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Application of Linearization and Approximation01:29

Application of Linearization and Approximation

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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Linearization and Approximation01:26

Linearization and Approximation

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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Measuring Psoriasis Severity at Home02:28

Measuring Psoriasis Severity at Home

This paper details the creation of a Psoriasis Thickness Reference Card, enabling psoriasis patients to self-assess their psoriasis plaque thickness without the need for physician assistance. Additionally, the precision of self-assessment for psoriasis redness and scaliness by employing reference images depicting various skin tones is...
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Recognition of Epidermal Transglutaminase by IgA and Tissue Transglutaminase 2 Antibodies in a Rare Case of Rhesus Dermatitis10:27

Recognition of Epidermal Transglutaminase by IgA and Tissue Transglutaminase 2 Antibodies in a Rare Case of Rhesus Dermatitis

Dermatitis herpetiformis (DH) is a chronic inflammatory condition characterized by an autoimmune reaction between IgA and epidermal transglutaminase (eTG). DH develops in a very small portion of gluten-sensitive and/or celiac patients. The results of this study indicate that DH can also develop in a rhesus monkey host with symptoms of idiopatic...
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Linear Circuits01:17

Linear Circuits

A linear circuit is characterized by its output having a direct proportionality to its input, adhering to the linearity property, which encompasses the principles of homogeneity (scaling) and additivity. Homogeneity dictates that when the input, also referred to as the excitation, is multiplied by a constant factor, the output, known as the response, is correspondingly scaled by the same constant factor. For instance, if the current is multiplied by a constant 'k,' the voltage likewise...
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Linear Momentum00:55

Linear Momentum

The term momentum is used in various ways in everyday language, most of which are consistent with the precise scientific definition. Generally, momentum implies a tendency to continue on course—to move in the same direction; we tend to speak of sports teams or politicians gaining and maintaining the momentum to win.  Momentum is also associated with great mass and speed and is often considered when talking about collisions. For example, when rugby players collide and fall to the...
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