Sentences Containing 'finite'
(locally finite implies point finite) Refinement.
A "thin" group is a group where the girth has an upper bound for all finite generating sets.
A curve "C" has at most a finite number of singular points.
A semigroup is said to be periodic if all of its elements are of finite order.
All finite-dimensional statistical manifolds can be understood in this way.
As light has a finite velocity, this theory also constrains the size of the directly observable Universe.
Based on his black-hole thermodynamics work, Bekenstein also demonstrated the Bekenstein bound: there is a maximum to the amount of information that can potentially be stored in a given finite region of space which has a finite amount of energy (which is similar to the holographic principle).
But when there is some sort of short-distance regulator on space time, the monopoles have a finite mass.
Every finite extension of a finite field is a cyclic extension.
Farrell extended Tate cohomology groups to the case of all groups "G" of finite virtual cohomological dimension.
Finite groups have virtual cohomological dimension 0, and in this case Farrell's cohomology groups are the same as those of Tate.
For more on the structure of finite semigroups, see Krohn–Rhodes theory.
He believed that the Universe, while not infinite, could not be held as finite as it lacked any bounds within which it could be contained.
Here consider them as finite cardinal numbers.
His 1928 paper "Über die endlichen Gruppen ohne das Gesetz der eindeutigen Umkehrbarkeit" ("On finite groups without the rule of unique invertibility") determined the structure of finite simple semigroups and showed that the minimal ideal (or Green's relations J-class) of a finite semigroup is simple.
If it is finite and nonempty, then it must contain at least one idempotent.
If this is finite, then "x" is said to be of finite order, otherwise it is of infinite order.
In combinatorics, enumeration means counting, i.e., determining the exact number of elements of finite sets, usually grouped into infinite families, such as the family of sets each consisting of all permutations of some finite set.
In mathematics, a topological space is feebly compact if every locally finite cover by nonempty open sets is finite.
In mathematics, in the realm of group theory, a group is said to be thin if there is a finite upper bound on the girth of the Cayley graph induced by any finite generating set.
In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.
In particular, a finitely generated group with property FA has finite abelianization.
In set theory, the notion of enumeration has a broader sense, and does not require the set being enumerated to be finite.
In theoretical physics, thermal quantum field theory or finite temperature field theory (or, shorter, thermal field theory) is a set of methods to calculate expectation values of physical observables of a quantum field theory at finite temperature.
In ZFC, a set formula_77 is finite if and only if there is formula_214 such that formula_215: further, define formula_193 as this "n" for finite "A".
Indeed, any subgroup of finite index in a T-group has property FA.
Just as the Fourier transform for an infinite interval is related to the Fourier series over a finite interval, so the Hankel transform over an infinite interval is related to the Fourier–Bessel series over a finite interval. Domain of definition.
Let "M" be a "GK"-module of finite order "m".
Let formula_8 be a finite set of events determined by these variables.
Methods capable of treating finite regions have been applied to stars and to atomic nuclei.
More can often be said when the order is finite.
Natural numbers can be considered either as finite ordinals or finite cardinals.
SRFI 41 enables the expression of both finite and infinite sequences with extraordinary economy.
That is, we have the estimate for all formula_4 for which the right-hand side is finite.
The base ring "R" is taken to be the finite field formula_2.
The Big Bang cosmology replaced this model (expanding, finite, and inhomogeneous universe).
The construction of MMH works in the finite field formula_24 for some prime integer formula_23.
The first element of the name is "not" which means "to fish using a seine" and the last element is the finite form of "odde" meaning "headland".
The last element "-fjorden" (the finite form of fjord) is a later addition.
The name derives from this bijection (one-to-one correspondence) between the set of non-negative integers and the set of finite strings using a finite set of symbols (the "digits").
The sea had jeeringly kept his finite body up, but drowned the infinite of his soul.
The set of possible output values may be finite or countably infinite.
The term is used in English in 1908 in Harold Hinton's "Theory of Groups of Finite Order".
The theory of finite semigroups has been of particular importance in theoretical computer science since the 1950s because of the natural link between finite semigroups and finite automata.
This finite volume is denoted by formula_1 and its bounding surface formula_2.
This has been shown to be a useful tool in studying the behavior of quantum field theories at finite temperature.
This leaves open the question as to whether the Universe is finite or infinite.
Universal hashing can be defined as a mapping from a finite set "A" with size "a" to a finite set "B" with size "b".
We can also state the "Symmetric Algorithmic Lovász Local Lemma": Let formula_40 be a finite set of mutually independent random variables and formula_4 be a finite set of events determined by these variables as before.
We may as well assume that the tree has no finite branches, as finite branches can be "unravelled" so make no difference.
More Vocab Words::: amnesia - loss of memory
::: rococo - ornate; highly decorated; N. CF. 18th century
::: inflated - exaggerated; pompous; enlarged (with air or gas)
::: vagary - capricious happening; caprice; whim; CF. wander
::: incriminate - accuse of or implicate in a crime; serve as evidence against; cause to seem or make guilty of a crime; Ex. incriminating evidence
::: dissection - analysis; cutting apart in order to examine
::: drone - idle person who lives on other people's work; male bee
::: mystic - of hidden meaning and spiritual power; Ex. mystic ceremonies; N. CF. mysticism
::: gape - open widely; open the mouth wide; stare wonderingly with the mouth open; CF. agape
::: antidote - remedy to counteract a poison or disease; Ex. antidote to the economic troubles