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

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 ( 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 the program for which the halting problem is to be solved be N bits long.

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

Let X be a measurable space, let μ be a measure on X, and let N be a measurable set in X.

Let M and N be ( left or right ) modules over the same ring, and let f: M → N be a module homomorphism.

Let N be a function assigning to each x in X a non-empty set N ( x ) of subsets of X.

Let S be the group of all permutations of N, the natural numbers, that fixes all but finitely many numbers then:

Let F: J → C be a diagram of type J in a category C. A cone to F is an object N of C together with a family ψ < sub > X </ sub >: N → F ( X ) of morphisms indexed by the objects of J, such that for every morphism f: X → Y in J, we have F ( f ) o ψ < sub > X </ sub >

Let S be a subgroup of G, and let N be a normal subgroup of G. Then:

Let N and K be normal subgroups of G, with

Let G be a group with identity element e, N a normal subgroup of G ( i. e., N ◁ G ) and H a subgroup of G. The following statements are equivalent:

Let M and N be smooth manifolds and be a smooth map.

Let ( M, g ) and ( N, h ) be Riemannian manifolds.

) Let N be the ( possibly fractional ) number of submovements required to fall within the target.

Let N =

Let p be the nth decimal of the nth number of the set E ; we form a number N having zero for the integral part and p + 1 for the nth decimal, if p is not equal either to 8 or 9, and unity in the contrary case.

Let N represent the common nine-point center and P be an arbitrary point in the plane of the orthocentric system.

Let denote the Bézier curve determined by the points P < sub > 0 </ sub >, P < sub > 1 </ sub >, ..., P < sub > n </ sub >.

Let P < sub > F </ sub > be the domain of a prefix-free universal computable function F. The constant Ω < sub > F </ sub > is then defined as

Let M be a smooth manifold and let x be a point in M. Let T < sub > x </ sub > M be the tangent space at x.

Let M be a smooth manifold and let x be a point in M. Let I < sub > x </ sub > be the ideal of all functions in C < sup >∞</ sup >( M ) vanishing at x, and let I < sub > x </ sub >< sup > 2 </ sup > be the set of functions of the form, where f < sub > i </ sub >, g < sub > i </ sub > ∈ I < sub > x </ sub >.

Let M be a smooth manifold and let f ∈ C < sup >∞</ sup >( M ) be a smooth function.

Let e be the error in b. Assuming that A is a square matrix, the error in the solution A < sup >− 1 </ sup > b is A < sup >− 1 </ sup > e.

Let us for simplicity take, then < math > 0 < c =- 2a </ math > and.

Let the function g ( t ) be the altitude of the car at time t, and let the function f ( h ) be the temperature h kilometers above sea level.

Let R be the radius of Earth and h be the altitude of a telecommunication station.

Let c, h, s be the sides of three squares associated with the right

Let vectors < u > a </ u >, < u > b </ u >, < u > c </ u > and < u > h </ u > determine the position of each of the four orthocentric points and let < u > n </ u > = (< u > a </ u > + < u > b </ u > + < u > c </ u > + < u > h </ u >) / 4 be the position vector of N, the common nine-point center.

Let h be the jump intensity.

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

Let g be a Lie algebra, h a maximal commutative Lie subalgebra consisting of semi-simple elements ( sometimes called Cartan subalgebra ) and let V be a finite dimensional representation of g. If g is semisimple, then g = g and so all weights on g are trivial.

Let h *< sub > 0 </ sub > be the real subspace of h * ( if it is complex ) generated by the roots of g.

Let f, g, and h be functions defined on I, except possibly at a itself.

Let X be any Lie algebra over K. Given a unital associative K-algebra U and a Lie algebra homomorphism: h: X → U < sub > L </ sub >, ( notation as above ) we say that U is the universal enveloping algebra of X if it satisfies the following universal property: for any unital associative K-algebra A and Lie algebra homomorphism f: X → A < sub > L </ sub > there exists a unique unital algebra homomorphism g: U → A such that: f (-) = g < sub > L </ sub > ( h (-)).

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 us call ( e ), ( f ), ( g ), ( h ), the successive frames deduced from the initial ( e ) reference frame by the successive intrinsic rotations described above.

Let R < sub > h </ sub > denote the ( right ) action of h ∈ H on P. The derivative of this action defines a vertical vector field on P for each element ξ of: if h ( t ) is a 1-parameter subgroup with h ( 0 )= e ( the identity element ) and h '( 0 )= ξ, then the corresponding vertical vector field is

Let P be a principal H-bundle on M, equipped with a Cartan connection η: TP → g. If g is a reductive module for H, meaning that g admits an Ad ( H )- invariant splitting of vector spaces g = h ⊕ m, then the m-component of η generalizes the solder form for an affine connection.

Genesis 1: 9 " And God said, Let the waters be collected ". Letters in black, < font color ="# CC0000 "> niqqud in red </ font >, < font color ="# 0000CC "> cantillation in blue </ font >

* Let D < sub > 1 </ sub > and D < sub > 2 </ sub > be directed sets.