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Singularities of inner functions associated with hyperbolic maps

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2019年第1期477卷 536-550页

作者： Evdoridou, Vasiliki Fagellab, Nuria Jarque, Xavier Sixsmith, David J. Open Univ Sch Math & Stat Walton Hall Milton Keynes MK7 6AA Bucks England Univ Barcelona Inst Matemat Dept Matemat & Informat Gran Via 585 E-08007 Barcelona Spain Barcelona Grad Sch Math BGSMath Gran Via 585 Barcelona 08007 Spain Univ Liverpool Dept Math Sci Liverpool L69 7ZL Merseyside England

Let f be a function in the Eremenko-Lyubich class B, and let U be an unbounded, forward invariant Fatou component of f. We relate the number of singularities of an inner function associated to f vertical bar(U) with the number of tracts of f. In particular, we show that if f lies in either of two large classes of functions in B, and also has finitely many tracts, then the number of singularities of an associated inner function is at most equal to the number of tracts of f. Our results imply that for hyperbolic functions of finite order there is an upper bound - related to the order - on the number of singularities of an associated inner function. Crown Copyright (C) 2019 Published by Elsevier Inc. All rights reserved.

关键词： Transcendental dynamics Inner functions hyperbolic functions

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On the stability of submerged gas jet in temporal mode

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PHYSICS OF FLUIDS 2025年第1期37卷

作者： Wang, Chao Hu, Yi-Ming Zheng, Xin Zhao, Da-Gang Chen, Xi-Lin Han, Yang Sun, Cong Siginer, Dennis A. Harbin Engn Univ Coll Shipbldg Engn Harbin 150001 Peoples R China Univ Santiago Chile Dept Ingn Mecan Ave Libertador Bernardo OHiggins 3363Estn Cent Santiago Chile

The temporal mode stability of incompressible submerged axisymmetric gas jets is comprehensively investigated by linear stability analysis. The basic velocity profile is constructed using the hyperbolic tangent function approach. The influences of basic velocity profile, Reynolds Re, and Weber We numbers, and physical properties of the surrounding liquid on the stability of the gas jet are investigated and stability maps are constructed. We find that the jet breakup propagation velocity shows a strong linear relationship with the velocity of the two-phase interface, and the shear on the interface can greatly change the instability modes of submerged gas jet system. Large surface tension triggers long-wave instability of the jet and local shear at the interface leads to the unsteady transition to short-wave instability. Moreover, it is found that there is a strong linear relationship between the most unstable growth rate and dimensionless parameters directly or indirectly, and R-2 is above 0.95. In addition, the instability of the submerged gas jet shows a double-mode feature when the velocity profile parameters exceed their thresholds.

关键词： hyperbolic functions

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Finite-time fault-tolerant control of attitude control system of quadrotor UAV based on neural network disturbance observer

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Neural Computing and Applications 2025年第7期37卷 5597-5606页

作者： Li, Boning Chen, Ming Qi, Shuchang Peng, Kaixiang School of Electronic and Information Engineering University of Science and Technology Liaoning Liaoning Anshan China School of Automation University of Science and Technology Beijing Beijing China

This paper investigates a new finite-time fault-tolerant control scheme for a quadrotor unmanned aerial vehicle (UAV). Firstly, a novel neural network disturbance observer with an auxiliary system is designed to compensate for actuator faults and external disturbances. In addition, in order to ensure the system’s rapidity, the finite-time theory is incorporated into the observer design and the controller design. The hyperbolic tangent function is also introduced to process the input signals, which ensures that the UAV receives relatively the smooth input signals. The design scheme takes into account the rapidity and robustness of the system, which makes the performance of the UAV better. Finally, the advantages of the proposed scheme are demonstrated through comparative experiments and the feasibility of the scheme is further verified through actual physical experiments. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2025.

关键词： hyperbolic functions

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Bifurcation analysis, phase portrait, and exploring exact traveling wave propagation of M-fractional (3 + 1) dimensional nonlinear equation in the fluid medium

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Optical and Quantum Electronics 2025年第4期57卷 1-23页

作者： Roshid, Md. Mamunur Uddin, Mahtab Abdalla, Mohamed Ullah, Md. Ahsan Department of Mathematics Hamdard University Bangladesh Munshigang Bangladesh Institute of Natural Sciences United International University Dhaka Bangladesh Department of Mathematics Faculty of Science King Khalid University Abha61471 Saudi Arabia Department of Computer Science and Engineering University of Liberal Arts Bangladesh Dhaka Bangladesh

This work studies the bifurcation analysis, phase portrait, and dynamics behavior of exact traveling wave solutions for the time M-fractional (3 + 1)-dimensional Painlevé integrable model. This model is used to describe some complex phenomena in nonlinear science and is crucial for addressing various practical challenges, including key models in areas like quantum mechanics, statistical physics, nonlinear optics, and celestial Mechanics. By bifurcation theory, we find the phase portrait of the proposed model. Bifurcation analysis in the proposed systems helps figure out how small changes in parameters can cause big changes in how the system behaves, like going from stable states to chaotic dynamics. It pinpoints critical thresholds where these transitions occur, aiding in the prediction and control of complex behaviors. We also present some traveling wave solutions according to the phase portrait orbit. Furthermore, the exact traveling wave solutions of the time M-fractional (3 + 1)-dimensional Painlevé integrable model are investigated by using the modified simple equation technique. This method provides the solutions directly without any predefined solutions. Under the condition, the solutions are real and complex valued in terms of exponential, trigonometric, and hyperbolic function form. For the special ideals of free parameters, we will include the bright bell wave, dark bell wave, interaction of kink and periodic lump wave, double periodic wave, double dark bell wave, and so on. By visualizing, the three, two-dimensional and density diagrams, the dynamic properties of the proposed model are examined and illustrated, enhancing the comprehension and application of time M-fractional (3 + 1)-dimensional Painlevé integrable model. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

关键词： hyperbolic functions

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The superposition solution of positive quadratic function and arbitrary positive function of a (3+1)-dimensional soliton equation under vector representation

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Optical and Quantum Electronics 2025年第4期57卷 1-17页

作者： Sun, Wenlong Bilige, Sudao Shao, Hangbing Wang, Wenjing Department of Mathematics Inner Mongolia University of Technology Hohhot010051 China Inner Mongolia Key Laboratory of Statistical Analysis Theory for Life Data and Neural Network Modeling Hohhot010051 China

The Hirota bilinear method was utilized to study a (3+1)-dimensional soliton equation, and we achieved success in obtaining a variety of solutions to the equation. Successfully yielding various solutions, such as lump solutions, rogue wave solutions, and interaction solutions. The first step in research is to transform the orginal equation into Hirota bilinear form. Through the symbolic calculation and the Cole-Hopf transformation, we obtain the solution of the original equation. Especially, we introduced vectors as tools to get the rational solutions of the equation. We make plots according to select different values of parameters, and the plots of various forms of solutions are dynamically analyzed to understand their physical significance. For the selection of trial functions, the first type is the positive quadratic functions, which can be used to obtain lump solutions and rogue wave solutions. The second type is the superposition of positive quadratic functions and positive arbitrary functions, resulting in an interaction solution consisting of both rational solution and arbitrary function solutions. We will provide examples to illustrate the interaction solutions formed by the superposition of positive quadratic and exponential functions, the superposition of positive quadratic, exponential and trigonometric functions, and the superposition of positive quadratic, exponential, trigonometric and hyperbolic functions. In short, we constructed different trial functions, so various new superposition solutions and wave motion were obtained. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

关键词： hyperbolic functions

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Elliptic, hyperbolic, complex gamma functions and QFT in various dimensions

Elliptic, hyperbolic, complex gamma functions and QFT in var...

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2021 RDP Online PhD School and Workshop "Aspects of Symmetry", Regio 2021

作者： Sarkissian, Gor Spiridonov, Vyacheslav Laboratory of Theoretical Physics JINR Joliot-Curie 6 Dubna141980 Russia Petersburg Department of the Steklov Mathematical Institute of Russian Academy of Sciences Fontanka 27 St. Petersburg191023 Russia Yerevan Physics Institute Brothers Alikhanian 2 Yerevan0036 Armenia

We present new relations for integrals of complex gamma functions. We show that starting from properties of the elliptic hypergeometric integrals, and using some limiting procedures, one can get vast number of identities for integrals of products of the hyperbolic and complex gamma functions. The latter integrals have physical interpretation of partition functions for different types of quantum field theories dualities in various dimensions, and the corresponding limiting procedures can be viewed as dimensional reduction and multiplet decoupling. © Copyright owned by the author(s) under the terms of the Creative Commons

关键词： hyperbolic functions

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Construction of German machine translation model combining Long Short-Term Memory and multi-subspace attention mechanism 2

Construction of German machine translation model combining L...

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2nd International Conference on Big Data, Computational Intelligence, and Applications, BDCIA 2024

作者： Liu, Lingshan Xi'an Fanyi University Xi'an710105 China

ISBN: (纸本)9781510689053

In the context of rapid development of information technology, the development of intelligent algorithms has greatly promoted the progress of natural language processing technology. This study addresses the inefficiency and gradient problem of the traditional neural machine translation model in dealing with German long sequence data, and proposes a German machine translation model that integrates the hyperbolic tangent long short-term memory network and the multisubspace attention mechanism. The outcomes indicated that the new model has a bilingual evaluation substitution index of 0.98, an explicitly ordered translation evaluation index of 0.99, a translation editing rate of 99.87%, and an average response time of 2.54 seconds, which are all higher than the comparison model and significantly better than the comparison model. It shows faster translation speed and higher stability. In addition to increasing the accuracy of German translation, this study offers new technology for a number of fields that need precise and quick translation. © 2025 SPIE.

关键词： hyperbolic functions

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Potential Function, A-Polynomial and Reidemeister Torsion of hyperbolic Links 13th

Potential Function, A-Polynomial and Reidemeister Torsion of...

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13th International Workshop on Low Dimensional Topology and Number Theory, LDT and NT 2022

作者： Murakami, Jun Tran, Anh T. Department of Mathematics Faculty of Science and Engineering Waseda University 3-4-1 Ohkubo Tokyo Shinjuku-ku169-8555 Japan Department of Mathematical Sciences The University of Texas at Dallas RichardsonTX75080-3021 United States

ISBN: (纸本)9789819737772

We propose conjectural methods to get the A-polynomial and the twisted Reidemeinster torsion from the colored Jones invariant of knots and links. For some families of knots and links, it is checked that our methods work well by comparing with these invariants computed from PSL(2,C) representations of the fundamental groups of the knot/link complements. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： hyperbolic functions

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Observation-Transformed Distributed Detection in Sensor Networks 59

Observation-Transformed Distributed Detection in Sensor Netw...

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59th Annual Conference on Information Sciences and Systems, CISS 2025

作者： Cao, Lei Viswanathan, Ramanarayanan University of Mississippi Dept. of Electrical and Computer Engineering OxfordMS38677 United States

ISBN: (纸本)9798331513269

Distributed detection (DD) plays a crucial role in sensor networks, where sensors gather data from a region of interest and report their observations to a fusion center (FC). The FC then makes a decision regarding a specific task, such as determining the presence or absence of a target. Given the constraints imposed by the transmission power, bandwidth, and noise impact in both sensing and data reporting channels, what should be reported from the sensors significantly affects the final detection accuracy. Existing methods include observation-untransformed DD (UDD), codewords-based DD (CDD), and quantized-but-uncoded DD (QDD). In this paper, we attempt to find the optimal sensor decision rule, i.e., the best transform for the observed data to be reported, by formulating the task as a functional optimization problem. To bypass the difficulty of theoretically solving the problem, we present two methods: an approximation function and a numerical solution for the Gaussian noise case. Our simulation results demonstrate that a variation of the hyperbolic tangent function can be an effective approximation of the optimal transform. This work could lead to further studies on the optimal design for distributed detection. © 2025 IEEE.

关键词： hyperbolic functions

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Model for Forecasting Rural Travel Demand Using Feed Forward—Backpropagation Neural Network and Minimized Akaike Information Criterion Algorithm 4th

Model for Forecasting Rural Travel Demand Using Feed Forward...

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4th International Civil Engineering and Architecture Conference, CEAC 2024

作者： Sahagun, Reynaldo P. Silva, Dante L. Diona, Russell L. Cabuñas, Jay T. De Jesus, Kevin Lawrence M. School of Graduate Studies Mapua University 658 Muralla St. Intramuros Manila1002 Philippines School of Civil Environmental and Geological Engineering Mapua University 658 Muralla St. Intramuros Manila1002 Philippines Information and Technology Department University of Technology and Applied Sciences PO Box 74 Al Khuwair Muscat133 Oman College of Engineering Mapua Malayan Colleges Mindanao Davao City Philippines Department of Civil Engineering College of Engineering FEU Institute of Technology P. Paredes St. Sampaloc Manila1015 Philippines

ISBN: (纸本)9789819754762

Transportation is critical, especially in rural areas as it provides the mobility to people to access different activities satisfying their daily needs. The purpose of this research is to create an artificial neural network (ANN) trip generation model (TGM). 500 households (HH) were surveyed to obtain the independent variables used in the modeling process including the HH size (HHS), number of children in the HH below 7 years old (NCHHBS), number of HH member from 7 to 59 years old (NHHMSF), number of HH member above 59 years old (NHHAF), number of working member of the HH (NWMHH), number of school children in the HH (NSCHH), number of helpers in the HH (NHHH), number of motorize vehicles in the HH (NMVHH), HH income (HHI), highest educational attainment (HEA), head of HH age (HHHA), and number of driver’s license holder in the HH (NDLHHH). Using the Levenberg–Marquardt algorithm (LMA) as the training algorithm (TA) and hyperbolic tangent sigmoid (HTS) function as the activation function (AF), the governing TGM was observed in the 12–25-1 network structure with the highest R value = 0.98476 and least Mean Absolute Percentage Error (MAPE) of 9.04%. Moreover, the governing network structure achieved the minimized Akaike Information Criterion (AIC) value at 25 hidden neurons (HN) indicating that the network has already been generalized and was the best model among those observed in this study. The outcomes of the research showed the efficacy of artificial neural networks in developing trip generation prediction models (PM). © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： hyperbolic functions

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