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Let be a hypergraph such that.
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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 hypergraph
Let and such
* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )
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 ).
Records such as " Let Me Be the One " by Safire, " I Remember What You Like " by Jenny Burton, " Running " by Information Society, " Give Me Tonight " by Shannon and " It Works For Me " by Pam Russo enjoyed heavy New York radio airplay.
Let Marcion then exhibit, as gifts of his god, some prophets, such as have not spoken by human sense, but with the Spirit of God, such as have both predicted things to come, and have made manifest the secrets of the heart ; let him produce a psalm, a vision, a prayer -- only let it be by the Spirit, in an ecstasy, that is, in a rapture, whenever an interpretation of tongues has occurred to him ; let him show to me also, that any woman of boastful tongue in his community has ever prophesied from amongst those specially holy sisters of his.
Let us call the class of all such formulas R. We are faced with proving that every formula in R is either refutable or satisfiable.
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.
Ashcroft composed a paean called " Let the Eagle Soar " which he sang at the Gordon-Conwell Theological Seminary in February 2002, which was satirically featured in Michael Moore's 2004 movie Fahrenheit 9 / 11 and has been frequently mocked by comedians such as David Letterman, Stephen Colbert and David Cross, to name a few.
* Let be the least number such that there is a file with length bits that compresses to something shorter.
Proof: Let d be the position of the leftmost ( most significant ) nonzero bit in the binary representation of s, and choose k such that the dth bit of x < sub > k </ sub > is also nonzero.
Let be the space of real-valued continuous functions on X which vanish at infinity ; that is, a continuous function f is in if, for every, there exists a compact set such that on
If V is a real vector space, then we replace V by its complexification V ⊗< sub > R </ sub > C and let g denote the induced bilinear form on V ⊗< sub > R </ sub > C. Let W be a maximal isotropic subspace, i. e. a maximal subspace of V such that g |< sub > W </ sub > = 0.
Let the distance from the Sun to Saturn be taken as 100, then Mercury is separated by 4 such parts from the Sun.
" Let them produce the original records of their churches ; let them unfold the roll of their bishops, running down in due succession from the beginning in such a manner that first bishop of theirs bishop shall be able to show for his ordainer and predecessor some one of the apostles or of apostolic men, — a man, moreover, who continued steadfast with the apostles.
Let K be a topological field, namely a field with a topology such that addition, multiplication, and division are continuous.
Let F: J → C be a diagram of type J in a category C. A cone to F is an object N of C together with a family ψ < sub > X </ sub >: N → F ( X ) of morphisms indexed by the objects of J, such that for every morphism f: X → Y in J, we have F ( f ) o ψ < sub > X </ sub >
Let us assume that the waveguide is made of a metal that is such a good conductor that we can consider it to be a perfect conductor.
Let T: X → X be a contraction mapping on X, i. e.: there is a nonnegative real number q < 1 such that
0.351 seconds.