Search results
Results from the WOW.Com Content Network
More generally, the restriction (or domain restriction or left-restriction) of a binary relation between and may be defined as a relation having domain , codomain and graph ( ) = {(,) ():}. Similarly, one can define a right-restriction or range restriction R B . {\displaystyle R\triangleright B.}
Similarly, every additive function that is not linear (that is, not of the form for some constant ) is a nowhere continuous function whose restriction to is continuous (such functions are the non-trivial solutions to Cauchy's functional equation). This raises the question: can such a dense subset always be found?
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
In the general case, constraint problems can be much harder, and may not be expressible in some of these simpler systems. "Real life" examples include automated planning, [6] [7] lexical disambiguation, [8] [9] musicology, [10] product configuration [11] and resource allocation. [12] The existence of a solution to a CSP can be viewed as a ...
What links here; Related changes; Upload file; Permanent link; Page information; Cite this page; Get shortened URL; Download QR code
A problem is called extremely-benevolent if it satisfies the following three conditions: Proximity is preserved by the transition functions: For any r>1, for any transition function f in F, for any input-vector x, and for any two state-vectors s 1,s 2, the following holds: if s 1 is (d,r)-close to s 2, then f(s 1,x) is (d,r)-close to f(s 2,x).
In calculus, a real-valued function of a real variable or real function is a partial function from the set of the real numbers to itself. Given a real function f : x ↦ f ( x ) {\displaystyle f:x\mapsto f(x)} its multiplicative inverse x ↦ 1 / f ( x ) {\displaystyle x\mapsto 1/f(x)} is also a real function.
Blumberg theorem – even if a real function : is nowhere continuous, there is a dense subset of such that the restriction of to is continuous. Thomae's function (also known as the popcorn function) – a function that is continuous at all irrational numbers and discontinuous at all rational numbers.