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Let us denote the mutually orthogonal single-particle states by and so on.
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Let and us
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 not confuse the issue by labeling the objective or the method `` psychoanalytic '', for this is a well established term of art for the specific ideas and procedures initiated by Sigmund Freud and his followers for the study and treatment of disordered personalities.
Let us quote once more from R. G. Collingwood: `` History is properly concerned with the actions of human beings Regarded from the outside, an action is an event or series of events occurring in the physical world ; ;
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 us, like the French, have outdoor cafes where we may relax, converse at leisure and enjoy the passing crowd.
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 us now put some flesh on the theoretical bones we have assembled by giving illustrations of roleplaying used for evaluation and analysis.
Let us also assume the existence of only one class or type of service, all of which is supplied at the same voltage, phase, etc. to residential, commercial, and industrial customers.
Let us therefore consider each of the three types of cost in turn, recognizing that this simplified classification is used only for illustrative purposes ; ;
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 and denote
Let denote the Bézier curve determined by the points P < sub > 0 </ sub >, P < sub > 1 </ sub >, ..., P < sub > n </ sub >.
Let '~' denote an equivalence relation over some nonempty set A, called the universe or underlying set.
Let G denote the set of bijective functions over A that preserve the partition structure of A: ∀ x ∈ A ∀ g ∈ G ( g ( x ) ∈ ).
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 n denote a complete set of ( discrete ) quantum numbers for specifying single-particle states ( for example, for the particle in a box problem we can take n to be the quantized wave vector of the wavefunction.
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 line of symmetry intersect the parabola at point Q, and denote the focus as point F and its distance from point Q as f. Let the perpendicular to the line of symmetry, through the focus, intersect the parabola at a point T. Then ( 1 ) the distance from F to T is 2f, and ( 2 ) a tangent to the parabola at point T intersects the line of symmetry at a 45 ° angle.
That is, Alice has one half, a, and Bob has the other half, b. Let c denote the qubit Alice wishes to transmit to Bob.
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 < sub > x </ sub >, defined by
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.
A possible definition of spoiling based on vote splitting is as follows: Let W denote the candidate who wins the election, and let X and S denote two other candidates.
Let be a sequence of independent and identically distributed variables with distribution function F and let denote the maximum.
0.088 seconds.