Relevant bibliographies by topics / Number theory. Error analysis (Mathematics)

Contents

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

Academic literature on the topic 'Number theory. Error analysis (Mathematics)'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Number theory. Error analysis (Mathematics)"

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T., V., Solomon G. Mikhlin, and Reinhard Lehmann. "Error Analysis in Numerical Processes." Mathematics of Computation 60, no. 201 (1993): 431. http://dx.doi.org/10.2307/2153180.

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Wu, Xinyuan, and Zhengyu Wang. "A new iterative refinement with roundoff error analysis." Numerical Linear Algebra with Applications 18, no. 2 (2010): 275–82. http://dx.doi.org/10.1002/nla.723.

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Stewart, G. W. "Error Analysis of QR Updating with Exponential Windowing." Mathematics of Computation 59, no. 199 (1992): 135. http://dx.doi.org/10.2307/2152984.

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Calvetti, Daniela. "A stochastic roundoff error analysis for the convolution." Mathematics of Computation 59, no. 200 (1992): 569. http://dx.doi.org/10.1090/s0025-5718-1992-1134719-8.

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Stewart, G. W. "Error analysis of $QR$ updating with exponential windowing." Mathematics of Computation 59, no. 199 (1992): 135. http://dx.doi.org/10.1090/s0025-5718-1992-1134738-1.

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MROZEC, MARIAN. "Rigorous Error Analysis of Numerical Algorithms via Symbolic Computations." Journal of Symbolic Computation 22, no. 4 (1996): 435–58. http://dx.doi.org/10.1006/jsco.1996.0061.

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Buccimazza, Biagio, Bal Kishan Dass, and Sapna Jain. "High-density-burst error detection." Journal of Discrete Mathematical Sciences and Cryptography 7, no. 1 (2004): 5–21. http://dx.doi.org/10.1080/09720529.2004.10697984.

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Hou, Thomas Y., and Philippe G. LeFloch. "Why nonconservative schemes converge to wrong solutions: error analysis." Mathematics of Computation 62, no. 206 (1994): 497. http://dx.doi.org/10.1090/s0025-5718-1994-1201068-0.

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Deckelnick, Klaus, and Gerhard Dziuk. "Error analysis for the elastic flow of parametrized curves." Mathematics of Computation 78, no. 266 (2008): 645–71. http://dx.doi.org/10.1090/s0025-5718-08-02176-5.

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Calvetti, Daniela. "A stochastic roundoff error analysis for the fast Fourier transform." Mathematics of Computation 56, no. 194 (1991): 755. http://dx.doi.org/10.1090/s0025-5718-1991-1068824-0.

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Dissertations / Theses on the topic "Number theory. Error analysis (Mathematics)"

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Lau, Yuk-kam, and 劉旭金. "Error terms in the summatory formulas for certain number-theoretic functions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31238804.

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Lau, Yuk-kam. "Error terms in the summatory formulas for certain number-theoretic functions /." Hong Kong : University of Hong Kong, 1999. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20897509.

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Buchanan, Dan Matthews. "Analytic Number Theory and the Prime Number Theorem." Youngstown State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1525451327211365.

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Anglin, William Sherron Raymond. "The nature of solutions in mathematics /." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=72100.

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What constitutes an adequate solution to a mathematical problem? When is an adequate solution a 'good' solution? In this thesis I consider these questions in relation to two Diophantine equations, namely, x$ sp2$ + k = y$ sp3$ and 6y$ sp2$ = x(x + 1)(2x + 1). The first dates back to Diophantus himself (c. 250 AD) while the second can be traced to a puzzle proposed by Edouard Lucas in 1875. Each of these equations has attracted a number of solutions and each solution reveals something about its era. An examination and comparison of these solutions will give us an opportunity to reflect on some
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Wang, Stephen. "Zeta Function Regularization and its Relationship to Number Theory." Digital Commons @ East Tennessee State University, 2021. https://dc.etsu.edu/etd/3895.

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While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and
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Huang, Fang-Lun. "Error analysis and tractability for multivariate integration and approximation." HKBU Institutional Repository, 2004. http://repository.hkbu.edu.hk/etd_ra/515.

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Harper, John-Paul. "The class number one problem in function fields." Thesis, Stellenbosch : Stellenbosch University, 2003. http://hdl.handle.net/10019.1/53619.

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Thesis (MComm)--Stellenbosch University, 2003.<br>ENGLISH ABSTRACT: In this dissertation I investigate the class number one problem in function fields. More precisely I give a survey of the current state of research into extensions of a rational function field over a finite field with principal ring of integers. I focus particularly on the quadratic case and throughout draw analogies and motivations from the classical number field situation. It was the "Prince of Mathematicians" C.F. Gauss who first undertook an in depth study of quadratic extensions of the rational numbers and the corre
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Lennon, Craig. "On the likely number of stable marriages." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1194991095.

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欒世武 and Shiwu Luan. "Structural inference of linear models for some families of error distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B31237502.

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Luan, Shiwu. "Structural inference of linear models for some families of error distributions /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B19979368.

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Books on the topic "Number theory. Error analysis (Mathematics)"

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Hejhal, Dennis A. Emerging Applications of Number Theory. Springer New York, 1999.

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Sheĭnin, O. B., and O. B. Sheĭnin. The history of the theory of errors. Hänsel-Hohenhausen, 1996.

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Paul, Sally, ed. Number, shape, and symmetry: An introduction to number theory, geometry, and group theory. A K Peters, 2012.

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Ramakrishnan, Dinakar. Fourier Analysis on Number Fields. Springer New York, 1999.

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Latent class analysis of survey error. Wiley, 2011.

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Pearls of discrete mathematics. Taylor & Francis, 2009.

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Erickson, Martin J. Pearls of discrete mathematics. Taylor & Francis, 2009.

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Grinberg, E. L., S. Berhanu, M. Knopp, G. Mendoza, and E. T. Quinto, eds. Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis. American Mathematical Society, 2000. http://dx.doi.org/10.1090/conm/251.

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Jorgenson, Jay. Basic analysis of regularized series and products. Springer-Verlag, 1993.

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Kotulski, Zbigniew. Error analysis with applications in engineering. Springer, 2010.

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Book chapters on the topic "Number theory. Error analysis (Mathematics)"

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Rashed, Roshdi. "Number Theory and Combinatorial Analysis." In The Development of Arabic Mathematics: Between Arithmetic and Algebra. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-017-3274-1_5.

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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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Whitty, Robin, and Robin Wilson. "Introducing Turing’s mathematics." In The Turing Guide. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198747826.003.0048.

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Alan Turing’s mathematical interests were deep and wide-ranging. From the beginning of his career in Cambridge he was involved with probability theory, algebra (the theory of groups), mathematical logic, and number theory. Prime numbers and the celebrated Riemann hypothesis continued to preoccupy him until the end of his life. As a mathematician, and as a scientist generally, Turing was enthusiastically omnivorous. His collected mathematical works comprise thirteen papers, not all published during his lifetime, as well as the preface from his Cambridge Fellowship dissertation; these cover group theory, probability theory, number theory (analytic and elementary), and numerical analysis. This broad swathe of work is the focus of this chapter. But Turing did much else that was mathematical in nature, notably in the fields of logic, cryptanalysis, and biology, and that work is described in more detail elsewhere in this book. To be representative of Turing’s mathematical talents is a more realistic aim than to be encyclopaedic. Group theory and number theory were recurring preoccupations for Turing, even during wartime; they are represented in this chapter by his work on the word problem and the Riemann hypothesis, respectively. A third preoccupation was with methods of statistical analysis: Turing’s work in this area was integral to his wartime contribution to signals intelligence. I. J. Good, who worked with Turing at Bletchley Park, has provided an authoritative account of this work, updated in the Collected Works. By contrast, Turing’s proof of the central limit theorem from probability theory, which earned him his Cambridge Fellowship, is less well known: he quickly discovered that the theorem had already been demonstrated, the work was never published, and his interest in it was swiftly superseded by questions in mathematical logic. Nevertheless, this was Turing’s first substantial investigation, the first demonstration of his powers, and was certainly influential in his approach to codebreaking, so it makes a fitting first topic for this chapter. Turing’s single paper on numerical analysis, published in 1948, is not described in detail here. It concerned the potential for errors to propagate and accumulate during large-scale computations; as with everything that Turing wrote in relation to computation it was pioneering, forward-looking, and conceptually sound. There was also, incidentally, an appreciation in this paper of the need for statistical analysis, again harking back to Turing’s earliest work.
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Pulkkinen, Jarmo. "The Neo-Kantians and the ‘Logicist’ Definition of Number." In The Paideia Archive: Twentieth World Congress of Philosophy. Philosophy Documentation Center, 1998. http://dx.doi.org/10.5840/wcp20-paideia199834568.

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The publication of Russell's The Principles of Mathematics (1903) and Couturat's Les principes des mathematiques (1905) incited several prominent neo-Kantians to make up their mind about the logicist program. In this paper, I shall discuss the critiques presented by the following neo-Kantians: Paul Natorp, Ernst Cassirer and Jonas Cohn. They argued that Russell's attempt to deduce the number concept from the class concept is a petitio principii. Russell replied that the sense in which every object is 'one' must be distinguished from the sense in which 'one' is a number. I claim that Russell was wrong in dismissing the neo-Kantian argument as an elementary logical error. To accept Russell's distinction would be to accept at least part of Russell's logicist program. The expression 'a class with one member' would presuppose the number 'one' only if one simultaneously accepted the analysis which mathematical logic provides for it (the class u has one member when u is not null and 'x and y are us' implies 'x and y are identical'). My point is that the aforementioned analysis provided by mathematical logic was something that the neo-Kantians were not ready to accept.
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Datta, D. "Mathematics of Probabilistic Uncertainty Modeling." In Advances in Computational Intelligence and Robotics. IGI Global, 2014. http://dx.doi.org/10.4018/978-1-4666-4991-0.ch009.

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This chapter presents the uncertainty modeling using probabilistic methods. Probabilistic method of uncertainty analysis is due to randomness of the parameters of a model. Randomness of parameters is characterized by specified probability distribution such as normal, log normal, exponential etc., and the corresponding samples are generated by various methods. Monte Carlo simulation is applied to explore the probabilistic uncertainty modeling. Monte Carlo simulation being a statistical process is based on the random number generation from the specified distribution of the uncertain random parameters. Sample size is generally very large in Monte Carlo simulation which is required to have small errors in the computation. Latin hypercube sampling and importance sampling are explored in brief. This chapter also presents Polynomial Chaos theory based probabilistic uncertainty modeling. Polynomial Chaos theory is an efficient Monte Carlo simulation in the sense that sample size here is very small and dictated by the number of the uncertain parameters and by choice of the order of the polynomial selected to represent the uncertain parameter.
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Porter, Theodore M. "The Errors of Art and Nature." In The Rise of Statistical Thinking, 1820-1900. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691208428.003.0005.

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This chapter analyzes the law of facility of errors. All the early applications of the error law could be understood in terms of a binomial converging to an exponential, as in Abrahan De Moivre's original derivation. All but Joseph Fourier's law of heat, which was never explicitly tied to mathematical probability except by analogy, were compatible with the classical interpretation of probability. Just as probability was a measure of uncertainty, this exponential function governed the chances of error. It was not really an attribute of nature, but only a measure of human ignorance—of the imperfection of measurement techniques or the inaccuracy of inference from phenomena that occur in finite numbers to their underlying causes. Moreover, the mathematical operations used in conjunction with it had a single purpose: to reduce the error to the narrowest bounds possible. With Adolphe Quetelet, all that began to change, and a wider conception of statistical mathematics became possible. When Quetelet announced in 1844 that the astronomer's error law applied also to the distribution of human features such as height and girth, he did more than add one more set of objects to the domain of this probability function; he also began to break down its exclusive association with error.
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Moreno, A., E. Soria, J. García, J. D. Martín, and R. Magdalena. "Neural Models for Rainfall Forecasting." In Soft Computing Methods for Practical Environment Solutions. IGI Global, 2010. http://dx.doi.org/10.4018/978-1-61520-893-7.ch021.

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This chapter is focused on obtaining an optimal forecast of one month lagged rainfall in Spain. It is assessed by analyzing 22 years of both satellite observations of vegetation activity (e.g. NDVI) and climatic data (precipitation, temperature). The specific influence of non-spatial climatic indices such as NAO and SOI is also addressed. The approaches considered for rainfall forecasting include classical Auto-Regressive Moving-Average with Exogenous Inputs (ARMAX) models and Artificial Neural Networks (ANN), the so-called Multilayer Perceptron (MLP), in particular. The use of neural models is proven to be an adequate mathematical prediction tool in this problem due the non-linearity of the problem. These models enable us to predict, with one month foresight, the general rainfall dynamics, with average errors of 44 mm (RMSE) in a test series of 4 years with a rainfall standard deviation equal to 73 mm. Also, the sensitivity analysis in the neural network models reveals that observations in the status of the vegetation cover in previous months have a predictive power greater than other considered variables. Linear models yield average results of 55 mm (RMSE) although they need a large number of error terms (12) to obtain acceptable models. Nevertheless, they provide means for assessing the seasonal influence of the precipitation regime with the aid of linear dummy regression parameters, thereby offering an immediate interpretation (e.g. coherent maps) of the causality between vegetation cover and rainfall.
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Shahriari, Kyarash. "Identification and Response Prediction of Switching Dynamic Systems Using Interval Analysis." In Cybernetics and Systems Theory in Management. IGI Global, 2010. http://dx.doi.org/10.4018/978-1-61520-668-1.ch015.

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A novel method based on interval analysis is proposed in this work for modeling and response prediction of SISO uncertain switching dynamic systems. To describe the system’s dynamic in any operating mode, a local linear model is used. The validity domain of any local model is determined in system’s input-output space. To take into account the modeling error, adjustable parameters of local models are considered time-varying and characterized by intervals of real numbers. A model whose parameters are characterized by intervals is called an interval model. A procedure is also developed to perform nstep prediction of system’s response using the multi-mode interval model. Since the model parameters are intervals, the predicted response at any instant is not a real number anymore but an interval of real numbers. The set of predicted intervals at different instances generates a tube through time called wrapping envelope. However, the identification/characterization procedure proposed in the early stage of this work guarantees that the wrapping envelope includes the system’s response taking into account possible modeling error and perturbations. This envelope can be used in diagnosis to supervise healthy operation of the system as well as in process safety analysis to guarantee that the physical variables of the system never enter in forbidden operating zones and the system remains in safe operating conditions.
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Wagner, Roi. "Mathematics and Cognition." In Making and Breaking Mathematical Sense. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691171715.003.0006.

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This chapter introduces the notion of embodied mathematical cognition by reviewing some neuro-cognitive theories of mathematical concept formation. It first considers the neuro-cognitive debate on the mental representation of numbers, focusing on Stanislas Dehaene's notion of “number sense” and Vincent Walsh's ATOM (acronym for a theory of magnitude), before presenting the cognitive theory of mathematical metaphor and relating it to Water J. Freeman III's theory of meaning. It also examines Gilles Deleuze's Logic of Sensation in the context of mathematical practice, the link between the history of mathematics and neuro-cognition through an analysis of theories that explicitly engage the formation of higher mathematical concepts, and some challenges to the theory of mathematical metaphors.
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Flowerdew, Robin. "Modelling Migration with Poisson Regression." In Technologies for Migration and Commuting Analysis. IGI Global, 2010. http://dx.doi.org/10.4018/978-1-61520-755-8.ch014.

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Most statistical analysis is based on the assumption that error is normally distributed, but many data sets are based on discrete data (the number of migrants from one place to another must be a whole number). Recent developments in statistics have often involved generalising methods so that they can be properly applied to non-normal data. For example, Nelder and Wedderburn (1972) developed the theory of generalised linear modelling, where the dependent or response variable can take a variety of different probability distributions linked in one of several possible ways to a linear predictor, based on a combination of independent or explanatory variables. Several common statistical techniques are special cases of the generalised linear models, including the usual form of regression analysis, Ordinary Least Squares regression, and binomial logit modelling. Another important special case is Poisson regression, which has a Poisson-distributed dependent variable, linked logarithmically to a linear combination of independent variables. Poisson regression may be an appropriate method when the dependent variable is constrained to be a non-negative integer, usually a count of the number of events in certain categories. It assumes that each event is independent of the others, though the probability of an event may be linked to available explanatory variables. This chapter illustrates how Poisson regression can be carried out using the Stata package, proceeding to discuss various problems and issues which may arise in the use of the method. The number of migrants from area i to area j must be a non-negative integer and is likely to vary according to zone population, distance and economic variables. The availability of high-quality migration data through the WICID facility permits detailed analysis at levels from the region to the output areas. A vast range of possible explanatory variables can also be derived from the 2001 Census data. Model results are discussed in terms of the significant explanatory variables, the overall goodness of fit and the big residuals. Comparisons are drawn with other analytic techniques such as OLS regression. The relationship to Wilson’s entropy maximising methods is described, and variants on the method are explained. These include negative binomial regression and zero-censored and zero-truncated models.
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Conference papers on the topic "Number theory. Error analysis (Mathematics)"

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Sotiropoulos, Megaklis Th, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Stochastic-Conceptual Models Applied to Number Theory." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636750.

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Ghanem, Roger, and Manuel Pellissetti. "A Method for the Validation of Predictive Computations Using a Stochastic Approach." In ASME 2002 21st International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/omae2002-28071.

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The task of model validation deals with quantifying the extent to which predictions from a particular model can be relied upon as representatives of the true behavior of the system being modeled. This issue is of great importance in assessing the reliability and safety of structures since in most cases their quantification relies on predictions from sophisticated probabilistic models. The paper describes a formalism that will extend the realm of the model to include all aspects of data collection and parameter calibration. Error estimators are developed that permit the quantification of the va
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Susandi, Ardi Dwi, Cholis Sa'dijah, Abdur Rahman Asari, and Susiswo Susiswo. "Error Analysis on Prospective Teacher in Solving the Problem of Critical Thinking Mathematics with Apos Theory." In 1st Annual International Conference on Mathematics, Science, and Education (ICoMSE 2017). Atlantis Press, 2018. http://dx.doi.org/10.2991/icomse-17.2018.13.

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Yu¨mer, M. Ersin, Ender Cig˘erog˘lu, and H. Nevzat O¨zgu¨ven. "Mistuning Identification of Bladed Disks Utilizing Neural Networks." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-22129.

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Mistuning affects forced response of bladed disks drastically; therefore, its identification plays an essential role in the forced response analysis of realistic bladed disk assemblies. Forced response analysis of mistuned bladed disk assemblies has drawn wide attention of researchers but there are a very limited number of studies dealing with identification of mistuning, especially if the component under consideration is a blisk (integrally bladed disk). This paper presents two new methods to identify mistuning of a rotor from the assembly modes via utilizing neural networks. It is assumed th
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Shevchenko, Maksim, Sergiy Yepifanov, and Igor Loboda. "Ridge Estimation and Principal Component Analysis to Solve an Ill-Conditioned Problem of Estimating Unmeasured Gas Turbine Parameters." In ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-94496.

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This paper addresses the problem of estimation of unmeasured gas turbine engine variables using statistical analysis of measured data. Possible changes of an engine health condition and lack of information about these changes caused by limited instrumentation are taken into account. Engine thrust is under consideration as one of the most important unmeasured parameters. Two common methods of aircraft gas turbine engine (GTE) thrust monitoring and their errors due to health condition changes are analyzed. Additionally, two mathematical techniques that allow reducing in-flight thrust estimation
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Ahlfeld, Richard, and Francesco Montomoli. "A Single Formulation for Uncertainty Propagation in Turbomachinery: SAMBA PC." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-56573.

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This work newly proposes an uncertainty quantification method named SAMBA PC (Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos) that offers a single solution to many current problems in turbomachinery applications. At the moment every specific case is characterized by a variety of different input types such as histograms (from experimental data), normal PDFs (design rules) or fat tailed PDFs (for rare events). Thus, the application of UQ requires the adaptation of ad hoc methods for each individual case. A second problem is that parametric PDFs have to be determined for all inpu
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Khan, Mohammad Rasheed, Shams Kalam, and Rizwan Ahmed Khan. "Development of a Computationally Intelligent Model to Estimate Oil Formation Volume Factor." In Offshore Technology Conference. OTC, 2021. http://dx.doi.org/10.4043/31312-ms.

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Abstract This investigation presents a powerful predictive model to determine crude oil formation volume factor (FVF) using state-of-the-art computational intelligence (CI) techniques. FVF is a vital pressure-volume-temperature (PVT) parameter used to characterize hydrocarbon systems and is pivotal to reserve evaluation studies and reservoir engineering calculations. Ideally, FVF is measured at the laboratory scale; however, prognostic tools to evaluate this parameter can aid in optimizing time and cost estimates. The database utilized in this study is obtained from open literature and covers
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Tao, Mo, Jun Wu, Zhiwu Ke, Xianling Li, and Yong Li. "A Novel High-Power Magnetic Transmission System Based on Magnetic Conductivity Modulation Principle." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-67959.

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Due to the increasingly complexity of the nuclear power device system, the demands for its performance and security become rather high. There is a large number of rotating machinery working in the nuclear power plant.The static and dynamic misalignment between the rotating mechanical rotors may exist for various reasons like installation error, loading deformation, thermal expansion deformation and etc.Both of the radial vibration and the axial vibration can be generated by the misalignment. The security of nuclear power is severely threatened by these vibrations. Compared with the mechanical
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Niknam, Seyed Ali, Azziz Tiabi, Imed Zaghbani, Rene Kamguem, and Victor Songmene. "Milling Burr Size Estimation Using Acoustic Emission and Cutting Forces." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63824.

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Burr formation is one of the main concerns usually faced by machining industries. Its presence leads to additional part edge finishing operations that are costly and time consuming. Burrs must be removed as they are source of dimensional errors, jamming and misalignment during assembly. In many cases burrs may injure workers during handling of machined part. Due to burr effect on machined part quality, manufacturing costs and productivity, more focus has been given to burr measurement/estimation methods. Large number of burr measurement methods has been introduced according to various criteria
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10

Motriuk, Roman W., Timothy Schmidt, John Webster, and Thangavel Thevar. "Determination of Dynamic Velocity and Strain Using Wide Field Holographic Interferometry: Verification." In 2000 3rd International Pipeline Conference. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/ipc2000-276.

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Abstract:
High power and high capacity turbo-compressor systems frequently sustain acoustically induced vibrations. Higher order acoustic modes generated by turbo-compressors often couple selectively with structural pipe resonances producing significant increase in pipe wall vibration. In some instances, these coincidences generate high local stress levels that fatigue pipe shell or pipe attachments. In order to judge the level of dynamic strain and stress in piping systems, elaborate theories are employed. However, these are frequently not practical and relatively difficult to use in industrial applica
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