Relevant bibliographies by topics / Hyperbolic function models

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Hyperbolic function models'

Author: Grafiati
Published: 3 June 2025
Last updated: 22 June 2025

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Journal articles on the topic "Hyperbolic function models"

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Li, Yunyue, Yang Zhang, and Jon Claerbout. "Hyperbolic estimation of sparse models from erratic data." GEOPHYSICS 77, no. 1 (2012): V1—V9. http://dx.doi.org/10.1190/geo2011-0099.1.

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We have developed a hyperbolic penalty function for image estimation. The center of a hyperbola is parabolic like that of an [Formula: see text] norm fitting. Its asymptotes are similar to [Formula: see text] norm fitting. A transition threshold must be chosen for regression equations of data fitting and another threshold for model regularization. We combined two methods: Newton’s and a variant of conjugate gradient method to solve this problem in a manner we call the hyperbolic conjugate direction (HYCD) method. We tested examples of (1) velocity transform with strong noise (2) migration of aliased data, and (3) blocky interval velocity estimation. For the linear experiments we performed in this study, nonlinearity is introduced by the hyperbolic objective function, but the convexity of the sum of the hyperbolas assures the convergence of gradient methods. Because of the sufficiently reliable performance obtained on the three mainstream geophysical applications, we expect the HYCD solver method to become our default method.
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Miguel, E. San, S. Monserrat, C. Fernández, et al. "Growth models and longevity of freshwater pearl mussels (Margaritifera margaritifera) in Spain." Canadian Journal of Zoology 82, no. 8 (2004): 1370–79. http://dx.doi.org/10.1139/z04-113.

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Growth rates of populations of the freshwater pearl mussel, Margaritifera margaritifera (L., 1758), in northwestern Spain were analysed based on measurements of annual annuli and using two nonlinear functions for length-at-age data sets: von Bertalanffy's growth model and a hyperbolic function. These populations reach the smallest maximum shell length (90.5 mm) and have the shortest life-span (35 years) and the highest growth rate (k in von Bertalanffy's model >0.1·year–1, on average) known for this species. The two models were similar in performance and were well fitted (around 99%) to shell-length-at-age data, although the hyperbolic function appears to be applicable only from 6 years of age. The growth rate (either k or k' from the hyperbolic function) showed a large and significant variation across populations, both among and within drainages.
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Cahyono, Muhammad. "Hybrid Models for Solving the Colebrook–White Equation Using Artificial Neural Networks." Fluids 7, no. 7 (2022): 211. http://dx.doi.org/10.3390/fluids7070211.

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This study proposes hybrid models to solve the Colebrook–White equation by combining explicit equations available in the literature to solve the Colebrook–White equation with an error function. The hybrid model is in the form of fH=fo−eA. fH is the friction factor value f predicted by the hybrid model, fo is the value of f calculated using several explicit formulas for the Colebrook–White equation, and eA is the error function determined using the neural network procedures. The hybrid equation consists of a series of hyperbolic tangent functions whose number corresponds to the number of neurons in the hidden layer. The simulation results showed that the hybrid models using five hyperbolic tangent functions could produce reasonable predictions of friction factors, with the maximum absolute relative error (MAXRE) around one tenth, or ten times lower than that produced by the corresponding existing formula. The simplified hybrid models are also given using four and three tangent hyperbolic functions. These simplified models still provide accurate results with MAXRE of less than 0.1%.
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Safak, Suleyman. "A New Hyperbolic Function Approach of Rock Fragmentation Size Distribution Prediction Models." Symmetry 16, no. 8 (2024): 979. http://dx.doi.org/10.3390/sym16080979.

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It is well known that the first stage of mine-to-mill optimization is rock fragmentation by blasting. The degree of rock fragmentation can be expressed in terms of average grain (X50) size and size distribution. There are approaches in which exponential functions are used to estimate the size distribution of the pile that will be formed before blasting. The most common of these exponential functions used to estimate the average grain size is the Kuz–Ram and KCO functions. The exponential functions provide a curve from 0% to 100% using the mean grain size (X50), characteristic size (XC), and uniformity index (n) parameters. This distribution curve can make predictions in the range of fine grains and coarse grains outside the acceptable error limits in some cases. In this article, the usability of the hyperbolic tangent function, which is symmetrical at origin, in the estimation of the size distribution as an alternative to the exponential distribution functions used in almost all estimation models is investigated. As with exponential functions, the hyperbolic tangent function can express the aggregated size distribution as a percentage with reference to the variables X50 and XC. It has been shown that the hyperbolic tangent function provides 99% accuracy to the distribution of fine grains and coarse grains of the pile formed as a result of blasting data for the characteristic size (XC) parameter and the uniformity index (n).
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Ivanov, Roman V. "The Semi-Hyperbolic Distribution and Its Applications." Stats 6, no. 4 (2023): 1126–46. http://dx.doi.org/10.3390/stats6040071.

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This paper studies a subclass of the class of generalized hyperbolic distribution called the semi-hyperbolic distribution. We obtain analytical expressions for the cumulative distribution function and, specifically, their first and second lower partial moments. Using the received formulas, we compute the value at risk, the expected shortfall, and the semivariance in the semi-hyperbolic model of the financial market. The formulas depend on the values of generalized hypergeometric functions and modified Bessel functions of the second kind. The research illustrates the possibility of analysis of generalized hyperbolic models using the same methodology as is employed for the well-established variance-gamma model.
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PARISI, J., and R. STOOP. "THE GENERALIZED THERMODYNAMIC FORMALISM APPLIED TO HYPERBOLIC AND NONHYPERBOLIC MODELS." Modern Physics Letters B 06, no. 24 (1992): 1513–18. http://dx.doi.org/10.1142/s0217984992001216.

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In this contribution, scaling properties of hyperbolic and nonhyperbolic model systems are discussed by using the generalized thermodynamic formalism. The central quantity for the investigation is the generalized entropy function. With the help of this approach, insight into the possible occurrence of phase transitions in the various entropy-like scaling functions can be gained. It is shown how this effect is determined by the existence of a critical line in the surface described by the generalized entropy function.
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Al-Amry, M. S., and E. F. Al-Abdali. "New Exact Solutions for Generalized of Combined with Negative Calogero-Bogoyavlenskii Schiff and Generalized Yu–Toda–Sassa–Fukuyama Equations." University of Aden Journal of Natural and Applied Sciences 28, no. 1 (2024): 25–30. http://dx.doi.org/10.47372/uajnas.2024.n1.a04.

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In this paper, we present generalized model of combined Calogero-Bogoyavlenskii Schiff and negative-order Calogero-Bogoyavlenskii Schiff G(CBS-nCBS) equation and generalized Yu–Toda–Sassa–Fukuyama g(YTSF) equation. We apply the extended hyperbolic function method, to solve generalized models. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions solutions of these equations from the method with the aid of the computer program Maple.
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Hoon Lim, Siew. "Accounting for environmental pollution in production function." Management of Environmental Quality: An International Journal 25, no. 6 (2014): 679–95. http://dx.doi.org/10.1108/meq-08-2013-0087.

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Purpose – Traditionally, economic production models consider pollution as bads that may be modeled as either outputs or inputs in economic models. The purpose of this paper is to examine the implications of these modeling choices on the measurements of productive efficiency and private costs of pollution control. Design/methodology/approach – The authors apply the hyperbolic distance functions to measure trucking efficiency and the private costs of pollution control. Findings – The results show: (i) regardless of the choice of modeling, when only one bad was incorporated in hyperbolic distance functions, the efficiency loss and private abatement cost measures derived from the two models were equivalent, but potential pollution reduction and good output expansion differed; (ii) when more than one bad were introduced, the equivalence of efficiency loss measure in (i) did not hold; and (iii) the potential amounts of pollution reduction and good output expansion were larger when bads were modeled as inputs. With multiple bads, private abatement costs varied considerably under the two modeling treatments. Practical implications – From a policy standpoint, the results suggest that one should consider the modeling options with caution when multiple economic bads are involved, because the resulting measures of economic burden of pollution control differ. Originality/value – The paper shows that the traditional conceptual framework for modeling pollution in hyperbolic distance functions could yield inconsistent results.
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AKARÇAY, Özlem, and Nimet YAPICI PEHLİVAN. "FUZZY MULTI-OBJECTIVE NONLINEAR PROGRAMMING PROBLEMS UNDER VARİOUS MEMBERSHIP FUNCTIONS: A COMPARATİVE ANALYSIS." Mühendislik Bilimleri ve Tasarım Dergisi 11, no. 3 (2023): 857–72. http://dx.doi.org/10.21923/jesd.1062118.

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Fuzzy sets have been applied to various decision-making problems when there is uncertainty in real-life problems. In decision-making problems, objective functions and constraints sometimes cannot be expressed linearly. In such cases, the problems discussed are expressed by nonlinear programming models. Fuzzy multi-objective programming models are problems containing multiple objective functions, where objective functions and/or constraints include fuzzy parameters. Membership functions are crucial to obtain optimal solution of fuzzy multi-objective programming model. In this study, a green supply chain network model with fuzzy parameters is proposed. Proposed model with nonlinear constraints is a fuzzy multi-objective nonlinear programming model that minimizes both transportation costs and emissions generated by two vehicle types during transportation. The model is used in Zimmermann's Min-Max approach by considering triangular, hyperbolic and exponential membership functions and optimal solutions are obtained. When optimal solutions are compared, it is seen that optimal solution obtained using the hyperbolic membership function is better than the optimal solutions obtained from triangular and exponential ones. Maximum common satisfaction level calculated using hyperbolic membership function for proposed model is λ=0.97. Sensitivity analysis is also carried out by taking into account distances between suppliers, manufacturers, distribution centers and customers, as well as customer demands.
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Sakai, Motoki. "Estimation of Heart Rate from Vocal Frequency Based on Support Vector Machine." International Journal of Advances in Scientific Research 2, no. 1 (2016): 16. http://dx.doi.org/10.7439/ijasr.v2i1.2849.

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Heart rate (HR) is one of the vital signs used to assess our physical condition; it would be beneficial if HR could easily be obtained without special medical instruments. In this study, a feature of vocal frequency was used to estimate HR, because it can easily be recorded with a common device such as a smartphone. Previous studies proposed that a support vector machine (SVM) that adopted the inner product as the kernel function was efficient for estimating HR to a certain extent. However, these studies did not present the effectiveness of other kernel functions, such as the hyperbolic tangent function. Therefore, this study identified a combination of kernel functions of the kernel ridge regression (KRR). In addition, features of vocal frequency to effectively estimate HR were investigated. To evaluate the effectiveness, experiments were conducted with two subjects. In the experiment, 60 sets of HRs and voice data were measured per subject. To identify the most effective kernel function, four kernel functions (the inner function, Gaussian function, polynomial function, and hyperbolic tangent function) were compared. Moreover, effective features of vocal frequency were selected with the sequential feature selection (SFS) method. As a consequence, the hyperbolic tangent function worked best, and high-frequency components of voice were efficient. However, results of this research indicated that effective vocal spectrum components to estimate HR differ depending on prediction models.
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Dissertations / Theses on the topic "Hyperbolic function models"

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Ström, David. "The Open Mapping Theorem for Analytic Functions and some applications." Thesis, Karlstad University, Faculty of Technology and Science, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-210.

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<p>This thesis deals with the Open Mapping Theorem for analytic functions on domains in the complex plane: A non-constant analytic function on an open subset of the complex plane is an open map.</p><p>As applications of this fundamental theorem we study Schwarz’s Lemma and its consequences concerning the groups of conformal automorphisms of the unit disk and of the upper halfplane.</p><p>In the last part of the thesis we indicate the first steps in hyperbolic geometry.</p><br><p>Denna uppsats behandlar satsen om öppna avbildningar för analytiska funktioner på domäner i det komplexa talplanet: En icke-konstant analytisk funktion på en öppen delmängd av det komplexa talplanet är en öppen avbildning.</p><p>Som tillämpningar på denna fundamentala sats studeras Schwarz’s lemma och dess konsekvenser för grupperna av konforma automorfismer på enhetsdisken och på det övre halvplanet.</p><p>I uppsatsens sista del antyds de första stegen inom hyperbolisk geometri.</p>
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El-Khatib, Mayar. "Highway Development Decision-Making Under Uncertainty: Analysis, Critique and Advancement." Thesis, 2010. http://hdl.handle.net/10012/5741.

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While decision-making under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous. In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model. This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decision-making. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavy-tailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives. Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decision-making process. This furthers the quest for optimality in highway projects and beyond.
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Books on the topic "Hyperbolic function models"

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Laibson, David I. Hyperbolic discount functions, undersaving, and savings policy. National Bureau of Economic Research, 1996.

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Stoica, Ion. Evaluating the hyperbolic model on a variety of architectures. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1996.

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Stoica, Ion. A simple hyperbolic model for communication in parallel processing environments. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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Center, Ames Research, ed. Generation of three-dimensional body-fitted grids by solving hyperbolic partial differential equations. National Aeronautics and Space Administration, Ames Research Center, 1989.

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Center, Ames Research, ed. Generation of three-dimensional body-fitted grids by solving hyperbolic partial differential equations. National Aeronautics and Space Administration, Ames Research Center, 1989.

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Center, Ames Research, ed. Generation of three-dimensional body-fitted grids by solving hyperbolic partial differential equations. National Aeronautics and Space Administration, Ames Research Center, 1989.

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Center, Ames Research, ed. Generation of three-dimensional body-fitted grids by solving hyperbolic partial differential equations. National Aeronautics and Space Administration, Ames Research Center, 1989.

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C, Constanda, ed. Variational and potential methods for a class of linear hyperbolic evolutionary processes. Springer, 2005.

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Shlomo, Ta'asan, and Institute for Computer Applications in Science and Engineering., eds. The large discretization step method for time-dependent partial differential equations. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1995.

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Ninul, Anatolij Sergeevič. Tenzornaja trigonometrija: Teorija i prilozenija / Theory and Applications /. Mir Publisher, 2004.

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Book chapters on the topic "Hyperbolic function models"

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Popa, Cosmin Radu. "Hyperbolic Functions’ Synthesizers." In Current-Mode Analog Nonlinear Function Synthesizer Structures. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-01035-9_3.

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Toh, Kar-Ann, Xudong Jiang, and Wei-Yun Yau. "A Hyperbolic Function Model for Multiple Biometrics Decision Fusion." In Biometric Authentication. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-25948-0_89.

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Cerejeiras, P. "Sn-1-Harmonic Functions for the Spherical Model of Hyperbolic Spaces." In Proceedings of the Second ISAAC Congress. Springer US, 2000. http://dx.doi.org/10.1007/978-1-4613-0271-1_76.

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Bartecki, Krzysztof. "Rational Transfer Function Approximation Model for $$2 \times 2$$ Hyperbolic Systems with Collocated Boundary Inputs." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-50936-1_5.

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Kuroe, Yasuaki, Shinpei Tanigawa, and Hitoshi Iima. "Models of Hopfield-Type Clifford Neural Networks and Their Energy Functions - Hyperbolic and Dual Valued Networks -." In Neural Information Processing. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-24955-6_67.

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Alshalif, Sarah Abdulkarem, Noraini Ibrahim, and Tutut Herawan. "Artificial Neural Network with Hyperbolic Tangent Activation Function to Improve the Accuracy of COCOMO II Model." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-51281-5_9.

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Chang, D. W., and T. M. Chou. "Developing a two-dimensional nonlinear vertical spring model for mat foundation in clays using hyperbolic function." In Smart Geotechnics for Smart Societies. CRC Press, 2023. http://dx.doi.org/10.1201/9781003299127-362.

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Liang, Qiuyu, Weihua Wang, Feilong Bao, and Guanglai Gao. "Fully Hyperbolic Rotation for Knowledge Graph Embedding." In Frontiers in Artificial Intelligence and Applications. IOS Press, 2024. http://dx.doi.org/10.3233/faia240668.

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Hyperbolic rotation is commonly used to effectively model knowledge graphs and their inherent hierarchies. However, existing hyperbolic rotation models rely on logarithmic and exponential mappings for feature transformation. These models only project data features into hyperbolic space for rotation, limiting their ability to fully exploit the hyperbolic space. To address this problem, we propose a novel fully hyperbolic model designed for knowledge graph embedding. Instead of feature mappings, we define the model directly in hyperbolic space with the Lorentz model. Our model considers each relation in knowledge graphs as a Lorentz rotation from the head entity to the tail entity. We adopt the Lorentzian version distance as the scoring function for measuring the plausibility of triplets. Extensive results on standard knowledge graph completion benchmarks demonstrated that our model achieves competitive results with fewer parameters. In addition, our model get the state-of-the-art performance on datasets of CoDEx-s and CoDEx-m, which are more diverse and challenging than before. Our code is available at https://github.com/llqy123/FHRE.
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Tayler, A. B. "Elliptic Problems." In Mathematical Models in Applied Mechanics. Oxford University PressOxford, 2002. http://dx.doi.org/10.1093/oso/9780198515593.003.0003.

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Abstract In Chapter 2 a linear partial differential equation in two independent variables was defined to be hyperbolic if there exist two real distinct characteristic directions at each point, which define curves across which discontinuities in the first derivatives of the unknown function &amp;lt;f&amp;gt;can occur.
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Vakili J. "An experimental study of clay based on a class of simple hypoelastic constitutive behavior." In Proceedings of the 17th International Conference on Soil Mechanics and Geotechnical Engineering. IOS Press, 2009. https://doi.org/10.3233/978-1-60750-031-5-506.

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The objective of this paper is to present a mathematically simple model to define the mechanical behavior of clay that can be utilized in determination of practical solutions for soil mechanics problems. Variable moduli models in the form of tangential stress-strain relationships according to the theory of hypoelsticity are used in this paper. The incremental constitutive relations are formulated directly based on the isotropic linear elastic formulation simply by replacing the elastic constants with variable tangential moduli which are functions of strain invariants. By examining an experimental stress-strain curve of a triaxial compression test, it has been demonstrated that the variable moduli, in this case, is a decreasing function of strain which starts at an initial value of E0and gradually reduces to zero at the ultimate deviator stress application. The stress-strain relationship, in this case, can be reduced to a simple hyperbolic from.
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Conference papers on the topic "Hyperbolic function models"

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Colorado, D., S. Serna-Barquera, J. A. Hernández, Y. Barrera-Rojas, M. Lucio-García, and B. Campillo. "Neural Network for Dispersion Strengthened Microalloyed Steel Sour Corrosion from Electrochemical Impedance Spectroscopy Laboratory Measurements." In CORROSION 2010. NACE International, 2010. https://doi.org/10.5006/c2010-10279.

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Abstract Microalloyed pipeline steels mechanical resistance can be improved by dispersion strengthening. The enhancement of steel dispersion strengthening by tempering at a suitable temperature has been studied at various holding times at 3, 6, 8 and 10 hours. Depending on the elapsed time, microalloying elements that were still located within steel iron lattice can be re-diffused, thus developing different nanoparticle sizes, densities and distribution. The steel yield strength and sulphide stress cracking resistance were significantly improved under sour environment. A systematic electrochemical impedance spectroscopy (EIS) corrosion study was carried out. The objective of the present work was to predict corrosion results from EIS collected data from the different steel tempering times and exposure temperatures to sour environment (room temperature and 50 °C) by means of an artificial neural network (ANN). For the ANN, an approach based on Levenberg–Marquardt learning algorithm, hyperbolic tangent sigmoid transfer function, and a linear transfer function was used. The model takes into account of the variations of the real impedance, time and steel exposure temperature. The developed model can be used for prediction at short simulation times illustrating the utility of the ANN. On the validation data set, the simulations and the theoretical data tests were in good agreement with R2 &amp;gt; 0.98 for all experimental databases. These results suggest that ANN may play a key role in making lifetime predictions for components based on laboratory measurements.
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Bartecki, Krzysztof. "A transfer function representation for a class of hyperbolic systems." In 2012 17th International Conference on Methods & Models in Automation & Robotics (MMAR). IEEE, 2012. http://dx.doi.org/10.1109/mmar.2012.6347815.

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Zhu, Yingying, Haiquan Zhao, and Pucha Song. "Hyperbolic Secant Function Algorithms for Nonlinear Active Noise Control models of Kernel Mapping Types." In 2021 IEEE 16th Conference on Industrial Electronics and Applications (ICIEA). IEEE, 2021. http://dx.doi.org/10.1109/iciea51954.2021.9516266.

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García-Barrachina, L. "Comparative studies of hyperbolic sine constitutive models for constant pressure superplastic tests." In Superplasticity in Advanced Materials. Materials Research Forum LLC, 2023. http://dx.doi.org/10.21741/9781644902615-30.

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Abstract. The constant pressure free-inflation test is a very versatile and simple tool for analyzing different features of superplastic forming. In recent years, different methods have been proposed to measure constitutive parameters of the stress–strain relationship for the superplastic material, specifically the K and m parameters of the power law model. However, this law is restricted to be used in narrow strain-rate ranges, and poor results are obtained when applied in a broader spectrum. To overcome this problem, numerous constitutive models covering the full strain-rate range applicable in superplastic forming have been proposed historically, including the hyperbolic sine equation. However, there is no clear consensus on the type of hyperbolic sine function to use. Some authors include a sensitivity parameter while others do not. This article aims to study the characteristics of the hyperbolic sine constitutive model, checking which of the historically proposed models achieves better results in the test at free deformation and constant pressure.
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Samuilik, Inna, Felix Sadyrbaev, and Svetlana Atslega. "On mathematical models of artificial neural networks." In 22nd International Scientific Conference Engineering for Rural Development. Latvia University of Life Sciences and Technologies, Faculty of Engineering, 2023. http://dx.doi.org/10.22616/erdev.2023.22.tf007.

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Artificial Neural Networks are in focus. The four-dimensional and the five-dimensional systems are considered. The activation function – hyperbolic tangent is used to model the Artificial Neural Networks. By changing one of the parameters in the system, different types of solutions are obtained: periodic solutions and chaotic solutions. The graphs of all solutions, the dynamics of Lyapunov exponents and 2D and 3D projections of attractors are provided using Wolfram Mathematica.
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Haque, Mohammad Shafinul, and Calvin M. Stewart. "Exploiting Functional Relationships Between MPC Omega, Theta, and Sinh-Hyperbolic Continuum Damage Mechanics Model." In ASME 2016 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/pvp2016-63089.

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The MPC Omega and Theta models for creep deformation and life prediction have become popular in recent years. Both models offer better prediction than classical constitutive models such as Norton Power law, Bailey-Norton law, and Norton-Soderberg law to name a few. The Omega model uses a strain hardening approach and requires two material constants for creep deformation and life prediction. An analytical solution to the constants are available and it is easy to manipulate and implement numerically. However, the analytical damage of the Omega model predicts an unrealistic linear damage evolution. The Theta model uses a time-hardening approach, and requires four constant that are a function of stress and temperature. For materials under isothermal conditions, with tertiary creep dominant deformation, the Theta model constants can be determined using only two constants. Life prediction using the Theta and Omega models depends on the final creep strain. The final creep strain observed in an experiment is stochastic; dependent on the material, testing conditions, and operator. The statistics of final creep strain must be investigated before the Theta or Omega models can be applied. In literature, some authors add a nonlinear damage variable to the Theta model; however, critical damage at rupture is not unity violating the assumptions of continuum damage mechanics. There is a superior Sin-hyperbolic continuum damage model available in the literature that can be used to overcome these problems. It is hypothesized that a functional relationships exist between the three models and these relationships can be exploited to achieve more accurate and easy to implement creep deformation and life predictions. In this study, the relationships between the constants of MPC Omega, Theta, and a Sin-hyperbolic CDM models are determined analytically. The sin-hyperbolic model incorporates a continuum damage variable in the creep strain rate equation. The damage function exhibits a more realistic elliptical path and is constructed such that damage is always unity at rupture. This function facilitates conversion of one models’ constants to the constants of the other two. The relationships between the constants are identified, while maintaining dimensional homogeneity. Using the derived relationships, the three models can be easily compared and the disadvantages of each respective model can be avoided. Experimental data at four different configurations of stress (6.3 to 36.5 ksi) and temperature (1200 to 1800°F) (sixteen data sets) for Hastelloy X is used to compare the models. Creep rupture data at seven temperature levels (600 to 1000°C) and a wide stress range (5 to 500 MPa) is used to analyze life prediction. The constants for each model are determined. Using one models’ constants and the derived relationships; the predictions of the other two models are generated. It is observed that the relationship generated curves agree with experimental data. Finally, it is demonstrated that using the derived relationships, the most useful aspects of each model can combined. An elliptical damage evolution curve is obtained for the Omega model. The final creep strain rate dependency problem of the Theta model can be avoided. It is observed that the Sinh model becomes more flexible and easy to implement.
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Sharma, Kal Renganathan. "Effect of Relativistic Transformation Methods on the Solutions of the Damped Wave Conduction and Relaxation Equation in Semi-Infinite Medium." In ASME 2009 Heat Transfer Summer Conference collocated with the InterPACK09 and 3rd Energy Sustainability Conferences. ASMEDC, 2009. http://dx.doi.org/10.1115/ht2009-88523.

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The expression for transient temperature during damped wave conduction and relaxation developed by Baumeister and Hamill by the method of Laplace transforms was further integrated. A Chebyshev polynomial approximation was used for the integrand with modified Bessel composite function in space and time. Telescoping power series leads to more useful expression for transient temperature. By the method of relativistic transformation the transient temperature during damped wave conduction and relaxation was developed. There are three regimes to the solution. A regime comprising of Bessel composite function in space and time and another regime comprising of modified Bessel composite function in space and time. The temperature solution at the wave front was also developed. The solution for transient temperature from the method of relativistic transformation is compared side by side with the solution for transient temperature from the method of Chebyshev economization. Both solutions are within 12% of each other. For conditions close to the wave front the solution from the Chebyshev economization is expected to be close to the exact solution and was found to be within 2% of the solution from the method of relativistic transformation. Far from the wave front, i.e., close to the surface the numerical error from the method of Chebyshev economization is expected to be significant and verified by a specific example. The solution for transient surface heat flux from the parabolic Fourier heart conduction model and the hyperbolic damped wave conduction and relaxation models are compared with each other. For τ&amp;gt; 1/2 the parabolic and hyperbolic solutions are within 10% of each other. The parabolic model has a “blow-up” at τ→0 and the hyperbolic model is devoid of singularities. The transient temperature from the Chebyshev economization is within an average of 25% of the error function solution for the parabolic Fourier heat conduction model. A penetration distance beyond which there is no effect of the step change in the boundary is predicted using the relativistic transformation model.
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8

Haque, Mohammad Shafinul. "Modification of the MPC Omega Model to Predict Primary and Tertiary Creep." In ASME 2019 Pressure Vessels & Piping Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/pvp2019-93100.

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Abstract The MPC Omega model has become popular in recent years for the prediction of creep deformation. Successful predictions of the tertiary creep for a wide range of materials are available. The Omega model relates the strain as a linear function of the natural logarithm of strain-rate. It is assumed that the primary creep is a short-lived phenomenon and can be neglected. The Omega model is unable to predict the primary creep deformation. Often primary creep is a long-lived phenomenon and cannot be neglected. A mathematical modification can be performed to incorporate the primary creep curve in the Omega model. A common approach is by adding a work hardening function to the original constitutive model. Approaches using power, or exponential, or logarithmic work-hardening function are available. However, it is difficult to discern which function is the best for accurate prediction. In this study, the Omega model is modified to predict the primary and tertiary creep deformation curve by adding a hyperbolic tangent work hardening function. A metamodel incorporating the four modified Omega sub-models (power, exponential, logarithmic and hyperbolic tangent) is developed. The metamodel enables the determination of the most suitable model for a given material and avoids the force fit of a preselected model. Short, medium, and long-term creep deformation data for alloy P91 (pipe) and G91 (plate) at two isotherms of 600°C and 650°C are used to calibrate the metamodel. The data include five stress levels ranging from 70 to 160 MPa including creep life from 233 to 1.1 × 105 hrs. A detail calibration process is provided. A numerical analysis is performed to compare the four submodels. It is observed that the selection of the most suitable function depends on the loading condition and material properties. Based on the analysis, a recommendation to select the suitable work-hardening function to predict the primary and tertiary creep deformation curve is presented.
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9

Kang, Seok-Jun, Hoomin Lee, Moon-Ki Kim, and Jae-Boong Choi. "Comparative Creep Life Evaluation of HR3C Using Creep Damage Models." In ASME 2017 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/pvp2017-65908.

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Recently, due to both environmental and energy efficiency, the designed life cycle of many power plant have been extended and also their operating temperature increased. When a material is exposed to high temperature over 50% of its melting temperature, it often shows unusual creep behavior in which the long time exposure of high temperature causes a microstructural degradation in the material and leads to creep rupture at a stress much lower than yield. Thus, there is a great significance in evaluating the creep life of high temperature components in power plant. In this study, accelerated uniaxial creep tests have been conducted to obtain material properties of HR3C at high temperature. The material properties of three damage models were derived from the accelerated short term creep tests in different stress conditions and the constitutive equation was the form of a power-law for the Kachanov and Liu-Murakami damage models and a hyperbolic sine function for the Dyson model, respectively. Based on these three damage models, the long term creep life was also evaluated. Using the creep rupture envelope, a modified grain boundary constrained cavitation coefficient function is proposed to resolve the constant failure strain problem. Also another modifications is made to the aging coefficient calculation by suggesting a new type of optimization function. By this, the classical problem of rupture time underestimation in the original Dyson model has been resolved. Consequently, the suggested creep life evaluation technique with a simple uniaxial creep example can be extended to more complicated engineering components at high temperature.
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10

Hagani, Fouad, M'hamed Boutaous, Ronnie Knikker, Shihe Xin, and Dennis Siginer. "Numerical Modeling of Non-Affine Viscoelastic Fluid Flow Including Viscous Dissipation Through a Square Cross-Section Duct: Heat Transfer Enhancement due to the Inertia and the Elastic Effects." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-23558.

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Abstract Non-isothermal laminar flow of a viscoelastic fluid including viscous dissipation through a square cross–section duct is analyzed. Viscoelastic stresses are described by Giesekus modele orthe Phan-Thien–Tanner model and the solvent shear stress is given by the linear Newtonian constitutive relationship. The flow through the tube is governed by the conservation equations of energy, mass, momentum associated with to one non–affine rheological model mentioned above. The mixed type of the governing system of equations (elliptic–parabolic–hyperbolic) requires coupling between discretisation methods designed for elliptic–type equations and techniques adapted to transport equations. To allow appropriate spatial discretisation of the convection terms, the system is rewritten in a quasi-linear first-order and homogeneous form without the continuity and energy equations. With the rheological models of the Giesekus type, the conformation tensor is by definition symmetrical and positive-definite, with the PTT model the hyperbolicity condition is subject to restrictions related to the rheological parameters. Based on this hyperbolicity condition, the contribution of the hyperbolic part is approximated by applying the characteristic method to extract pure advection terms which are then discretized by high ordre schemes WENO and HOUC. The algorithm thus developed makes it possible, to avoid the problems of instabilities related to the high Weissenberg number without the use of any stabilization method. Finally, a Nusselt number analysis is given as a function of inertia, elasticity, viscous dissipation, for constant solvent viscosity ratio and constant material and rheological parameters.
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