The Karush-Kuhn-Tucker (KKT) stationarity condition yields a system of equations that can be solved directly for the PC2 coefficients. This approach is a natural extension of the ordinary least squares (OLS) approach, as used in standard PCE [27], to incorporate known equality-type constraints...
Last summer, I worked out a simple, concrete example in detail, and this column will discuss the upshot of that, leaving out the details. If you’ve ever wondered, how exactly do quantum models work?—or even if you haven’t wondered, but are wondering now that I mention it—well, re...
For example, suppose that Bob measures Alice’s brain in the lab while she’s feeling happiness. Although they observe different properties, they actually measure the same phenomenon from different points of view. Because of their different kinds of measurements, different kinds of properties have b...
Work energy theorem. Potential energy of a spring. Mechanical energy and its conservation. Collision and its types. What is Work? Work happens when a force makes something move. For example, when a person climbs a mountain, work is being done because they are going against gravity to go up...
For more information on principles and implementation of physics in real-time rendering, see the articles Execution Sequence, Physics and Simulation of Physics. See Also The Creating a Car with Suspension Joints usage example demonstrating how to set up physics parameters A set of UnigineScript API...
"Put it in Context" examples. Each chapter contains one or more "context-rich" worked examples. Unlike standard worked examples, these include extra contextual information (such as descriptions of the real-life situation) and state the problem indirectly. For example, in a standard problem, the...
As example, assume a plane has a speed of 400 m/s and is in the wind of 100 m/s to east. Therefore, the plane’s speed relative to the ground will be: square root of (4002 + 1002) = 412.31 m/s. Let’s talk about another problem, Suppose the capsule that was transmitted in ...
solved using numerical integration techniques with an elastic coupling equation as a constraint. The least-squares method is typically used iteratively to find the values of the parameters that fit the frictional data with an average\(R^2\)> 0.9. In this work, we consider RSF parameters listed...
For example, I learned that the word “transistor” was chosen by polling employees at the lab where the first such device was successfully made; that an early example of network theory was a problem called the Seven Bridges of Königsberg, solved by Euler in 1736; and that both...
Not all forces are conservative; in our current example we could have included friction. Because friction is always in a direction that opposes the motion, to overcome it will always require (positive) work, and travel along a closed path (even if level) will have a value of w that depend...