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Journal articles on the topic 'Newton fractals'

Author: Grafiati

Published: 30 May 2022

Last updated: 31 July 2025

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1

Jovanovic, V. T., and K. Kazerounian. "Using Chaos to Obtain Global Solutions in Computational Kinematics." Journal of Mechanical Design 120, no. 2 (1998): 299–304. http://dx.doi.org/10.1115/1.2826972.

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In this paper we examine the sensitive dependence on the initial conditions of the Newton-Raphson search technique. It is demonstrated that this sensitivity has a fractal nature which can be effectively utilized to find all solutions to a nonlinear equation. The developed technique uses an important feature of fractals to preserve shape of basins of attraction on infinitely small scales.

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2

P.Soman, K., Manu Unni V.G, Praveen Krishnan, and V. Sowmya. "Enhancing Computational Thinking with Spreadsheet and Fractal Geometry: Part 2 Root-finding using Newton Method and Creation of Newton Fractals." International Journal of Computer Applications 55, no. 14 (2012): 9–15. http://dx.doi.org/10.5120/8821-2742.

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3

Triana Laverde, Juan Gabriel. "On the Newton-Raphson method and its modifications." Ciencia en Desarrollo 14, no. 2 (2023): 75–80. http://dx.doi.org/10.19053/01217488.v14.n2.2023.15157.

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The Newton-Raphson method, also known as Newton's method, is a method for finding successively better approximations to the roots of a real-valued function, starting with an initial guess, being useful even for generating fractals when we consider complex functions. It is a fast method, but convergence is not guaranteed, which is the reason why several modifications of that method have been proposed. Here we present some modifications of the Newton-Raphson method, and we study the convergence of those methods through cases.

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4

Cartwright, Julyan H. E. "Newton maps: fractals from Newton's method for the circle map." Computers & Graphics 23, no. 4 (1999): 607–12. http://dx.doi.org/10.1016/s0097-8493(99)00078-3.

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5

He, Yang-Hui. "Polynomial Roots and Calabi-Yau Geometries." Advances in High Energy Physics 2011 (2011): 1–15. http://dx.doi.org/10.1155/2011/719672.

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The examination of roots of constrained polynomials dates back at least to Waring and to Littlewood. However, such delicate structures as fractals and holes have only recently been found. We study the space of roots to certain integer polynomials arising naturally in the context of Calabi-Yau spaces, notably Poincaré and Newton polynomials, and observe various salient features and geometrical patterns.

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6

Carlson, Paul W. "Two artistic orbit trap rendering methods for Newton M-set fractals." Computers & Graphics 23, no. 6 (1999): 925–31. http://dx.doi.org/10.1016/s0097-8493(99)00123-5.

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7

Lazorenko, O., and L. Chernogor. "FRACTAL RADIOPHYSICS. PART 3. FRACTIONAL CALCULUS IN ELECTRODYNAMICS." Radio physics and radio astronomy 29, no. 1 (2024): 046–67. http://dx.doi.org/10.15407/rpra29.01.046.

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Subject and Purpose. At the beginning of the 21st century, a fundamentally new scientific direction was formed, currently known as fractal radiophysics. The present work is an overview of the principal theoretical and practical ideas concerning "fractalization" in radio physics. The purpose is a systematic presentation of the main practical results suitable for application of the fractional calculus in modern theoretical radiophysics. Methods and Methodology. The basic theoretical principles of fractional calculus are outlined in a structured form. Results of applying fractional calculus metho

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Christian, J. M., and H. A. J. Middleton-Spencer. "On the Nth Roots of –1 and Complex Basin Boundaries: Fractals from Newton–Raphson." College Mathematics Journal 51, no. 2 (2020): 95–104. http://dx.doi.org/10.1080/07468342.2020.1703452.

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9

Wang, Xiaofeng, and Wenshuo Li. "A Class of Sixth-Order Iterative Methods for Solving Nonlinear Systems: The Convergence and Fractals of Attractive Basins." Fractal and Fractional 8, no. 3 (2024): 133. http://dx.doi.org/10.3390/fractalfract8030133.

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In this paper, a Newton-type iterative scheme for solving nonlinear systems is designed. In the process of proving the convergence order, we use the higher derivatives of the function and show that the convergence order of this iterative method is six. In order to avoid the influence of the existence of higher derivatives on the proof of convergence, we mainly discuss the convergence of this iterative method under weak conditions. In Banach space, the local convergence of the iterative scheme is established by using the ω-continuity condition of the first-order Fréchet derivative, and the appl

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10

Akgül, Ali, and David Grow. "Fractal Newton Methods." Mathematics 11, no. 10 (2023): 2277. http://dx.doi.org/10.3390/math11102277.

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We introduce fractal Newton methods for solving f(x)=0 that generalize and improve the classical Newton method. We compare the theoretical efficacy of the classical and fractal Newton methods and illustrate the theory with examples.

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11

Sahari, M. L., and I. Djellit. "Fractal Newton basins." Discrete Dynamics in Nature and Society 2006 (2006): 1–16. http://dx.doi.org/10.1155/ddns/2006/28756.

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The dynamics of complex cubic polynomials have been studied extensively in the recent years. The main interest in this work is to focus on the Julia sets in the dynamical plane, and then is consecrated to the study of several topics in more detail. Newton's method is considered since it is the main tool for finding solutions to equations, which leads to some fantastic images when it is applied to complex functions and gives rise to a chaotic sequence.

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Terán Tarapués, Juneth Andrea, and Catalina María Rúa Alvarez. "El Método de Newton para raíces complejas. Fractales en el problema de Cayley." Revista EIA 15, no. 29 (2018): 97–108. http://dx.doi.org/10.24050/reia.v15i29.1131.

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Cuando la búsqueda de la solución de un problema de aplicación implica la resolución de ecuaciones no lineales se hace uso de métodos numéricos. Siendo el método de Newton uno de los más usados debido a su versatilidad y agilidad, es de gran interés emplearlo especialmente para aproximar soluciones de sistemas de ecuaciones no lineales. Solucionar ecuaciones con variable compleja a través del método de Newton tiene una aplicación muy interesante en el campo de los fractales como es la del problema de Cayley y las figuras fractales que se producen a partir de la convergencia, divergencia e incl

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Bray, Kasey, Jerry Dwyer, Roger W. Barnard, and G. Brock Williams. "Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions." International Journal of Mathematics and Mathematical Sciences 2020 (April 23, 2020): 1–10. http://dx.doi.org/10.1155/2020/1853467.

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The dynamical systems of trigonometric functions are explored, with a focus on tz=tanz and the fractal image created by iterating the Newton map, Ftz, of tz. The basins of attraction created from iterating Ftz are analyzed, and some bounds are determined for the primary basins of attraction. We further prove x- and y-axis symmetry of the Newton map and explore the nature of the fractal images.

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Chen, Huijuan, and Xintao Zheng. "Improved Newton Iterative Algorithm for Fractal Art Graphic Design." Complexity 2020 (November 27, 2020): 1–11. http://dx.doi.org/10.1155/2020/6623049.

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Fractal art graphics are the product of the fusion of mathematics and art, relying on the computing power of a computer to iteratively calculate mathematical formulas and present the results in a graphical rendering. The selection of the initial value of the first iteration has a greater impact on the final calculation result. If the initial value of the iteration is not selected properly, the iteration will not converge or will converge to the wrong result, which will affect the accuracy of the fractal art graphic design. Aiming at this problem, this paper proposes an improved optimization me

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15

Jeong, Soyeong, and Pilwon Kim. "A Population-Based Optimization Method Using Newton Fractal." Complexity 2019 (February 3, 2019): 1–9. http://dx.doi.org/10.1155/2019/5379301.

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We propose a deterministic population-based method for a global optimization, a Newton particle optimizer (NPO). The algorithm uses the Newton method with a guiding function and drives particles toward the current best positions. The particles’ movements are influenced by the fractal nature of the Newton method and are greatly diversified in the approach to the temporal best optimums. As a result, NPO generates a wide variety of searching paths, achieving a balance between exploration and exploitation. NPO differs from other metaheuristic methods in that it combines an exact mathematical opera

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Alsulami, Amer, Rasmiyah Alharb, Tahani Albogami, Nidal Eljaneid, Haroon Adam, and Sayed Saber. "Controlled chaos of a fractal-fractional Newton-Leipnik system." Thermal Science 28, no. 6 Part B (2024): 5153–60. https://doi.org/10.2298/tsci2406153a.

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In this study, fractal-fractional derivatives (FFD) with exponential decay laws kernels are applied to explain the chaotic behavior of a Newton-Leipnik system (NLS) with constant and time-varying derivatives. By using Caputo-Fabrizio fractal-fractional derivatives, fixed point theory verifies their existence and uniqueness. Using the implicit finite difference method, the Caputo-Fabrizio (CF) FF NLS is numerically solved. There are several numerical examples presented to illustrate the method?s applicability and efficiency. The CF fractal-fractional solutions are more general as compared to cl

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17

Singh, Manoj K., and Ioannis K. Argyros. "The Dynamics of a Continuous Newton-like Method." Mathematics 10, no. 19 (2022): 3602. http://dx.doi.org/10.3390/math10193602.

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The objective of the current work is to invent and introduce the continuous version of Newton’s method. This scheme is used to establish some interesting properties with examples. We have plotted the fractal pattern graphs for a Newton-like method and a Damped Newton-like method in the discrete case and hence we have introduced a new concept of streamline for the continuous version of the Newton-like method. The graph and streamlines of these patterns are in agreement with numerical results and describe the convergence and stability of the proposed method to different roots when the Newton met

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18

Deng, Jiao-Jiao, and Hsiao-Dong Chiang. "Convergence Region of Newton Iterative Power Flow Method: Numerical Studies." Journal of Applied Mathematics 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/509496.

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Power flow study plays a fundamental role in the process of power system operation and planning. Of the several methods in commercial power flow package, the Newton-Raphson (NR) method is the most popular one. In this paper, we numerically study the convergence region of each power flow solution under the NR method. This study of convergence region provides insights of the complexity of the NR method in finding power flow solutions. Our numerical studies confirm that the convergence region of NR method has a fractal boundary and find that this fractal boundary of convergence regions persists u

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19

Zhang, Wei, Xiao Chun Tang, and Jing Wang. "Research on a Class of Multi Parameter Fractal Interpolation Curved Surface Based on Iterative Function Image Generating Method." Applied Mechanics and Materials 687-691 (November 2014): 1457–61. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.1457.

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This paper extends the polynomial function to double logarithmic function, constructing a class of multi parameters iterative function, and uses this function to calculate the fractal interpolated surface for given interpolation points, and establishes the iterative function mathematical model of multi parameters fractal interpolation. In order to verify the effectiveness and reliability of this proposed model algorithm, this paper uses MATLAB numerical simulation method to calculate, and programs the Newton iterative function of multi parameters fractal interpolation surface, finally gets cal

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20

Cloutier, Aimée, Jerry Dwyer, Roger W. Barnard, William D. Stone, and G. Brock Williams. "Dynamics of Iterations of the Newton Map of sin(z)." Symmetry 16, no. 2 (2024): 162. http://dx.doi.org/10.3390/sym16020162.

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The dynamical systems of trigonometric functions are explored, with a focus on sz=sin(z) and the fractal image created by iterating the Newton map, Fs(z), of s(z). The basins of attraction created from iterating Fs(z) are analyzed, and some bounds are determined for the primary basins of attraction. We further prove x and y-axis symmetry of the Newton map as well as some interesting results on periodic points on the real axis.

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21

Najafi, Hashem, Sina Etemad, Nichaphat Patanarapeelert, Joshua Kiddy K. Asamoah, Shahram Rezapour, and Thanin Sitthiwirattham. "A Study on Dynamics of CD4+ T-Cells under the Effect of HIV-1 Infection Based on a Mathematical Fractal-Fractional Model via the Adams-Bashforth Scheme and Newton Polynomials." Mathematics 10, no. 9 (2022): 1366. http://dx.doi.org/10.3390/math10091366.

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In recent decades, AIDS has been one of the main challenges facing the medical community around the world. Due to the large human deaths of this disease, researchers have tried to study the dynamic behaviors of the infectious factor of this disease in the form of mathematical models in addition to clinical trials. In this paper, we study a new mathematical model in which the dynamics of CD4+ T-cells under the effect of HIV-1 infection are investigated in the context of a generalized fractal-fractional structure for the first time. The kernel of these new fractal-fractional operators is of the

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22

Zotos, Euaggelos E., Fredy L. Dubeibe, and A. Riaño-Doncel. "Fractal Basins of Convergence of a Seventh-Order Generalized Hénon–Heiles Potential." Advances in Astronomy 2021 (July 13, 2021): 1–11. http://dx.doi.org/10.1155/2021/6665238.

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This article aims to investigate the points of equilibrium and the associated convergence basins in a seventh-order generalized Hénon–Heiles potential. Using the well-known Newton–Raphson iterator, we numerically locate the positions of the points of equilibrium, while we also obtain their linear stability. Furthermore, we demonstrate how the two variable parameters, entering the generalized Hénon–Heiles potential, affect the convergence dynamics of the system as well as the fractal degree of the basin diagrams. The fractal degree is derived by computing the (boundary) basin entropy as well as

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23

Marín, María José, Fernando Giménez, and Juan A. Monsoriu. "Generación de fractales a partir del método de Newton." Modelling in Science Education and Learning 6 (June 2, 2013): 137. http://dx.doi.org/10.4995/msel.2013.1846.

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24

Bisoi, A. K. "Newton raphson method, scaling at fractal boundaries and mathematica." Mathematical and Computer Modelling 21, no. 10 (1995): 91–102. http://dx.doi.org/10.1016/0895-7177(95)00073-b.

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25

Ştefănuţ, Anne Claudia, Ştefan Ţălu, Viorel Miclăuş, Adriana Mureşan, Remus Moldovan, and Bianca Szabo. "Postnatal Development of the Retina in Rats Exposed to Hyperoxia: A Fractal Analysis." ISRN Biomedical Imaging 2013 (April 15, 2013): 1–6. http://dx.doi.org/10.1155/2013/589327.

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Purpose. The aim of this study was to investigate and quantify changes in the newborn rats retinal layers during the hyperoxia (80% O2) exposure using fractal analysis. Materials and Methods. This study was conducted on two groups of 20 newborn rats: a control (normal) group (10 rats) and an experimental group (10 rats). The control group was composed of 10 newborn rats, which were placed at 12 hours after birth, in a pediatric incubator, together with their mother, in conditions of normoxia for 21 days. The experimental group consisted of 10 newborn rats, which were placed at 12 hours after b

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Srivastava, Hari M., Khaled Mohammed Saad, and Walid M. Hamanah. "Certain New Models of the Multi-Space Fractal-Fractional Kuramoto-Sivashinsky and Korteweg-de Vries Equations." Mathematics 10, no. 7 (2022): 1089. http://dx.doi.org/10.3390/math10071089.

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The main objective of this paper is to introduce and study the numerical solutions of the multi-space fractal-fractional Kuramoto-Sivashinsky equation (MSFFKS) and the multi-space fractal-fractional Korteweg-de Vries equation (MSFFKDV). These models are obtained by replacing the classical derivative by the fractal-fractional derivative based upon the generalized Mittag-Leffler kernel. In our investigation, we use the spectral collocation method (SCM) involving the shifted Legendre polynomials (SLPs) in order to reduce the new models to a system of algebraic equations. We then use one of the kn

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27

Luo, You Xin, and Ling Fang Li. "Fractal–Based Newton Method and Mechanism Synthesis & Approximate Synthesis." Applied Mechanics and Materials 155-156 (February 2012): 420–23. http://dx.doi.org/10.4028/www.scientific.net/amm.155-156.420.

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Many questions in natural science and engineering are transformed into nonlinear equations to be found, Newton iterative method is an important technique to one dimensional and multidimensional variables and iterative process exhibits sensitive dependence on initial guess point. For the first time, utilizing a fractal iteration system to produce initial value, a new method to find all solutions of the nonlinear equations was proposed. The numerical examples in linkage synthesis and approximate synthesis show that the method is correct and effective.

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28

Ma, Ning. "SA-enhanced PSO Newton algorithm for fractal art graphic design." International Journal of Information and Communication Technology 26, no. 18 (2025): 86–99. https://doi.org/10.1504/ijict.2025.146692.

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29

Meftah, Badreddine, Wedad Saleh, Muhammad Uzair Awan, Loredana Ciurdariu, and Abdelghani Lakhdari. "Hybrid Integral Inequalities on Fractal Set." Axioms 14, no. 5 (2025): 358. https://doi.org/10.3390/axioms14050358.

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In this study, we introduce a new hybrid identity that effectively combines Newton–Cotes and Gauss quadrature, allowing us to recover well-known formulas such as Simpson’s second rule and the left- and right-Radau two-point rules, among others. Building upon this flexible framework, we establish several new biparametrized fractal integral inequalities for functions whose local fractional derivatives are of a generalized convex type. In addition to employing tools from local fractional calculus, our approach utilizes the Hölder inequality, the power mean inequality, and a refined version of the

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Addai, Emmanuel, Adejimi Adeniji, Olumuyiwa J. Peter, Janet O. Agbaje, and Kayode Oshinubi. "Dynamics of Age-Structure Smoking Models with Government Intervention Coverage under Fractal-Fractional Order Derivatives." Fractal and Fractional 7, no. 5 (2023): 370. http://dx.doi.org/10.3390/fractalfract7050370.

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The rising tide of smoking-related diseases has irreparably damaged the health of both young and old people, according to the World Health Organization. This study explores the dynamics of the age-structure smoking model under fractal-fractional (F-F) derivatives with government intervention coverage. We present a new fractal-fractional model for two-age structure smokers in the Caputo–Fabrizio framework to emphasize the potential of this operator. For the existence-uniqueness criterion of the given model, successive iterative sequences are defined with limit points that are the solutions of o

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Rezapour, Shahram, Sina Etemad, Joshua Kiddy K. Asamoah, Hijaz Ahmad, and Kamsing Nonlaopon. "A mathematical approach for studying the fractal-fractional hybrid Mittag-Leffler model of malaria under some control factors." AIMS Mathematics 8, no. 2 (2023): 3120–62. http://dx.doi.org/10.3934/math.2023161.

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<abstract><p>Malaria disease, which is of parasitic origin, has always been one of the challenges for human societies in areas with poor sanitation. The lack of proper distribution of drugs and lack of awareness of people in such environments cause us to see many deaths every year, especially in children under the age of five. Due to the importance of this issue, in this paper, a new five-compartmental $ (c_1, c_2) $-fractal-fractional $ \mathcal{SIR} $-$ \mathcal{SI} $-model of malaria disease for humans and mosquitoes is presented. We use the generalized Mittag-Leffler fractal-fr

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NAMAZI, HAMIDREZA, and SAJAD JAFARI. "ESTIMATING OF BRAIN DEVELOPMENT IN NEWBORNS BY FRACTAL ANALYSIS OF SLEEP ELECTROENCEPHALOGRAPHIC (EEG) SIGNAL." Fractals 27, no. 03 (2019): 1950021. http://dx.doi.org/10.1142/s0218348x1950021x.

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Analysis of the brain development is one of the major research areas in human neuroscience. In order to analyze the human brain development, scientists employ different brain imaging techniques. One of the typical techniques to measure the brain activity is electroencephalography (EEG). In this paper, we do complexity analysis on the EEG signal recorded from the newborns during their sleep, in different weeks of post conception. We analyze how the nonlinear structure of EEG signal changes for newborns with their ages by using fractal theory. The result of our analysis showed that the EEG signa

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Sharma, Janak Raj, Deepak Kumar, and Carlo Cattani. "An Efficient Class of Weighted-Newton Multiple Root Solvers with Seventh Order Convergence." Symmetry 11, no. 8 (2019): 1054. http://dx.doi.org/10.3390/sym11081054.

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In this work, we construct a family of seventh order iterative methods for finding multiple roots of a nonlinear function. The scheme consists of three steps, of which the first is Newton’s step and last two are the weighted-Newton steps. Hence, the name of the scheme is ‘weighted-Newton methods’. Theoretical results are studied exhaustively along with the main theorem describing convergence analysis. Stability and convergence domain of the proposed class are also demonstrated by means of using a graphical technique, namely, basins of attraction. Boundaries of these basins are fractal like sha

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Kongson, Jutarat, Chatthai Thaiprayoon, Apichat Neamvonk, Jehad Alzabut, and Weerawat Sudsutad. "Investigation of fractal-fractional HIV infection by evaluating the drug therapy effect in the Atangana-Baleanu sense." Mathematical Biosciences and Engineering 19, no. 11 (2022): 10762–808. http://dx.doi.org/10.3934/mbe.2022504.

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<abstract><p>In this paper, we apply the fractal-fractional derivative in the Atangana-Baleanu sense to a model of the human immunodeficiency virus infection of CD$ 4^{+} $ T-cells in the presence of a reverse transcriptase inhibitor, which occurs before the infected cell begins producing the virus. The existence and uniqueness results obtained by applying Banach-type and Leray-Schauder-type fixed-point theorems for the solution of the suggested model are established. Stability analysis in the context of Ulam's stability and its various types are investigated in order to ensure tha

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Alalhareth, Fawaz K., Mohammed H. Alharbi, Noura Laksaci, Ahmed Boudaoui, and Meroua Medjoudja. "Investigating a Fractal–Fractional Mathematical Model of the Third Wave of COVID-19 with Vaccination in Saudi Arabia." Fractal and Fractional 8, no. 2 (2024): 95. http://dx.doi.org/10.3390/fractalfract8020095.

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The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is responsible for coronavirus disease-19 (COVID-19). This virus has caused a global pandemic, marked by several mutations leading to multiple waves of infection. This paper proposes a comprehensive and integrative mathematical approach to the third wave of COVID-19 (Omicron) in the Kingdom of Saudi Arabia (KSA) for the period between 16 December 2022 and 8 February 2023. It may help to implement a better response in the next waves. For this purpose, in this article, we generate a new mathematical transmission model for coronavir

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Kumar, Deepak, Janak Raj Sharma, and Lorentz Jăntschi. "A Novel Family of Efficient Weighted-Newton Multiple Root Iterations." Symmetry 12, no. 9 (2020): 1494. http://dx.doi.org/10.3390/sym12091494.

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We propose a novel family of seventh-order iterative methods for computing multiple zeros of a nonlinear function. The algorithm consists of three steps, of which the first two are the steps of recently developed Liu–Zhou fourth-order method, whereas the third step is based on a Newton-like step. The efficiency index of the proposed scheme is 1.627, which is better than the efficiency index 1.587 of the basic Liu–Zhou fourth-order method. In this sense, the proposed iteration is the modification over the Liu–Zhou iteration. Theoretical results are fully studied including the main theorem of lo

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Pantic, Igor, Jovana Paunovic, Danijela Vucevic, et al. "Postnatal Developmental Changes in Fractal Complexity of Giemsa-Stained Chromatin in Mice Spleen Follicular Cells." Microscopy and Microanalysis 23, no. 5 (2017): 1024–29. http://dx.doi.org/10.1017/s1431927617012545.

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AbstractAlthough there are numerous recent works focusing on fractal properties of DNA and chromatin, many issues regarding changes in chromatin fractality during physiological aging remain unclear. In this study, we present results indicating that in mice, there is an age-related reduction of chromatin fractal complexity in a population of spleen follicular cells (SFCs). Spleen tissue was obtained from 16 mice and fixated in Carnoy solution. The youngest animal was newborn, and each animal was exactly 1 month older than the previous. We performed fractal analysis of SFC chromatin structure, s

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Chandra Sekhar, D., and R. Ganguli. "Fractal boundaries of basin of attraction of Newton–Raphson method in helicopter trim." Computers & Mathematics with Applications 60, no. 10 (2010): 2834–58. http://dx.doi.org/10.1016/j.camwa.2010.09.040.

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Iomin, Alexander. "Fractional Schrödinger equation in gravitational optics." Modern Physics Letters A 36, no. 14 (2021): 2140003. http://dx.doi.org/10.1142/s0217732321400034.

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This paper addresses issues surrounding the concept of fractional quantum mechanics, related to lights propagation in inhomogeneous nonlinear media, specifically restricted to a so-called gravitational optics. Besides Schrödinger–Newton equation, we have also concerned with linear and nonlinear Airy beam accelerations in flat and curved spaces and fractal photonics, related to nonlinear Schrödinger equation, where impact of the fractional Laplacian is discussed. Another important feature of the gravitational optics’ implementation is its geometry with the paraxial approximation, when quantum m

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40

Bashnin, Alexander, and Oscar Ozols. "Import Substitution of the Culture of Measurements." Economic Strategies 25, no. 4 (2023): 78–85. http://dx.doi.org/10.33917/es-4.190.2023.78-85.

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World turbulence has accelerated trends towards cultural changes that emerged at the end of the last century. Today transformation of traditional management forms, corresponding to changing cultural models, is adequate neither to the essence nor the pace of the new reality formation. It’s high time to start thinking about inevitability of losing the comfort of managing an enterprise as a profit-making machine. The well-known postulate “what cannot be measured cannot be controlled” raises a new question: what and how to measure? Possible way out could be the return to corporations of diversity

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Peralta Tapia, Benjamin A., Matías I. Ojeda Rojas, Pablo Pacheco Pérez, and Cristian Chávez Toro. "Algoritmos Fractales Aplicados al Diseño de Disipadores de Calor Compuestos por Multimicrocanales." Resúmenes de Mecánica Computacional 1, no. 18 (2024): 199. https://doi.org/10.70567/rmc.v1i18.220.

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El estudio se centra en el diseño de disipadores de calor compuestos por redes de microcanales. El enfoque metodológico se apoya en la utilización de algoritmos fractales para generar estructuras de multimicrocanales interconectadas en una disposición bidimensional que conforma el disipador térmico. La configuración de microcanales se genera de manera numérica mediante un algoritmo que identifica las intersecciones y conexiones de las geometrías fractales. Esta disposición es sometida a análisis termo-hidráulico, integrando las condiciones de contorno del problema y las propiedades de los flui

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Ackora-Prah, Joseph, Baba Seidu, Eric Okyere, and Joshua K. K. Asamoah. "Fractal-Fractional Caputo Maize Streak Virus Disease Model." Fractal and Fractional 7, no. 2 (2023): 189. http://dx.doi.org/10.3390/fractalfract7020189.

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Maize is one of the most extensively produced cereals in the world. The maize streak virus primarily infects maize but can also infect over 80 other grass species. Leafhoppers are the primary vectors of the maize streak virus. When feeding on plants, susceptible vectors can acquire the virus from infected plants, and infected vectors can transmit the virus to susceptible plants. However, because maize is normally patchy and leafhoppers are mobile, leafhoppers will always be foraging for food. Therefore, we want to look at how leafhoppers interact on maize farms using Holling’s Type III functio

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Zarin, Rahat, Amir Khan, Pushpendra Kumar, and Usa Wannasingha Humphries. "Fractional-order dynamics of Chagas-HIV epidemic model with different fractional operators." AIMS Mathematics 7, no. 10 (2022): 18897–924. http://dx.doi.org/10.3934/math.20221041.

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<abstract><p>In this research, we reformulate and analyze a co-infection model consisting of Chagas and HIV epidemics. The basic reproduction number $ R_0 $ of the proposed model is established along with the feasible region and disease-free equilibrium point $ E^0 $. We prove that $ E^0 $ is locally asymptotically stable when $ R_0 $ is less than one. Then, the model is fractionalized by using some important fractional derivatives in the Caputo sense. The analysis of the existence and uniqueness of the solution along with Ulam-Hyers stability is established. Finally, we solve the

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Szeto, H. H., P. Y. Cheng, J. A. Decena, Y. Cheng, D. L. Wu, and G. Dwyer. "Fractal properties in fetal breathing dynamics." American Journal of Physiology-Regulatory, Integrative and Comparative Physiology 263, no. 1 (1992): R141—R147. http://dx.doi.org/10.1152/ajpregu.1992.263.1.r141.

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The dynamic pattern of fetal breathing was studied in 17 fetal lambs with chronically implanted electromyographic electrodes in the diaphragm. The instantaneous breathing rate time series appeared similar on different time scales, with clusters of faster breathing rates interspersed with periods of relative quiescience, suggesting self-similarity. Distribution histograms of the interbreath intervals (IBIs) showed log-normal distribution for IBIs less than 1 s and inverse power-law distribution for IBIs greater than 1 s. The ratio of log-normal distribution to power-law distribution varied from

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Benedetti, M., D. Bortoluzzi, M. Da Lio, and V. Fontanari. "The Influence of Adhesion and Sub-Newton Pull-Off Forces on the Release of Objects in Outer Space." Journal of Tribology 128, no. 4 (2006): 828–40. http://dx.doi.org/10.1115/1.2345407.

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The theoretical background and the numerical modeling results of a ground-based verification activity of a critical space mission phase affected by adhesion issues are presented. Tribological models are first reviewed with an emphasis on the contact forces assessment and their relationship to the geometrical, material, and mechanical properties of the contacting metal bodies. An approach based on a finite element analysis of the contact, accounting for the adhesion forces, is then proposed for studying the contact behavior of smooth surfaces in vacuum. Some solutions aimed at reducing adhesion

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Asamoah, Joshua Kiddy K. "Fractal–fractional model and numerical scheme based on Newton polynomial for Q fever disease under Atangana–Baleanu derivative." Results in Physics 34 (March 2022): 105189. http://dx.doi.org/10.1016/j.rinp.2022.105189.

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AGISHTEIN, M. E., and A. A. MIGDAL. "THREE-DIMENSIONAL QUANTUM GRAVITY AS DYNAMICAL TRIANGULATION." Modern Physics Letters A 06, no. 20 (1991): 1863–84. http://dx.doi.org/10.1142/s0217732391002025.

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The dynamical triangulation model of 3-dimensional Quantum Gravity is defined and studied. We propose two different algorithms for numerical simulations, leading to consistent results. One is the 3-dimensional generalization of the bonds flip, another is more sophisticated algorithm, based on Schwinger–Dyson equations. We found such care necessary, because our results appear to be quite unexpected. We simulated up to 60000 tetrahedra and observed none of the feared pathologies like factorial growth of the partition function with volume, or collapse to the branched polymer phase. The volume of

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Naroda, Yuto, Yoshie Endo, Kenji Yoshimura, Hiroshi Ishii, Shin-Ichiro Ei, and Takashi Miura. "Noise-induced scaling in skull suture interdigitation." PLOS ONE 15, no. 12 (2020): e0235802. http://dx.doi.org/10.1371/journal.pone.0235802.

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Sutures, the thin, soft tissue between skull bones, serve as the major craniofacial growth centers during postnatal development. In a newborn skull, the sutures are straight; however, as the skull develops, the sutures wind dynamically to form an interdigitation pattern. Moreover, the final winding pattern had been shown to have fractal characteristics. Although various molecules involved in suture development have been identified, the mechanism underlying the pattern formation remains unknown. In a previous study, we reproduced the formation of the interdigitation pattern in a mathematical mo

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Ahmad, Hanan Haj, and Kariema A. Elnagar. "A novel quantile regression for fractiles based on unit logistic exponential distribution." AIMS Mathematics 9, no. 12 (2024): 34504–36. https://doi.org/10.3934/math.20241644.

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<p>Continuous developments in unit interval distributions have shown effectiveness in modeling proportional data. However, challenges persist in diverse dispersion characteristics in real-world scenarios. This study introduces the unit logistic-exponential (ULE) distribution, a flexible probability model built upon the logistic-exponential distribution and designed for data confined to the unit interval. The statistical properties of the ULE distribution were studied, and parameter estimation through maximum likelihood estimation, Bayesian methods, maximum product spacings, and least squ

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Hasan, Ali, Ali Akgül, Muhammad Farman, Faryal Chaudhry, Muhammad Sultan, and Manuel De la Sen. "Epidemiological Analysis of Symmetry in Transmission of the Ebola Virus with Power Law Kernel." Symmetry 15, no. 3 (2023): 665. http://dx.doi.org/10.3390/sym15030665.

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This study presents a mathematical model of non-integer order through the fractal fractional Caputo operator to determine the development of Ebola virus infections. To construct the model and conduct analysis, all Ebola virus cases are taken as incidence data. A symmetric approach is utilized for qualitative and quantitative analysis of the fractional order model. Additionally, stability is evaluated, along with the local and global effects of the virus that causes Ebola. Using the fractional order model of Ebola virus infections, the existence and uniqueness of solutions, as well the posednes

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