Assume that t seconds after his jump, his height above sea level in meters is given by.

and measure the parameter s from c. Assume r is to the right of c since the other case is implied by symmetry.

For systems where the volume is preserved by the flow, Poincaré discovered the recurrence theorem: Assume the phase space has a finite Liouville volume and let F be a phase space volume-preserving map and A a subset of the phase space.

Assume that Carol's key has been revoked ( e. g. by exceeding its expiration date, or because of a compromise of Carol's matching private key ).

Assume the wire costs are the same by weight.

Assume that a game is being played by four players: Alice, who is dealing ; Bob, who is sitting to her left ; Carol to his left ; David to Carol's left.

Let's say this interaction is described by a unitary transformation U acting upon H. Assume the initial state of the environment is

Assume there are four agents: two use the tit-for-tat strategy, and two are " defectors " who will simply try to maximize their own winnings by always giving evidence against the other.

Consider a polygon P and a triangle T, with one edge in common with P. Assume Pick's theorem is true for both P and T separately ; we want to show that it is also true to the polygon PT obtained by adding T to P. Since P and T share an edge, all the boundary points along the edge in common are merged to interior points, except for the two endpoints of the edge, which are merged to boundary points.

Assume, as was taken for granted in Galton's time, that surnames are passed on to all male children by their father.

Assume that each case of cooperation increases the chance of survival and reproduction by 10 units, which is divided among the interacting pair ( group of two ).

Assume a ( pseudo ) Riemann manifold is embedded into Euclidean space via a ( twice continuously ) differentiable mapping such that the tangent space at is spanned by the vectors

Assume the consumer utility function is defined by, where U is consumer utility, x and y are goods.

Assume “ that most if not all frontal functions can be explained by one construct ( homogeneity of function ) such as working memory or inhibition ” ( Stuss, 1999, p. 348 ; cf.

Proof by Contradiction: Assume that there is a non-empty set of natural numbers that are not interesting.

# Assume all other duties assigned it by the Constitution or by law.

Assume that the traditional sector pays workers one unit of output which is subsequently spent equally by them in all sectors.

Assume that a string x is read by a deterministic finite automaton, with the machine proceeding into state p. If y is another string read by the machine, also terminating in the same state p, then clearly one has.

Let V < sup > i </ sup > be the subspace of V on which L < sub > 0 </ sub > has eigenvalue i. Assume that V is acted on by a group G which preserves all of its structure.

Assume that the temperature leaving the coil is 10 ° C ( 50 ° F ) and is heated to room temperature ( not mixed with room air ), which is found by following the horizontal humidity ratio from the dew point or saturation line to the room dry bulb temperature line and reading the relative humidity.

Assume this spin can be represented by a real vector, pointing in any direction.

Assume that the combined system determined by two random variables X and Y has entropy, that is, we need bits of information to describe its exact state.

Assume uniform circular motion, which requires three things.

Assume a uniform prior of, and that trials are independent and identically distributed.

Assume the system is prepared in state.

Assume the system is prepared in state, which can be written in terms of the eigenbasis as

Assume that the earth releases a huge volume of carbon dioxide during an interval of excessive volcanism ; global temperatures rise due to the greenhouse effect ; global weathering rates and fluvial nutrient flux increase ; organic productivity in the oceans increases ; organic-carbon burial in the oceans increases ( OAE begins ); carbon dioxide is drawn down ( inverse greenhouse effect ); global temperatures fall, and the ocean – atmosphere system returns to equilibrium ( OAE ends ).

William Gale, Co-director of the Urban-Brookings Tax Policy Center, offers a simplified way to understand a consumption tax: Assume that our current tax system remains the same but remove limitations to contributing to and removing funds from a traditional Individual Retirement Account ( IRA ).

Assume the Earth is in L, at the second quadrature with Jupiter ( i. e. ALB is 90 °), and Io emerges from D. After several orbits of Io, at 42. 5 hours per orbit, the Earth is in K. Rømer reasoned that if light is not propagated instantaneously, the additional time it takes to reach K, that he reckoned about 3½ minutes, would explain the observed delay.

) Assume that this quantum state is not known to Alice and she would like to send this state to Bob.

Assume the SMTP server expects TCP connections on Port 25. one would configure Stunnel to map the SSL Port 465 to non-SSL port 25.

( Assume you are fairly ignorant about martial arts and would have great difficulty making a choice of who to bet on.

Assume that Japan wants to protect a domestic industry that is only able to produce and sell widgets at the price P < sub > tariff </ sub >.

Assume five candidates A, B, C, D and E with 27 voters with the following preferences:

on the domain V of infinitely differentiable functions of compact support on R. Assume ħ to be a fixed non-zero real number — in quantum theory ħ is ( up to a factor of 2π ) Planck's constant, which is not dimensionless ; it takes a small numerical value in terms of units of the macroscopic world.

Assume that the th sector, in order to produce 1 unit, must use units from sector.

Assume a player is given 16 rolls to obtain at least one win ( 1 − p ( rolling no ones )).

Assume also that Americans benefit from immigration ( at least in small amounts ) because they get cheap labor, etc.

Assume that the content of the memory is a 1, stored at Q.

Assume that the set O has at least one element.

Assume for a two-dimensional turbulent flow that one was able to locate a specific point in the fluid and measure the actual velocity of every particle that passed through that point at any given time.

Assume one is looking straight out of the train car's window at the adjacent track.

Assume customers arrive at the rate of 10 per hour and stay an average of 0. 5 hour.

Assume we notice that there are on average 2 customers in the queue and at the counter.

Assume the motion of the projectile is being measured from a Free fall frame which happens to be at ( x, y )=( 0, 0 ) at t = 0.

Assume that the time to maturity is, and that we will price the option at time < math > t < T </ math >, although the life of the option started at time zero.

Assume that is located at address 0x8130 in memory and at 0x8134 ; also assume this is a 32-bit machine such that an int is 32-bits wide.

Assume furthermore that f is flat at x in X.

* Assume f is flat at x in X.

* " Assume there is at least one other side or version to every story.

Assume that the function ƒ ( x ) has a unique global maximum at x < sub > 0 </ sub >.

Theorem ( Dini's test ): Assume a function f satisfies at a point t that

: Theorem: Assume T is a bounded linear operator from L < sup > p </ sup > to L < sup > p </ sup > and at the same time from L < sup > q </ sup > to L < sup > q </ sup >.