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The order of operations, that is, the order in which the operations in an expression are usually performed, results from a convention adopted throughout mathematics, science, technology and many computer programming languages.
Quantum superposition is a fundamental principle of quantum mechanics that states that linear combinations of solutions to the Schrödinger equation are also solutions of the Schrödinger equation.
Juxtaposition in literary terms is the showing contrast by concepts placed side by side. An example of juxtaposition are the quotes "Ask not what your country can do for you; ask what you can do for your country", and "Let us never negotiate out of fear, but let us never fear to negotiate", both by John F. Kennedy, who particularly liked juxtaposition as a rhetorical device. [1]
A multiplicative group structure, called the Hamilton product, denoted by juxtaposition, can be defined on the quaternions in the following way: The real quaternion 1 is the identity element. The real quaternions commute with all other quaternions, that is aq = qa for every quaternion q and every real quaternion a.
A general 3d rotation of a vector a, about an axis in the direction of a unit vector ω and anticlockwise through angle θ, can be performed using Rodrigues' rotation formula in the dyadic form a r o t = R ⋅ a , {\displaystyle \mathbf {a} _{\mathrm {rot} }=\mathbf {R} \cdot \mathbf {a} \,,}
Multiplication in group theory is typically notated either by a dot or by juxtaposition (the omission of an operation symbol between elements). So multiplying element a by element b could be notated as a b or ab. When referring to a group via the indication of the set and operation, the dot is used.
Repetition is the essential comedic device and is often used in combination with other devices to reinforce them. The "callback" in comedy writing—in which a statement or theme is recalled as the punchline or close of a scene—is a classic example of the tension and release that are possible using repetition.
Relief theory suggests humor is a mechanism for pent-up emotions or tension through emotional relief. In this theory, laughter serves as a homeostatic mechanism by which psychological stress is reduced [1] [3] [7] Humor may thus facilitate ease of the tension caused by one's fears, for example.