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Related Concept Videos

Linearization and Approximation01:26

Linearization and Approximation

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Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
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Application of Linearization and Approximation01:29

Application of Linearization and Approximation

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A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
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Accuracy, limits, and approximation01:28

Accuracy, limits, and approximation

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Accuracy, limits, and approximations are common in many fields, especially in engineering calculations. These concepts are imperative for ensuring that a given value is as close as possible to its true value.
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...
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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
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Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

362
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
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Formulation and Manufacturing Process: Physical Attributes of Generic Tablets and Capsules01:18

Formulation and Manufacturing Process: Physical Attributes of Generic Tablets and Capsules

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Bioequivalence in generic drugs, such as tablets and capsules, refers to their pharmaceutical equivalence to the brand-name counterparts. However, for therapeutic equivalence, manufacturers must also consider physical attributes like size, shape, and weight (FDA Guidance for Industry, December 2003). Discrepancies in these aspects could impact patient compliance and cause medication errors. For instance, swallowing difficulties, often experienced with larger tablets or capsules, can lead to...
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Approximating Future Generic Entry for New Drugs

Reed F Beall1, Jonathan J Darrow1, Aaron S Kesselheim1

  • 1Reed F. Beall, Ph.D., is an Assistant Professor at the Cummings School of Medicine and O'Brien Institute of Public Health, University of Calgary, Calgary, AB, Canada. He is also affiliated with the Program on Regulation, Therapeutics, and Law (PORTAL), Division of Pharmacoepidemiology and Pharmacoeconomics, Department of Medicine, Brigham and Women's Hospital and Harvard Medical School, Boston, MA, USA. Jonathan J. Darrow, S.J.D., J.D., M.B.A., is affiliated with the Program on Regulation, Therapeutics, and Law (PORTAL), Division of Pharmacoepidemiology and Pharmacoeconomics, Department of Medicine, Brigham and Women's Hospital and Harvard Medical School, Boston, MA, USA. Aaron S. Kesselheim, M.D., J.D., M.P.H., is affiliated with the Program on Regulation, Therapeutics, and Law (PORTAL), Division of Pharmacoepidemiology and Pharmacoeconomics, Department of Medicine, Brigham and Women's Hospital and Harvard Medical School, Boston, MA, USA.

The Journal of Law, Medicine & Ethics : a Journal of the American Society of Law, Medicine & Ethics
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PubMed
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No abstract available in PubMed .

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