Crossword-Solution: INTEGRABILITY
Dictionary
| Word | Word Type | Definition |
|---|---|---|
| Integrability | n. | The quality of being integrable. |
We have 1 clue for the answer “INTEGRABILITY”
| Clue | Answers |
|---|---|
| the state of being integrable | 1 answer |
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Hint 1 meaning
To cause to flow in a stream, as a liquid or anything
flowing like a liquid, either out of a vessel or into it; as, to pour
water from a pail; to pour wine into a decanter; to pour oil upon the
waters; to pour out sand or dust.
Hint 2 anagram
ORPU
Hint 3 another clue
Stream
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Sentences with INTEGRABILITY (3)
There is then only one total equation, say dz = adz + bdy; if we do not take account of the condition of integrability, which is in this case da/dy + bda/dz = db/dx + adb/dz, this equation may be regarded as defining through an arbitrary point (x0, y0, z0) of three-dimensioned space (about which a, b are developable) a plane, namely, z - z0 = a0(x - x0) + b0(y - y0), and therefore, through this arbitrary point [oo]² directions, namely, all those in the plane.
But we find d¹z0 = a0dx0 + b(x0 + dx0 , y0, z0 + a0dx0)dy0 = /db db \ a0dx0 + b0dy0 + dx0dy0( --- + a0--- ), \dx0 dz0/ and so at once reach the condition of integrability.
The integral of a function f(x) through a measurable domain H, which is a homogeneous part of the numerical continuum of n dimensions, is defined in just the same way as the integral through an interval, the extent of a square domain taking the place of the difference of the end-values of a partial interval; and the condition of integrability takes the same form as in the simple case.