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Что (кто) такое factorial duality - определение
EXPERIMENT WHOSE DESIGN CONSISTS OF TWO OR MORE FACTORS, EACH WITH DISCRETE POSSIBLE VALUES, AND WHOSE EXPERIMENTAL UNITS TAKE ON ALL POSSIBLE COMBINATIONS OF THESE LEVELS ACROSS ALL SUCH FACTORS
Factorial experiments; Factorial design; Fully-crossed design; Fully crossed design; Factorial designs; Factorial trial
![Pareto plot]] showing the relative magnitude of the factor coefficients.](https://commons.wikimedia.org/wiki/Special:FilePath/Pareto plot filtration rate.svg?width=200 "Pareto plot]] showing the relative magnitude of the factor coefficients.")
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Factorial
![[[Relative error]] in a truncated Stirling series vs. number of terms](https://commons.wikimedia.org/wiki/Special:FilePath/Stirling series relative error.svg?width=200 "[[Relative error]] in a truncated Stirling series vs. number of terms")
![TI SR-50A]], a 1975 calculator with a factorial key (third row, center right)](https://commons.wikimedia.org/wiki/Special:FilePath/Vintage Texas Instruments Model SR-50A Handheld LED Electronic Calculator, Made in the USA, Price Was $109.50 in 1975 (8715012843).jpg?width=200 "TI SR-50A]], a 1975 calculator with a factorial key (third row, center right)")
PRODUCT OF ALL INTEGERS BETWEEN 1 AND THE INTEGRAL INPUT OF THE FUNCTION
Factorial function; Factorials; Superduperfactorial; N!; Factorial number; Factoral; Factorial growth; X!; ! (math); Approximations of factorial; Negative factorial
In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial:
factorial
PRODUCT OF ALL INTEGERS BETWEEN 1 AND THE INTEGRAL INPUT OF THE FUNCTION
Factorial function; Factorials; Superduperfactorial; N!; Factorial number; Factoral; Factorial growth; X!; ! (math); Approximations of factorial; Negative factorial
<mathematics> The mathematical function that takes a
natural number, N, and returns the product of N and all
smaller positive integers. This is written
N! = N * (N-1) * (N-2) * ... * 1.
The factorial of zero is one because it is an {empty
product}.
Factorial can be defined recursively as
0! = 1
N! = N * (N-1)! , N > 0
The gamma function is the equivalent for real numbers.
(2005-01-07)
Factorial
PRODUCT OF ALL INTEGERS BETWEEN 1 AND THE INTEGRAL INPUT OF THE FUNCTION
Factorial function; Factorials; Superduperfactorial; N!; Factorial number; Factoral; Factorial growth; X!; ! (math); Approximations of factorial; Negative factorial
·adj Related to factorials.
II. Factorial ·adj Of or pertaining to a factory.
III. Factorial ·noun The product of the consecutive numbers from unity up to any given number.
IV. Factorial ·noun A name given to the factors of a continued product when the former are derivable from one and the same function F(x) by successively imparting a constant increment or decrement h to the independent variable. Thus the product F(x)·F(x + h)·F(x + 2h)· ... ·F(x + (n - 1)·h) is called a factorial term, and its several factors take the name of factorials.
Factorial experiment
In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design.
Factorial number system
![The factorial numbers of a given length form a [[permutohedron]] when ordered by the bitwise <math>\le</math> relation<br/><br/>These are the right inversion counts (aka Lehmer codes) of the permutations of four elements.](https://commons.wikimedia.org/wiki/Special:FilePath/Symmetric group 4; permutohedron 3D; Lehmer codes.svg?width=200 "The factorial numbers of a given length form a [[permutohedron]] when ordered by the bitwise <math>\le</math> relation<br/><br/>These are the right inversion counts (aka Lehmer codes) of the permutations of four elements.")
MIXED RADIX NUMERAL SYSTEM ADAPTED TO NUMBERING PERMUTATIONS; REPRESENTS A NUMBER AS A×0! + B×1! + C×2! + ⋯
Factoradix; Factorial base; Factoradic
In combinatorics, the factorial number system, also called factoradic, is a mixed radix numeral system adapted to numbering permutations. It is also called factorial base, although factorials do not function as base, but as place value of digits.
U-duality
SYMMETRY OF M-THEORY COMPACTIFICATIONS THAT INCLUDES T-DUALITY AND S-DUALITY AS SUBGROUPS; THE SUPERGRAVITY THEORY U-DUALITY GROUP IS AN E-SERIES LIE GROUP, WHILE STRINGY EFFECTS BREAK IT TO A DISCRETE SUBGROUP
U-duality group
In physics, U-duality (short for unified duality)S. Mizoguchi, "On discrete U-duality in M-theory", 2000.
Matlis duality
MATHEMATICAL THEOREM THAT, OVER A NOETHERIAN COMPLETE LOCAL RING, THE CATEGORIES OF NOETHERIAN AND ARTINIAN MODULES ARE ANTI-ISOMORPHIC
Matlis module; Macaulay duality
In algebra, Matlis duality is a duality between Artinian and Noetherian modules over a complete Noetherian local ring. In the special case when the local ring has a field mapping to the residue field it is closely related to earlier work by Francis Sowerby Macaulay on polynomial rings and is sometimes called Macaulay duality, and the general case was introduced by .
Coherent duality
Global duality theorem
In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the 'local' theory.
Eckmann–Hilton duality
Eckmann Hilton duality; Eckmann-Hilton duality
In the mathematical disciplines of algebraic topology and homotopy theory, Eckmann–Hilton duality in its most basic form, consists of taking a given diagram for a particular concept and reversing the direction of all arrows, much as in category theory with the idea of the opposite category. A significantly deeper form argues that the fact that the dual notion of a limit is a colimit allows us to change the Eilenberg–Steenrod axioms for homology to give axioms for cohomology.
Poincaré duality
DUALITY THAT RELATES HOMOLOGY AND COHOMOLOGY GROUPS FOR ORIENTED CLOSED MANIFOLDS
Poincare duality; Poincaré dual; Poincare dual; Torsion linking form; Poincaré duality theorem
In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds. It states that if M is an n-dimensional oriented closed manifold (compact and without boundary), then the kth cohomology group of M is isomorphic to the (n-k)th homology group of M, for all integers k
Википедия
Factorial experiment
In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design. Such an experiment allows the investigator to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable.
For the vast majority of factorial experiments, each factor has only two levels. For example, with two factors each taking two levels, a factorial experiment would have four treatment combinations in total, and is usually called a 2×2 factorial design. In such a design, the interaction between the variables is often the most important. This applies even to scenarios where a main effect and an interaction is present.
If the number of combinations in a full factorial design is too high to be logistically feasible, a fractional factorial design may be done, in which some of the possible combinations (usually at least half) are omitted.
