Relevant bibliographies by topics / Fitting functions(Mathematics)

Contents

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

Academic literature on the topic 'Fitting functions(Mathematics)'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "Fitting functions(Mathematics)"

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Gordon, Sheldon P. "FITTING SURGE FUNCTIONS TO DATA." PRIMUS 16, no. 1 (2006): 81–96. http://dx.doi.org/10.1080/10511970608984137.

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Rossa, Bernd, Dick Pulskamp, and Danny Otero. "REMARKS ON FITTING FUNCTIONS TO DATA." PRIMUS 8, no. 4 (1998): 289–304. http://dx.doi.org/10.1080/10511979808965905.

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Varah, J. M. "Least squares data fitting with implicit functions." BIT Numerical Mathematics 36, no. 4 (1996): 842–54. http://dx.doi.org/10.1007/bf01733795.

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Peker, Eli, and Ami Wiesel. "Fitting Generalized Multivariate Huber Loss Functions." IEEE Signal Processing Letters 23, no. 11 (2016): 1647–51. http://dx.doi.org/10.1109/lsp.2016.2612170.

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Kay, Steven. "Signal Fitting With Uncertain Basis Functions." IEEE Signal Processing Letters 18, no. 6 (2011): 383–86. http://dx.doi.org/10.1109/lsp.2011.2140397.

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Bottai, Matteo, and Nicola Orsini. "qmodel: A command for fitting parametric quantile models." Stata Journal: Promoting communications on statistics and Stata 19, no. 2 (2019): 261–93. http://dx.doi.org/10.1177/1536867x19854002.

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In this article, we introduce the qmodel command, which fits parametric models for the conditional quantile function of an outcome variable given covariates. Ordinary quantile regression, implemented in the qreg command, is a popular, simple type of parametric quantile model. It is widely used but known to yield erratic estimates that often lead to uncertain inferences. Parametric quantile models overcome these limitations and extend modeling of conditional quantile functions beyond ordinary quantile regression. These models are flexible and efficient. qmodel can estimate virtually any possible linear or nonlinear parametric model because it allows the user to specify any combination of qmodel-specific built-in functions, standard mathematical and statistical functions, and substitutable expressions. We illustrate the potential of parametric quantile models and the use of the qmodel command and its postestimation commands through realand simulated-data examples that commonly arise in epidemiological and pharmacological research. In addition, this article may give insight into the close connection that exists between quantile functions and the true mathematical laws that generate data.
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Einbeck, Jochen. "Multivariate Local Fitting with General Basis Functions." Computational Statistics 18, no. 2 (2003): 185–203. http://dx.doi.org/10.1007/s001800300140.

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Navascués, M. A., and M. V. Sebastián. "Fitting functions of Jackson type for three-dimensional data." International Journal of Computer Mathematics 97, no. 1-2 (2018): 157–74. http://dx.doi.org/10.1080/00207160.2018.1458099.

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Ameur, El Bachir, Driss Sbibih, and Paul Sablonniere. "A General Multiresolution Method for Fitting Functions on the Sphere." Numerical Algorithms 34, no. 2-4 (2003): 159–71. http://dx.doi.org/10.1023/b:numa.0000005360.94439.47.

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Wright, R. K. "Spline fitting discontinuous functions given just a few Fourier coefficients." Numerical Algorithms 9, no. 1 (1995): 157–69. http://dx.doi.org/10.1007/bf02143932.

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Dissertations / Theses on the topic "Fitting functions(Mathematics)"

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Altoumaimi, Rasha Talal. "Nonlinear Least-Square Curve Fitting of Power-Exponential Functions: Description and comparison of different fitting methods." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-38606.

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This thesis examines how to find the best fit to a series of data points when curve fitting using power-exponential models. We describe the different numerical methods such as the Gauss-Newton and Levenberg-Marquardt methods to compare them for solving non-linear least squares of curve fitting using different power-exponential functions. In addition, we show the results of numerical experiments that illustrate the effectiveness of this approach.Furthermore, we show its application to the practical problems by using different sets of data such as death rates and rocket-triggered lightning return strokes based on the transmission line model.
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Denka, Tshering. "Nonlinear Regression of Power-Exponential Functions : Experiment Design for Curve Fitting." Thesis, Mälardalens högskola, Utbildningsvetenskap och Matematik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-35897.

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This thesis explores how to best choose data when curve fitting using power exponential functions. The power exponential functions used are μ(b; x)=(xe1-x)b and Φ(ρ; x)=((1-x)ex)ρ . We use a number of designs such as the equidistant design, the Chebyshev design and the the D-optimal design to compare which design gives the best fit. A few examples including the logistic and the heidler function are looked at during the comparison. The measurement of the errors were made based on the sum of least squares errors in the first part and the maximum error in the second part. MATLAB was used in this comparison.
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Morad, Farhad. "Non-linear Curve Fitting." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-43600.

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The work done in this thesis is to examine various methods for curve fitting. Linear least squares and non-linear least squares will be described and compared, and the Newton method, Gauss--Newton method and Levenberg--Marquardt method will be applied to example problems.<br>Syftet med denna uppsats är att beskriva och använda olika metoder för kurvanpassning, det vill säga att passa matematiska funktioner till data. De metoder som undersöks är Newtons metod, Gauss--Newton metoden och Levenberg--Marquardt metoden. Även skillnaden mellan linjär minsta kvadrat anpassning och olinjär minsta kvadrat anpassning. Till sist tillämpas Newton, Gauss Newton och Levenberg--Marquardt metoderna på olika exempel.
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Hubrich, Simeon [Verfasser]. "The hierarchical finite cell method for nonlinear problems: moment fitting quadratures, basis function removel, and remeshing / Simeon Hubrich." Hamburg : Universitätsbibliothek der Technischen Universität Hamburg-Harburg, 2021. http://d-nb.info/1236991451/34.

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Atoui, Ibrahim Abdelhalim. "Data reduction techniques for wireless sensor networks using mathematical models." Thesis, Bourgogne Franche-Comté, 2018. http://www.theses.fr/2018UBFCD009.

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Dans ce travail, nous présentons des techniques de réduction de données et de sécurité conçues pour économiser de l’énergie dans les réseaux de capteurs sans fil. Premièrement, nous proposons un modèle d’agrégation de données basé sur la fonction de similarité servant à éliminer les données redondantes. En plus, nous avons travaillé sur l’envoi, le moins possible, de caractéristiques de données en se basant sur des fonctions d’ajustement qui expriment ces caractéristiques. Deuxièmement, nous nous sommes intéressés à l’hétérogénéité des données tout en étudiant la corrélation entre ces caractéristiques multi variantes après avoir éliminé les mesures identiques durant la phase d’agrégation. Finalement, nous donnons un cadre de sécurité rigoureux, conçu à partir de la cryptographie, qui satisfait le niveau d’exigence atteint normalement dans les réseaux de capteurs sans fil arborescents. Il empêche les pirates d’obtenir des informations à propos des données détectées en assurant une certaine confidentialité de bout-en-bout entre les nœuds du capteur et le puits. Afin de valider nos techniques proposées, nous avons implémenté les simulations de la première technique sur des données collectées en temps réel à partir du réseau Sensor Scope déployé à Grand-St-Bernard. Les simulations de la deuxième et de la troisième technique sont réalisées sur des données collectées en temps réel à partir de 54 capteurs déployés au laboratoire de recherche Intel Berkeley. L’efficacité de nos techniques est évaluée selon le taux de réduction de données, la consommation de l’énergie, la précision des données et la complexité de temps<br>In this thesis, we present energy-efficient data reduction and security techniques dedicated for wireless sensor networks. First, we propose a data aggregation model based on the similarity function that helps in removing the redundant data. In addition, based on the fitting functions we worked on sending less data features, accompanied with the fitting function that expresses all features. Second, we focus on heterogeneity of the data while studying the correlation among these multivariate features in order to enhance the data prediction technique that is based on the polynomial function, all after removing the similar measures in the aggregation phase using the Euclidean distance. Finally, we provide a rigorous security framework inherited from cryptography satisfies the level of exigence usually attained in tree-based WSNs. It prevents attackers from gaining any information about sensed data, by ensuring an end-to-end privacy between sensor nodes and the sink. In order to validate our proposed techniques, we implemented the simulations of the first technique on real readings collected from a small Sensor Scope network which is deployed at the Grand-St-Bernard, while the simulations of the second and the third techniques are conducted on real data collected from 54 sensors deployed in the Intel Berkeley Research Lab. The performance of our techniques is evaluated according to data reduction rate, energy consumption, data accuracy and time complexity
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Willersjö, Nyfelt Emil. "Comparison of the 1st and 2nd order Lee–Carter methods with the robust Hyndman–Ullah method for fitting and forecasting mortality rates." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-48383.

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The 1st and 2nd order Lee–Carter methods were compared with the Hyndman–Ullah method in regards to goodness of fit and forecasting ability of mortality rates. Swedish population data was used from the Human Mortality Database. The robust estimation property of the Hyndman–Ullah method was also tested with inclusion of the Spanish flu and a hypothetical scenario of the COVID-19 pandemic. After having presented the three methods and making several comparisons between the methods, it is concluded that the Hyndman–Ullah method is overall superior among the three methods with the implementation of the chosen dataset. Its robust estimation of mortality shocks could also be confirmed.
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Sulemana, Hisham. "Comparison of mortality rate forecasting using the Second Order Lee–Carter method with different mortality models." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-43563.

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Mortality information is very important for national planning and health of a country. Mortality rate forecasting is a basic contribution for the projection of financial improvement of pension plans, well-being and social strategy planning. In the first part of the thesis, we fit the selected mortality rate models, namely the Power-exponential function based model, the ModifiedPerks model and the Heligman and Pollard (HP4) model to the data obtained from the HumanMortality Database [22] for the male population ages 1–70 of the USA, Japan and Australia. We observe that the Heligman and Pollard (HP4) model performs well and better fit the data as compared to the Power-exponential function based model and the Modified Perks model. The second part is to systematically compare the quality of the mortality rate forecasting using the second order Lee–Carter method with the selected mortality rate models. The results indicate that Power-exponential function based model and the Heligman and Pollard (HP4) model gives a more reliable forecast depending on individual countries.
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Bothenna, Hasitha Imantha. "Approximation of Information Rates in Non-Coherent MISO wireless channels with finite input signals." University of Akron / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=akron1516369758012866.

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Olofsson, Anders. "Modern Stereo Correspondence Algorithms : Investigation and Evaluation." Thesis, Linköping University, Information Coding, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-57853.

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<p>Many different approaches have been taken towards solving the stereo correspondence problem and great progress has been made within the field during the last decade. This is mainly thanks to newly evolved global optimization techniques and better ways to compute pixel dissimilarity between views. The most successful algorithms are based on approaches that explicitly model smoothness assumptions made about the physical world, with image segmentation and plane fitting being two frequently used techniques.</p><p>Within the project, a survey of state of the art stereo algorithms was conducted and the theory behind them is explained. Techniques found interesting were implemented for experimental trials and an algorithm aiming to achieve state of the art performance was implemented and evaluated. For several cases, state of the art performance was reached.</p><p>To keep down the computational complexity, an algorithm relying on local winner-take-all optimization, image segmentation and plane fitting was compared against minimizing a global energy function formulated on pixel level. Experiments show that the local approach in several cases can match the global approach, but that problems sometimes arise – especially when large areas that lack texture are present. Such problematic areas are better handled by the explicit modeling of smoothness in global energy minimization.</p><p>Lastly, disparity estimation for image sequences was explored and some ideas on how to use temporal information were implemented and tried. The ideas mainly relied on motion detection to determine parts that are static in a sequence of frames. Stereo correspondence for sequences is a rather new research field, and there is still a lot of work to be made.</p>
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Books on the topic "Fitting functions(Mathematics)"

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Guido, Vanden Berghe, ed. Exponential fitting. Kluwer Academic Publishers, 2004.

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Gragg, William B. Downdating of Szego polynomials and data fitting applications. Naval Postgraduate School, 1992.

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Franke, Richard H. Least squares surface approximation to scattered data using multiquadric functions. Naval Postgraduate School, 1993.

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Tree structured function estimation with Haar wavelets. Verlag Dr. Kovač, 1999.

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Rubinstein, Robert. Rapid inversion of angular deflection data for certain axisymmetric refractive index distributions. National Aeronautics and Space Administration, 1994.

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Ixaru, Liviu Gr, and Guido Vanden Berghe. Exponential Fitting. Ixaru Liviu Gr Vanden Berghe Guido, 2010.

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Ixaru, Liviu Gr, and Guido Vanden Berghe. Exponential Fitting (Mathematics and Its Applications). Springer, 2004.

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Statistically generated weighted curve fit of residual functions for modal analysis of structures. National Aeronautics and Space Administration, George C. Marshall Space Flight Center, 1995.

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Book chapters on the topic "Fitting functions(Mathematics)"

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Bhattacharya, Binay, Sandip Das, and Tsunehiko Kameda. "Linear-Time Fitting of a k-Step Function." In Algorithms and Discrete Applied Mathematics. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29221-2_8.

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Georgieva, Irina, Clemens Hofreither, and Rumen Uluchev. "Least Squares Fitting of Harmonic Functions Based on Radon Projections." In Mathematical Methods for Curves and Surfaces. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-54382-1_9.

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Georgiev, Alexander A. "Local Properties of Function Fitting Estimates with Application to System Identification." In Mathematical Statistics and Applications. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5438-0_10.

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Garrett, Steven L. "Comfort for the Computationally Crippled." In Understanding Acoustics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44787-8_1.

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Abstract The difference between engineering and science, and all other human activity, is the fact that engineers and scientists make quantitative predictions about measurable outcomes and can specify their uncertainty in such predictions. Because those predictions are quantitative, they must employ mathematics. This chapter is intended as review of some of the more useful mathematical concepts, strategies, and techniques that are employed in the description of vibrational and acoustical systems and in the calculation of their behavior. Topics in this review include techniques such as Taylor series expansions, integration by parts, and logarithmic differentiation. Equilibrium and stability considerations lead to relations between potential energies and forces. The concept of linearity leads to superposition and Fourier analysis. Complex numbers and phasors are introduced along with the techniques for their algebraic manipulation. The discussion of physical units is extended to include their use for predicting functional dependencies of resonance frequencies, quality factors, propagation speeds, flow noise, and other system behaviors using similitude and the Buckingham Π-theorem to form dimensionless variables. Linearized least-squares fitting is introduced as a method for extraction of experimental parameters and their uncertainties and error propagation is presented to allow those uncertainties to be combined.
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Wang, ZhiLiang, Yanling Zhao, Lele Zou, and Masaeake Nagai. "An Objective Function of Artificial Psychology for a Computer System of Fashion Fitting." In Lecture Notes in Economics and Mathematical Systems. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-56038-5_12.

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Moreno-Quintero, Eric. "Modelling the Route Choice." In Handbook of Research on Military, Aeronautical, and Maritime Logistics and Operations. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-4666-9779-9.ch009.

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The issue of route choice is a key factor for the freight transport performance. Congestion at roads encourages hauliers to change routes to minimize the delays and keep lead times in a reliable range. In the context of transport planning, the route choice problem can be assessed by modelling the travel times needed to reach a destination through the different routes in a road network. Is in this point where the volume-delay functions become relevant. A Volume-Delay Function (VDF) is a mathematical representation of the increase of the travel time as more and more vehicles utilize the routes, causing congestion on the road networks. The related literature and practitioners report on the use of some known functional forms, as the BPR function, the Conical volume-delay function or the Akcelik's function, which are widely utilized in flow's assignation modelling in transport planning. A successful application of VDFs requires a proper fitting of the function's parameters. In a classical focus these parameters can be deduced from speed-flow surveys carried out at the routes or links of interest; these surveys generally require time money and personnel. As an alternative to this classical focus, particularly when facing scarcity of resources, this work carries out a mathematical analysis of the VDF functional forms, as well with an interpretation of their parameters in relation to road's operation. The results of these analyses clarifies the meaning of the functional forms for the VDFs and their parameters, and suggest other ways to assess those parameters which may be more practical for the purpose of modelling the choice of route in freight transport. Some considerations to put into practice this in Mexico are discussed at the end of this work.
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"Curve Fitting for Mechanical and Tribological Problems." In Advances in Systems Analysis, Software Engineering, and High Performance Computing. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-7078-4.ch009.

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This chapter devoted to matching the data with mathematical expressions. Here the functions using fitting by polynomial and non-polynomial expressions is represented by examples from the mechanics and tribology (M&amp;T) fields. The Basic Fitting tool and examples of its use are described. Single and multivariate fitting through optimization are discussed. Application examples are demonstrate the curve fitting for the following data: fuel efficiency-velocity, yield strength-grain diameter, friction coefficient-time, and machine diagnostic parameter.
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Churchland, Patricia S., and Terrence J. Sejnowski. "Computational Overview." In The Computational Brain. The MIT Press, 2016. http://dx.doi.org/10.7551/mitpress/9780262533393.003.0003.

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This chapter provides an overview of computational principles that may be useful when addressing the question of computation in nervous systems as well as questions of biological systems. It begins by introducing several key mathematical concepts, including “function,” and the distinction between computable and noncomputable functions, and between linear and nonlinear functions. It then considers a number of computational principles, such as the look-up table and linear associators, before discussing a new type of principle that can accomplish the satisfaction of constraints by a process of “relaxation.” In particular, it describes Hopfield networks and Boltzmann machines. It also examines learning in neural nets, competitive learning, curve fitting, feedforward nets, and recurrent nets. Finally, it assesses the importance of optimization procedures to neuroscience, along with the use of realistic and abstract network models in neuroscience.
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Hassan, Said Ali, and Miral Hossam Khodeir. "A Model for Reducing the Cost of Refueling in a Flight Route Problem With Discounted Fuel Prices." In Advances in Logistics, Operations, and Management Science. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-8040-0.ch001.

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Acquiring and purchasing fuel represents a significant part of operating and managing expenses for an airline, so commercial airline companies are implementing strategies for minimizing costs of fuel for their flight routes. A nonlinear mathematical model for the airline refueling problem is presented to minimize the total cost in a flight route problem. The model is enhanced to include possible discounts in fuel prices, which are performed by adding dummy variables and some restrictive constraints, or by fitting a suitable function that relates prices to the purchased amounts. The obtained fuel plan explains exactly the amounts of fuel to be purchased from each airport in the route. A case study is introduced for a certain flight rotation in a domestic US air aviation company. The mathematical model including stepped discounted fuel prices is formulated, and the results show that introducing the discounted fuel prices dramatically change the strategy of fuel purchase amounts in the aircraft flight problem.
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Conference papers on the topic "Fitting functions(Mathematics)"

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Cardone, A., B. Paternoster, and G. Santomauro. "Exponential fitting quadrature rule for functional equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756358.

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Batcha, Siti Rahimah, Hamzah Sakidin, and Asmala Ahmad. "Simpler hydrostatics component of UNBabc mapping function using nonlinear curve fitting method." In ADVANCES IN INDUSTRIAL AND APPLIED MATHEMATICS: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences (SKSM23). Author(s), 2016. http://dx.doi.org/10.1063/1.4954572.

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Lanzafame, R., and M. Messina. "Experimental Data Extrapolation by Using V Order Logarithmic Polynomials." In ASME 2002 Internal Combustion Engine Division Spring Technical Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/ices2002-458.

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In this work, the authors consider the possibility to extrapolate experimental data on fuels specific heat at constant pressure, beyond the range of temperature investigated in the experimental measurements. With a proper extrapolation it is possible to avoid the necessary but empirical linear extrapolation, often used by CFD programs. Mathematical functions obtained from fitting experimental data are very useful when computational models on ICE are implemented. To obtain reliable results from these models, a great precision is required to the mathematical functions. In this work a new polynomial, used in order to fit experimental data on gases properties at low pressure, is presented. The new mathematical function presented has the functional form of a fifth order Logarithmic Polynomial, and it is evaluated through the least squares method, on the basis of experimental thermodynamic data found in literature. This new function presents three great advantage in respect to traditional polynomials used in literature: 1) it offers a great fitting precision (correlation factor R2 greater than 0.99); 2) it is able to cover wide range of temperature with a single polynomial; 3) it gives the possibility to extrapolate data beyond experimental temperature range.
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García-Bermúdez, Rodolfo, Camilo Velázquez, Fernando Rojas, et al. "A Comparison of Two Fitting Functions for Sacadic Pulse Component Mathematical Modelling." In International Workshop on Artificial Neural Networks and Intelligent Information Processing. SCITEPRESS - Science and and Technology Publications, 2014. http://dx.doi.org/10.5220/0005136800880094.

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Carminelli, Antonio, and Giuseppe Catania. "Curve and Surface Fitting by Means of Rational B-Spline Functions." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-67422.

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This paper presents a method to obtain the mathematical model of a free-form curve or a surface fitting a set of point coordinates by a rational B-spline (NURBS) formulation in the homogeneous R4 space. A method to evaluate the control points R4 coordinates is proposed by means of a two step process. In the first step, NURBS weights are evaluated by means of an optimization procedure making it possible to evaluate the best fitting parameterization as well. In the second step, the control point coordinates are computed by means of a linear least squares approach.
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Jiang, Ren-qiang, Yue-lei Wu, Zhi-rong Lu, and Tie-jun Zhang. "The Optimization of Mathematic Model of Penumbral Imaging System’s Point Spread Function." In 18th International Conference on Nuclear Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/icone18-29743.

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In inertial confinement fusion (ICF) project, there are many diagnostic methods. Neutron penumbral imaging is one of the important technologies to diagnose the information about neutron spatial and temporal distribution in burn region of the core of a compressed pellet in the low yield fusion. In this study, a linear space invariant neutron penumbral imaging system was designed and established with Monte Carlo method, the system’s point spread function (PSF) was obtained. By fitting the obtained PSF, several mathematic models were obtained and compared. The improved “logistic function” mathematic model was chosen to reconstruct the coded penumbral image and the original neutron source image “T” was successfully was obtained.
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Lanzafame, R., and M. Messina. "Fuels Characterization for Use in Internal Combustion Engines." In ASME 2001 Internal Combustion Engine Division Fall Technical Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/2001-ice-421.

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Abstract It is important provide mathematical functions able to fit with great precision experimental data on gases properties, in order to obtain reliable results when computerized models on IC engines are used. On the basis of experimental data on equilibrium constants (for dissociation phenomena occurring during combustion process in IC engines) new mathematical functions have been determined to fit experimental data. In comparison to traditional fitting polynomials, these new mathematical functions present a great accuracy in matching experimental data. These new mathematical functions have the functional forms of a V order Logarithmic Polynomial, and their coefficients have been evaluated on the basis of the least square method. The new V order Logarithmic Polynomials have been determined for several dissociation reactions according to internal combustion processes applications. V order Logarithmic Polynomials have been implemented also to describe the trend of specific heat at constant pressure Vs temperature and enthalpy Vs temperature. These new Logarithmic Polynomials have been calculated for several gases and fuels for IC engines applications. The new Logarithmic Polynomials pointed out a better precision in comparison to the others polynomial functions used in literature, and the possibility to utilize a single Logarithmic Polynomial for a wide temperature range, according to a good accuracy with experimental data. Another advantage of the Logarithmic Polynomials is the possibility to extrapolate experimental data on a wide temperature range (25% of experimental T range) in order to supply to the experimental data shortage.
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Galvin, Daniel D. "Tuning of a Rear Electronic Control Engine Mount." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0584.

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Abstract This paper refers to mathematical tuning, by the sinusoidal steady-state transfer function method, of an adjustable hydraulic rear engine mount for reduction of perceived vibration during engine idle situations. The problem being addressed, in particular, is the reduction of “idle shake”. The accuracy of this method is confirmed by individual component testing along with in situ vibration measurements. During this work, a general approach to transfer function calculation is given by evaluating the system components with the linear-graph system of modeling. This is complemented by component verification and curve-fitting to arrive at the final transfer function which reveals the inherent tendencies of the overall system. Secondary measurements are then employed to rectify the contradiction between mathematical values and subjective results.
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Chen, Yih-Jen D. "Smooth Surface Fitting and Finite Element Mesh Generation for Irregularly Distributed Data Points." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0372.

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Abstract This paper presents two computational methods for geometric modeling of curved surfaces represented by irregularly distributed data points. The study emphasizes irregularly distributed data points since this represents the most general case in geometric data interpretation. The first method is a direct mesh mapping procedure, which projects an relatively regular mesh to the complicated real surface. The second method is a surface fitting technique that reconstructs the mathematical surface model using piecewise bi-cubic parametric functions or B-spline functions. This data reconstruction method uses a normal-distance least-squares concept to generate the best fit. Recursive subdivision algorithm and quad tree data structure are applied to optimize the number of patches needed within the desired precision and thus minimize the computing time in the further processing of the surface model. A computer program based on the two computational methods in surface modeling has been developed and demonstrated by its engineering application. Its development provides an automated tool for design engineers and structure analysts to interpret and model complex surfaces derived from data points.
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Gray, Allison, and Allan Lewandowski. "Sensitivities in Fitting a Parabolic Trough Facet." In ASME 2012 6th International Conference on Energy Sustainability collocated with the ASME 2012 10th International Conference on Fuel Cell Science, Engineering and Technology. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/es2012-91453.

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The collector accuracy requirements for parabolic trough systems are a function of the concentrator and receiver geometry. As the current trend is to use larger trough designs the need for higher accuracy is generally more important. Concentrating solar power (CSP) companies developing and deploying collectors need to meet stringent optical performance requirements and thus require accurate surface characterization instruments to validate that performance. All reflective characterization processes are sensitive to the instrument resolution, experimental setup, data fitting process, and analysis. Small changes in any of these factors can impact the estimated optical performance. It is desirable to have total local surface measurement uncertainties less than 0.5 milliradians (mrad) for a parabolic trough reflector and many instruments are capable of achieving this. Most surface characterization instruments perform a fitting process on measured data that yields a best fit description of the collector surface using some sort of polynomial. Because of this relationship it is desirable to have a robust fitting process. The type and order of the fitted polynomial and fitting process are the two major contributors to describing a facet’s surface based on the measured data. The order of the polynomial can increase or decrease the accuracy of surface description relative to the true surface. This is a function of the existing aberrations in the facet and the surface naturally described by the polynomial. An accurate description of a surface is typically obtained by performing a least squares fit on measured surface data relative to the polynomial. The best analytical description of the surface is achieved when residual errors relative to the polynomial are minimized. The difference between measured data and the best fit description is completed using an iterative process. However, not all surface imperfections on a single reflector can be accurately described with a polynomial as an exact mathematical description of the surface can never be truly achieved. Local positional errors exist in isolated areas of a facet cannot always be fit accurately. The sensitivity in the best fit description of the surface and the surface resulting from the fitting process using higher order polynomials will be discussed in this paper. The change in calculated facet location and surface slope are compared to determine the sensitivity of the process. The results are then used to calculate the intercept factor using ray tracing and estimate the sensitivity in this calculated performance metric.
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