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 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 )

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 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.

Let Q ( x ) denote the number of square-free ( quadratfrei ) integers between 1 and x.

Let Q be P's right child.

Beginning with From Russia with Love in 1963, Llewelyn appeared as Q, the quartermaster of the MI6 gadget lab ( also known as Q branch ), in almost every Bond film until his death ( 17 ), only missing appearances in Live and Let Die in 1973, and Never Say Never Again, the latter of which is not part of the official James Bond film series.

Let Q and R be the points of intersection of these two circles.

Let C be a non-singular algebraic curve of genus g over Q.

Let K be the rational number field Q and

Let Q ( H ) be the expected number of values we have to choose before finding the first collision.

Let h < sub > 0 </ sub > be the hour angle when Q becomes positive.

Let K be a field lying between Q and its p-adic completion Q < sub > p </ sub > with respect to the usual non-Archimedean p-adic norm

|| x ||< sub > p </ sub > on Q for some prime p. Let R be the subring of K defined by

Let A =( Q < sub > A </ sub >, Σ, Δ < sub > A </ sub >, I < sub > A </ sub >, F < sub > A </ sub >) and B =( Q < sub > B </ sub >, Σ, Δ < sub > B </ sub >, I < sub > B </ sub >, F < sub > B </ sub >) be Büchi automata and C =( Q < sub > C </ sub >, Σ, Δ < sub > C </ sub >, I < sub > C </ sub >, F < sub > C </ sub >) be a finite automaton.

Let ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.

Let us for simplicity take m = k as an example.

Let f and g be any two elements of G. By virtue of the definition of G, = and =, so that =.

Let s = x < sub > 1 </ sub > ⊕ ... ⊕ x < sub > n </ sub > and t = y < sub > 1 </ sub > ⊕ ... ⊕ y < sub > n </ sub >.

Let the directrix be the line x = − p and let the focus be the point ( p, 0 ).

Let be a non-negative real-valued function of the interval, and let < math > S =

Let us assume the bias is V and the barrier width is W. This probability, P, that an electron at z = 0 ( left edge of barrier ) can be found at z = W ( right edge of barrier ) is proportional to the wave function squared,

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 x = rnd * 20! Let the value ' x ' equal a random number between ' 0 ' and ' 20 '

LET y = rnd * 20! Let the value ' y ' equal a random number between ' 0 ' and ' 20 '

Let A =

:: Let n = 0

:: Let repeat = TRUE

Let ( S, f ) be a game with n players, where S < sub > i </ sub > is the strategy set for player i, S = S < sub > 1 </ sub > × S < sub > 2 </ sub > ... × S < sub > n </ sub > is the set of strategy profiles and f =( f < sub > 1 </ sub >( x ), ..., f < sub > n </ sub >( x )) is the payoff function for x S. Let x < sub > i </ sub > be a strategy profile of player i and x < sub >- i </ sub > be a strategy profile of all players except for player i. When each player i < nowiki >

Let X = " to make something that its maker cannot lift ".

* Let TQBF =

* The ring of continuous functions from the real numbers to the real numbers is not Noetherian: Let I < sub > n </ sub > be the ideal of all continuous functions f such that f ( x ) = 0 for all x ≥ n. The sequence of ideals I < sub > 0 </ sub >, I < sub > 1 </ sub >, I < sub > 2 </ sub >, etc., is an ascending chain that does not terminate.

# Let p = ( p < sub > 1 </ sub >, p < sub > 2 </ sub >) and q = ( q < sub > 1 </ sub >, q < sub > 2 </ sub >) be elements of W, that is, points in the plane such that p < sub > 1 </ sub > = p < sub > 2 </ sub > and q < sub > 1 </ sub > = q < sub > 2 </ sub >.

Let ƒ be a function whose domain is the set X, and whose range is the set Y.

Let ( M, g ) be a Riemannian manifold and ƒ: M < sup > m </ sup > → R < sup > n </ sup > a short C < sup >∞</ sup >- embedding ( or immersion ) into Euclidean space R < sup > n </ sup >, where n ≥ m + 1.

Let ƒ and g be functions.

Let ƒ and g be two functions satisfying the above hypothesis that ƒ is continuous on I and is continuous on the closed interval.

Let ƒ ( x ) be any rational function over the real numbers.

Let k be an algebraically closed field and let A < sup > n </ sup > be an affine n-space over k. The polynomials ƒ in the ring k ..., x < sub > n </ sub > can be viewed as k-valued functions on A < sup > n </ sup > by evaluating ƒ at the points in A < sup > n </ sup >, i. e. by choosing values in k for each x < sub > i </ sub >.

Let k be the field of complex numbers C. Let A < sup > 2 </ sup > be a two dimensional affine space over C. The polynomials f in the ring Cy can be viewed as complex valued functions on A < sup > 2 </ sup > by evaluating ƒ at the points in A < sup > 2 </ sup >.

Let ƒ be measurable, E (| ƒ |) < ∞, and T be a measure-preserving map.

Let ƒ be the fraction of the circumference subtended by the golden angle, or equivalently, the golden angle divided by the angular measurement of the circle.

Let M and N be differentiable manifolds and ƒ: M → N be a differentiable map between them.

where stands for all partial derivatives of ƒ up to order k. Let us exchange every variable in for new independent variables

Let Ω be a connected open set in the complex plane C and ƒ: Ω → C a holomorphic function.

Let γ be a simple rectifiable loop in X around P. The ramification index of ƒ at P is

Let ƒ: X → Y be a morphism of algebraic curves.

Let ƒ ( x ) = ƒ ( x, y ) be a continuous function vanishing outside some large disc in the Euclidean plane R < sup > 2 </ sup >.

Let K be the sheaf of meromorphic functions and O the sheaf of holomorphic functions on M. A global section ƒ of K passes to a global section φ ( ƒ ) of the quotient sheaf K / O.

Let V and W be handlebodies of genus g, and let ƒ be an orientation reversing homeomorphism from the boundary of V to the boundary of W. By gluing V to W along ƒ we obtain the compact oriented 3-manifold