Suppose Af is defined in the sub-interval Af.

Suppose that Af, and that the average operation requires only Af sec..

: Suppose X is a compact Hausdorff space and A is a subalgebra of C ( X, R ) which contains a non-zero constant function.

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 M is a C < sup >∞</ sup > manifold.

Suppose that U: D → C is a functor from a category D to a category C, and let X be an object of C. Consider the following dual ( opposite ) notions:

* Suppose & B is equivalent to & D. If we acquire new information A and then acquire further new information B, and update all probabilities each time, the updated probabilities will be the same as if we had first acquired new information C and then acquired further new information D. In view of the fact that multiplication of probabilities can be taken to be ordinary multiplication of real numbers, this becomes a functional equation

Suppose the maximum temperature is 125 ° C, and the ambient temperature is 25 ° C ; then ΔT is 100 ° C.

Suppose that C is a twice continuously differentiable immersed plane curve, which here means that there exists parametric representation of C by a pair of functions such that the first and second derivatives of x and y both exist and are continuous, and

Suppose U is an open subset of the complex plane C, f: U → C is a holomorphic function and the closed disk

Suppose that A, B, and C are the matrices representing the transformations T, S, and ST with respect to the given bases.

I accept A and B and C and D. Suppose I still refused to accept Z?

Suppose X is a normed vector space over R or C. We denote by its continuous dual, i. e. the space of all continuous linear maps from X to the base field.

To illustrate his thoughts he used the following example: Suppose an object C, on which an infinite small plane zz and a sphere centered about zz is drawn.

The theorem can also be used to deduce that the domain of a non-constant elliptic function f cannot be C. Suppose it was.

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 M is a compact smooth manifold, and a V is a smooth vector bundle over M. The space of smooth sections of V is then a module over C < sup >∞</ sup >( M ) ( the commutative algebra of smooth real-valued functions on M ).

Suppose A, B, C, D are respectively

Suppose we are willing to accept that should be true when both and are true, and false when is true but is false.

Suppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting upon it.

Suppose that when the rock is lowered into water, it displaces water of weight 3 newtons.

Suppose you are riding a bicycle on a day when there is no wind.

Suppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting upon it.

Suppose that when the rock is lowered into water, it displaces water of weight 3 newtons.

Suppose one wants to turn the inductor off: when the current goes to zero, if the gate is not fed, the TRIAC attempts to turn off, but this causes a step in the voltage across it due to the afore-mentioned phase shift.

Suppose that he raises his stake to when he wins, but does not reduce his stake when he loses.

Jasper says to Puffer at the end of the book: " Suppose you had something in your mind ; something you were going to do ... Should you do it in your fancy, when you were lying here doing this ?...

Suppose a two-level atom whose ground state is shown by g and excited state by e. Efficient laser cooling occurs when the frequency of the laser beam is tuned to the red sideband i. e.

Lewis is perhaps using Puddleglum to give a somewhat existential statement of faith when he writes, " Suppose we have only dreamed, or made up, all of those things — trees and grass and sun and moon and stars and Aslan himself.

Suppose a light source has luminosity L ( d ) when observed from a distance of parsecs, and luminosity L ( 10 ) when observed from a distance of 10 parsecs.

Suppose is a plane curve with curvature which makes a convex curve when closed by the chord connecting its endpoints, and is a curve of the same length with curvature.

Suppose, however, for a moment, all existing space to be bounded, and that a man runs forward to the uttermost borders, and stands upon the last verge of things, and then hurls forward a winged javelin ,— suppose you that the dart, when hurled by the vivid force, shall take its way to the point the darter aimed at, or that something will take its stand in the path of its flight, and arrest it?

Suppose, in the reference frame of the observer, the source is moving with speed at an angle relative to the vector from the observer to the source at the time when the light is emitted.

`` Suppose you take Mr. Hearst's morning American at $10,000 a year '', Brisbane proposed.

Suppose John Jones, who, for 1960, filed on the basis of a calendar year, died June 20, 1961.

Here's how the scheme works: Suppose the operator pulls the lever to clear a particular signal.

Suppose that the minimal polynomial for T decomposes over F into a product of linear polynomials.

Suppose, he says, that the tables were turned, and we were in the Soviets' position: `` There would be more than 2,000 modern Soviet fighters, all better than ours, stationed at 250 bases in Mexico and the Caribbean.

`` Suppose you tell me the real reason '', he drawled.

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

`` Suppose you let me explain.

`` Suppose it was not us that killed these aliens.

Suppose it is something right on the planet, native to it.

Suppose we have sample space.

Suppose a chain consists of squares 8D, 8E, and 8F.

Suppose there is a chain at 1A, 2A, 3A, and 4A, along with another chain at 6A and 7A.

If two players tie for minority, they will share the minority shareholder bonus. Suppose Festival is the chain being acquired.

Alex is the majority shareholder, and Betty is the minority shareholder. Suppose now that Worldwide is the chain being acquired.

Suppose that R ( x, y ) is a relation in the xy plane.

Take as an example a program that looks up a specific entry in a sorted list of size n. Suppose this program were implemented on Computer A, a state-of-the-art machine, using a linear search algorithm, and on Computer B, a much slower machine, using a binary search algorithm.

) 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