On the Piano Movers Problem Iv Various Decomposable Two Dimensional Motion Pl
On the Piano Movers Problem Iv Various Decomposable Two Dimensional Motion Pl
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Then for each i=l k for which the orientation ^i is a touch, 6 j^ is not an isolated point of 0^ (X), and is not the end-point of more than one arc of 0^*(X). Moreover, Sj^(6j^, X) contains just one wall section W.
Lemma 1. 6: The set of points satisfying the hypotheses (*) and (**) of Lemma 1. 5 is open.
Lemma 1. 7: Let X satisfy the hypotheses of Lemma 1. 5. Then there exists an open neighborhood N of X such that for Y e N we have a(Y) = a(X), and for each i=l, ... , k. , 0^*(Y) consists of e...xactly as many arcs as 0^*(X). Moreover if [W. W ] c o^(x) = ai(Y) then i^i(Y, W) (resp. '*^i'(Y, W')) depends continuously on Y for Y e N.
Let V be the locus of all points violating one of the conditions (*), (**) of Lemma 1. 5. We will see below that V is the union of a finite collection of curves, which we call the critical curves of our case of the mover's problem. Removal of these critical curves divides the two dimensional space of all admissible points into a finite collection of connected open regions R, which we call the noncritical regions of our problem.
What to read after On the Piano Movers Problem Iv Various Decomposable Two Dimensional Motion Pl?
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To quickly assess the difficulty of the text, read a short excerpt:
Then for each i=l k for which the orientation ^i is a touch, 6 j^ is not an isolated point of 0^ (X), and is not the end-point of more than one arc of 0^*(X). Moreover, Sj^(6j^, X) contains just one wall section W.
Lemma 1. 6: The set of points satisfying the hypotheses (*) and (**) of Lemma 1. 5 is open.
Lemma 1. 7: Let X satisfy the hypotheses of Lemma 1. 5. Then there exists an open neighborhood N of X such that for Y e N we have a(Y) = a(X), and for each i=l, ... , k. , 0^*(Y) consists of e...xactly as many arcs as 0^*(X). Moreover if [W. W ] c o^(x) = ai(Y) then i^i(Y, W) (resp. '*^i'(Y, W')) depends continuously on Y for Y e N.
Let V be the locus of all points violating one of the conditions (*), (**) of Lemma 1. 5. We will see below that V is the union of a finite collection of curves, which we call the critical curves of our case of the mover's problem. Removal of these critical curves divides the two dimensional space of all admissible points into a finite collection of connected open regions R, which we call the noncritical regions of our problem.
What to read after On the Piano Movers Problem Iv Various Decomposable Two Dimensional Motion Pl?
You can find similar books in the "Read Also" column, or choose other free books by Micha Sharir to read onlineMoreLess
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