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Suppose and S

Suppose S is normal.

Suppose that L is a lattice of determinant d ( L ) in the n-dimensional real vector space R n and S is a convex subset of R n that is symmetric with respect to the origin, meaning that if x is in S then − x is also in S.

Suppose f were injective, which means the pieces of S cut out by the squares stack up in a non-overlapping way.

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

Suppose V is a subset of R n ( 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

Suppose a stock price follows a Geometric Brownian motion given by the stochastic differential equation dS = S ( σdB + μ dt ).

Suppose r is an element of R which is not in Rad ( I ), and let S be the set

Suppose that the image of the embedding is a surface S in R 3 .

Suppose S ' is in relative uniform motion to S with velocity v. Consider a point object whose position is given by r

Suppose that a tangent vector to the sphere S is given at the north pole, and we are to define a manner of consistently moving this vector to other points of the sphere: a means for parallel transport.

Suppose that P ( t ) is a curve in S. Naïvely, one may consider a vector field parallel if the coordinate components of the vector field are constant along the curve.

* Suppose that is the infinite cyclic group and the set S consists of the standard generator 1 and its inverse (− 1 in the additive notation ) then the Cayley graph is an infinite chain.

Suppose that we can find a n by m matrix S

Suppose we have some set S of objects, with an equivalence relation.

Suppose a planar closed loop carries an electric current I and has vector area S ( x, y, and z coordinates of this vector are the areas of projections of the loop onto the yz, zx, and xy planes ).

Suppose that c is a simple closed curve in a closed, orientable surface S. Let A be a tubular neighborhood of c. Then A is an annulus and so is homeomorphic to the Cartesian product of

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 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 and is

Suppose Af is defined in the sub-interval Af.

Suppose they both had ventured into realms which their colleagues thought infidel: is this the way gentlemen settle frank differences of opinion??

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

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

Suppose there is a program

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.

) Then X i 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 i and variance σ i 2 for all times i. Then the definition of the autocorrelation between times s and t is

Suppose that a car is driving up a tall mountain.

Suppose that the car is ascending at 2. 5 km / h.

Suppose the vector field describes the velocity field of a fluid flow ( such as a large tank of liquid or gas ) and a small ball is located within the fluid or gas ( the centre of the ball being fixed at a certain point ).

Suppose that F is a partial function that takes one argument, a finite binary string, and possibly returns a single binary string as output.

Suppose, says Searle, that this computer performs its task so convincingly that it comfortably passes the Turing test: it convinces a human Chinese speaker that the program is itself a live Chinese speaker.

; Dennett's reply from natural selection: Suppose that, by some mutation, a human being is born that does not have Searle's " causal properties " but nevertheless acts exactly like a human being.

Suppose that is a complex-valued function which is differentiable as a function.

Suppose a mass is attached to a spring which exerts an attractive force on the mass proportional to the extension / compression of the spring.

Suppose that in a mathematical language L, it is possible to enumerate all of the defined numbers in L. Let this enumeration be defined by the function G: W → R, where G ( n ) is the real number described by the nth description in the sequence.

Suppose and immersed

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 and submanifold

Suppose an enveloping manifold M has n dimensions ; then any submanifold of M of n − 1 dimensions is a hypersurface.

Suppose and M

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

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

Suppose M is a C ∞ manifold.

Suppose block M is a dominator with several incoming edges, some of them being back edges ( so M is a loop header ).

Suppose M is some 2-dimensional Riemannian manifold ( not necessarily compact ), and we specify a " triangle " on M formed by three geodesics.

Suppose M is an m × n matrix whose entries come from the field K, which is either the field of real numbers or the field of complex numbers.

Suppose we have an n-dimensional oriented Riemannian manifold, M and a target manifold T. Let be the configuration space of smooth functions from M to T. ( More generally, we can have smooth sections of a fiber bundle over M .)

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 Ω is given in the standard form and let M be a 2n × 2n block matrix given by

Suppose that x i are local coordinates on the base manifold M. In terms of these base coordinates, there are fibre coordinates p i : a one-form at a particular point of T * M has the form p i dx i ( Einstein summation convention implied ).

Suppose we zero-pad to a length M ≥ 2N – 1.

Suppose we are given an element e 0 ∈ E P at P = γ ( 0 ) ∈ M, rather than a section.

Suppose f is bounded: i. e. there exists a constant M such that | f ( z )| ≤ M for all z.

Suppose that f is entire and | f ( z )| is less than or equal to M | z |, for M a positive real number.

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 ∞( M ) ( the commutative algebra of smooth real-valued functions on M ).

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