Exponential Fitting

In this book, a series of aspects is covered, ranging from the theory of the procedure up to direct applications and sometimes including ready to use programs. The book can also be used as a textbook for graduate students.

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Author: Liviu Gr. Ixaru

Publisher: Springer Science & Business Media

ISBN: 1402020996

Category: Mathematics

Page: 308

View: 140

Exponential Fitting is a procedure for an efficient numerical approach of functions consisting of weighted sums of exponential, trigonometric or hyperbolic functions with slowly varying weight functions. This book is the first one devoted to this subject. Operations on the functions described above like numerical differentiation, quadrature, interpolation or solving ordinary differential equations whose solution is of this type, are of real interest nowadays in many phenomena as oscillations, vibrations, rotations, or wave propagation. The authors studied the field for many years and contributed to it. Since the total number of papers accumulated so far in this field exceeds 200 and the fact that these papers are spread over journals with various profiles (such as applied mathematics, computer science, computational physics and chemistry) it was time to compact and to systematically present this vast material. In this book, a series of aspects is covered, ranging from the theory of the procedure up to direct applications and sometimes including ready to use programs. The book can also be used as a textbook for graduate students.

Exponential Data Fitting and Its Applications

"Real and complex exponential data fitting is an important activity in many different areas of science and engineering, ranging from Nuclear Magnetic Resonance Spectroscopy and Lattice Quantum Chromodynamics to Electrical and Chemical ...

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Author: Victor Pereyra

Publisher: Bentham Science Publishers

ISBN: 9781608050482

Category: Computers

Page: 195

View: 228

"Real and complex exponential data fitting is an important activity in many different areas of science and engineering, ranging from Nuclear Magnetic Resonance Spectroscopy and Lattice Quantum Chromodynamics to Electrical and Chemical Engineering, Vision a"

Least Squares Fitting of Exponential Functions

This paper develops two methods for dealing with the above difficulty. The first method employs Newton's Formula to fit the general form f(x) = alpha + beta(x to the power a)(e to the power(gamma(x to the power b))).

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Author: V. Behrns

Publisher:

ISBN: OCLC:227589784

Category:

Page: 35

View: 690

In attempting to fit an exponential function to a set of data points by the method of least squares, the general situation is that the equations resulting from partial differentiation are transcendental in one or more of the parameters and cannot be solved by the usual algebraic methods. This paper develops two methods for dealing with the above difficulty. The first method employs Newton's Formula to fit the general form f(x) = alpha + beta(x to the power a)(e to the power(gamma(x to the power b))). The second method employs numerical analytic methods to fit the form f(x) = alpha + beta(e to the power(gamma x)). (Author).

A Method for Nonlinear Exponential Regression Analysis

Foss , S. D .: A Method of Exponential Curve Fitting by Numerical Integration . Biometrics , December 1970 , pp . 815-821 . 5 . Behrns , V .: Least Squares ...

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Author: Bobby G. Junkin

Publisher:

ISBN: NASA:31769000531684

Category: Mathematical models

Page: 94

View: 533

Exponential Fitting

In this book, a series of aspects is covered, ranging from the theory of the procedure up to direct applications and sometimes including ready to use programs. The book can also be used as a textbook for graduate students.

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Author: Liviu Gr. Ixaru

Publisher: Springer

ISBN: 9401569827

Category: Mathematics

Page: 308

View: 345

Exponential Fitting is a procedure for an efficient numerical approach of functions consisting of weighted sums of exponential, trigonometric or hyperbolic functions with slowly varying weight functions. This book is the first one devoted to this subject. Operations on the functions described above like numerical differentiation, quadrature, interpolation or solving ordinary differential equations whose solution is of this type, are of real interest nowadays in many phenomena as oscillations, vibrations, rotations, or wave propagation. The authors studied the field for many years and contributed to it. Since the total number of papers accumulated so far in this field exceeds 200 and the fact that these papers are spread over journals with various profiles (such as applied mathematics, computer science, computational physics and chemistry) it was time to compact and to systematically present this vast material. In this book, a series of aspects is covered, ranging from the theory of the procedure up to direct applications and sometimes including ready to use programs. The book can also be used as a textbook for graduate students.

Intermediate Statistics For Dummies

For more details on what shape to look for, see the section “Recollecting exponential models.” 2. Use Minitab to fit a line to the log(y) data.

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Author: Deborah J. Rumsey

Publisher: John Wiley & Sons

ISBN: 9780470147740

Category: Mathematics

Page: 362

View: 442

Need to know how to build and test models based on data? Intermediate Statistics For Dummies gives you the knowledge to estimate, investigate, correlate, and congregate certain variables based on the information at hand. The techniques you’ll learn in this book are the same techniques used by professionals in medical and scientific fields. Picking up right where Statistics For Dummies left off, this straightforward, easy-to-follow book guides you beyond Central Limit Theorem and hypothesis tests and immerses you in flavors of regression, ANOVA, and nonparametric procedures. Unlike regular statistics books, this guide provides full explanations of intermediate statistical ideas; computer input dissection; an extensive number of examples, tips, strategies, and warnings; and clear, concise step-by-step procedures—all in a language you can understand. You’ll soon discover how to: Analyze data and base models off of your data Make predictions using regression Compare many means with ANOVA Test models using Chi-square Dealing with abnormal data In addition, this book includes a list of wrong statistical conclusions and common questions that professors ask using computer output. This book also adopts a nonlinear approach, making it possible to skip to the information you need without having to read previous chapters. With Intermediate Statistics For Dummies, you’ll have all the tools you need to make important decisions in all types of professional areas—from biology and engineering to business and politics!

Imaging from Cells to Animals In Vivo

Commercial soft- ware such as SPCImage (Becker and Hickl), SymPhoTime (PicoQuant), and DAS6 (Horiba) use exponential curve fitting for two components: ...

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Author: Margarida Barroso

Publisher: CRC Press

ISBN: 9781351704502

Category: Science

Page: 356

View: 640

Imaging from Cells to Animals In Vivo offers an overview of optical imaging techniques developed over the past two decades to investigate biological processes in live cells and tissues. It comprehensively covers the main imaging approaches used as well as the application of those techniques to biological investigations in preclinical models. Among the areas covered are cell metabolism, receptor-ligand interactions, membrane trafficking, cell signaling, cell migration, cell adhesion, cytoskeleton and other processes using various molecular optical imaging techniques in living organisms, such as mice and zebrafish. Features Brings together biology and advanced optical imaging techniques to provide an overview of progress and modern methods from microscopy to whole body imaging. Fills the need for a comprehensive view of application-driven development and use of new tools to ask new biological questions in the context of a living system. Includes basic chapters on key methods and instrumentation, from fluorescence microscopy and imaging to endoscopy, optical coherence tomography and super-resolution imaging. Discusses approaches at different length scales and biomedical applications to the study of single cell, whole organ, and whole organism behavior. Addresses the impact on discovery, such as cellular function as implicated in human disease and translational medicine, for example in cancer diagnosis. Margarida M. Barroso is a Professor in the Department of Molecular and Cellular Physiology, Albany Medical College (Albany, New York). Xavier Intes is a Professor in the Biomedical Engineering Department and Co-Director of the Center for Modeling, Simulation and Imaging for Medicine (CeMSIM) at Rensselaer Polytechnic Institute (Troy, New York).

Mechanisms of Catalysis

approaches to data analysis: first, the conventional fitting of data to ... Thus for a single exponential, the fitting process provides the amplitude (A), ...

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Author: David S. Sigman

Publisher: Academic Press

ISBN: 9780121227203

Category: Science

Page: 546

View: 407

Discrete Event Simulation

These are usually available from the software fitting applications or are easily ... For exponential fitting, the mode is at zero and the tailexponential.

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Author: George S. Fishman

Publisher: Springer Science & Business Media

ISBN: 9781475735529

Category: Computers

Page: 537

View: 869

"This is an excellent and well-written text on discrete event simulation with a focus on applications in Operations Research. There is substantial attention to programming, output analysis, pseudo-random number generation and modelling and these sections are quite thorough. Methods are provided for generating pseudo-random numbers (including combining such streams) and for generating random numbers from most standard statistical distributions." --ISI Short Book Reviews, 22:2, August 2002

Practical Handbook of Curve Fitting

The book demonstrates how to analyze World data bases and graph and map the results. Default settings in software packages can produce attractive graphs of data imported into the software.

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Author: Sandra Arlinghaus

Publisher: CRC Press

ISBN: 0849301432

Category: Mathematics

Page: 272

View: 871

Practical Handbook of Curve Fitting is a reference work assembled by Arlinghaus and a set of editors with well over a century of combined experience in various disciplines and activities related to curve fitting. The book demonstrates how to analyze World data bases and graph and map the results. Default settings in software packages can produce attractive graphs of data imported into the software. Often, however, the default graph has no equation associated with it and cannot therefore be used as a tool for further analysis or projection of the data. The same software can often be used to generate curves from equations. The reader is shown directly, and in a series of steps, how to fit curves to data using Lotus 1-2-3. There are traditional unbounded curve fitting techniques-lines of least squares, exponentials, logistic curves, and Gompertz curves. There is the bounded curve fitting technique of cubic spline interpolation. Beyond these, there is a detailed application of Feigenbaum's graphical analysis from chaos theory, and there is a hint as to how fractal geometry might come into play. Curve fitting algorithms take on new life when they are actually used on real-world data. They are used in numerous worked examples drawn from electronic data bases of public domain information from the Stars data base of The World Bank and from the WRD data base of the World Resources Institute. The applications are current and reflect a state-of-the-art interest in the human dimensions of global change.

College Algebra Concepts and Contexts

I 3.5 Fitting Exponential Curves to Data I Finding Exponential Models for Data I Is an Exponential Model Appropriate? I Modeling Logistic Growth m we learn ...

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Author: James Stewart

Publisher: Cengage Learning

ISBN: 9781111780708

Category: Mathematics

Page: 816

View: 416

This text bridges the gap between traditional and reform approaches to algebra encouraging students to see mathematics in context. It presents fewer topics in greater depth, prioritizing data analysis as a foundation for mathematical modeling, and emphasizing the verbal, numerical, graphical and symbolic representations of mathematical concepts as well as connecting mathematics to real life situations drawn from the students' majors. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Fitting Statistical Distributions

As we have already considered fitting a largest extreme value distribution, ... 2.4.14 The Double Exponential Distribution The double exponential ...

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Author: Zaven A. Karian

Publisher: CRC Press

ISBN: 9781420038040

Category: Mathematics

Page: 438

View: 491

Throughout the physical and social sciences, researchers face the challenge of fitting statistical distributions to their data. Although the study of statistical modelling has made great strides in recent years, the number and variety of distributions to choose from-all with their own formulas, tables, diagrams, and general properties-continue to create problems. For a specific application, which of the dozens of distributions should one use? What if none of them fit well? Fitting Statistical Distributions helps answer those questions. Focusing on techniques used successfully across many fields, the authors present all of the relevant results related to the Generalized Lambda Distribution (GLD), the Generalized Bootstrap (GB), and Monte Carlo simulation (MC). They provide the tables, algorithms, and computer programs needed for fitting continuous probability distributions to data in a wide variety of circumstances-covering bivariate as well as univariate distributions, and including situations where moments do not exist. Regardless of your specific field-physical science, social science, or statistics, practitioner or theorist-Fitting Statistical Distributions is required reading. It includes wide-ranging applications illustrating the methods in practice and offers proofs of key results for those involved in theoretical development. Without it, you may be using obsolete methods, wasting time, and risking incorrect results.

Environmental Statistics and Data Analysis

Tail Exponential Method Although the exponential model may fit the tail of a distribution fairly well , it does not necessarily also fit the rest of the ...

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Author: Wayne R. Ott

Publisher: CRC Press

ISBN: 0873718488

Category: Mathematics

Page: 336

View: 291

This easy-to-understand introduction emphasizes the areas of probability theory and statistics that are important in environmental monitoring, data analysis, research, environmental field surveys, and environmental decision making. It communicates basic statistical theory with very little abstract mathematical notation, but without omitting important details and assumptions. Topics include Bayes' Theorem, geometric distribution, computer simulation, histograms and frequency plots, maximum likelihood estimation, the tail exponential method, Bernoulli processes, Poisson processes, diffusion and dispersion of pollutants, normal distribution, confidence intervals, and stochastic dilution; gamma, chi-square, and Weibull distributions; and the two- and three-parameter lognormal distributions. The author also presents the Statistical Theory of Rollback, which allows data analysts and regulatory officials to estimate the effect of different emission control strategies on environmental quality frequency distributions. Assuming only a basic knowledge of algebra and calculus, Environmental Statistics and Data Analysis provides an outstanding reference and collection of statistical procedures for analyzing environmental data and making accurate environmental predictions.

Experimental Vibration Analysis for Civil Structures

The fitting result is shown in Figure 33.9. When the Two-term Exponential fitting is adopted, since the acceleration response skewness is almost 0, ...

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Author: Jian Zhang

Publisher: CRC Press

ISBN: 9781000178654

Category: Technology & Engineering

Page: 586

View: 639

Experimental Vibration Analysis for Civil Structures: Testing, Sensing, Monitoring, and Control covers a wide range of topics in the areas of vibration testing, instrumentation, and analysis of civil engineering and critical infrastructure. It explains how recent research, development, and applications in experimental vibration analysis of civil engineering structures have progressed significantly due to advancements in the fields of sensor and testing technologies, instrumentation, data acquisition systems, computer technology, computational modeling and simulation of large and complex civil infrastructure systems. The book also examines how cutting-edge artificial intelligence and data analytics can be applied to infrastructure systems. Features: Explains how recent technological developments have resulted in addressing the challenge of designing more resilient infrastructure Examines numerous research studies conducted by leading scholars in the field of infrastructure systems and civil engineering Presents the most emergent fields of civil engineering design, such as data analytics and Artificial Intelligence for the analysis and performance assessment of infrastructure systems and their resilience Emphasizes the importance of an interdisciplinary approach to develop the modeling, analysis, and experimental tools for designing more resilient and intelligent infrastructures Appropriate for practicing engineers and upper-level students, Experimental Vibration Analysis for Civil Structures: Testing, Sensing, Monitoring, and Control serves as a strategic roadmap for further research in the field of vibration testing and instrumentation of infrastructure systems.

Maple and Mathematica

Fit, fitting a model function to data, ExponentialFit, LogarithmicFit, fitting exponential and logarithmic functions to data, LinearFit, NonlinearFit, ...

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Author: Inna K. Shingareva

Publisher: Springer Science & Business Media

ISBN: 9783211994337

Category: Computers

Page: 484

View: 539

In the history of mathematics there are many situations in which cal- lations were performed incorrectly for important practical applications. Let us look at some examples, the history of computing the number ? began in Egypt and Babylon about 2000 years BC, since then many mathematicians have calculated ? (e. g. , Archimedes, Ptolemy, Vi` ete, etc. ). The ?rst formula for computing decimal digits of ? was disc- ered by J. Machin (in 1706), who was the ?rst to correctly compute 100 digits of ?. Then many people used his method, e. g. , W. Shanks calculated ? with 707 digits (within 15 years), although due to mistakes only the ?rst 527 were correct. For the next examples, we can mention the history of computing the ?ne-structure constant ? (that was ?rst discovered by A. Sommerfeld), and the mathematical tables, exact - lutions, and formulas, published in many mathematical textbooks, were not veri?ed rigorously [25]. These errors could have a large e?ect on results obtained by engineers. But sometimes, the solution of such problems required such techn- ogy that was not available at that time. In modern mathematics there exist computers that can perform various mathematical operations for which humans are incapable. Therefore the computers can be used to verify the results obtained by humans, to discovery new results, to - provetheresultsthatahumancanobtainwithoutanytechnology. With respectto our example of computing?, we can mention that recently (in 2002) Y. Kanada, Y. Ushiro, H. Kuroda, and M.

Chemical Modelling

2.1.7 Open Problems in Exponential Fitting. – In future years it will be interesting to investigate the following about exponential fitting: 1.

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Author: Alan Hinchliffe

Publisher: Royal Society of Chemistry

ISBN: 9781847553317

Category: Science

Page: 524

View: 932

Chemical Modelling: Applications and Theory comprises critical literature reviews of molecular modelling, both theoretical and applied. Molecular modelling in this context refers to modelling the structure, properties and reactions of atoms, molecules & materials. Each chapter is compiled by experts in their fields and provides a selective review of recent literature. With chemical modelling covering such a wide range of subjects, this Specialist Periodical Report serves as the first port of call to any chemist, biochemist, materials scientist or molecular physicist needing to acquaint themselves of major developments in the area. Specialist Periodical Reports provide systematic and detailed review coverage in major areas of chemical research. Compiled by teams of leading authorities in the relevant subject areas, the series creates a unique service for the active research chemist, with regular, in-depth accounts of progress in particular fields of chemistry. Subject coverage within different volumes of a given title is similar and publication is on an annual or biennial basis. Current subject areas covered are Amino Acids, Peptides and Proteins, Carbohydrate Chemistry, Catalysis, Chemical Modelling. Applications and Theory, Electron Paramagnetic Resonance, Nuclear Magnetic Resonance, Organometallic Chemistry. Organophosphorus Chemistry, Photochemistry and Spectroscopic Properties of Inorganic and Organometallic Compounds. From time to time, the series has altered according to the fluctuating degrees of activity in the various fields, but these volumes remain a superb reference point for researchers.

A Higher Order Exponential Function for Fitting Nonlinear Curves

Numerous mathematical methods have evolved over the years for fitting curves that exhibit nonlinear character.

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Author:

Publisher:

ISBN: OCLC:227786799

Category:

Page: 19

View: 424

Numerous mathematical methods have evolved over the years for fitting curves that exhibit nonlinear character. In this technical memorandum, the authors present a continuous function, the Rachele/Kilmer (R/K) optical profile function, that was originally configured by R/K to fit model simulated vertical profiles of extinction and backscatter coefficients in very low stratus clouds and subcloud regions. The R/K function fits most of the nonlinear optical profiles so well that the authors were encouraged to investigate its potential for fitting nonlinear curves that were produced by other physical/mathematical models. Results are presented that demonstrate the versatility and power of the R/K function when fitting simulated data from three different models.