Supposing that the bounding surface goes out to infinity, and plugging in this expression for the Green's function, this gives the familiar expression for electric potential in terms of electric charge density ( in the CGS unit system ) as

Supposing that the voltage noise on one wire is uncorrelated to the noise on the other one, the result is that it takes twice as much noise to cause an error with the differential system as with the single-ended system.

Supposing we exclude the degenerate case where ABCD has zero area, there is a unique such affine transformation T. Drawing out a whole grid of parallelograms based on ABCD, the image T ( P ) of any point P is determined by noting that T ( A ) = A ′, T applied to the line segment AB is A ′ B ′, T applied to the line segment AC is A ′ C ′, and T respects scalar multiples of vectors based at A.

Supposing u is the velocity of gross matter, v is the velocity of the gravific particles and ρ the density of the medium.

Supposing there is a veto player, any coalition not containing a veto player is losing.

Supposing this is password i, this password is already useless for subsequent authentications, because each password can only be used once.

Supposing the bodies tied by a rope to hold them together ( rather than gravity, which is ignored in this example ), the rope is under tension if the bodies are rotating relative to absolute space ( according to Rotating spheres | Newton ), or because they rotate relative to the Universe itself ( according to Mach's principle | Mach ), or because they rotate relative to an inertial frame of reference according to modern ideas.

Supposing her to be with her sister, Philoclea, Dametas barges into Philoclea's bed chamber and finds, of course, not Pamela, but " Cleophila ," who is naked and in bed with Philoclea, and who is evidently not a woman.

Supposing that the gas pressure is small compared to the magnetic pressure, i. e.,

Supposing the inhabitants were to view rods believed to be rigid, or measure distance with light rays.

Supposing that the kidnappers would contact the family, they tapped the phones and surveilled the house in order that the family would not try to deal directly with the kidnappers.

Supposing that the premises are both true ( the dog will bark if it detects an intruder, and does indeed not bark ), it follows then that no intruder has been detected.

Supposing that an animator wants the beam size of the light to change smoothly from one value to another within a predefined period of time, that could be achieved by using keyframes.

Supposing that light waves propagate from A to B by all possible routes AB < sub > j </ sub >, unrestricted initially by rules of geometrical or physical optics.

Supposing you or I were being accused in this manner, and yet we were doing our level best to carry on our work.

Supposing the 15-year-old Chulalongkorn also to be dying, King Mongkut on his deathbed had written, “ My brother, my son, my grandson, whoever you all the senior officials think will be able to save our country will succeed my throne, choose at your own will .” Si Suriyawongse, the most powerful government official of the day, managed the succession of Chulalongkorn to the throne, and his own appointment as regent.

Supposing Bunnicula will die of starvation otherwise, Harold brings him into the dining room to feast on the Monroe's salad.

In 1966, Tolkien referred to " cellar door " in an interview, using it as an example of the way in which words will shape his stories: " Supposing you say some quite ordinary words to me, ' cellar door ', say ," he said.

Supposing the phenomena described have a real physical base, numerous atmospheric phenomena could be the cause.

Supposing all setup data has been shared, the STS protocol proceeds as follows.

Supposing that groups of 4 digits are chosen.

Create a free market here, give us a sound, debt-free money system, and we'll compete with anyone, Europe and Asia combined.

Not only is this kind of duplication wasteful, but it gives the combined system the ability to take freight traffic away from the New York Central and other railroads serving the area.

The APG III system ( 2009 ) differs only in that the Limnocharitaceae are combined with the Alismataceae ; it was also suggested that the genus Maundia ( of the Juncaginaceae ) could be separated into a monogeneric family, Maundiaceae, but the authors noted that more study was necessary before Maundiaceae could be recognized.

When the Ming Dynasty Chinese astronomer Xu Guangqi adapted the European southern hemisphere constellations to the Chinese system in The Southern Asterisms, he combined Apus with some of the stars in Octans to form the " Exotic Bird " ( 異雀, Yìquè ).

Because field artillery mostly uses indirect fire the guns have to be part of a system that enables them to attack targets invisible to them in accordance with the combined arms plan.

The standard system is a tiled leach field combined with a septic tank.

In some cities, such as the Victorian era London sewers or much of the old City of Toronto, the storm water system is combined with the sanitary sewer system.

However, they are much less toxic than their predecessors, the barbiturates, and death rarely results when a benzodiazepine is the only drug taken ; however, when combined with other central nervous system depressants such as alcohol and opiates, the potential for toxicity and fatal overdose increases.

* S-Bahn, the combined city center and suburban railway system metro in Austria, Germany, Switzerland and Denmark

To provide modularity, memory and I / O buses can be combined into a unified system bus.

Coleco was also able to design and market the Gemini game system which was an exact clone of the 2600, but with combined joystick / paddle controllers.

The second point cannot in any reasonable way be combined with the first point, as long as the axiom system is genuinely finitary.

[...] A linguistic system is a series of differences of sound combined with a series of differences of ideas ; but the pairing of a certain number of acoustical signs with as many cuts made from the mass thought engenders a system of values.

Baudot combined these, together with original ideas of his own, to produce a complete multiplex system.

An extensive system of affixes may be freely combined with roots to generate vocabulary ; and the rules of word formation are straightforward, allowing speakers to communicate with a much smaller root vocabulary than in most other languages.

The results of each race are combined with a points system to determine two annual World Championships, one for the drivers and one for the constructors.

It is one of the world's best-selling game system lines, with a combined 200 + million units sold worldwide.

* dual gauge: 23 km combined 1. 435 m and 1. 000-m gauges ( three rail system ) ( 2004 )

A very popular type of system for reproducing music from the 1970s onwards was the integrated music centre which combined phonograph, radio tuner, tape player, preamp and power amplifier in one package, often sold with its own separate, detachable or integrated speakers.

During the course of the next thirty years, these same numbers were combined with filing codes used by the Navy's clerks to create an informal version of the system that was put in place in 1920.

* When insulin pump technology is combined with a continuous blood glucose monitoring system, the technology seems promising for real-time control of the blood sugar level.

The Hagia Sophia architects innovatively combined the longitudinal structure of a Roman basilica and the central plan of a drum-supported dome, in order to withstand the high magnitude earthquakes of the Marmara Region, “ However, in May 558, little more than 20 years after the Church ’ s dedication, following the earthquakes of August 553 and December 557, parts of the central dome and its supporting structure system collapsed .” The Hagia Sophia was repeatedly cracked by earthquakes and was quickly repaired.

which is simply the canonical way of constructing a basis for a tensor product space of the combined system from the individual spaces.