Let the open enemy to it be regarded as a Pandora with her box opened ; ;

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 him be now ''!!

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 T be a linear operator on the finite-dimensional vector space V over the field F.

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 Af be the null space of Af.

Let N be a linear operator on the vector space V.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

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 this be denoted by Af.

Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.

Let not your heart be troubled, neither let it be afraid ''.

The same God who called this world into being when He said: `` Let there be light ''!!

For those who put their trust in Him He still says every day again: `` Let there be light ''!!

Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.

Let her out, let her out -- that would be the solution, wouldn't it??

Let ε ( n ) denote the energy of a particle in state n. As the particles do not interact, the total energy of the system is the sum of the single-particle energies.

Let the potential energy difference across the surface due to effective surface dipole be.

Next, take a Hamiltonian invariant under T. Let | a > and T | a > be two quantum states of the same energy.

Let the number of particles with the same energy be, the number of particles possessing another energy be, and so forth for all the possible energies

Let V be a Hamiltonian representing a weak physical disturbance, such as a potential energy produced by an external field.

Let us label with s ( s = 1, 2, 3, ...) the exact states ( microstates ) that the system can occupy, and denote the total energy of the system when it is in microstate s as E < sub > s </ sub >.

Let the ecosystem ( i. e., solar energy ) subsidize the management effort rather than the other way around.

Let the energy of e, be

Let the total energy of the traffic graph be the sum of the energies of every edge in the graph.

Let be total energy of the traffic graph, and consider what happens when the route is removed.

Paxton's 1979 album, Up and Up, contains the song " Let the Sunshine ", which addresses issues concerning environmentalism and solar energy.

" It was parodied by the band Dash Rip Rock with their single entitled “ Let ’ s Go Smoke Some Pot ”, and by NRBQ during the 1973 energy crisis under the title, " Get That Gasoline.

Let denote the time-independent Hamiltonian, and let and denote the two energy eigenstates of the system, with respective eigenvalues and.

Let us hope, then, that you can use your energy to overcome your moth-eaten thirty tyrants of the various German states.

Let the energy difference between the states be so that is the transition frequency of the system.

Let us suppose the Russians decide to build a rail-mobile ICBM force.

Let us suppose that the animal did not in fact fall into the trap and did not suffer at all, but that we mistakenly believe it did, and say as before that its suffering was an evil thing.

Let us focus on an atom of calcium from the tip of the bone of my finger and let us suppose that I swallow a magic Alice In Wonderland growing pill.

Let us suppose ( as is the practical case ) that the star is sufficiently distant that all light from the star travels in parallel paths to the Earth observer, regardless of where the Earth is in its orbit.

Let ( A < sub > i </ sub >)< sub > i ∈ I </ sub > be a family of groups and suppose we have a family of homomorphisms f < sub > ij </ sub >: A < sub > j </ sub > → A < sub > i </ sub > for all i ≤ j ( note the order ) with the following properties:

In his Commentary on Daniel, he noted, “ Let us not follow the opinion of some commentators and suppose him to be either the Devil or some demon, but rather, one of the human race, in whom Satan will wholly take up his residence in bodily form .” In interpreting 2 Thessalonians's claim that the Antichrist will sit in God's temple, Jerome preferred the view that the " temple " should be interpreted as the Church, not as the Temple in Jerusalem.

Let us suppose now that there is at least a positive solution, and let be the minimal one.

Let us suppose that L is a complete lattice and let f be a monotonic function from L into L. Then, any x ′ such that f ′( x ′) ≤ x ′ is an abstraction of the least fixed-point of f, which exists, according to the Knaster – Tarski theorem.

Let A be an observable of the system, and suppose the ensemble is in a mixed state such that each of the pure states occurs with probability p < sub > j </ sub >.

* "' Let me not suppose that she dares go about, Emma Woodhouse-ing me!

Let U be a measurable subset of R < sup > n </ sup > and φ: U → R < sup > n </ sup > an injective function, and suppose for every x in U there exists < span > φ '</ span >( x ) in R < sup > n, n </ sup > such that φ ( y ) = φ ( x ) + < span > φ '</ span >( x ) ( y − x ) + o (|| y − x ||) as y → x.

Let V be a finite-dimensional vector space over some field K and suppose T: V → V is a linear map.

Let f = uv and suppose u and v are positive functions of x.

Let us suppose also that a choice of positive roots Φ < sup >+</ sup > has been fixed.

Let us suppose we have a point positive charge of a certain true

Let X be the wedge sum of two spaces K and L, and suppose furthermore that the identified basepoint is a deformation retract of open neighborhoods U ⊂ K and V ⊂ L. Letting A

Let φ: M → N be a smooth map between ( smooth ) manifolds M and N, and suppose f: N → R is a smooth function on N. Then the pullback of f by φ is the smooth function φ < sup >*</ sup > f on M defined by

Let be an observable, and suppose that it has discrete eigenstates ( in bra-ket notation ) for and corresponding eigenvalues, no two of which are equal.

Let be an observable, and suppose that it has a continuous spectrum of eigenvalues filling the interval ( a, b ).

* K ( X, Y ) is a closed subspace of B ( X, Y ): Let T < sub > n </ sub >, n ∈ N, be a sequence of compact operators from one Banach space to the other, and suppose that T < sub > n </ sub > converges to T with respect to the operator norm.

Let be a random sample from the distribution where the mean is known, and suppose that we wish to test for against.

Theorem ( Calvin Richard Putnam ) Let T, M, N be linear operators on a complex Hilbert space, and suppose that M and N are normal and MT

Let e =( e < sub > α </ sub >)< sub > α = 1, 2 ,..., k </ sub > be a local frame on E. This frame can be used to express locally any section of E. For suppose that ξ is a local section, defined over the same open set as the frame e, then

This identity is derived from the divergence theorem applied to the vector field: Let φ and ψ be scalar functions defined on some region U in R < sup > 3 </ sup >, and suppose that φ is twice continuously differentiable, and ψ is once continuously differentiable.

Let the spiritually illiterate suppose what they may, it was the Jewish denial and rejection of the Holy One of Israel, whom their fathers worshiped in the beauty of holiness, that has made them a hiss and a byword in all nations and that has taken millions of their fair sons and daughters to untimely graves.