Relevant bibliographies by topics / Optics – Testing – Mathematical models

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

Academic literature on the topic 'Optics – Testing – Mathematical models'

Author: Grafiati
Published: 4 June 2021
Last updated: 14 February 2022

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Journal articles on the topic "Optics – Testing – Mathematical models"

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Wac-Wlodarczyk, A., R. Goleman, D. Czerwinski, and T. Gizewski. "Mathematical models applied in inductive non-destructive testing." Journal of Magnetism and Magnetic Materials 320, no. 20 (2008): e1044-e1048. http://dx.doi.org/10.1016/j.jmmm.2008.04.179.

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Stojek, Jerzy, and Rafał Dańko. "Model Testing of Flow Phenomena in the Squeeze Chamber of a Cold-Chamber Diecasting Machine." Solid State Phenomena 177 (July 2011): 151–58. http://dx.doi.org/10.4028/www.scientific.net/ssp.177.151.

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A review of the studies carried out on this subject so far was made, and the available mathematical models applicable at Phase I of the diecasing process were presented. Own model testing of the examined process phase was described. The tests were conducted on a laboratory station designed and constructed to serve this purpose. Basing on the obtained results, the fundamental Garber's model was modified and extended further to include the coefficient of liquid metal viscosity.
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Peng, Dong Lin, Ji Sen Yang, Xi Hou Chen, and Zi Ran Chen. "The Principle and Structure of Novel High-Precision Linear Time Grating Displacement Sensors." Applied Mechanics and Materials 236-237 (November 2012): 1216–21. http://dx.doi.org/10.4028/www.scientific.net/amm.236-237.1216.

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The existing grating type sensors such as optical grating sensor, have long been designed to rely on the precise mechanical space division technology, which is hard to develop without heavy investment. A theoretical concept, time-space coordinate transformation, was presented to realize measuring spatial displacement with time difference. Similar to the principle of circular time grating based on rotating electrical machine, linear time grating is designed based on the principle of linear motor, with which the physical and mathematical models of linear time grating are established. Based on these models linear time grating mechanical structure is designed, which has commercialization value. The resolution of linear time grating can achieve 0.1μm tested by National Institute of Measurement and Testing Technology.
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Elkatatny, Salaheldin. "Real-Time Prediction of Rate of Penetration in S-Shape Well Profile Using Artificial Intelligence Models." Sensors 20, no. 12 (2020): 3506. http://dx.doi.org/10.3390/s20123506.

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Rate of penetration (ROP) is defined as the amount of removed rock per unit area per unit time. It is affected by several factors which are inseparable. Current established models for determining the ROP include the basic mathematical and physics equations, as well as the use of empirical correlations. Given the complexity of the drilling process, the use of artificial intelligence (AI) has been a game changer because most of the unknown parameters can now be accounted for entirely at the modeling process. The objective of this paper is to evaluate the ability of the optimized adaptive neuro-fuzzy inference system (ANFIS), functional neural networks (FN), random forests (RF), and support vector machine (SVM) models to predict the ROP in real time from the drilling parameters in the S-shape well profile, for the first time, based on the drilling parameters of weight on bit (WOB), drillstring rotation (DSR), torque (T), pumping rate (GPM), and standpipe pressure (SPP). Data from two wells were used for training and testing (Well A and Well B with 4012 and 1717 data points, respectively), and one well for validation (Well C) with 2500 data points. Well A and Well B data were combined in the training-testing phase and were randomly divided into a 70:30 ratio for training/testing. The results showed that the ANFIS, FN, and RF models could effectively predict the ROP from the drilling parameters in the S-shape well profile, while the accuracy of the SVM model was very low. The ANFIS, FN, and RF models predicted the ROP for the training data with average absolute percentage errors (AAPEs) of 9.50%, 13.44%, and 3.25%, respectively. For the testing data, the ANFIS, FN, and RF models predicted the ROP with AAPEs of 9.57%, 11.20%, and 8.37%, respectively. The ANFIS, FN, and RF models overperformed the available empirical correlations for ROP prediction. The ANFIS model estimated the ROP for the validation data with an AAPE of 9.06%, whereas the FN model predicted the ROP with an AAPE of 10.48%, and the RF model predicted the ROP with an AAPE of 10.43%. The SVM model predicted the ROP for the validation data with a very high AAPE of 30.05% and all empirical correlations predicted the ROP with AAPEs greater than 25%.
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Zambon, Ivan, Anja Vidović, and Alfred Strauss. "Reliability of Existing Concrete Structures Determined with Physical Models - Carbonation Induced Corrosion." Solid State Phenomena 259 (May 2017): 255–60. http://dx.doi.org/10.4028/www.scientific.net/ssp.259.255.

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The main goal of transportation infrastructure management is to optimize the use of infrastructure in the most beneficiary way while respecting the predefined requirements. One of the crucial parts in management strategy is the prediction of behaviour of vital transportation elements. Used prediction models should accurately describe the process of degradation and allow forecasting of structural condition by considering environment, usage and maintenance actions. Deterioration models can be divided into mathematical (statistical), physical and empirical models. Statistical models are based on data that describe condition of structure, such as for example condition rating. Physical models describe damage-causing processes and empirical models are experience based. The focus of this paper is to present the physical model of carbonation in assessment of performance of existing reinforced concrete structures in transportation networks. Assessment is done through determining the probability of limit state of depassivation. In order to determine the carbonation without testing, a special attention has to be given to environmental and material parameter identification. Herein, the identification takes into account weather specifics and construction practice in Austria. Finally, the reliability of existing reinforced concrete structures for combination of different exposure classes and material characteristics is analysed. Based on the analysis of reliability, the carbonation nomogram for engineering use is presented, showing the reliability indices β for the service life of 50 years.
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Linkeová, Ivana, and Vít Zelený. "APPLICATION OF RULED SURFACES IN FREEFORM AND GEAR METROLOGY." Acta Polytechnica 61, SI (2021): 99–109. http://dx.doi.org/10.14311/ap.2021.61.0099.

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An application of two ruled surfaces (i.e., surfaces generated by a motion of a straight line), a surface of hyperbolic paraboloid and a tangent surface of a cylindrical helix in freeform and gear metrology is introduced in this paper. Both surfaces have been implemented as the main functional figures in several artefacts – metrological calibration standards intended for testing the freeform capabilities of various measuring technologies (e.g., tactile point-to-point measurement and tactile scanning on coordinate measuring machine, optical scanning, computer tomography). Geometrical and mathematical properties of the surface used are summarised, CAD models of all the developed standards are presented and photos of the manufactured standards are shown.
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Porciatti, Vittorio, and Tsung-Han Chou. "Modeling Retinal Ganglion Cell Dysfunction in Optic Neuropathies." Cells 10, no. 6 (2021): 1398. http://dx.doi.org/10.3390/cells10061398.

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As in glaucoma and other optic neuropathies cellular dysfunction often precedes cell death, the assessment of retinal ganglion cell (RGC) function represents a key outcome measure for neuroprotective strategies aimed at targeting distressed but still viable cells. RGC dysfunction can be assessed with the pattern electroretinogram (PERG), a sensitive measure of electrical activity of RGCs that is recorded non-invasively in human subjects and mouse models. Here, we offer a conceptual framework based on an intuitive state-transition model used for disease management in patients to identify progressive, potentially reversible stages of RGC dysfunction leading to cell death in mouse models of glaucoma and other optic neuropathies. We provide mathematical equations to describe state-transitions with a set of modifiable parameters that alter the time course and severity of state-transitions, which can be used for hypothesis testing and fitting experimental PERG data. PERG dynamics as a function of physiological stimuli are also used to differentiate phenotypic and altered RGC response dynamics, to assess susceptibility to stressors and to assess reversible dysfunction upon pharmacological treatment.
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Kamrud, Alexander, Brett Borghetti, and Christine Schubert Kabban. "The Effects of Individual Differences, Non-Stationarity, and the Importance of Data Partitioning Decisions for Training and Testing of EEG Cross-Participant Models." Sensors 21, no. 9 (2021): 3225. http://dx.doi.org/10.3390/s21093225.

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EEG-based deep learning models have trended toward models that are designed to perform classification on any individual (cross-participant models). However, because EEG varies across participants due to non-stationarity and individual differences, certain guidelines must be followed for partitioning data into training, validation, and testing sets, in order for cross-participant models to avoid overestimation of model accuracy. Despite this necessity, the majority of EEG-based cross-participant models have not adopted such guidelines. Furthermore, some data repositories may unwittingly contribute to the problem by providing partitioned test and non-test datasets for reasons such as competition support. In this study, we demonstrate how improper dataset partitioning and the resulting improper training, validation, and testing of a cross-participant model leads to overestimated model accuracy. We demonstrate this mathematically, and empirically, using five publicly available datasets. To build the cross-participant models for these datasets, we replicate published results and demonstrate how the model accuracies are significantly reduced when proper EEG cross-participant model guidelines are followed. Our empirical results show that by not following these guidelines, error rates of cross-participant models can be underestimated between 35% and 3900%. This misrepresentation of model performance for the general population potentially slows scientific progress toward truly high-performing classification models.
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D’Emilia, Giulio, and Emanuela Natale. "Validation of Methods for the Optical Characterisation of the Wettability of Polymeric Films for Food Packaging." Journal of Industrial Engineering 2014 (October 23, 2014): 1–6. http://dx.doi.org/10.1155/2014/623510.

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A methodology is described for the theoretical-experimental evaluation of the measurement uncertainty of the polar and dispersive components of the surface free energy (SFE) in polypropylene films; these parameters are related to the film wettability of adhesives and inks. The proposed method is based on the measurement by means of a vision system of the contact angles of liquid drops deposited on the film itself, which allows for obtaining, through mathematical models drawn from the literature, the physical quantities of interest. The effect of the principal influence parameters has been experimentally evaluated, and testing has allowed the defining of the technical procedures readily transferable in the industry. The uncertainty assessment is interesting not only to correctly evaluate experimental data but also to characterise the reproducibility of the effects of techniques for improving the wettability of films, such as surface treatments.
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Poghosyan, Arnak, Ashot Harutyunyan, Naira Grigoryan, et al. "An Enterprise Time Series Forecasting System for Cloud Applications Using Transfer Learning." Sensors 21, no. 5 (2021): 1590. http://dx.doi.org/10.3390/s21051590.

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The main purpose of an application performance monitoring/management (APM) software is to ensure the highest availability, efficiency and security of applications. An APM software accomplishes the main goals through automation, measurements, analysis and diagnostics. Gartner specifies the three crucial capabilities of APM softwares. The first is an end-user experience monitoring for revealing the interactions of users with application and infrastructure components. The second is application discovery, diagnostics and tracing. The third key component is machine learning (ML) and artificial intelligence (AI) powered data analytics for predictions, anomaly detection, event correlations and root cause analysis. Time series metrics, logs and traces are the three pillars of observability and the valuable source of information for IT operations. Accurate, scalable and robust time series forecasting and anomaly detection are the requested capabilities of the analytics. Approaches based on neural networks (NN) and deep learning gain an increasing popularity due to their flexibility and ability to tackle complex nonlinear problems. However, some of the disadvantages of NN-based models for distributed cloud applications mitigate expectations and require specific approaches. We demonstrate how NN-models, pretrained on a global time series database, can be applied to customer specific data using transfer learning. In general, NN-models adequately operate only on stationary time series. Application to nonstationary time series requires multilayer data processing including hypothesis testing for data categorization, category specific transformations into stationary data, forecasting and backward transformations. We present the mathematical background of this approach and discuss experimental results based on implementation for Wavefront by VMware (an APM software) while monitoring real customer cloud environments.
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Dissertations / Theses on the topic "Optics – Testing – Mathematical models"

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CHENG, YEOU-YEN. "MULTIPLE-WAVELENGTH PHASE SHIFTING INTERFEROMETRY (OPTICAL-TESTING, ASPHERIC SURFACE)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/187928.

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The problems of combining ideas of phase shifting interferometry (PSI) and synthetic-wavelength techniques to extend the phase measurement range of conventional single-wavelength PSI are investigated. This combination of PSI and synthetic-wavelengths gives multiple-wavelength phase-shifting interferometry the advantages of: (1) larger phase measurement range and (2) higher accuracy of phase measurement. Advantages, error sources, and limitations of single-wavelength PSI are discussed. Some practical methods to calibrate the piezoelectric transducer (PZT), used to phase shift the reference beam, are presented with experimental results. Two methods of two-wavelength PSI are used to solve the 2π ambiguity problem of single-wavelength PSI. For the first method, two sets of phase data (with 2π ambiguities) for shorter wavelengths are calculated and stored in the computer which calculates the new phase data for the equivalent-wavelength λ(eq). The "error magnification effect," which reduces the measurement precision of the first method, is then investigated. The second, more accurate method, uses the results of the first method as a reference to correct the 2π ambiguities in the single-wavelength phase data. Experimental results are included to confirm theoretical predictions. The enhancement of two-wavelength PSI is investigated, and requires the phase data of a third wavelength. Experiments are performed to verify the capability of multiple-wavelength PSI. For the wavefront being measured, the difference of the optical-path-difference (OPD) between adjacent pixels is as large as 3.3 waves. After temporal averaging of five sets of data, the repeatability of the measurement is better than 2.5 nm (0.0025%) rms (λ = 632.8 nm). This work concludes with recommendations for future work that should make the MWLPSI a more practical technique for the testing of steep aspheric surfaces.
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Caccavano, Adam. "Optics and Spectroscopy in Massive Electrodynamic Theory." PDXScholar, 2013. https://pdxscholar.library.pdx.edu/open_access_etds/1485.

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The kinematics and dynamics for plane wave optics are derived for a massive electrodynamic field by utilizing Proca's theory. Atomic spectroscopy is also examined, with the focus on the 21 cm radiation due to the hyperfine structure of hydrogen. The modifications to Snell's Law, the Fresnel formulas, and the 21 cm radiation are shown to reduce to the familiar expressions in the limit of zero photon mass.
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Tsang, Suk-chong, and 曾淑莊. "A numerical study of coupled nonlinear Schrödinger equations arising in hydrodynamics and optics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B26652651.

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Seid, Hamid Jemila. "New residuals in multivariate bilinear models : testing hypotheses, diagnosing models and validating model assumptions /." Uppsala : Dept. of Biometry and Engineering, Swedish University of Agricultural Sciences, 2005. http://epsilon.slu.se/200583.pdf.

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Alluri, Chandra M. "Testing calculation engines using input space partitioning and automation." Fairfax, VA : George Mason University, 2008. http://hdl.handle.net/1920/3228.

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Thesis (M.S.)--George Mason University, 2008.<br>Vita: p. 158. Thesis director: Jeff Offutt. Submitted in partial fulfillment of the requirements for the degree of Master of Science in Software Engineering. Title from PDF t.p. (viewed Aug. 27, 2008). Includes bibliographical references (p. 156-157). Also issued in print.
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Banan, Roshan Aerospace Civil &amp Mechanical Engineering Australian Defence Force Academy UNSW. "An engineering approach to modelling ballistic impact on hybrid polymer laminates." Publisher:University of New South Wales - Australian Defence Force Academy. Information Technology & Electrical Engineering, 2009. http://handle.unsw.edu.au/1959.4/44094.

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Hybrid polymer laminates of polycarbonate and PMMA have generated considerable interest among researchers as an alternative to traditional glass armours because of their potential for reduced cost and weight. Generally, the development of ballistic armour is carried out experimentally which is an expensive task in terms of time and cost. Numerical simulation provides a much greater facility to understand the phenomenon of ballistic impact and the effects of various parameters on the response to such impact. In addition it provides an easy means of comparing the impact performance of different materials as well as combination of materials forming hybrid laminates. The aim of this research was to develop a numerical modelling capability to simulate the ballistic response of hybrid polymer laminates, specifically polycarbonate and PMMA, using a commercially available finite element code LS-DYNA. The challenge was to work within the limitations of the material models and the failure algorithms available within LS-DYNA, and still try to reproduce the behaviour observed experimentally by previous researchers, initially on monolithic plates of polycarbonate and PMMA and then on hybrid laminates. The first part of the study focuses on a detailed literature survey on mechanical and dynamic characterisation of polycarbonate and PMMA as well as experimental and numerical studies previously conducted on ballistic behaviour of these materials as well as their combinations. The material properties of the polymers compiled from this literature survey were used as input for the selected LS-DYNA material model. Impact simulations were carried on monolithic and laminated media of polycarbonate and PMMA and where possible these were compared to experimental results. It was observed that the results agreed with the experimental data qualitatively. Quantitatively the results showed some discrepancies which were attributed to the limitations faced in simulating the exact test conditions numerically. Numerical simulations were carried out to study the effects of variations in laminate thickness and plate support diameters as well as to examine the influence of the bond between the layers. Finally the impact response of four different combinations of polycarbonate and PMMA are compared to each other for different laminate thicknesses.
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Kleinow, Torsten. "Testing continuous time models in financial markets." Doctoral thesis, [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=965412091.

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Azadeh, Mohammad. "Reflection and Refraction of Light from Nonlinear Boundaries." PDXScholar, 1994. https://pdxscholar.library.pdx.edu/open_access_etds/4715.

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This thesis deals with the topic of reflection and refraction of light from the boundary of nonlinear materials in general, and saturating amplifiers in particular. We first study some of the basic properties of the light waves in nonlinear materials. We then develop a general formalism to model the reflection and refraction of light with an arbitrary angle of incidence from the boundary of a nonlinear medium. This general formalism is then applied to the case of reflection and refraction from the boundary of linear dielectrics. It will be shown that in this limit, it reduces to the well known Fresnel and Snell's formulas. We also study the interface of a saturating amplifier. The wave equation we use for this purpose is approximate, in the sense that it assumes the amplitude of the wave does not vary significantly in a distance of a wave length. The limits and implications of this approximation are also investigated. We derive expressions for electric field and intensity reflection and transmission coefficients for such materials. In doing so, we make sure that the above mentioned approximation is not violated. These results are compared with the case of reflection and refraction from the interface of a linear dielectric.
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Carroll, James M. "The psychometrics of a bipolar valence activation model of self-reported affect." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ56520.pdf.

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Scholey, Kenneth Erwin. "Heat tranfser and crack formation in water-cooled zinc fuming furnace jackets." Thesis, University of British Columbia, 1991. http://hdl.handle.net/2429/30078.

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In the zinc slag fuming process, zinc is extracted from lead blast furnace slag by reduction with a coal/air mixture injected into the slag through submerged tuyeres. The furnace is constructed of water-cooled jackets to contain the molten bath and freeze a protective slag layer. The slag layer greatly reduces vessel wear caused by the corrosive and violently agitated bath. However, the jackets are known to develop cracks in the working face panel that initiate on the slag face and propagate towards the water cavity. If the cracks reach the water cavity explosions may result should the molten slag come into contact with the water. In this study an analysis of heat transfer in the jacket has been carried out using in-plant measurements and mathematical modelling. The working face of a water jacket was instrumented with thermocouples and positioned in a fuming furnace at the Trail smelter of Cominco Ltd. Measurements revealed the presence of large thermal transients or temperature "spikes" in the panel approximately 20 cm above the tuyeres. The transients were observed during charging and tapping of the furnace and are likely associated with slag fall-off due to surface wave action and gas injection effects when the bath level is low. Temperatures at the mid-thickness were seen to rise by as much as 180 °C above the steady-state level. Under these conditions large compressive stresses are produced in the panel that are sufficient to cause yielding. Over time, the transients lead to low-cycle fatigue of the working face panel with crack formation initiating at pre-existing surface flaws. A mathematical modelling analysis of the transient freezing phenomena has been carried out using the finite element method. The results indicate that the temperature spikes are associated with the sudden removal of patches of slag and molten slag coming into direct contact with the jacket. The temperature spikes are large enough to generate compressive stresses that cause yielding of the material in the exposed area. In order to reduce the damage caused by the removal of the slag shell an increased number of anchoring studs should be used in critical areas and a higher water circulation velocity should be employed to increase the size of the frozen slag layer and its strength.<br>Applied Science, Faculty of<br>Materials Engineering, Department of<br>Graduate
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Books on the topic "Optics – Testing – Mathematical models"

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Bates, David S. Testing option pricing models. National Bureau of Economic Research, 1995.

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United States. Advanced Research Projects Agency., ed. An optical signal processing model for the interferometric fiber optic gyro. RAND, 1995.

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Leamer, Edward E. Testing trade theory. National Bureau of Economic Research, 1992.

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Bagdonavičius, V. Semiparametric models in accelerated life testing. Queen's University, 1995.

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Lehmann, Bruce Neal. Empirical testing of asset pricing models. National Bureau of Economic Research, 1992.

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Mueller, Uli. Testing models of low-frequency variability. National Bureau of Economic Research, 2006.

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Bagdonavicius, V. Semiparametric models in accelerated life testing. Queen's University, 1995.

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Probability, statistical optics, and data testing: A problem solving approach. 2nd ed. Springer-Verlag, 1991.

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Probability, statistical optics, and data testing: A problem solving approach. 3rd ed. Springer, 2001.

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Daniela, Milovic, and Edwards Matthew (Thomas Matthew), eds. Mathematical theory of dispersion-managed optical solitons. Springer, 2010.

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Book chapters on the topic "Optics – Testing – Mathematical models"

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Diffey, B. L. "Mathematical Models for the Ultraviolet Optics of Human Epidermis." In Skin Models. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-70387-4_42.

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Taler, Dawid. "Mathematical Models of Heat Exchangers." In Numerical Modelling and Experimental Testing of Heat Exchangers. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91128-1_9.

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Aceto, Luca, Rocco Nicola, and Alessandro Fantechi. "Testing equivalences for event structures." In Mathematical Models for the Semantics of Parallelism. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/3-540-18419-8_9.

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Wefelmeyer, Wolfgang. "Testing hypotheses on independent, not identically distributed models." In Mathematical Statistics and Probability Theory. Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-3963-9_20.

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Bayarri, M. J., James O. Berger, and Gauri S. Datta. "Objective Bayes testing of Poisson versus inflated Poisson models." In Institute of Mathematical Statistics Collections. Institute of Mathematical Statistics, 2008. http://dx.doi.org/10.1214/074921708000000093.

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Urbain, Jean-Pierre. "Testing for Weak Exogeneity in Error Correction Models." In Lecture Notes in Economics and Mathematical Systems. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-95706-2_4.

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Yamamoto, Watalu, Chiharu Kumazaki, and Kazuyuki Suzuki. "Estimation of Archival Lifetime Distribution for Writable Optical Disks from Accelerated Testings." In Mathematical and Statistical Models and Methods in Reliability. Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4971-5_24.

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Baker, Rose. "Software Reliability Growth Models for Discrete and Incomplete Testing." In Lecture Notes in Economics and Mathematical Systems. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-59105-1_19.

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Folmer, Henk. "Autocorrelation Pre-Testing in Linear Models with AR(1) Errors." In Lecture Notes in Economics and Mathematical Systems. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-61564-1_3.

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Han, Cheng Shun, Long Jiang Zhang, and Shen Dong. "Research on Mathematical Models of New Diamond Turning for Non-Axisymmetric Aspheric Mirrors." In Optics Design and Precision Manufacturing Technologies. Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/0-87849-458-8.35.

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Conference papers on the topic "Optics – Testing – Mathematical models"

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Booij, Silvia, Hedser van Brug, and Oliver W. Fähnle. "A mathematical model for machining spot in fluid jet polishing explained." In Optical Fabrication and Testing. OSA, 2000. http://dx.doi.org/10.1364/oft.2000.otua3.

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Zhang, Fengdong, Xuejun Zhang, and Jingchi Yu. "Mathematics model of magnetorheological finishing." In International Topical Symposium on Advanced Optical Manufacturing and Testing Technology, edited by Li Yang, Harvey M. Pollicove, Qiming Xin, and James C. Wyant. SPIE, 2000. http://dx.doi.org/10.1117/12.402796.

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Fang, Hui, Peiji Guo, and Jingchi Yu. "Research on the mathematical model of fluid jet polishing." In 2nd international Symposium on Advanced Optical Manufacturing and Testing Technologies, edited by Li Yang, Shangming Wen, Yaolong Chen, and Ernst-Bernhard Kley. SPIE, 2006. http://dx.doi.org/10.1117/12.674206.

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Qiu, Gu-feng. "Mathematical model of contacting aspheric surface profile measurement." In 4th International Symposium on Advanced Optical Manufacturing and testing technologies: Optical Test and Measurement Technology and Equipment, edited by Yudong Zhang, James C. Wyant, Robert A. Smythe, and Hexin Wang. SPIE, 2009. http://dx.doi.org/10.1117/12.828713.

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Hargett, Zachary, Manuel Gutierrez, and Melinda Harman. "Verification of Manual Digitization Methods During Experimental Simulation of Knee Motion." In ASME 2019 Verification and Validation Symposium. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/vvs2019-5158.

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Abstract Cadaveric testing is a common approach for verifying mathematical models used in computational modeling work. In the case of a knee joint model for calculating ligament tension during total knee replacement (TKR) motion, model inputs include rigid body motions defined using the Grood-Suntay coordinate system as a spatial linkage between the tibial component orientation relative to the femoral component. Using this approach requires the definition of coordinate systems for each rigid TKR component (i.e. tibial and femoral) based on fiducial points, manual digitization of a point cloud within the experimental setup, and registration of the orientation relative to the relevant bone marker array. The purpose of this study was to compare the variability between two different manual point digitization methods (a hand-held stylus and pivot tool each calibrated in the optical tracking system), using a TKR femoral component in a simulated cadaver limb experimental setup as an example. This was accomplished by verifying the mathematical algorithm used to calculate the coordinate system from the digitized points, quantifying the variability of the manual digitization methods, and discussing how any error could affect the computational model. For the hand-held stylus method, the standard deviation of the origin and, x-, y-, and z-axis calculations were 0.50mm, 1.31 degrees, 0.51 degrees, and 0.62 degrees, respectively. It is important to note that there is an additional error created using the hand-held stylus from required manual digitization of each rigid marker array. This average additional error was 0.54mm for the origin and 1.70, 1.66, and 0.98 degrees for the x-, y-, and z-axes, respectively. For the pivot tool method, the standard deviation was 0.35mm, 0.37 degrees, 1.27 degrees, and 1.24 degrees for the origin, x-, y-, and z-axes, respectively. It is essential to minimize experimental error, as small errors in alignment can substantially alter model outputs. In this study of cadaver simulation of limb motion, the pivot tool is the better option for minimizing error. Careful definition of fiducial points and repeatable manual digitization of the point cloud is critical for meaningful computational models of TKR motion based on cadaver experimental work.
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Liu, Haitao, Zhige Zeng, Fan Wu, and Bin Fan. "Mathematical model for active lap to achieve unsymmetrical fabrication." In 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies (AOMATT 2012), edited by Li Yang, Eric Ruch, and Shengyi Li. SPIE, 2012. http://dx.doi.org/10.1117/12.975689.

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Stork, Milan, Jaroslav Novak, and Pavel Broz. "Cardiac Mathematical Models for Exercise Testing on Treadmill Ergometer." In 2019 International Conference on Applied Electronics (AE). IEEE, 2019. http://dx.doi.org/10.23919/ae.2019.8866998.

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Mitrea, Alexandru I., and Paulina Mitrea. "Deformable models: Software implementation based on mathematical fundamentals." In 2008 IEEE International Conference on Automation, Quality and Testing, Robotics. IEEE, 2008. http://dx.doi.org/10.1109/aqtr.2008.4588948.

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Hodge, Ryan D., and Caner Demirdogen. "Case Studies on the Use of Two and Three Degree of Freedom Models to Understand Fundamental Vibration Behavior of Complex Systems." In ASME 2014 Internal Combustion Engine Division Fall Technical Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/icef2014-5486.

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Mathematical models of simple two and three degree of freedom vibrating systems are beneficial to ease understanding of a complex system by providing an opportunity to readily identify the effect of one degree of freedom on another. When dealing with short timelines in industry, simple models provide the opportunity to quickly develop potential solutions to excessive vibration issues or understand unexpected results. Simple models are not always appropriate and may have significant uncertainties but such an option may still add value when compared to the time and effort required to develop larger, detailed models. This paper presents two cases regarding the use of simple models to develop understanding of a complex system. In each case, the focus is on the insights that can be gained from a simple model rather than the detailed calculations and calibrations necessary to ensure its complete accuracy. Case 1 employs a two degree of freedom system to relate how an experimental modal test of an engine component can be affected by the base structure on which it is mounted. This study directly relates to the experimental modal testing of large engine components which are tested both in laboratories and on engines. Two charts are presented to evaluate the error of a measured natural frequency as a function of both the mass and natural frequency of the component to be tested and the base structure. Case 2 utilizes a three degree of freedom system built in a commercial finite element analysis (FEA) code and solved via a multi-disciplinary optimizer to determine the ideal parameters of a vibration absorber to effect the greatest possible reduction in vibration levels of a component. The lessons learned from this study are applicable to developing a vibration absorber to be installed on an engine component that is being excited by global modes of a generator set. Both cases display the significant lessons that can be learned from extremely simple systems.
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Tahhan, Antonio, Cody Muchmore, Larinda Nichols, et al. "Development of Experimental and Computational Procedures for Nuclear Power Plant Component Testing Under Flooding Conditions." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-67985.

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Idaho State University (ISU), with support from Idaho National Laboratory, is actively engaged in enhancing nuclear power plant risk modeling. The ISU team is significantly increasing the understanding of non-containment, nuclear power plant component performance under flooding conditions. The work involves experimentation activities and development of mathematical models, using data from component flooding experiments. The research consists in developing experimentation procedures that comprised small scale component testing, followed by simple and then complex full scale component testing. The research is taking place in the Component Flooding Evaluation Laboratory (CFEL). Tests in CFEL will include water rise, spray, and wave impact experiments on passive and active components. Initial development work focused on small scale components, radios and simulated doors, that served as a low-risk and low-cost proof-of-concept options. Following these tests, full-scale component tests were performed in the Portal Evaluation Tank (PET). The PET is a semi-cylindrical 7500-1 capacity steel tank, with an opening to the environment of 2.4 m. × 2.4 m. The opening allows installation of doors, feedthroughs, pipes, or other components. The first set of experiments with the PET were conducted in 2016 using hollow doors subjected to a water rise scenario. Data collected during the door tests is being analyzed using Bayesian regression methods to determine the parameters of influence and inform future experiments. A practical method of simulating full scale wave impacts on components and structures is also being researched to further enhance CFEL capabilities. Early on, the team determined full scale wave impacts could not be simulated using traditional wave flumes or pools; therefore, closed conduit flow is under consideration. Computational fluid dynamics software is being used to simulate fluid velocities associated with tsunami waves of heights up to 6-m, and to design a wave impact simulation device capable of accurately recreating a near vertical wave section with variable height and fluid velocity. The component flooding simulation activities associated with this project involve use of smoothed particle dynamics codes. These particle-based simulation methods do not require a mesh to be applied to the fluid, which allows for more natural flows to be simulated. Finally, CFEL can be described as a pioneering element, comprised of several ongoing research and experimental projects, that are vital to the development of risk analysis methods for the nuclear industry.
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