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Journal articles on the topic 'R-function method'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 May 2022

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1

Proskurin, A. V., and A. M. Sagalakov. "Modeling duct flow by the R-function method." Journal of Applied and Industrial Mathematics 10, no. 3 (July 2016): 429–34. http://dx.doi.org/10.1134/s1990478916030133.

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2

Dmitriev, V. I., and J. G. Ingtem. "The Regularized Spline (R-Spline) Method for Function Approximation." Computational Mathematics and Modeling 30, no. 3 (July 2019): 198–206. http://dx.doi.org/10.1007/s10598-019-09447-w.

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3

Veretel'nik, V. V., V. F. Kravchenko, and V. L. Rvachev. "Design of groove waveguides by the R-function method." Measurement Techniques 36, no. 2 (February 1993): 216–19. http://dx.doi.org/10.1007/bf00977862.

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4

Hong-wei, Lu, Sun Ying, Lin Min, Li Pi-ding, and Zheng Zheng. "A probability density function method for detecting atrial fibrillation using R–R intervals." Medical Engineering & Physics 31, no. 1 (January 2009): 116–23. http://dx.doi.org/10.1016/j.medengphy.2008.04.013.

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5

Pál, Ambrus, and Endre Szabó. "The fibration method over real function fields." Mathematische Annalen 378, no. 3-4 (August 15, 2020): 993–1019. http://dx.doi.org/10.1007/s00208-020-02053-x.

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Abstract Let $$\mathbb R(C)$$ R ( C ) be the function field of a smooth, irreducible projective curve over $$\mathbb R$$ R . Let X be a smooth, projective, geometrically irreducible variety equipped with a dominant morphism f onto a smooth projective rational variety with a smooth generic fibre over $$\mathbb R(C)$$ R ( C ) . Assume that the cohomological obstruction introduced by Colliot-Thélène is the only one to the local-global principle for rational points for the smooth fibres of f over $$\mathbb R(C)$$ R ( C ) -valued points. Then we show that the same holds for X, too, by adopting the fibration method similarly to Harpaz–Wittenberg.

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6

Chrapoński, Jacek, Marian Maliński, Janusz Szala, and Jan Cwajna. "FGM Structure Characterization by Distance Functions and Systematic Scanning Method." Materials Science Forum 567-568 (December 2007): 153–56. http://dx.doi.org/10.4028/www.scientific.net/msf.567-568.153.

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The distance functions such as G(r), K(r), H(r), g(r) and systematic scanning method connected with variance analysis have been used for quantitative characterization of functionally gradient materials structures. The methods have been tested on computer generated 3D model polycrystalline structures with diverse type of gradient function. Usefulness of the presented methods for quantitative description of FGM structures has been evaluated.

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7

Uvarova, E. A. "R -function method as a supportive extension for the ritz method and least squares method." Journal of Mathematical Sciences 171, no. 4 (November 7, 2010): 466–73. http://dx.doi.org/10.1007/s10958-010-0150-4.

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8

Rvachev, V. L., and L. V. Kurpa. "Solving stability problems of plates by the R-function method." Strength of Materials 19, no. 6 (June 1987): 843–46. http://dx.doi.org/10.1007/bf01522846.

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9

Xia, Fengfei, and Shanqing Li. "R-Function and variation method for bending problem of clamped thin plate with complex shape." Advances in Mechanical Engineering 13, no. 7 (July 2021): 168781402110348. http://dx.doi.org/10.1177/16878140211034832.

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Solving ordinary thin plate bending problem in engineering, only a few analytical solutions with simple boundary shapes have been proposed. When using numerical methods (e.g. the variational method) to solve the problem, the trial functions can be found only it exhibits a simple boundary shape. The R-functions can be applied to solve the problem with complex boundary shapes. In the paper, the R-function theory is combined with the variational method to study the thin plate bending problem with the complex boundary shape. The paper employs the R-function theory to express the complex area as the implicit function, so it is easily to build the trial function of the complex shape thin plate, which satisfies with the complex boundary conditions. The variational principle and the R-function theory are introduced, and the variational equation of thin plate bending problem is derived. The feasibility and correctness of this method are verified by five numerical examples of rectangular, I-shaped, T-shaped, U-shaped, and L-shaped thin plates, and the results of this method are compared with that of other literatures and ANSYS finite element method (FEM). The results of the method show a good agreement with the calculation results of literatures and FEM.

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10

Diógenes, A. N., L. O. E. dos Santos, and C. P. Fernandes. "PARTICLE SIZE DISTRIBUTION CORRECTION METHOD USING A SIMULATED ANNEALING TECHNIQUE." Revista de Engenharia Térmica 10, no. 1-2 (December 31, 2011): 39. http://dx.doi.org/10.5380/reterm.v10i1-2.61950.

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The procedure for obtaining the particle size distribution by visual inspection of a sample involves stereological errors, given the cut of the sample. A cut particle, supposedly spherical, with radius R, will be counted as a circular particle with radius r, r≤R. The difference between r and R depends on how far from the center of the sphere the cut was performed. This introduces errors when the extrapolation of the properties from two to three dimensions during the analysis of a sample. The usual method is to correct the distribution by probabilistic functions, which have large errors. This paper presents a method to reduce the error inherent to this problem. The method is to compute a simulation of the preparation process in a sample whose structure can be described by non-penetrating spheres of various diameters which meet a known probability distribution function, for example, a log-logistic function, or even a constant function. For each distribution radius, a number of spheres is generated and virtually cut, generating a bi-dimensional (2D) distribution. The 2D curves of the spheres distribution obtained in this simulation are compared with that obtained by the experimental procedure and then the parameters of the threedimensional distribution function are adjusted until the 2D curves are similar to the experimental one using the optimization method Simulated Annealing for the curve-fitting. In future this method will be applied to the analysis of the oil reservoir rocks.

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11

BOUGAEV, ANTON, ALEKSEY URMANOV, LEFTERI TSOUKALAS, and KENNY GROSS. "METHOD OF KEY VECTORS EXTRACTION USING R-CLOUD CLASSIFIERS." New Mathematics and Natural Computation 03, no. 03 (November 2007): 419–26. http://dx.doi.org/10.1142/s1793005707000884.

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A novel method for reducing a training data set in the context of nonparametric classification is proposed. The new method is based on the method of R-clouds. The advantages of the R-cloud classification method introduced recently are being investigated. The separating boundary of the R-cloud classifier is represented using Rvachev functions. The method of key vectors extraction uses the value of the R-cloud function to quantify the disturbance of the separating boundary, which is caused by removal of one data vector from the design dataset. The R-cloud method was found instructive and practical in a number of engineering problems related to pattern classification.

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12

Ababneh, O., and N. Zomot. "New Iterative Method with Application." JOURNAL OF ADVANCES IN MATHEMATICS 20 (October 15, 2021): 424–30. http://dx.doi.org/10.24297/jam.v20i.8289.

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13

Sizova, Natal'ya Dmitrievna, and Victor Filippovich Kravchenko. "Investigation of Some Heat Conductivity Problems by the R-Function Method." Telecommunications and Radio Engineering 58, no. 5-6 (2002): 46. http://dx.doi.org/10.1615/telecomradeng.v58.i5-6.30.

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14

Wolfenden, A., JD Landes, Z. Zhou, K. Lee, and R. Herrera. "Normalization Method for Developing J-R Curves with the LMN Function." Journal of Testing and Evaluation 19, no. 4 (1991): 305. http://dx.doi.org/10.1520/jte12574j.

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15

Breslavsky, I. D., and K. V. Avramov. "Nonlinear modes of cylindrical panels with complex boundaries. R-function method." Meccanica 46, no. 4 (August 4, 2010): 817–32. http://dx.doi.org/10.1007/s11012-010-9340-x.

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16

Rvachev, V. L., L. V. Kurpa, Kh F. Nasriddinov, and A. N. Shevchenko. "The r-function method in problems of nonlinear deformation of plates." Soviet Applied Mechanics 23, no. 9 (September 1987): 861–66. http://dx.doi.org/10.1007/bf00887791.

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17

Petersen, DR, RE Link, CJFO Fortes, and FL Bastian. "A Modified Normalization Method for Developing J-R and CTOD-R Curves with the LMN Function." Journal of Testing and Evaluation 25, no. 3 (1997): 302. http://dx.doi.org/10.1520/jte11342j.

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18

Gao, Liuyang, Nae Zheng, Yinghua Tian, and Jingzhi Zhang. "Target Signal Extraction Method Based on Enhanced ICA with Reference." Mathematical Problems in Engineering 2019 (August 21, 2019): 1–12. http://dx.doi.org/10.1155/2019/4128438.

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Target signal extraction has a great potential for applications. To solve the problem of error extraction of target signals in the current constrained independent component analysis (cICA) method, an enhanced independent component analysis with reference (EICA-R) method is proposed. The new algorithm establishes a unified cost function, which combines the negative entropy contrast function and the distance metric function. The EICA-R method transforms the constrained optimization problem into unconstrained optimization problem to overcome the problem of threshold setting of distance metric function in constrained optimization problem. The theoretical analysis and simulation experiment show that the proposed EICA-R algorithm overcomes the problem of the error extraction of the existing algorithm and improves the reliability of the target signal extraction.

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19

Jiang, Wen Wen, and Zhi Bin Xie. "Research of Design Method of Product Function Analysis and Combination." Applied Mechanics and Materials 201-202 (October 2012): 886–89. http://dx.doi.org/10.4028/www.scientific.net/amm.201-202.886.

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This paper adopts methods of longitudinal comparison, classification research, expand competition field to research for design method of product function analysis and combination based on user research. It found initiative combination of product function and technique could share technology platform and spare module organization to form different varieties of product in functional detail, market orientation, and functional emphasis, avoid to carrying out fierce competition with competitor in narrow market area. It is benefit for company pursuing different strategy. R&D team should maintain validity and direction of design, analysis, and manufacturing work. High efficient pursuing situation from competitor, sale situation from user market would increase urgency and psychological pressure of R&D team and manufacturer, thus improve efficiency of research and development. The results show that fundamental goal of R&d team carries on product function analysis is tightly grasp functional use essence of future products to allocate various of resources to achieve product function index, satisfy user demand by best way.

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20

Lahav, Ofer, Donald Lynden-Bell, and Steve F. Gull. "From 2-D to 3-D by Maximum Entropy Method." Symposium - International Astronomical Union 130 (1988): 559. http://dx.doi.org/10.1017/s0074180900136885.

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We present a method of estimating distances to clusters of galaxies from twodimensional catalogues. The angular diameters (or magnitudes) of galaxies are used as distance indicators. The mapping from 2-D to 3-D is done by using a ‘diameter function’ (analogous to a luminosity function), which is based on a redshift survey from a section of the sky. The problem is formulated as follows. The number of galaxies with a metric diameter D in a volume element d3r is: where n(r) is the ‘true’ number density of galaxies at position r, n& is the mean number density of galaxies in the universe and ϕ(D)dD is the diameter function. We assume that within a narrow cone n(r) = n(r) and then express N(> θ), the number of galaxies greater than a certain angular diameter θ. In a discrete form we write the relation as: where ni is the density at the i – th distance bin and Pik is our ‘point spread function’, which is a function of the diameter function and Galactic obscuration. We express (2) in terms of χ2 statistics over the measurements, and require it to be less than a certain value. The entropy of the image is expressed as:

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21

Kravchenko, V. F., and M. A. Basarab. "Generalized method of eigenmodes and R function in problems of wave diffraction." Doklady Physics 49, no. 5 (May 2004): 270–74. http://dx.doi.org/10.1134/1.1763613.

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22

Cao, Weiming, Weizhang Huang, and Robert D. Russell. "An Error Indicator Monitor Function for an r-Adaptive Finite-Element Method." Journal of Computational Physics 170, no. 2 (July 2001): 871–92. http://dx.doi.org/10.1006/jcph.2001.6770.

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23

Bogolyubov, A. N., and M. I. Svetkin. "Application of V.L. Rvachev R-function method to solving mathematical modeling problems." Физические основы приборостроения 10, no. 3 (2021): 93–104. http://dx.doi.org/10.25210/jfop-2103-093104.

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24

González-Gaxiola, O. "Optical soliton solutions for Triki–Biswas equation by Kudryashov’s R function method." Optik 249 (January 2022): 168230. http://dx.doi.org/10.1016/j.ijleo.2021.168230.

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25

Altiparmakov, D. "Analytical Representation Of ZED-2 Reactor Geometry by Means of The R-Function Method." AECL Nuclear Review 2, no. 1 (June 1, 2013): 27–37. http://dx.doi.org/10.12943/anr.2013.00004.

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The R-function method is applied to model the geometry of the critical facility ZED-2 as an illustrative example. Each material region is represented by a real, continuous and differentiable function of spatial coordinates that is referred to as the domain function. Instead of using particular functions for individual elements, a single function is constructed to represent all spatial domains that contain the same material, for instance all fuel pins, etc. Owing to continuity and differentiability, the domain functions can be used to construct a basis for approximate solution of the related boundary-value problems. A study of the approximation ability of the domain functions is carried out using the two-group spatial neutron flux distribution in the ZED-2 facility as a model problem. The least squares method is used to determine the unknown coefficients by minimizing the discrepancy between the reference MCNP solution and a power series of domain functions. The results show that a modest number of terms in the series is able to produce a good approximation of the neutron flux distribution specified on a mesh grid of 500 x 500 points.

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26

Christoffersen, Berit, Ulla Ribel, Kirsten Raun, Valeria Golozoubova, and Giovanni Pacini. "Evaluation of different methods for assessment of insulin sensitivity in Göttingen minipigs: introduction of a new, simpler method." American Journal of Physiology-Regulatory, Integrative and Comparative Physiology 297, no. 4 (October 2009): R1195—R1201. http://dx.doi.org/10.1152/ajpregu.90851.2008.

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The use of animal models in diabetes research requires reliable tests for evaluation of insulin sensitivity and β-cell function. Minipigs are being increasingly used in metabolic research, and the aim of this study was to compare different tests and indexes for evaluation of insulin sensitivity and β-cell function in Göttingen minipigs. Hyperinsulinemic, isoglycemic clamp, intravenous (IVGTT) and oral glucose tolerance tests (OGTT), and a modified insulin tolerance test were performed in minipigs fed either low- or high-energy diet. Furthermore, the reproducibility of IVGTT-derived parameters was assessed. Previously described insulin sensitivity indexes [steady-state glucose infusion rate/glucose concentration/insulin concentration from clamp (M/G/I); oral glucose insulin sensitivity (OGIS) and ISIcomp from OGTT; SI from minimal model analysis of IVGTT; and quantitative insulin sensitivity check index from fasting values] were calculated together with an insulin sensitivity index from the modified insulin tolerance test (ISIITT) and a new simple index (S2) derived from the first 30 min of the IVGTT. β-Cell function was assessed from the IVGTT and the OGTT. Reproducibility of the IVGTT-derived parameters was calculated as median intraindividual coefficient of variation (CV%).M/G/I correlated significantly only with S2 ( P < 0.05, r = 0.54). S2 furthermore correlated with SI ( P < 0.001, r = 0.81), ISIITT ( P < 0.001, r = 0.57), and the two indexes from OGTT, ISIcomp ( P < 0.001, r = 0.78) and OGIS ( p < 0.05, r = 0.48). No correlation was found between β-cell function indexes from OGTT and IVGTT. The median CV% of the new S2 index was 13. In conclusion, the new simple index of insulin sensitivity, S2, was revealed to be useful for evaluation of insulin sensitivity in pigs.

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27

Merchela, Wassim. "One method for investigating the solvability of boundary value problems for an implicit differential equation." Russian Universities Reports. Mathematics, no. 136 (2021): 404–13. http://dx.doi.org/10.20310/2686-9667-2021-26-136-404-413.

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The article concernes a boundary value problem with linear boundary conditions of general form for the scalar differential equation f(t,x(t),x ̇(t))=y ̂(t), not resolved with respect to the derivative x ̇ of the required function. It is assumed that the function f satisfies the Caratheodory conditions, and the function y ̂ is measurable. The method proposed for studying such a boundary value problem is based on the results about operator equation with a mapping acting from a metric space to a set with distance (this distance satisfies only one axiom of a metric: it is equal to zero if and only if the elements coincide). In terms of the covering set of the function f(t,x_1,•): R→R and the Lipschitz set of the function f(t,•,x_2): R →R, conditions for the existence of solutions and their stability to perturbations of the function f generating the differential equation, as well as to perturbations of the right-hand sides of the boundary value problem: the function y ̂ and the value of the boundary condition, are obtained.

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28

Esfandiari, Aakbar, and Masoud Sanayei. "Discussion on: Function-weighted frequency response function sensitivity method for analytical model updating, by R. M. Lin." Journal of Sound and Vibration 432 (October 2018): 699–705. http://dx.doi.org/10.1016/j.jsv.2018.06.038.

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29

Li, Shan Qing, and Hong Yuan. "Application of the R-Function Theory and Variational Method for Torsion Problem with Complicated Cross-Section." Applied Mechanics and Materials 353-356 (August 2013): 3320–23. http://dx.doi.org/10.4028/www.scientific.net/amm.353-356.3320.

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The R-function theory and variational method are employed to solve the torsion problem of the bar with a complicated cross-section. When the variational method is used to solve the elastic torsion problem alone, the stress function can be set to meet the boundary condition, only with the simple cross-section such as the rectangle and ellipse. For the complicated cross-section, it is hard to find a stress function to meet the boundary condition. The R-function theory can solve the problem, and it can be used to describe the complicated cross-section by implicit function form. Introducing the R-function theory can be easy to construct the stress function that satisfied the boundary of the complicated cross-section. A numerical example demonstrates the feasibility and efficiency of the present method.

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30

Rvachev, Vladimir Logvinovich, Vadim Valerievich Torchinov, and Victor Filippovich Kravchenko. "The R-Function Method in Electrodynamic's Boundary Value Problems with Arbitrary Boundary Conditions." Telecommunications and Radio Engineering 54, no. 11-12 (2000): 3–22. http://dx.doi.org/10.1615/telecomradeng.v54.i11-12.10.

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31

Kurpa, L. V., and A. V. Chistilina. "R-function method in studying the vibrations of orthotropic shells with varying thickness." International Applied Mechanics 45, no. 7 (July 2009): 742–53. http://dx.doi.org/10.1007/s10778-009-0222-7.

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32

Kurpa, L. V., and A. V. Arkhipov. "R-function method in problems of elastoplastic bending of plates of arbitrary shape." International Applied Mechanics 35, no. 1 (January 1999): 76–80. http://dx.doi.org/10.1007/bf02682066.

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33

Graef, John, Lingju Kong, Feliz Minhós, and João Fialho. "On the lower and upper solution method for higher order functional boundary value problems." Applicable Analysis and Discrete Mathematics 5, no. 1 (2011): 133–46. http://dx.doi.org/10.2298/aadm110221010g.

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The authors consider the nth-order differential equation ?(?(u(n?1)(x)))?= f(x, u(x), ..., u(n?1)(x)), for 2?(0, 1), where ?: R? R is an increasing homeomorphism such that ?(0) = 0, n?2, I:= [0,1], and f : I ?Rn ? R is a L1-Carath?odory function, together with the boundary conditions gi(u, u?, ..., u(n?2), u(i)(1)) = 0, i = 0, ..., n? 3, gn?2 (u, u?, ..., u(n?2), u(n?2)(0), u(n?1)(0)) = 0, gn?1 (u, u?, ..., u(n?2), u(n?2)(1), u(n?1)(1)) = 0, where gi : (C(I))n?1?R ? R, i = 0, ..., n?3, and gn?2, gn?1 : (C(I))n?1?R2 ? R are continuous functions satisfying certain monotonicity assumptions. The main result establishes sufficient conditions for the existence of solutions and some location sets for the solution and its derivatives up to order (n?1). Moreover, it is shown how the monotone properties of the nonlinearity and the boundary functions depend on n and upon the relation between lower and upper solutions and their derivatives.

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34

Podhornyj, O. R., and M. V. Sidorov. "Mathematical modeling of fluid flows through the piecewise homogeneous porous medium by R-function method." Mathematical Modeling and Computing 8, no. 3 (2021): 499–508. http://dx.doi.org/10.23939/mmc2021.03.499.

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The stationary fluid flow through a piecewise homogeneous porous medium is considered under the assumption that Darcy's law holds. The mathematical model of this problem is defined as an elliptic equation for the stream function, supplemented by the second-type boundary conditions at the water boundaries and the first-type boundary conditions at the impervious to liquid boundaries. The problem statement also includes the conditions of conjugation at the separation line between two soils and the unknown value of fluid discharge, which can be established from the additional integral ratio. It is proposed to use the structure-variational method of R-functions in order to numerically analyze and solve the current problem. The complete solution structure for the boundary value problem of stream function regarding the R-functions method is established, moreover, the application of the Ritz method for approximating an unspecified structural formula component is substantiated. Then, the approximate value of the fluid discharge and the approximate solution of the original problem are found from the additional integral ratio. The computational experiment was carried out with different coefficients of permeability within the area, which has the shape of the lower half ring. It is established that as the number of coordinate functions increases, the value of fluid discharge becomes constant, indicating the convergence of the proposed method.

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Poltorak, K. "Cross-Approximation Method for Solving Dynamics Problems of Arbitrarily Shaped Plates." Journal of Applied Mechanics 57, no. 2 (June 1, 1990): 370–75. http://dx.doi.org/10.1115/1.2891999.

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This paper deals with a new method for solving dynamics problems of arbitrarily shaped plates. The method consists in cross approximation of functions satisfying solely an equation of motion and functions satisfying solely boundary conditions on irregular plate edges. This approach is applied in the paper to the case of free and forced vibration of homogeneous and sandwich plates with edges of various shapes. Functions satisfying boundary conditions are determined by the Rvachev’s R-function method. The validity of the method is discussed.

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36

Li, Ping Ping, Hong Yuan, and Shan Qing Li. "Application of the R-Function Theory and Least Square Method for Torsion Problem with H-Shaped Cross-Section." Applied Mechanics and Materials 217-219 (November 2012): 2313–16. http://dx.doi.org/10.4028/www.scientific.net/amm.217-219.2313.

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The R-function theory and least square method are employed to solve the torsion problem of the bar with H-shaped cross-section. When the least square method is used to solve the elastic torsion problem alone, the stress function can be set to meet the boundary condition, only with the simple cross-section such as the rectangle and ellipse. For the H-shaped cross-section, it is hard to find a stress function to meet the boundary condition. The R-function theory can solve the problem, and it can be used to describe H-shaped cross-section by implicit function form. Introducing the R-function theory can be easy to construct the stress function that satisfied the boundary of H-shaped cross-section. A numerical example demonstrates the feasibility and efficiency of the present method.

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37

Headd, Jeffrey J., Nathaniel Echols, Pavel V. Afonine, Ralf W. Grosse-Kunstleve, Vincent B. Chen, Nigel W. Moriarty, David C. Richardson, Jane S. Richardson, and Paul D. Adams. "Use of knowledge-based restraints in phenix.refine to improve macromolecular refinement at low resolution." Acta Crystallographica Section D Biological Crystallography 68, no. 4 (March 16, 2012): 381–90. http://dx.doi.org/10.1107/s0907444911047834.

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Traditional methods for macromolecular refinement often have limited success at low resolution (3.0–3.5 Å or worse), producing models that score poorly on crystallographic and geometric validation criteria. To improve low-resolution refinement, knowledge from macromolecular chemistry and homology was used to add three new coordinate-restraint functions to the refinement program phenix.refine. Firstly, a `reference-model' method uses an identical or homologous higher resolution model to add restraints on torsion angles to the geometric target function. Secondly, automatic restraints for common secondary-structure elements in proteins and nucleic acids were implemented that can help to preserve the secondary-structure geometry, which is often distorted at low resolution. Lastly, we have implemented Ramachandran-based restraints on the backbone torsion angles. In this method, a φ,ψ term is added to the geometric target function to minimize a modified Ramachandran landscape that smoothly combines favorable peaks identified from nonredundant high-quality data with unfavorable peaks calculated using a clash-based pseudo-energy function. All three methods show improved MolProbity validation statistics, typically complemented by a lowered R free and a decreased gap between R work and R free.

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38

Schuitemaker, Alie, Bart NM van Berckel, Marc A. Kropholler, Reina W. Kloet, Cees Jonker, Philip Scheltens, Adriaan A. Lammertsma, and Ronald Boellaard. "Evaluation of Methods for Generating Parametric (R)-[11C]PK11195 Binding Images." Journal of Cerebral Blood Flow & Metabolism 27, no. 9 (February 21, 2007): 1603–15. http://dx.doi.org/10.1038/sj.jcbfm.9600459.

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Activated microglia can be visualised using ( R)-[11C]PK11195 (1-[2-chlorophenyl]- N-methyl- N-[1-methyl-propyl]-3-isoquinoline carboxamide) and positron emission tomography (PET). In previous studies, various methods have been used to quantify ( R)-[11C]PK11195 binding. The purpose of this study was to determine which parametric method would be best suited for quantifying ( R)-[11C]PK11195 binding at the voxel level. Dynamic ( R)-[11C]PK11195 scans with arterial blood sampling were performed in 20 healthy and 9 Alzheimer's disease subjects. Parametric images of both volume of distribution ( Vd) and binding potential ( BP) were obtained using Logan graphical analysis with plasma input. In addition, BP images were generated using two versions of the basis function implementation of the simplified reference tissue model, two versions of Ichise linearisations, and Logan graphical analysis with reference tissue input. Results of the parametric methods were compared with results of full compartmental analysis using nonlinear regression. Simulations were performed to assess accuracy and precision of each method. It was concluded that Logan graphical analysis with arterial input function is an accurate method for generating parametric images of Vd. Basis function methods, one of the Ichise linearisations and Logan graphical analysis with reference tissue input provided reasonably accurate and precise estimates of BP. In pathological conditions with reduced flow rates or large variations in blood volume, the basis function method is preferred because it produces less bias and is more precise.

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Gong, Zhi Hua, Peng Wei Duan, Xu Xu, and Hai Dong Lv. "Study on the Multi-Optical Theodolites Positioning Method Based on Function Restriction." Applied Mechanics and Materials 511-512 (February 2014): 227–33. http://dx.doi.org/10.4028/www.scientific.net/amm.511-512.227.

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Aiming at the shortcoming of the classical method of optical theodolite projection intersection named ́R ́ method and traditional data fusion method named point-by-point EMBET method, this paper advances the function restriction EMBET method which is based on multi-optical theodolites. Comparing with the three methods by simulation experiment, it demonstrates that the function restriction EMBET method has higher positioning accuracy and stronger practicability than two traditional methods. Furthermore, this method supplies the important reference value for engineering application.

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BUNDSCHUH, PETER, and KEIJO VÄÄNÄNEN. "ALGEBRAIC INDEPENDENCE OF CERTAIN MAHLER FUNCTIONS AND OF THEIR VALUES." Journal of the Australian Mathematical Society 98, no. 3 (November 11, 2014): 289–310. http://dx.doi.org/10.1017/s1446788714000524.

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This paper considers algebraic independence and hypertranscendence of functions satisfying Mahler-type functional equations $af(z^{r})=f(z)+R(z)$, where $a$ is a nonzero complex number, $r$ an integer greater than 1, and $R(z)$ a rational function. Well-known results from the scope of Mahler’s method then imply algebraic independence over the rationals of the values of these functions at algebraic points. As an application, algebraic independence results on reciprocal sums of Fibonacci and Lucas numbers are obtained.

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CHAMPION, BRODIE, RICHARD L. HALL, and NASSER SAAD. "ASYMPTOTIC ITERATION METHOD FOR SINGULAR POTENTIALS." International Journal of Modern Physics A 23, no. 09 (April 10, 2008): 1405–15. http://dx.doi.org/10.1142/s0217751x08039852.

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The asymptotic iteration method (AIM) is applied to obtain highly accurate eigenvalues of the radial Schrödinger equation with the singular potential V(r) = r2+λ/rα(α,λ>0) in arbitrary dimensions. Certain fundamental conditions for the application of AIM, such as a suitable asymptotic form for the wave function, and the termination condition for the iteration process, are discussed. Several suggestions are introduced to improve the rate of convergence and to stabilize the computation. AIM offers a simple, accurate, and efficient method for the treatment of singular potentials, such as V(r), valid for all ranges of coupling λ.

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RHANIZAR, Bouchta x. "On a New Optimization Method With Constraints." Journal of Mathematics Research 12, no. 5 (August 24, 2020): 27. http://dx.doi.org/10.5539/jmr.v12n5p27.

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We consider the constrained optimization problem  defined by: $$f(x^*) = \min_{x \in  X} f(x) \eqno (1)$$ where the function  $f$ : $ \pmb{\mathbb{R}}^{n} \longrightarrow \pmb{\mathbb{R}}$ is convex  on a closed convex set X. In this work, we will give a new method to solve problem (1) without bringing it back to an unconstrained problem. We study the convergence of this new method and give numerical examples.

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Yun, Beong In. "Improving Fourier Partial Sum Approximation for Discontinuous Functions Using a Weight Function." Abstract and Applied Analysis 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/1364914.

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We introduce a generalized sigmoidal transformation wm(r;x) on a given interval [a,b] with a threshold at x=r∈(a,b). Using wm(r;x), we develop a weighted averaging method in order to improve Fourier partial sum approximation for a function having a jump-discontinuity. The method is based on the decomposition of the target function into the left-hand and the right-hand part extensions. The resultant approximate function is composed of the Fourier partial sums of each part extension. The pointwise convergence of the presented method and its availability for resolving Gibbs phenomenon are proved. The efficiency of the method is shown by some numerical examples.

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Sangiorgi, Davide. "From enhanced coinduction towards enhanced induction." Proceedings of the ACM on Programming Languages 6, POPL (January 16, 2022): 1–29. http://dx.doi.org/10.1145/3498679.

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There exist a rich and well-developed theory of enhancements of the coinduction proof method, widely used on behavioural relations such as bisimilarity. We study how to develop an analogous theory for inductive behaviour relations, i.e., relations defined from inductive observables. Similarly to the coinductive setting, our theory makes use of (semi)-progressions of the form R->F(R), where R is a relation on processes and F is a function on relations, meaning that there is an appropriate match on the transitions that the processes in R can perform in which the process derivatives are in F(R). For a given preorder, an enhancement corresponds to a sound function, i.e., one for which R->F(R) implies that R is contained in the preorder; and similarly for equivalences. We introduce weights on the observables of an inductive relation, and a weight-preserving condition on functions that guarantees soundness. We show that the class of functions contains non-trivial functions and enjoys closure properties with respect to desirable function constructors, so to be able to derive sophisticated sound functions (and hence sophisticated proof techniques) from simpler ones. We consider both strong semantics (in which all actions are treated equally) and weak semantics (in which one abstracts from internal transitions). We test our enhancements on a few non-trivial examples.

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Yamada, Hirokazu, and Yuji Nakayama. "Japanese R&D Profitability." International Journal of Systems and Service-Oriented Engineering 8, no. 2 (April 2018): 16–29. http://dx.doi.org/10.4018/ijssoe.2018040102.

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This article examines the contribution to profit from research and development (R&D) using industry-level accounting panel data for eight industries in Japan from 1986 to 2012. Problematically, simple least-squares regression estimation of production functions, where the authors specify sales or value-added as the explained variable and investment in R&D as the explanatory variable, involve endogeneity. Two possible ways of addressing this are the instrumental variables method and another that utilizes the orthogonality between error terms and appropriately time-lagged explanatory variables. The authors compare how both these methods eliminate endogeneity in the estimated production function and thus improve the accuracy of estimates of the rate of return on R&D. These findings thus contribute to the managerial decision-making process on R&D strategy by providing insights into the precise contribution of firm R&D to profit.

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Zaprawa, Paweł, Anna Futa, and Magdalena Jastrzębska. "On Coefficient Functionals for Functions with Coefficients Bounded by 1." Mathematics 8, no. 4 (April 1, 2020): 491. http://dx.doi.org/10.3390/math8040491.

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In this paper, we discuss two well-known coefficient functionals a 2 a 4 - a 3 2 and a 4 - a 2 a 3 . The first one is called the Hankel determinant of order 2. The second one is a special case of Zalcman functional. We consider them for functions in the class Q R ( 1 2 ) of analytic functions with real coefficients which satisfy the condition ( ) f ( z ) z > 1 2 for z in the unit disk Δ . It is known that all coefficients of f ∈ Q R ( 1 2 ) are bounded by 1. We find the upper bound of a 2 a 4 - a 3 2 and the bound of | a 4 - a 2 a 3 | . We also consider a few subclasses of Q R ( 1 2 ) and we estimate the above mentioned functionals. In our research two different methods are applied. The first method connects the coefficients of a function in a given class with coefficients of a corresponding Schwarz function or a function with positive real part. The second method is based on the theorem of formulated by Szapiel. According to this theorem, we can point out the extremal functions in this problem, that is, functions for which equalities in the estimates hold. The obtained estimates significantly extend the results previously established for the discussed classes. They allow to compare the behavior of the coefficient functionals considered in the case of real coefficients and arbitrary coefficients.

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Regmi, Rajendra Prasad. "Application of differential equation in L-R and C-R circuit analysis by classical method." Janapriya Journal of Interdisciplinary Studies 5 (July 21, 2017): 114–23. http://dx.doi.org/10.3126/jjis.v5i0.17844.

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The paper deals with the analysis of L-R and C-R circuit by using linear differential equation of first order. A circuit containing an inductance L or a capacitor C and resistor R with current and voltage variable given by differential equation. The general solution of differential equation have two parts complementary function (C.F) and particular integral(P.I) in which C.F. represent transient response and P.I. represent steady response. The general solution of differential equation represent the complete response of network. In this connection, this paper includes L-R, C-R circuit and ordinary differential equation of first order and its solution. Janapriya Journal of Interdisciplinary Studies, Vol. 5 (December 2016), page: 114-123

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Semerich, Yuriy. "ANALYTICAL MODELLING OF PERFORATED GEOMETRICAL DOMAINS BY THE R-FUNCTIONS." Mathematical Modelling and Analysis 25, no. 3 (July 8, 2020): 490–504. http://dx.doi.org/10.3846/mma.2020.11174.

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This paper deals with the construction of boundary equations for geometric domains with perforation. Different types of perforated geometric domains are considered. The R-functions method for analytical modelling of perforated geometrical domains is used. For all constructed equations, function plots are obtained.

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Riello, P., P. Canton, and G. Fagherazzi. "A semi-empirical asymmetry function for X-ray diffraction peak profiles." Powder Diffraction 10, no. 3 (September 1995): 204–6. http://dx.doi.org/10.1017/s0885715600014743.

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A new semi-empirical approximation for the asymmetry function to be used in the X-ray Rietveld analysis has resulted in lower values of the so-called goodness-of-fit index, defined as S = Rwp/Rexp, where Rwp is the R-weighted pattern and Rexp is the R-expected [R. A. Young, The Rietveld Method (Oxford U.P., Oxford, 1993)], with respect to the corresponding values obtained with the classical approximation used by Rietveld in his fundamental paper. A comparing test of the two asymmetry functions was carried out for the cubic Y2O3 and for αAl2O3 using either pseudo-Voigt or Pearson VII symmetrical functions and two diffractometers. As in the case of the Rietveld approximation, the present one, which employs an exponential function, is optimized using only one fitting parameter. Experimentally, the asymmetry can be considerably diminished by using Soller slits with a small opening angle (≤2°).

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50

Shklennik, Maria A., and Alexander N. Moiseev. "Method of Markovian summation for study the repeated flow in queueing tandem M|GI|∞ → GI|∞." Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 21, no. 1 (February 24, 2021): 125–37. http://dx.doi.org/10.18500/1816-9791-2021-21-1-125-137.

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The paper presents a mathematical model of queueing tandem M|GI|∞ → GI|∞ with feedback. The service times at the first stage are independent and identically distributed (i.i.d.) with an arbitrary distribution function B1(x). Service times at the second stage are i.i.d. with an arbitrary distribution function B2(x). The problem is to determine the probability distribution of the number of repeated customers (r-flow) during fixed time period. To solve this problem, the Markov summation method was used, which is based on the consideration of Markov processes and the solution of the Kolmogorov equation. In the course of the solution, the so-called local r-flow was studied — the number of r-flow calls generated by one incoming customer received by the system. As a result, an expression is obtained for the characteristic probability distribution function of the number of calls in the local r-flow, which can be used to study queuing systems with a similar service discipline and non-Markov incoming flows. As a result of the study, an expression is obtained for the characteristic probability distribution function of the number of repeated calls to the system at a given time interval during non-stationary regime, which allows one to obtain the probability distribution of the number of calls in the flow under study, as well as its main probability characteristics.

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