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As the gradual degradation with same failure mechanism has some regularity in macro, there would be certain relation between an arbitrary point of the degradation process and the correspondent RUL.
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Gap functions have turned out to be very useful in deriving the error bounds, which provide a measure of the distance between solution set and an arbitrary point.
Besides these, gap functions also turned out to be very useful in designing new globally convergent algorithms, in analyzing the rate of convergence of some iterative methods, and in obtaining the error bounds, which provide a measure of the distance between solution set and an arbitrary point.
Now, let ( x 0, y 0 ) be an arbitrary point between W s ( E y ¯ ) and W s ( E x ¯ ).
Finally, let ( x 0, y 0 ) be an arbitrary point between W s ( E y ¯ ) and W s ( E x ¯ − ).
To capture the shielding effects between discharge wires in a multi-wire ESP, the corona-discharge-induced space charge density at an arbitrary point between the discharge wire and grounded plates is specified as the sum of two components: (i) a uniform value on the wire surface which is resolved individually for each wire; and (ii) a space-dependent variation relative to the uniform part.
Our model for an active region had the form of an isotropic Gaussian field, that is, (2) where ‖ u, v ‖ is the Euclidean distance between the field center u and an arbitrary point v.
Take an arbitrary point (x^{ast}inGamma).
Let be an arbitrary point in for.
Let be an arbitrary point in.
We fix an arbitrary point x ∈ Ϝ.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com