With " multivalued state coding " a single variable can be used to distinguish states of automaton, the number of states is equal to the number of values this variable can take on.
42.
In other parts of mathematics, non-single-valued relations are similarly conflated with functions : these are called " multivalued functions ", with the corresponding term single-valued function for ordinary functions.
43.
(If we instead restrict to the domain, then the inverse is the negative of the square root of . ) Alternatively, there is no need to restrict the domain if we are content with the inverse being a multivalued function:
44.
For specifying the branch, that is defining which value of the multivalued function is considered at each point, one generally define it at a particular point, and deduce the value everywhere in the domain of definition of the principal value by analytic continuation.
45.
Michael Z . Zgurovsky, Pavlo O . Kasyanov Multivalued Dynamics of Solutions for Autonomous Operator Differential Equations in Strongest Topologies / / Continuous and Distributed Systems : Theory and Applications, Solid Mechanics and Its Applications, Volume 211, 2014, pp 149-162
46.
Since each email address can be the ID of a record in separate file ( in SQL terms, an outer join; in U2 terms, a " translate " ), this provides the reason why U2 may be classified as a MultiValued database.
47.
There is, moreover, nothing to prevent us from doing this incorrectly : we might add Cheese Crust rows for all but one of A1 Pizza's delivery areas, thereby failing to respect the multivalued dependency { Restaurant } \ twoheadrightarrow { Pizza Variety }.
48.
Also note that the table is in 4NF, since there are no multivalued dependencies ( 2-part join dependencies ) in the table : no column ( which by itself is not a candidate key or a superkey ) is a determinant for the other two columns.
49.
However, in using the inverse trigonometric functions, there is alway the issue what principal values to use, or to consider all solutions, since these inverse functions are tricky indeed : properly speaking they are not functions but relations, or so-called multivalued functions.
50.
However, since most central forces do not produce closed orbits ( see Bertrand's theorem ), the analogous vector \ mathcal { A } rarely has a simple definition and is generally a multivalued function of the angle ? between "'r "'and \ mathcal { A }.
