Assuming that the system has reached steady state, the particles will assume a characteristic radius dependent upon the force balance.

Assuming that they stayed in the United States, and that no other Israelis came to the United States via other countries, the " gross balance " of Israelis residing in the United States would be 290, 500.

Assuming that the loan, now a $ 10 asset on the bank's balance sheet, carries a risk weighting of 90 %, the bank now holds risk-weighted assets of $ 9 ($ 10 * 90 %).

Assuming office in 1770, he had a controversial career during which land title disputes and factional conflict slowed the initial attempts to populate and develop the island under a feudal system.

Assuming that the second particle is at rest before the collision, the angles of deflection of the two particles, and, are related to the angle of deflection in the system of the center of mass by

Assuming the goal of a system has been articulated and its measurements defined, the steps are:

Assuming the demand for labor to be a given monotonically decreasing function of the real wage rate, the theory then predicted that, in the long-run equilibrium of the system, labor supply ( i. e. population ) will be equated to the numbers demanded at the subsistence wage.

Assuming an origin of the system in 786 BCE, this results in an identical system as that of the classical tropical zodiac, shifted by 25. 5 days, i. e., if in tropical astrology, Aries is taken to begin at March 21, sidereal Aries will begin on April 15.

Using the quasi-stationary equilibrium approximation, that is, Assuming that the system is only slightly non-equilibrium, we have

Assuming the system is allowed this ideal growth without unexpected changes, it eventually consumes those resources.

Assuming the magnetic-field dependence is linear, the Hamiltonian matrix for the system with the field applied can be written

Assuming the fans are fitted with inverter speed controls, set to maintain a constant pressure in the ventilation system, then the reduced pressure drop leads to a slowing of the fan motor and thus reducing power consumption, and in turn improves the seasonal efficiency of the system.

Assuming such a statistical ensemble consists of an overall collection of N microscopic states, the ensemble is constructed so that the proportion p < sub > i </ sub >/ N of members of the ensemble which are in microscopic state i is proportional to the probability, over time, of finding the real-world system in that microscopic state i. Thus the ensemble is an imaginary static collection of microscopic states created to mirror the statistics of the successive fluctuations of the macroscopic physical system which is being modeled.

Assuming these are in general position, i. e. four distinct intersections, we get another interpretation of the linear system as the conics passing through the four given points ( note that the codimension four here matches the dimension, one, in the five-dimensional space of conics ).

Assuming that it isn't too difficult for anyone to replicate arbitrary Unicode on their keyboards, this can make the URI system more worldly and accessible.

Assuming that the system is symmetrical in the x and y directions ( around and along the axon, respectively ), only the z direction need be considered ; thus, the voltage E < sub > m </ sub > is the integral of the z component of the electric field across the membrane.

Assuming the formation of the wavefunctions is a fast process compared to the scattering between states, the time independent solutions to the Schrödinger equation may be applied and the system can be modelled using rate equations.

Assuming that air resistance is not significant, there are only two forces exerted on the system as a whole: ( 1 ) gravity, and ( 2 ) the reaction force caused by the ignited gases being expelled from the rocket's nozzle at high speed.

Assuming the lower figure for the big blast and one shot estimated by the Japanese at 10 megatons, a conservative computation is that the 24 announced tests produced a total yield of at least 60 megatons.

Assuming the weather is halfway decent that day, hundreds of thousands of persons will mass along this thoroughfare as President John F. Kennedy and retiring President Dwight D. Eisenhower leave Capitol Hill following the oath-taking ceremonies and ride down this historic ceremonial route.

Assuming ZF is consistent, Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model ( the constructible universe ) which satisfies ZFC and thus showing that ZFC is consistent.

Assuming ZF is consistent, Paul Cohen employed the technique of forcing, developed for this purpose, to show that the axiom of choice itself is not a theorem of ZF by constructing a much more complex model which satisfies ZF ¬ C ( ZF with the negation of AC added as axiom ) and thus showing that ZF ¬ C is consistent.

Assuming that the pixel color is expressed using straight ( non-premultiplied ) RGBA tuples, a pixel value of ( 0. 0, 0. 5, 0. 0, 0. 5 ) implies a pixel which has 50 % of the maximum green intensity and 50 % opacity.

Assuming that the ion is accelerated during a very short interval, the ion can be assumed to be travelling at constant velocity.

Assuming that 10 – 15 % of bread is thrown away as stale, if it could be made to stay fresh another 5 – 7 days then perhaps 2 million tons of flour per year would be saved.

Assuming average population densities of 0. 25 animals per km² in regions where it is known to be common or abundant, and 0. 02 per km² elsewhere, and with a total area of occupancy of 327, 000 km², a total population estimate of approximately 28, 000 is suggested.

Assuming a fixed sample size, the technique gives more accurate results when most of the variation in the population is within the groups, not between them.

:< u > The Copenhagen Interpretation </ u >: Assuming wave functions are not real, wave-function collapse is interpreted subjectively.

Assuming the Axiom of choice, is regular for each α.

Let e be the error in b. Assuming that A is a square matrix, the error in the solution A < sup >− 1 </ sup > b is A < sup >− 1 </ sup > e.

Assuming that the strength of the cable is proportional to its density per unit length, the weight, w, per unit length of the chain can be written T / c, where c is constant, and the analysis for nonuniform chains can be applied.

Assuming that the rule is known, one can derive the function that is used above in the classical heat calculation with respect to pressure.

Assuming that translation is not used transformations can be combined by simply multiplying the associated transformation matrices.

Assuming we can define at least one nonreal complex number, however, a complex number is definable if and only if both its real part and its imaginary part are definable.

Assuming that the visible material makes up only a small part of the cluster is the most straightforward way of accounting for this.

Assuming that the balls travel at a constant velocity and the pitcher is stationary, the man will catch one ball every second.

Assuming a flow is bounded on one side only, and that a rectilinear flow passing over a stationary flat plate which lies parallel to the flow, the flow just upstream of the plate has a uniform velocity.

Assuming the homeowner leaves his or her house to investigate, the game becomes one of chicken, where the players try to outlast each other in remaining silent and stationary in front of the homeowner's house without giving in from embarrassment ( and leaving ) or giving in to laughter.

Assuming no loss of time when moving a car from one station to another, the longest stage on the assembly line determines the throughput ( 20 minutes for the engine installation ) so a car can be produced every 20 minutes, once the first car taking 35 minutes has been produced.

Assuming there are no complications, the remaining portion of the first day's dose is then given.

Assuming one has overcome the mind's initial flight response in those first torturous minutes, the body fights back by invoking a " blood rush ".

Assuming that X makes the first move every time:

Assuming that X makes the first move every time:

Assuming that decision-makers make cost-benefit analyses when deciding to use force, China's doctrine calls for acquiring a nuclear arsenal only large enough to destroy an adversary ’ s " strategic points " in such a way that the expected costs of a first strike outweigh the anticipated benefits.

* January 1 – Assuming that the copyright laws are not changed further, all works published in 1923 enter the public domain in the U. S., the first works to do so since the passage of the 1998 Sonny Bono Copyright Term Extension Act.

Assuming all projects require the same amount of up-front investment, the project with the highest IRR would be considered the best and undertaken first.

Assuming that capture of the Chinese capital would be the decisive turning point in the war, there was an eagerness to be among the first to claim the honor of victory.

Assuming that Sewell is counted as the first Prime Minister, thirty-eight people have held the office since it was established.

Assuming these conditions the first law is rewritten as:

Assuming Gudfred had more than one sibling, Hemming and Reginold could also be paternal first cousins.

Assuming the official scorer agrees the shortstop could not have thrown the batter-runner out at first with ordinary effort, this play will be scored as a base hit and not FC.

Assuming that the image has been pre-smoothed by Gaussian smoothing and a scale space representation at scale has been computed, we can require that the gradient magnitude of the scale space representation, which is equal to the first-order directional derivative in the-direction, should have its first order directional derivative in the-direction equal to zero

Assuming the axiom of choice, is the first infinite cardinal which is singular ( the first infinite ordinal which is singular is ).

Assuming that is closed, there is a canonical symplectic form defined as which is compatible with, hence satisfying the first definition.

Assuming that Jeconiah's reign ended on the day that the Babylonians captured Jerusalem the first time, 2 Adar ( 16 March ) 597 BC, and further assuming that the Jewish calendar in the sixth century BC had the same number of days in the two preceding months as in the modern Jewish calendar, Jehoiachin's reign of three months and ten days () would have started on 21 Heshvan ( 9 December ) 598 BC.

Assuming it could be established in the first place, a beachhead on the Cotentin peninsula would be blocked off and attacked by land, sea and air.

Assuming command of a last-place team, Schuerholz went to work and recruited half of a new infield by first signing Sid Bream to a contract, then getting Pendleton to sign a four year, $ 10. 2 million contract with the Atlanta Braves on December 3, 1990.

Assuming this connection is found, the first breakpoint is reached.

Assuming that Richard A. Locke was the author, his intentions were probably, first, to create a sensational story which would increase sales of the New York Sun, and, second, to ridicule some of the more extravagant astronomical theories that had recently been published.

Assuming the part for the first time in 1785, Praskovia sang Eliane for 12 years — a first in the history of serf theatre.