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MATLAB (an abbreviation of "MATrix LABoratory" [18]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
In many applications, objective functions, including loss functions as a particular case, are determined by the problem formulation. In other situations, the decision maker’s preference must be elicited and represented by a scalar-valued function (called also utility function) in a form suitable for optimization — the problem that Ragnar Frisch has highlighted in his Nobel Prize lecture. [4]
For a partial differential equation, for example, + =, where denotes the Laplace operator, the Dirichlet boundary conditions on a domain Ω ⊂ R n take the form = (), where f is a known function defined on the boundary ∂Ω.
Function symbols are used, together with constants and variables, to form terms. The theory of uninterpreted functions is also sometimes called the free theory, because it is freely generated, and thus a free object, or the empty theory, being the theory having an empty set of sentences (in analogy to an initial algebra).
At that time, only real-valued functions of a real variable were considered, and all functions were assumed to be smooth. But the definition was soon extended to functions of several variables and to functions of a complex variable. In the second half of the 19th century, the mathematically rigorous definition of a function was introduced, and ...
In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form + ′ + ″ + () = where a 0 (x), ..., a n (x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y (n) are the successive derivatives of an unknown function y of ...
Using the XOR swap algorithm to exchange nibbles between variables without the use of temporary storage. In computer programming, the exclusive or swap (sometimes shortened to XOR swap) is an algorithm that uses the exclusive or bitwise operation to swap the values of two variables without using the temporary variable which is normally required.