2015.10.001.

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40

Almusawa, Hassan, Hasanen A. Hammad, and Nisha Sharma. "Approximation of the Fixed Point for Unified Three-Step Iterative Algorithm with Convergence Analysis in Busemann Spaces." Axioms 10, no. 1 (February 27, 2021): 26. http://dx.doi.org/10.3390/axioms10010026.

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Анотація:
In this manuscript, a new three-step iterative scheme to approximate fixed points in the setting of Busemann spaces is introduced. The proposed algorithms unify and extend most of the existing iterative schemes. Thereafter, by making consequent use of this method, strong and Δ-convergence results of mappings that satisfy the condition (Eμ) in the framework of uniformly convex Busemann space are obtained. Our results generalize several existing results in the same direction.
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41

SUN, YUNG-NIEN, and SHU-CHIEN HUANG. "GENETIC ALGORITHMS FOR ERROR-BOUNDED POLYGONAL APPROXIMATION." International Journal of Pattern Recognition and Artificial Intelligence 14, no. 03 (May 2000): 297–314. http://dx.doi.org/10.1142/s0218001400000209.

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Анотація:
A new polygonal approximation algorithm, employing the concept of genetic evolution, is presented. In the proposed method, a chromosome is used to represent a polygon by a binary string. Each bit, called a gene, represents a point on the given curve. Three genetic operators, including selection, crossover, and mutation, are designed to obtain the approximated polygon whose error is bounded by a given norm. Many experiments show that the convergence is guaranteed and the optimal or near-optimal solutions can be obtained. Compared with the Zhu–Seneviratne algorithm,24 the proposed algorithm successfully reduced the number of segments under the same error condition in the polygonal approximation.
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42

Anakira, N. R., O. Y. Ababneh, A. S. Heilat, and I. M. Batiha. "A New Accurate Approximate Solution of Singular Two-Point Boundary Value Problems." General Letters in Mathematics 12, no. 1 (March 2022): 31–39. http://dx.doi.org/10.31559/glm2022.12.1.4.

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Анотація:
In this paper, A new accurate solutions are obtained for classes of singular two-point boundary value problems (BVPs) using a new solution procedure based on the construction of the auxiliary functions of the standard optimal homotopy asymptotic method (OHAM). This procedure give us accurate approximate solutions using only one order of approximation compared with the solutions obtained previously by the standard OHAM approximation of three order. The obtained numerical results which are displayed in tables and plotted graphically in figures leads to concluded that this procedure is efficient and of third order reliable for finding the solutions of singular two BVPs.
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43

Neamah, Kawther Abood. "Mathematical Model for Handling Unstable Time Series by Using a Linear Approximation Technique." Webology 19, no. 1 (January 20, 2022): 2835–52. http://dx.doi.org/10.14704/web/v19i1/web19189.

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Анотація:
Time series are typically built on basic assumptions that include stationarity, linearity and normality. The three characteristics are crucial for estimating and building time series models. Studies on time series include these assumptions. To deal with unstable time series that are based on its basis, mathematical models that are suitable for such series are adopted in this study. A nonlinear self-regression model, called the rational model, is proposed. This model is a fraction in which the numerator is the complete sine function and the denominator is an exponential self-regression model. The fixed point and limit cycle of the model are simulated and determined, and its stability is studied using a linear approximation technique.
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44

Schreuder, H. T., Z. Ouyang, and M. Williams. "Point-Poisson, point-pps, and modified point-pps sampling: efficiency and variance estimation." Canadian Journal of Forest Research 22, no. 8 (August 1, 1992): 1071–78. http://dx.doi.org/10.1139/x92-142.

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Анотація:
Modified point-pps (probability proportional to size) sampling selects at least one sample tree per point and yields a fixed sample size. Point-Poisson sampling is as efficient as this modified procedure but less efficient than regular point-pps sampling in a simulation study estimating total volume using either the Horvitz–Thompson (ŶHT) or the weighted regression estimator (Ŷwr). Point-pps sampling is somewhat more efficient than point-Poisson sampling for all estimators except ŶHT, and point-Poisson sampling is always somewhat more efficient than modified point-pps sampling across.all estimators. For board foot volume the regression estimators are more efficient than ŶHT for all three procedures. Point-pps sampling is always most efficient, except for ŶHT, and point-Poisson sampling is always more efficient than the modified point-pps procedure. We recommend using Ŷgr (generalized regression estimator), Ŷwr, or ŶHT for total volume and Ŷgr for board foot volume. Three variance estimators estimate the variances of the regression estimates with small bias; we recommend the simple bootstrap variance estimator because it is simple to compute and does as well as its two main competitors. It does well for ŶHT, too, for all three procedures and should be used for ŶHT in point-Ppisson sampling in preference to the Grosenbaugh variance approximation. An unbiased variance estimator is given for ŶHT with the modified point-pps procedure, but the simple bootstrap variance is equally good.
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45

Gopal, Venu, R. K. Mohanty, and Navnit Jha. "New Nonpolynomial Spline in Compression Method of for the Solution of 1D Wave Equation in Polar Coordinates." Advances in Numerical Analysis 2013 (September 30, 2013): 1–8. http://dx.doi.org/10.1155/2013/470480.

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Анотація:
We propose a three-level implicit nine point compact finite difference formulation of order two in time and four in space direction, based on nonpolynomial spline in compression approximation in -direction and finite difference approximation in -direction for the numerical solution of one-dimensional wave equation in polar coordinates. We describe the mathematical formulation procedure in detail and also discussed the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.
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46

Xu, Xiangyang, and Hao Yang. "Network method for deformation analysis of three-dimensional point cloud with terrestrial laser scanning sensor." International Journal of Distributed Sensor Networks 14, no. 11 (November 2018): 155014771881413. http://dx.doi.org/10.1177/1550147718814139.

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Анотація:
The complexity of structural materials is increasing the importance of the technology for high accuracy measurement. How to obtain the displacement information of structural feature points accurately and efficiently is the key issue of deformation analysis. In this article, displacement analysis of a composite arched structure is investigated based on the terrestrial laser scanning technique. A new method based on the measured point cloud is proposed to analyze the displacement of surficial points, resulting in not only the displacement size but also the displacement direction. The innovation lies in extracting the displacement information with a network and remapped point cloud, which is called the network method. The displacement map obtained demonstrates that the transverse displacement in the experiment plays an important role in the safety of the structure, which could not be observed and obtained by the surface approximation method. Therefore, the panorama- and pointwise displacement analysis technologies contribute to ensure the safety of increasingly complex constructions.
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47

ALIGIA, A. A., and M. AVIGNON. "ALLOY ANALOG APPROACH AND THE GUTZWILLER APPROXIMATION AS PARTICULAR CASES OF A MEAN-FIELD THEORY." International Journal of Modern Physics B 06, no. 20 (October 20, 1992): 3341–52. http://dx.doi.org/10.1142/s021797929200147x.

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Анотація:
We develop a new mean field-theory for systems with on-site correlations, like the Hubbard and Anderson models. It consists in a generalization of the saddle-point approximation to the functional integral representation proposed by Kotliar and Ruckenstein to more than one saddle point. It contains also the alloy analog approximation proposed by Hubbard as a particular case. For a half-filled Hubbard model and a model density of states appropriate for three dimensions, we obtain a metal to insulator transition as U increases. The effective Hamiltonian for the insulating phase contains two split bands (rather than only one with an extremely heavy mass) which reproduce correctly the Green’s functions of the atomic limit.
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48

Weber, Richard R., and Gideon Weiss. "Addendum to ‘On an index policy for restless bandits'." Advances in Applied Probability 23, no. 02 (June 1991): 429–30. http://dx.doi.org/10.1017/s0001867800023582.

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Анотація:
We show that the fluid approximation to Whittle's index policy for restless bandits has a globally asymptotically stable equilibrium point when the bandits move on just three states. It follows that in this case the index policy is asymptotic optimal.
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49

Weber, Richard R., and Gideon Weiss. "Addendum to ‘On an index policy for restless bandits'." Advances in Applied Probability 23, no. 2 (June 1991): 429–30. http://dx.doi.org/10.2307/1427757.

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Анотація:
We show that the fluid approximation to Whittle's index policy for restless bandits has a globally asymptotically stable equilibrium point when the bandits move on just three states. It follows that in this case the index policy is asymptotic optimal.
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50

Wapenaar, Kees, Evert Slob, and Roel Snieder. "On seismic interferometry, the generalized optical theorem, and the scattering matrix of a point scatterer." GEOPHYSICS 75, no. 3 (May 2010): SA27—SA35. http://dx.doi.org/10.1190/1.3374359.

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Анотація:
We have analyzed the far-field approximation of the Green’s function representation for seismic interferometry. By writing each of the Green’s functions involved in the correlation process as a superposition of a direct wave and a scattered wave, the Green’s function representation is rewritten as a superposition of four terms. When the scattered waves are modeled with the Born approximation, it appears that a three-term approximation of the Green’s function representation (omitting the term containing the crosscorrelation of the scattered waves) yields a nearly exact retrieval, whereas the full four-term expression leads to a significant nonphysical event. This is because the Born approximation does not conserve energy and therefore is an insufficient model to explain all aspects of seismic interferometry. We use the full four-term expression of the Green’s function representation to derive the generalized optical theorem. Unlike other recent derivations, which use stationary phase analysis, our derivation uses reciprocity theory. From the generalized optical theorem, we derive the nonlinear scattering matrix of a point scatterer. This nonlinear model accounts for primary and multiple scattering at the point scatterer and conforms with well-established scattering theory of classical waves. The model is essential to explain fully the results of seismic interferometry, even when it is applied to the response of a single point scatterer. The nonlinear scattering matrix also has implications for modeling, inversion, and migration.
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