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Let G be a cycle graph of odd length greater than three ( a so-called " odd hole ").
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Let and G
Suppose that in a mathematical language L, it is possible to enumerate all of the defined numbers in L. Let this enumeration be defined by the function G: W → R, where G ( n ) is the real number described by the nth description in the sequence.
Let G denote the set of bijective functions over A that preserve the partition structure of A: ∀ x ∈ A ∀ g ∈ G ( g ( x ) ∈ ).
Moving to groups in general, let H be a subgroup of some group G. Let ~ be an equivalence relation on G, such that a ~ b ↔ ( ab < sup >− 1 </ sup > ∈ H ).
Let G be a set and let "~" denote an equivalence relation over G. Then we can form a groupoid representing this equivalence relation as follows.
Let E be the intersection of the diagonals, and let F be on side DA and G be on side BC such that FEG is parallel to AB and CD.
Let F and G be a pair of adjoint functors with unit η and co-unit ε ( see the article on adjoint functors for the definitions ).
Let and be
Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.
Let us assume that it would be possible for an enemy to create an aerosol of the causative agent of epidemic typhus ( Rickettsia prowazwki ) over City A and that a large number of cases of typhus fever resulted therefrom.
Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.
Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.
Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.
Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.
Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.
Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.
Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.
Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.
Let and cycle
Among his other songs, the charming Shakespeare settings in the cycle Let Us Garlands Bring ( 1942 ) are the best known.
Let f ( z ) be the ordinary generating function ( OGF ) of the objects, then the OGF of the configurations is given by the substituted cycle index
In addition, the couple's weddings have been reported by mainstream media. Melody Thomas Scott has said, " Let ’ s face facts: Victor and Nikki will always be a huge dynamic, they ’ ve been in a circular cycle for over 30 years!
Let an AC voltage of sufficiently large magnitude be superimposed on the dc bias, such that during the positive cycle of the AC voltage, the diode is driven deep into the avalanche breakdown.
0.283 seconds.