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Let and φ

Let φ be a formula of degree k + 1 ; then we can write it as

Let H be a Hilbert space, and let H * denote its dual space, consisting of all continuous linear functionals from H into the field R or C. If x is an element of H, then the function φ x , defined by

Let φ ( ξ, η, ζ ) be an arbitrary function of three independent variables, and let the spherical wave form F be a delta-function: that is, let F be a weak limit of continuous functions whose integral is unity, but whose support ( the region where the function is non-zero ) shrinks to the origin.

Let ρ, θ, and φ be spherical coordinates for the source point P. Here θ denotes the angle with the vertical axis, which is contrary to the usual American mathematical notation, but agrees with standard European and physical practice.

Let G and H be groups, and let φ: G → H be a homomorphism.

Let a sphere have radius r, longitude φ, and latitude θ.

Let φ range from 0 to 2π, and let θ range from 0 to π / 2.

Let there be a set of differentiable fields φ defined over all space and time ; for example, the temperature T ( x, t ) would be representative of such a field, being a number defined at every place and time.

Let the action be invariant under certain transformations of the space – time coordinates x μ and the fields φ

Let B contains all the sentences of A except ¬ φ.

Let ρ denote the number density of electrons, and φ the electric potential.

Let U be an open set in R n and φ: U → R n an injective differentiable function with continuous partial derivatives, the Jacobian of which is nonzero for every x in U. Then for any real-valued, compactly supported, continuous function f, with support contained in φ ( U ),

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

Let φ: X → Y be a continuous and absolutely continuous function ( where the latter means that ρ ( φ ( E )) = 0 whenever μ ( E ) = 0 ).

* Let I be any directed set with a greatest element m. The direct limit of any corresponding direct system is isomorphic to X m and the canonical morphism φ m : X m → X is an isomorphism.

Let F and G be two sheaves on X with values in the category C. A morphism φ: G → F consists of a morphism φ ( U ): G ( U ) → F ( U ) for each open set U of X, subject to the condition that this morphism is compatible with restrictions.

Let and be

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 and net

Let the net cash flow at time t be denoted by R t , i. e.:

* Let serve — A serve that touches the top of the net and lands in the proper service court ( it is replayed without penalty ).

Let and on

Let Old Knife come up and kill you and your people, or would you steer him on someone else ''??

Let us look in on one of these nerve centers -- SAC at Omaha -- and see what must still happen before a wing of B-52 bombers could drop their Aj.

Let us survey for a moment the development of modern thought -- turning our attention from the Reformation toward the revolutionary and romantic movements that follow and dwelling finally on more recent decades.

Let them offer on behalf of those creatures whose melody has been the joy of mankind since time began, the hymn `` Abide With Me ''.

Let me say at the outset that the music sounded as sparkling on the last playing as it did on the first.

Let us speculate a little on the maximum size of the anaconda.

Let us now regard D as a linear operator on the subspace V.

Let us now put some flesh on the theoretical bones we have assembled by giving illustrations of roleplaying used for evaluation and analysis.

Let us put to ourselves the hypothesis that we had not come on the scene and that the rabbit never was discovered.

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 your pupils learn on someone else, Doctor.

* 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 )

Parsons had already acted as assistant engineer on The Beatles ' Abbey Road and Let It Be, had recently engineered Pink Floyd's The Dark Side of the Moon, and had produced several acts for EMI Records.

During the January 1969 sessions for the Let It Be album, the Beatles played a slow impromptu version of " Mailman, Bring Me No More Blues " — although not written by Holly, it was popularized by him — with Lennon mimicking Holly's vocal style ; the recording was eventually released in the mid-1990s on Anthology 3.

Labour campaigned on the theme of " Let Us Face the Future " and positioned themselves as the party best placed to rebuild Britain after the war, while the Conservatives ' campaign centred around Churchill.

Let g be a smooth function on N vanishing at f ( x ).

Let c be the lowest point on the chain, called the vertex of the catenary,

2.419 seconds.