) 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 a definition of " good " is " pleasure-causing.

Suppose one wants to come up with a definition of " right " in the moral sense.

Suppose that g and h are total computable functions that are used in a recursive definition for a function f:

Suppose R is a commutative ring and A is an n × n matrix with entries from R. The definition of the adjugate of A is a multi-step process, drawing on the Laplace expansion:

Let π: E → X be a fibre bundle over a topological space X with structure group G and typical fibre F. By definition, there is a left action of G ( as a transformation group ) on the fibre F. Suppose furthermore that this action is effective.

For a precise definition, suppose that S is a compact surface properly embedded in a 3-manifold M. Suppose that D is a disk, also embedded in M, with

Suppose, says Dr. Lyttleton, the proton has a slightly greater charge than the electron ( so slight it is presently immeasurable ).

Suppose that has an inverse function.

Suppose a particle has position in a stationary frame of reference.

Suppose Alice has a qubit in some arbitrary quantum state.

Suppose Alice has a qubit that she wants to teleport to Bob.

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

Suppose the typewriter has 50 keys, and the word to be typed is banana.

Suppose this fuzzy system has the following rule base:

Suppose a lossless antenna has a radiation pattern given by:

Suppose a partially ordered set P has the property that every chain ( i. e. totally ordered subset ) has an upper bound in P. Then the set P contains at least one maximal element.

Suppose a non-empty partially ordered set P has the property that every non-empty chain has an upper bound in P. Then the set P contains at least one maximal element.

:" Moses said to God, ' Suppose I go to the Israelites and say to them, " The God of your fathers has sent me to you ," and they ask me, ‘ What is his name ?’ Then what shall I tell them ?” God said to Moses, “ I AM WHO I AM " — Exodus 3: 13-14 ( New International Version ) ( see Tetragrammaton ).

Suppose a computer has three CD drives and three processes.

Suppose, for example, that A is a 3 × 3 rotation matrix which has been computed as the composition of numerous twists and turns.

Suppose that a taxi firm has three taxis ( the agents ) available, and three customers ( the tasks ) wishing to be picked up as soon as possible.

Suppose V is a subset of R < sup > n </ sup > ( in the case of n = 3, V represents a volume in 3D space ) which is compact and has a piecewise smooth boundary S. If F is a continuously differentiable vector field defined on a neighborhood of V, then we have

INTERVIEWER: Suppose someone called you and said there was a kid, nineteen or twenty years old, who has been a very good boy, but all of a sudden this week he started walking around the neighborhood carrying a large cross.

Suppose Eve has intercepted the cryptogram below, and it is known to be encrypted using a simple substitution cipher:

Suppose that one has a table listing the population of some country in 1970, 1980, 1990 and 2000, and that one wanted to estimate the population in 1994.

Suppose the table has r rows and c columns ; the row sums are and the column sums are.

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 P is an exact category ; associated to P a new category QP is defined, objects of which are those of P and morphisms from M ′ to M ″ are isomorphism classes of diagrams

Suppose that certain outcomes are associated with three states of nature, so that ; This set of outcomes,, can be assumed to be a calculable money-prize in a controlled game of chance, unique up to one positive proportionality factor depending on the currency unit.

# Suppose there exists a function called Insert designed to insert a value into a sorted sequence at the beginning of an array.

Suppose that the signal to be sent ( called the modulating or message signal ) is and the carrier onto which the signal is to be modulated is

Suppose there is a sequence of independent Bernoulli trials, each trial having two potential outcomes called “ success ” and “ failure ”.

Suppose C is a category, and f: X → Y is a morphism in C. The morphism f is called a constant morphism ( or sometimes left zero morphism ) if for any object W in C and any g, h: W → X, fg

Suppose that F is a ( 1-dimensional ) formal group law over R. Its formal group ring ( also called its hyperalgebra or its covariant bialgebra ) is a cocommutative Hopf algebra H constructed as follows.

Suppose finally that the curve in S does not bound a disk inside of S. Then D is called a compressing disk for S and we also call S a compressible surface in M. If no such disk exists and S is not the 2-sphere, then we call S incompressible ( or geometrically incompressible ).

Suppose X is a Tychonoff space, also called a T < sub > 3. 5 </ sub > space, and C ( X ) is the algebra of continuous real-valued functions on X.

Suppose C is the complexity class of problems solvable in logarithmithic space with probabilistic Turing machines that never accept incorrectly but are allowed to reject incorrectly less than 1 / 3 of the time ; this is called one-sided error.

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

Suppose that the machine has several states, called FindIncrements, FindSubExprs and Completed.

Suppose we are given a Hilbert space and a Hermitian operator over it called the Hamiltonian H. Ignoring complications about continuous spectra, we look at the discrete spectrum of H and the corresponding eigenspaces of each eigenvalue λ ( see spectral theorem for Hermitian operators for the mathematical background ):

Suppose that the partial differential equation is defined on R < sup > n </ sup > and consider a smooth manifold S ⊂ R < sup > n </ sup > of dimension n − 1 ( S is called the Cauchy surface ).