) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is

Suppose that u and v satisfy the Cauchy – Riemann equations in an open subset of R < sup > 2 </ sup >, and consider the vector field

Suppose n < sub > 1 </ sub >, n < sub > 2 </ sub >, …, n < sub > k </ sub > are positive integers which are pairwise coprime.

Suppose random variable X can take value x < sub > 1 </ sub > with probability p < sub > 1 </ sub >, value x < sub > 2 </ sub > with probability p < sub > 2 </ sub >, and so on, up to value x < sub > k </ sub > with probability p < sub > k </ sub >.

Suppose that a speaker can have the concept of water we do only if the speaker lives in a world that contains H < sub > 2 </ sub > O.

Suppose that one particle is in the state n < sub > 1 </ sub >, and another is in the state n < sub > 2 </ sub >.

Suppose we have N particles with quantum numbers n < sub > 1 </ sub >, n < sub > 2 </ sub >, ..., n < sub > N </ sub >.

Suppose both ISPs have trans-Atlantic links connecting their two networks, but A < nowiki >' s </ nowiki > link has latency 100 ms and B's has latency 120 ms.

Suppose, for concreteness, that we have an algorithm for examining a program p and determining infallibly whether p is an implementation of the squaring function, which takes an integer d and returns d < sup > 2 </ sup >.

Suppose that whenever P ( β ) is true for all β < α, then P ( α ) is also true ( including the case that P ( 0 ) is true given the vacuously true statement that P ( α ) is true for all ).

Suppose M is a C < sup > k </ sup > manifold ( k ≥ 1 ) and x is a point in M. Pick a chart φ: U → R < sup > n </ sup > where U is an open subset of M containing x.

Suppose two curves γ < sub > 1 </ sub >: (- 1, 1 ) → M and γ < sub > 2 </ sub >: (- 1, 1 ) → M with γ < sub > 1 </ sub >( 0 )

Unicity: Suppose satisfies, then by Theorem 1. 8,.

Player 1 moves first and chooses either F or U. Player 2 sees Player 1s move and then chooses A or R. Suppose that Player 1 chooses U and then Player 2 chooses A, then Player 1 gets 8 and Player 2 gets 2.

Suppose an array A with elements indexed 1 to n is to be searched for a value x.

Suppose that you add blue, then the blue – red – black tree defined like red – black trees but with the additional constraint that no two successive nodes in the hierarchy will be blue and all blue nodes will be children of a red node, then it becomes equivalent to a B-tree whose clusters will have at most 7 values in the following colors: blue, red, blue, black, blue, red, blue ( For each cluster, there will be at most 1 black node, 2 red nodes, and 4 blue nodes ).

Suppose that a certain slot machine costs $ 1 per spin and has a return to player ( RTP ) of 95 %.

Suppose a line runs through two points: P = ( 1, 2 ) and Q = ( 13, 8 ).

Suppose that, instead of an exact observation, x, the observation is the value in a short interval ( x < sub > j − 1 </ sub >, x < sub > j </ sub >), with length Δ < sub > j </ sub >, where the subscripts refer to a predefined set of intervals.

Suppose in a year an object moves from coordinates ( α, δ ) to coordinates ( α < sub > 1 </ sub >, δ < sub > 1 </ sub >), with angles measured in seconds of arc.

Suppose that N = N < sub > 1 </ sub > N < sub > 2 </ sub >, where N < sub > 1 </ sub > and N < sub > 2 </ sub > are relatively prime.

Suppose for some unknown constants and unobserved random variables, where and, where < math > k < p </ math >, we have

Suppose that one is summing n values x < sub > i </ sub >, for i = 1 ,..., n. The exact sum is:

Suppose w = z < sup > 1 / 2 </ sup >, and z starts at 4 and moves along a circle of radius 4 in the complex plane centered at 0.

Suppose U < sub > 1 </ sub >, ..., U < sub > n </ sub > are independent standard normally distributed random variables, and an identity of the form

Suppose X < sub > 1 </ sub >, ..., X < sub > n </ sub > are independent and identically distributed, and are normally distributed with unknown expected value μ and known variance 1.

Suppose that R ( y, x < sub > 1 </ sub >,.

Suppose that C is a smooth algebraic curve of genus g. If g is zero, then C is P < sup > 1 </ sup >, and the canonical class is the class of − 2P, where P is any point of C. This follows from the calculus formula d ( 1 / t ) = − dt / t < sup > 2 </ sup >, for example, a meromorphic differential with double pole at the point at infinity on the Riemann sphere.

Suppose an experimenter performs 10 measurements all at exactly the same value of independent variable vector X ( which contains the independent variables X < sub > 1 </ sub >, X < sub > 2 </ sub >, and X < sub > 3 </ sub >).

Suppose now that X < sub > 1 </ sub >, ..., X < sub > n </ sub > are independent and identically distributed samples from the distribution above.

Suppose we are given boundary conditions, i. e., a specification of the value of φ at the boundary if M is compact, or some limit on φ as x approaches ∞.

Suppose that φ: M → N is a smooth map between smooth manifolds M and N ; then there is an associated linear map from the space of 1-forms on N ( the linear space of sections of the cotangent bundle ) to the space of 1-forms on M. This linear map is known as the pullback ( by φ ), and is frequently denoted by φ < sup >*</ sup >.

# Suppose φ: X → Y is a morphism of schemes of locally finite type over C. Then there exists a continuous map φ < sup > an </ sup >: X < sup > an </ sup > → Y < sup > an </ sup > such λ < sub > Y </ sub > ° φ < sup > an </ sup >

Suppose L / K is an unramified extension of local fields, with ring of integers O < sub > K </ sub > of K such that the residue field, the integers of K modulo their unique maximal ideal φ, is a finite field of order q.

Suppose that X is some datatype, called the fundamental datatype, and that Φ is a set of ( partial ) relations φ: X → X.

Suppose φ and χ are fields such that, if x and y are spacelike-separated points and i and j represent the spinor / tensor indices,

Suppose that φ: M → N is a smooth map between smooth manifolds ; then the differential of φ at a point x is, in some sense, the best linear approximation of φ near x.

Suppose that the field F has an endomorphism σ whose square is the Frobenius endomorphism: σ² = φ.

Suppose the muon happens to have fallen into an orbit around a deuteron initially, which it has about a 50 % chance of doing if there are approximately equal numbers of deuterons and tritons present, forming an electrically neutral muonic deuterium atom ( d-μ )< sup > 0 </ sup > that acts somewhat like a " fat, heavy neutron " due both to its relatively small size ( again, about 207 times smaller than an electrically neutral electronic deuterium atom ( d-e )< sup > 0 </ sup >) and to the very effective " shielding " by the muon of the positive charge of the proton in the deuteron.

Suppose that a proportion of the population q ( where q < q < sub > c </ sub >) is immunised at birth against an infection with R < sub > 0 </ sub >> 1.

Suppose M ( t, p < sub > 1 </ sub >, ..., p < sub > n </ sub >) is a function of time t and n variables which themselves depend on time.

Suppose f is in L < sup > p </ sup >( R < sup > d </ sup >) and g is in L < sup > q </ sup >( R < sup > d </ sup >) and

* Suppose that ( q < sup > 1 </ sup >, ..., q < sup > n </ sup >, p < sub > 1 </ sub >, ..., p < sub > n </ sub >) are canonical coordinates on M ( see above ).