Differential Invariants Under the Inversion Group
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2 . 3 ••• n If, inQ, f=g=h = 0, Q has a double point at the origin and its equation becomes Q': {x^ + y^y + {ax + by)ix'' + y^) + cr^ + 2dxy + ey^ = 0. Since there are five independent constants in Q', one member of the family may have contact of order five with c at the origin P, and this curve will serve as the geometric image for the fifth derivative. Expressing the fact that a member of the family Q' may osculate c at P we have Q' subject to the five conditions 1. C+2y'd + y"e = 0, 2. (1 + ...y")a + 2/'(l + y")b + y'^d + yY'e = 0, 3. 12(1 + yy+ \2y'y"a + W + I82/V - ]h + 4y'"d+[3y"'+4yy"]e = 0, 4. 242/'2/"(l + y") + Wy'" + 32/"1a + W" + Qy'Y' + ^y'y"']h + ^^^ci + [2y'Y' + yY'']e = 0, 5. 2402/'^'"(l + 2/'^) + 1802/"^(1 + 3i/'^) + [SOi/'i/'" + 602/'y "]a + [15y^^ + 45?/'V'^ + ISOyYy'" + 452/'"]6 + 6r
What to read after Differential Invariants Under the Inversion Group?
You can find similar books in the "Read Also" column, or choose other free books by George W George Walker Mullins to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
2 . 3 ••• n If, inQ, f=g=h = 0, Q has a double point at the origin and its equation becomes Q': {x^ + y^y + {ax + by)ix'' + y^) + cr^ + 2dxy + ey^ = 0. Since there are five independent constants in Q', one member of the family may have contact of order five with c at the origin P, and this curve will serve as the geometric image for the fifth derivative. Expressing the fact that a member of the family Q' may osculate c at P we have Q' subject to the five conditions 1. C+2y'd + y"e = 0, 2. (1 + ...y")a + 2/'(l + y")b + y'^d + yY'e = 0, 3. 12(1 + yy+ \2y'y"a + W + I82/V - ]h + 4y'"d+[3y"'+4yy"]e = 0, 4. 242/'2/"(l + y") + Wy'" + 32/"1a + W" + Qy'Y' + ^y'y"']h + ^^^ci + [2y'Y' + yY'']e = 0, 5. 2402/'^'"(l + 2/'^) + 1802/"^(1 + 3i/'^) + [SOi/'i/'" + 602/'y "]a + [15y^^ + 45?/'V'^ + ISOyYy'" + 452/'"]6 + 6r
What to read after Differential Invariants Under the Inversion Group?
You can find similar books in the "Read Also" column, or choose other free books by George W George Walker Mullins to read onlineMoreLess
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