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Assuming dark energy remains constant ( an unchanging cosmological constant ), so that the expansion rate of the universe continues to accelerate, there is a " future visibility limit " beyond which objects will never enter our observable universe at any time in the infinite future, because light emitted by objects outside that limit can never reach points that expand away from us at less than the speed of light.
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Assuming and dark
Assuming the sky is clear, the Earth's shadow is visible in the opposite half of the sky to the sunset or sunrise, and is seen right above the horizon as a dark blue band.
Assuming and energy
Assuming the field is weak and the motion of the electron non-relativistic, we have the total energy of the electron approximately equal to its rest energy, and the momentum going over to the classical value,
Assuming that all atoms in a crystal vibrate with the same frequency ν, the average thermal energy can be estimated using the equipartition theorem as
Assuming the gamma-ray explosion to be spherical, the energy output of GRB 080319B would be within a factor of two of the rest-mass energy of the Sun ( the energy which would be released were the Sun to be converted entirely into radiation ).
Assuming that the relic anti-neutrino is at rest, the energy of the incident cosmic neutrino has to be:
Assuming no absorption, conservation of energy requires T + R = 1.
Assuming smallness of | ψ | and smallness of its gradients, the free energy has the form of a field theory.
Assuming that the quantum particle started in orbit number n, emitted a photon, then ended up in orbit number m, the energy of the photon is E < sub > n </ sub > − E < sub > m </ sub >, which means that its frequency is.
Assuming the energy required scales with the mass of the fusion plasma ( E < sub > laser </ sub > ~ ρR < sup > 3 </ sup > ~ ρ < sup >- 2 </ sup >), compressing the fuel to 10 < sup > 3 </ sup > or 10 < sup > 4 </ sup > times solid density would reduce the energy required by a factor of 10 < sup > 6 </ sup > or 10 < sup > 8 </ sup >, bringing it into a realistic range.
Assuming a zero vacuum energy density, if is larger than unity, the space sections of the universe are closed ; the universe will eventually stop expanding, then collapse.
Assuming the wheel and axle does not dissipate or store energy, the power generated by forces applied to the wheel must equal the power out at the axle.
Assuming the field is weak and the motion of the electron non-relativistic, we have the total energy of the electron approximately equal to its rest energy, and the momentum reducing to the classical value,
and compute the gradient of the energy over distance to obtain the force F. Assuming that the cantilever deflects along the z-axis, and the tip is magnetized along a certain direction ( e. g. the z-axis ), then the equations can be simplified to
Assuming the source of deep ocean water is environmentally friendly and replenished by natural mechanisms, it forms a more innovative basis for cleaner energy than current fossil-fuel-derived energy.
Assuming energy demand does not change, this reduces the carbon dioxide emitted.
Assuming no change in the height of the particle, this will be the total gravitational potential energy of the particle at all times.
Assuming his post on July 13, 2005, Schulte was charged with advancing the President ’ s agenda in countering proliferation, terrorism, organized crime, and corruption, while promoting the peaceful use of nuclear energy.
Assuming and remains
Assuming something to be true for all numbers when it has been shown for over 906 million cases would not generally be considered hasty, but in mathematics a statement remains a conjecture until it is shown to be universally true.
Assuming that the turnover of total production capital invested remains constant, the proportion of total investment which just maintains the stock of total capital, rather than enlarging it, will typically increase as the total stock increases.
Assuming that the number of colonies in an area remains constant over time, on average only one queen among the many thousands sent out by a colony successfully founds a new one.
Assuming and constant
Assuming that the ion is accelerated during a very short interval, the ion can be assumed to be travelling at constant velocity.
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 the diffusion coefficient D to be a constant we can exchange the orders of the differentiation and multiply by the constant:
Assuming that the air is incompressible, the rate of flow ( e. g. liters or gallons per minute ) must be constant within each streamtube since matter is not created or destroyed.
Assuming that the masses are constant, the virial G is one-half the time derivative of this moment of inertia
Assuming constant pressure and volume, the thermodynamic properties of the cell are related strictly to the behavior of its emf by:
Assuming that the balls travel at a constant velocity and the pitcher is stationary, the man will catch one ball every second.
Assuming to be a constant not depending on the amount of fuel left this relation is integrated to
Assuming that the fluid is at rest at infinity and that the pressure is defined to be zero there, this constant is zero, and thus
Assuming a constant density throughout the star, this integration yields the formula
Assuming a constant density ρ for the cloud
Assuming this survivorship is constant through the adult life of a mosquito, less than 10 % of female A. gambiae would survive longer than a 14-day extrinsic incubation period.
Assuming a Gaussian profile for the bleaching beam, the diffusion constant D can be simply calculated from:
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 that the factor costs are constant ( that is, that the firm is a perfect competitor in all input markets ), a firm experiencing constant returns will have constant long-run average costs, a firm experiencing decreasing returns will have increasing long-run average costs, and a firm experiencing increasing returns will have decreasing long-run average costs.
Assuming that the input signal is zero-mean ( i. e. contains no DC component ), minimal distortion is attained when this constant is set to zero.
Assuming a constant rate c of propagule generation from each of the N occupied patches, during a time dt, each unoccupied patch can become occupied with a colonization probability cNdt.
Assuming a constant rate of mutation, Luria hypothesized that if mutations occurred after and in response to exposure to the selective agent, the number of survivors would be distributed according to a Poisson distribution with the mean equal to the variance.
Assuming that factor prices are constant, the production function determines all cost functions.
Assuming and ),
Assuming perfect combustion conditions, such as complete combustion under adiabatic conditions ( i. e., no heat loss or gain ), the adiabatic combustion temperature can be determined.
( Assuming the axiom of choice ), the following are equivalent.
Assuming Ignatius ' view was the Apostolic teaching and practice, the line of succession was unbroken and passed through the four ancient Patriarchal sees ( those local churches known to be founded by apostles ), Rome, Jerusalem, Antioch and Alexandria.
Assuming a specific Nazi usage of the term " Vaterland " ( which in fact never existed ), the direct English translation " fatherland " featured in news reports associated with Nazi Germany and in domestic anti-Nazi propaganda during World War II.
), the total human biomass is the average weight multiplied by the current human population of approximately 6. 5 billion ( see, e. g., ): Assuming 60 – 70 kg to be the average human mass ( approximately 130 – 150 lb on the average ), an approximation of total global human mass of between 390 billion ( 390 × 10 < sup > 9 </ sup >) and 455 billion kg ( between 845 billion and 975 billion lb, or about 423 million – 488 million short tons ).
For instance, raising the note B to B is equal to the note C. Assuming all such equivalences, the complete chromatic scale adds five additional pitch classes to the original seven lettered notes for a total of 12 ( the 13th note completing the octave ), each separated by a half-step.
Assuming that a TNT explosion releases 1, 000 small ( thermochemical ) calories per gram ( 4. 2 kJ / g ), one tonne of TNT is equivalent to 4. 2 gigajoules.
* Assuming that the Atlantic multidecadal oscillation runs through a 70-year quasi-cycle ( after peaks in ≈ 1880 and ≈ 1950 ), its current warm phase is likely to peak during this decade.
Assuming a full-scale sine wave signal ( that is, the quantizer is designed such that it has the same minimum and maximum values as the input signal ), the quantization noise approximates a sawtooth wave with peak-to-peak amplitude of one quantization level and uniform distribution.
Assuming opener bids 1 and partner responds 2 ; opener will know from this bid that partner has 9 losers ( using basic LTC ), if opener has 5 losers rather than the systemically assumed 7, then the calculation changes to ( 5 + 9
Assuming that the transcriptions are not intended to be precise, only 11 of the 26 — Bravo, Echo, Hotel, Juliet ( t ), Kilo, Mike, Papa, Quebec, Romeo, Whiskey, and Zulu — are given English pronunciations by all these agencies, though not always the same English pronunciations.
Assuming that birthdays are equally likely to happen on each of the 365 days of the year, the probability, P ( 2 ), that Person 2 has a different birthday than Person 1 is 364 / 365.
Assuming zero empirical mean ( the empirical mean of the distribution has been subtracted from the data set ), the principal component w < sub > 1 </ sub > of a data set X can be defined as:
Assuming the identity of " John Smith " ( the English equivalent of his natural German name ), Skull decided that he would reinvent himself and his quest for absolute power as a means to celebrate his cheating death.
Assuming the responsibility of mediator between the two sides, and with Erasmus ' willing participation ( the robot being left as the leader and controlling-force of the thinking machines ), Duncan does something similar to Bene-Gesserit Sharing with the robot ; possibly along with what seems to be a physical-bonding ( similar to what Leto II did with the sandtrout ) into something of a human-machine hybrid.
Assuming the material expands with temperature ( enriched Uranium-235 at room temperature for example ), at an exactly critical state, it will become subcritical if warmed to lower density or become supercritical if cooled to higher density.
Assuming all of the voters vote sincerely ( strategic voting is discussed below ), the results would be as follows, by percentage:
If the tested number n is composite, the strong liars a coprime to n are contained in a proper subgroup of the group, which means that if we test all a from a set which generates, one of them must be a witness for the compositeness of n. Assuming the truth of the generalized Riemann hypothesis ( GRH ), it is known that the group is generated by its elements smaller than O (( log n )< sup > 2 </ sup >), which was already noted by Miller.
Assuming the medium is linear, isotropic, and homogeneous ( see polarization density ), we have the constitutive equation:
Assuming the fulfillment of certain technical criteria ( such as the sentencing of the accused whose punishment was not yet executed ), wherever it is possible to punish the conspirators with exactly the same punishment through which they had planned to harm their fellow, the court carries out this direct reciprocal justice ( including when the punishment constitutes the death penalty ).
Assuming further for simplicity ( all arrows are lost after just one shot, so that they are circulating capital ), the absolute competitive prices of beavers and deer become:
Assuming the title of samdech ( prince ), Sihanouk explained that this action was necessary in order to give him a free hand to engage in politics.
* Assuming the shadow position ( with any handhold ), the leader leads the follower into chicken walks.
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