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Let denote the length function on W.
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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.
Let and length
Let now x ' and y ' be tuples of previously unused variables of the same length as x and y respectively, and let Q be a previously unused relation symbol which takes as many arguments as the sum of lengths of x and y ; we consider the formula
* Let be the least number such that there is a file with length bits that compresses to something shorter.
According to some translations, the segment CE, representing the intelligible world, is divided into the same ratio as AC, giving the subdivisions CD and DE ( it can be readily verified that CD must have the same length as BC < ref > Let the length of AE be equal to and that of AC equal to, where < math >
Let ℓ ( e ) be the length of the edge e and θ ( e ) be the dihedral angle between the two faces meeting at e, measured in radians.
Let us now consider a three-dimensional cubical box that has a side length L ( see infinite square well ).
Their new album " Es werde Nicht " ( translates to " Let there be Nothing ", a pun on " Es werde Licht "-" Let there be Light ") will be released in September 2011, followed by a big tour with concerts of regular length.
Let be a set called the instance space or the encoding of all the samples, and each instance have length assigned.
Let R be the radius of the circle, θ is the central angle in radians, α is the central angle in degrees, c the chord length, s the arc length, h the height of the segment, and d the height of the triangular portion.
Let 0 → G < sub > n </ sub > → … → G < sub > 0 </ sub > → 0 denote a finite complex of free R-modules such that ⊕< sub > i </ sub > H < sub > i </ sub >( G < sub >•</ sub >) has finite length but is not 0.
Let 0 → G < sub > n </ sub > → … → G < sub > 0 </ sub > → 0 denote a finite complex of free R-modules such that H < sub > i </ sub >( G < sub >•</ sub >) has finite length for i > 0 and H < sub > 0 </ sub >( G < sub >•</ sub >) has a minimal generator that is killed by a power of the maximal ideal of R. Then dim R ≤ n.
Let the return value of the function be the length of the input accepted by, or 0 if that rule does not accept any input at that offset in the string.
0.267 seconds.