On Solutions of Deltau Fu
On Solutions of Deltau Fu
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In our eReader you can find the full English version of the book. Read On Solutions of Deltau Fu Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book On Solutions of Deltau Fu
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, if v were not spherically symmetric, a different solution could be obtained by rotating v, and that would contradict the uniqueness of the solution. Therefore v ■ v(r), and the equations satisfied by v become (13) v + 2dk v = h(v), rr r r v " (1U) v r (0) =0, - 6 - (15) v(R) = a. Equations (13) and (15) are just (6) and (7) written explicitly, and n denotes the dimension of the space. Equation (lU) is a consequence of the regularity of v at r = 0. Every real a uniquely determines v(0) wnich i...s a monotonic increasing function of a. Therefore a is itself uniquely determined by v(0). Thus we may replace (1$) by (16) v(0) = v Q . As v Q increases, a = v(R) increases. We will show that a = v(R) is infinite for some value of v . This value of v is the lim v, which was defined before o o o a->oo as g(R). It is convenient to rewrite (13) in the form (17) ^\) = r^hCv). R r Integrating (17) from to r yields (18) r (r) - r 1 " 11 f x 11 " 1 h[v(x)]dx From (18) we see that v > 0. Therefore v is a nondecreasing function so we can obtain from (18) (19) y Upon inserting (19) into (13) we get r (r) £M.
What to read after On Solutions of Deltau Fu?
You can find similar books in the "Read Also" column, or choose other free books by Joseph Bishop Keller to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
, if v were not spherically symmetric, a different solution could be obtained by rotating v, and that would contradict the uniqueness of the solution. Therefore v ■ v(r), and the equations satisfied by v become (13) v + 2dk v = h(v), rr r r v " (1U) v r (0) =0, - 6 - (15) v(R) = a. Equations (13) and (15) are just (6) and (7) written explicitly, and n denotes the dimension of the space. Equation (lU) is a consequence of the regularity of v at r = 0. Every real a uniquely determines v(0) wnich i...s a monotonic increasing function of a. Therefore a is itself uniquely determined by v(0). Thus we may replace (1$) by (16) v(0) = v Q . As v Q increases, a = v(R) increases. We will show that a = v(R) is infinite for some value of v . This value of v is the lim v, which was defined before o o o a->oo as g(R). It is convenient to rewrite (13) in the form (17) ^\) = r^hCv). R r Integrating (17) from to r yields (18) r (r) - r 1 " 11 f x 11 " 1 h[v(x)]dx From (18) we see that v > 0. Therefore v is a nondecreasing function so we can obtain from (18) (19) y Upon inserting (19) into (13) we get r (r) £M.
What to read after On Solutions of Deltau Fu?
You can find similar books in the "Read Also" column, or choose other free books by Joseph Bishop Keller to read onlineMoreLess
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