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Mathieu function. In mathematics, Mathieu functions, sometimes called angular Mathieu functions, are solutions of Mathieu's differential equation. where a, q are real -valued parameters. Since we may add π/2 to x to change the sign of q, it is a usual convention to set q ≥ 0.
Inverted pendulum. Balancing cart, a simple robotics system circa 1976. The cart contains a servo system that monitors the angle of the rod and moves the cart back and forth to keep it upright. An inverted pendulum is a pendulum that has its center of mass above its pivot point. It is unstable and falls over without additional help.
The polyhedral model (also called the polytope method) is a mathematical framework for programs that perform large numbers of operations -- too large to be explicitly enumerated -- thereby requiring a compact representation. Nested loop programs are the typical, but not the only example, and the most common use of the model is for loop nest ...
β = 0 , {\displaystyle \beta =0,} the Duffing equation describes a damped and driven simple harmonic oscillator, γ {\displaystyle \gamma } is the amplitude of the periodic driving force; if. γ = 0 {\displaystyle \gamma =0} the system is without a driving force, and. ω {\displaystyle \omega } is the angular frequency of the periodic driving ...
The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, [3] linguistics, [4] and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different ...
Van der Pol oscillator. In the study of dynamical systems, the van der Pol oscillator (named for Dutch physicist Balthasar van der Pol) is a non- conservative, oscillating system with non-linear damping. It evolves in time according to the second-order differential equation where x is the position coordinate —which is a function of the time t ...
e. Active learning is a special case of machine learning in which a learning algorithm can interactively query a human user (or some other information source), to label new data points with the desired outputs. The human user must possess knowledge/expertise in the problem domain, including the ability to consult/research authoritative sources ...
A class diagram exemplifying the singleton pattern. In Object-oriented programming, the singleton pattern is a software design pattern that restricts the instantiation of a class to a singular instance. One of the well-known "Gang of Four" design patterns, which describes how to solve recurring problems in object-oriented software. [ 1 ]