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Journal articles on the topic 'R-function method'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 July 2025

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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 (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 (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 (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 (2009): 116–23. http://dx.doi.org/10.1016/j.medengphy.2008.04.013.

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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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6

Pál, Ambrus, and Endre Szabó. "The fibration method over real function fields." Mathematische Annalen 378, no. 3-4 (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

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7

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 (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 th

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8

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 (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 p

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9

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 (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 practic

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10

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

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11

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 (2010): 466–73. http://dx.doi.org/10.1007/s10958-010-0150-4.

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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 (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 (1987): 861–66. http://dx.doi.org/10.1007/bf00887791.

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17

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 fun

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18

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(

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19

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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20

Stetsyuk, Petro, Aleksandr Pylypovskyi, and Olha Khomiak. "GNU Octave and Python Implementation of Shor's r-Algorithm with Adaptive Step Control." Cybernetics and Computer Technologies, no. 3 (November 29, 2022): 98–112. http://dx.doi.org/10.34229/2707-451x.22.3.10.

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r-algorithms, or subgradient methods with dilation of space in the direction of the difference of two sequential subgradients, were proposed by N.Z.Shor in 1970 in his doctoral thesis. Respective software implementations proved to be competitive with the most effective methods for smooth ill-conditioned problems, both in terms of reliability and calculation time and accuracy of results. The article is devoted to the description of two software implementations of Shor's r-algorithm modification with a constant coefficient of space dilation and adaptive step control. The first program is impleme

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21

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

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22

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 (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

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23

Langarshoev, Mukhtor R. "The best approximation of analytic in a unit circle functions in the Bergman weight space B_(2,μ)". Russian Universities Reports. Mathematics, № 145 (2024): 65–76. http://dx.doi.org/10.20310/2686-9667-2024-29-145-65-76.

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The paper studies the issues of the best approximation of analytical functions in the Bergman weight space B_(2,μ). In this space, for best approximations of functions analytic in the circle by algebraic complex polynomials we obtain the exact inequalities by means of generalized modules of continuity of higher order derivatives Ω_m (z^r f^((r) ),t),m∈N,r∈Z. For classes of functions analytic in the unit circle defined by the characteristic Ω_m (z^r f^((r) ),t), and the majorant Φ, the exact values of some n-widths are calculated. When proving the main results of this work, we use methods for s

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24

Ngoc Huy, Dinh Tran, Pham Anh Dung, Le Ngoc Nuong, Le Thi Han, Dinh Tran Ngoc Hien, and Pham Hung Nhan. "Analysis of Relation Between Economic Innovation Models and R&D Function." Mediterranean Journal of Basic and Applied Sciences 08, no. 03 (2024): 143–51. http://dx.doi.org/10.46382/mjbas.2024.8315.

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The goal of this article focuses on Analysis of Relation between Economic Innovation Models and R&D Function in recent years. Method: Methodology includes Qualitative research method: synthesis and inductive methods. George, M., et al. (2009) mentioned some variables can be considered for R&D such as: R&D expenses, R&D personnel and patents of new tech. We also expand SWOT model by adding Value part analysis on it. Results: Authors stated opportunities for values adding including but not limited to: R&D will emphasize more the vital roles of technological change in improvin

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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 (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 bo

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26

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

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27

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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28

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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29

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

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30

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 (2001): 871–92. http://dx.doi.org/10.1006/jcph.2001.6770.

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31

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-

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32

Liu, Chein-Shan, Chih-Wen Chang, and Chung-Lun Kuo. "Memory-Accelerating Methods for One-Step Iterative Schemes with Lie Symmetry Method Solving Nonlinear Boundary-Value Problem." Symmetry 16, no. 1 (2024): 120. http://dx.doi.org/10.3390/sym16010120.

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In this paper, some one-step iterative schemes with memory-accelerating methods are proposed to update three critical values f′(r), f″(r), and f‴(r) of a nonlinear equation f(x)=0 with r being its simple root. We can achieve high values of the efficiency index (E.I.) over the bound 22/3=1.587 with three function evaluations and over the bound 21/2=1.414 with two function evaluations. The third-degree Newton interpolatory polynomial is derived to update these critical values per iteration. We introduce relaxation factors into the Dzˇunic´ method and its variant, which are updated to render four

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33

Wang, Tianji, and Qingdao Huang. "Research on Three-Dimensional Extension of Barzilai-Borwein-like Method." Mathematics 13, no. 2 (2025): 215. https://doi.org/10.3390/math13020215.

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The Barzilai-Borwein (BB) method usually uses BB stepsize for iteration so as to eliminate the line search step in the steepest descent method. In this paper, we modify the BB stepsize and extend it to solve the optimization problems of three-dimensional quadratic functions. The discussion is divided into two cases. Firstly, we study the case where the coefficient matrix of the quadratic term of quadratic function is a special third-order diagonal matrix and prove that using the new modified stepsize, this case is R-superlinearly convergent. In addition to that, we extend it to n-dimensional c

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34

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 m

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35

Headd, Jeffrey J., Nathaniel Echols, Pavel V. Afonine, et al. "Use of knowledge-based restraints in phenix.refine to improve macromolecular refinement at low resolution." Acta Crystallographica Section D Biological Crystallography 68, no. 4 (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

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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 theo

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37

Yang, Zhipeng, Wei Zhang, and Fukun Zhao. "Existence and concentration results for fractional Schrodinger-Poisson system via penalization method." Electronic Journal of Differential Equations 2021, no. 01-104 (2021): 14. http://dx.doi.org/10.58997/ejde.2021.14.

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This article concerns the positive solutions for the fractional Schrodinger-Poisson system $$\displaylines{ \varepsilon^{2s}(-\Delta)^su+V(x)u+\phi u=f(u)\quad \text{in }\mathbb{R}^3,\cr \varepsilon^{2t}(-\Delta)^t\phi=u^2\quad \text{in }\mathbb{R}^3, }$$ where \(\varepsilon>0\) is a small parameter, \((-\Delta)^\alpha\) denotes the fractional Laplacian of orders \(\alpha=s,t\in(3/4,1)\), \(V\in C(\mathbb{R}^3,\mathbb{R})\) is the potential function and \(f:\mathbb{R}\to\mathbb{R}\) is continuous and subcritical. Under a local condition imposed on the potential function, we relate the numbe

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38

Poltorak, K. "Cross-Approximation Method for Solving Dynamics Problems of Arbitrarily Shaped Plates." Journal of Applied Mechanics 57, no. 2 (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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39

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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40

Bhalgamiya, Bhavika, and Mark A. Novotny. "Exact solutions for the inverse problem of the time-independent Schrödinger equation." American Journal of Physics 92, no. 12 (2024): 975–79. http://dx.doi.org/10.1119/5.0172824.

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We introduce an “inverse method” for solving the time-independent Schrödinger equation. Rather than derive wave functions that are solutions for a given external potential V(r→), we ask the inverse question of which V(r→) will have a given probability density function P(r→). Several examples of ground states in one, two, and three dimensions are presented for both well-known and more exotic probability density functions in position space.

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41

BUNDSCHUH, PETER, and KEIJO VÄÄNÄNEN. "ALGEBRAIC INDEPENDENCE OF CERTAIN MAHLER FUNCTIONS AND OF THEIR VALUES." Journal of the Australian Mathematical Society 98, no. 3 (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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42

Sangiorgi, Davide. "From enhanced coinduction towards enhanced induction." Proceedings of the ACM on Programming Languages 6, POPL (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

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43

Wang, G., T. L. Rhodes, and W. A. Peebles. "Analysis method for calculating radial correlation length of electron temperature turbulence from correlation electron cyclotron emission radiometer." Review of Scientific Instruments 93, no. 11 (2022): 113511. http://dx.doi.org/10.1063/5.0101680.

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The radial correlation length ( L r) is one of the essential quantities to measure in order to more fully characterize and understand turbulence and anomalous transport in magnetic fusion plasmas. The analysis method for calculating L r of electron temperature (Te) turbulence from correlation electron cyclotron emission (correlation ECE or CECE) radiometer measurements has not been fully developed partly due to the fact that the turbulent electron temperature fluctuations are generally imbedded in much larger amplitude thermal noise, which leads to a greatly reduced cross correlation coefficie

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44

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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45

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 (1999): 76–80. http://dx.doi.org/10.1007/bf02682066.

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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 (2009): 742–53. http://dx.doi.org/10.1007/s10778-009-0222-7.

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Rinki, Hada. "A Study Of Correlation Of Pulmonary Functions And Percentage Of Body Fat In Normal And Overweight Medical Students." International Journal of Basic and Applied Physiology 1, no. 1 (2021): 61–95. https://doi.org/10.5281/zenodo.4468641.

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Background & Objectives: Clinically less severe obesity like overweight is not generally thought to have significant effect on ventilator function. The purpose of our study is to explore effects of body fat percentage and its distribution on ventilatory functions. We hypothesized that there is significant difference in Pulmonary Function among normal and overweight young healthy adults. Objectives: To assess & compare the difference in Pulmonary Function Tests among normal and overweight young healthy adults and to detect the correlation between Pulmonary Function Tests and Body fat pe

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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 (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 w

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Zhang, Guangxun. "The additional proof and application of Cauchy-Riemann Equation." Highlights in Science, Engineering and Technology 38 (March 16, 2023): 158–67. http://dx.doi.org/10.54097/hset.v38i.5801.

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As far back as the seventeenth century, Newton and Leibniz introduced and refined the idea of calculus, and the concepts of derivative and differentiation gradually entered the mathematical world as powerful tools. However, after the appearance of the theory of complex functions in the 18th century, the conventional methods used to analyze the properties of complex functions were somewhat limited. Thus, mathematicians Cauchy and Riemann came up with the idea of the “C-R equation” and provided the necessary and sufficient conditions in derivable complex functions based on the research done by d

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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

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