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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.
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]
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.
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.
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.
Here, ∗ is used to replace the symbol of the operation, which may be any symbol, and even the absence of symbol (juxtaposition) as for multiplication.
There has been some debate attempting to clarify the roles of juxtaposition and shifting in humor, hence, the discussion in the series Humor Research between John Morreall and Robert Latta. [30] Though Morreall himself endorses a cognitive shift theory, in this particular dialogue he indicated examples of simultaneous contrast, while Latta ...