In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept...
19 KB (2,467 words) - 04:06, 27 August 2024
absolutely monotonic function and a completely monotonic function are two very closely related concepts. Both imply very strong monotonicity properties...
10 KB (1,414 words) - 23:16, 27 August 2024
well the relationship between two variables can be described using a monotonic function. The Spearman correlation between two variables is equal to the Pearson...
32 KB (4,260 words) - 09:36, 22 August 2024
mathematical functions Injective metric space – Type of metric space Monotonic function – Order-preserving mathematical function Univalent function – Mathematical...
16 KB (2,493 words) - 13:11, 1 June 2024
{\displaystyle g:\mathbb {R} \to \mathbb {R} } be a monotonic function, then the resulting density function is f Y ( y ) = f X ( g − 1 ( y ) ) | d d y ( g...
30 KB (4,937 words) - 11:29, 22 August 2024
}\left(1\wedge x\right)\mu (dx)<\infty .} Absolutely and completely monotonic functions and sequences S. N. Bernstein (1928). "Sur les fonctions absolument...
3 KB (344 words) - 11:14, 24 March 2024
Square (algebra) (redirect from Square function)
square function preserves the order of positive numbers: larger numbers have larger squares. In other words, the square is a monotonic function on the...
15 KB (1,988 words) - 07:48, 23 August 2024
inputs. Strict monotonic function: preserves the given order. Real function: a function whose domain is real. Complex function: a function whose domain...
13 KB (1,407 words) - 21:21, 26 January 2023
Logarithm (redirect from Logarithmic function)
determined by reverse look up in the same table, since the logarithm is a monotonic function. The product and quotient of two positive numbers c and d were routinely...
97 KB (11,603 words) - 06:14, 29 August 2024
Sequence (redirect from Monotonic sequence)
sequence. This is a special case of the more general notion of a monotonic function. The terms nondecreasing and nonincreasing are often used in place...
39 KB (6,156 words) - 04:01, 4 August 2024
be a complete lattice and let f : L → L be an order-preserving (monotonic) function w.r.t. ≤ . Then the set of fixed points of f in L forms a complete...
19 KB (2,415 words) - 04:32, 29 July 2024
since it allows convex analysis to be used. Since squaring is a monotonic function of non-negative values, minimizing squared distance is equivalent...
25 KB (3,187 words) - 10:11, 23 August 2024
mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above the graph between...
35 KB (5,850 words) - 04:14, 7 June 2024
each point and exactly one inflection point. In general, a sigmoid function is monotonic, and has a first derivative which is bell shaped. Conversely, the...
13 KB (1,688 words) - 07:27, 10 May 2024
concave function can be quasiconvex. For example, x ↦ log ( x ) {\displaystyle x\mapsto \log(x)} is both concave and quasiconvex. Any monotonic function is...
12 KB (1,448 words) - 04:32, 22 May 2024
value zero for x = 1, is a differentiable function called the natural logarithm. A real function f is monotonic in an interval if the sign of f ( x ) −...
75 KB (11,265 words) - 23:35, 31 August 2024
Curvature (section Graph of a function)
arc length s is a differentiable monotonic function of the parameter t, and conversely that t is a monotonic function of s. Moreover, by changing, if needed...
44 KB (6,460 words) - 20:41, 28 August 2024
privacy that a person achieves. Third, privacy is described as a non-monotonic function. More privacy is not necessarily better. A person seeks an optimal...
8 KB (1,057 words) - 16:01, 8 August 2023
sound approximation of the semantics of computer programs, based on monotonic functions over ordered sets, especially lattices. It can be viewed as a partial...
24 KB (2,924 words) - 16:16, 17 April 2024
more than once, the function fails the horizontal line test and is not injective. Vertical line test Inverse function Monotonic function Stewart, James (2003)...
3 KB (399 words) - 19:22, 19 February 2024
) or inverse distribution function. With reference to a continuous and strictly monotonic cumulative distribution function F X : R → [ 0 , 1 ] {\displaystyle...
16 KB (2,186 words) - 22:23, 17 June 2024
Monotone preferences (redirect from Monotonic preferences)
preferences which are weakly monotonic but not strongly monotonic are those represented by a Leontief utility function. If an agent has monotone preferences...
2 KB (333 words) - 18:29, 21 December 2023
temperature ranges (negative thermal expansion). Temperature is a monotonic function of the average molecular kinetic energy of a substance. As energy...
49 KB (6,073 words) - 04:54, 14 August 2024
cubic function is strictly monotonic. See the figure for an example of the case Δ0 > 0. The inflection point of a function is where that function changes...
12 KB (1,746 words) - 17:03, 28 August 2024
well the relationship between two variables can be described by a monotonic function. The Kendall tau rank correlation coefficient is a measure of the...
6 KB (665 words) - 21:58, 26 March 2024
and equivalence and often occurs in the context of inequality and monotonic functions. It is often attached to a technical term to indicate that the exclusive...
3 KB (420 words) - 17:57, 28 October 2023
hereditary, monotone, or minor-closed if the function formalizing the invariant forms a monotonic function from the corresponding partial order on graphs...
9 KB (1,170 words) - 06:58, 8 October 2022
Examples of non-monotonic queries are aggregation queries, or queries with set difference. Identifying whether a query is monotonic can be crucial for...
3 KB (432 words) - 18:32, 16 April 2024
MR 2356043. Gelbaum, Bernard R.; Olmsted, John M. H. (1964), "18: A monotonic function whose points of discontinuity form an arbitrary countable (possibly...
28 KB (3,452 words) - 11:11, 8 January 2024