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In computer science and logic, a dependent type is a type whose definition depends on a value. It is an overlapping feature of type theory and type systems.In intuitionistic type theory, dependent types are used to encode logic's quantifiers like "for all" and "there exists".
Parameter dependent systems [ edit ] In control engineering , a state-space representation is a mathematical model of a physical system as a set of input, u {\displaystyle u} output, y {\displaystyle y} and state variables, x {\displaystyle x} related by first-order differential equations.
The system + =, + = has exactly one solution: x = 1, y = 2 The nonlinear system + =, + = has the two solutions (x, y) = (1, 0) and (x, y) = (0, 1), while + + =, + + =, + + = has an infinite number of solutions because the third equation is the first equation plus twice the second one and hence contains no independent information; thus any value of z can be chosen and values of x and y can be ...
The only cases where the overdetermined system does in fact have a solution are demonstrated in Diagrams #4, 5, and 6. These exceptions can occur only when the overdetermined system contains enough linearly dependent equations that the number of independent equations does not exceed the number of unknowns. Linear dependence means that some ...
A variant of ML called Dependent ML has been created based on this type system, but because type checking for conventional dependent types is undecidable, not all programs using them can be type-checked without some kind of limits. Dependent ML limits the sort of equality it can decide to Presburger arithmetic.
Two linear systems using the same set of variables are equivalent if each of the equations in the second system can be derived algebraically from the equations in the first system, and vice versa. Two systems are equivalent if either both are inconsistent or each equation of each of them is a linear combination of the equations of the other one.
From psychophysiological perspective, the human movement system is a highly intricate network of co-dependent sub-systems (e.g. respiratory, circulatory, nervous, skeletomuscular, perceptual) that are composed of a large number of interacting components (e.g. blood cells, oxygen molecules, muscle tissue, metabolic enzymes, connective tissue and ...
Systems theory is the transdisciplinary [1] study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or artificial.Every system has causal boundaries, is influenced by its context, defined by its structure, function and role, and expressed through its relations with other systems.