Counting Inversions, Offline Orthogonal Range Counting, and Related Problems Timothy M. Chan
... and n axis-aligned rectangles, compute the number size and optimal O(lg n/ lg lg√n) query time, which can of points inside each rectangle. The problem has be constructed faster in O(n lg n) time. The generalization of the result in dimenan immediate application to 2-d orthogonal segment intersection ...
... and n axis-aligned rectangles, compute the number size and optimal O(lg n/ lg lg√n) query time, which can of points inside each rectangle. The problem has be constructed faster in O(n lg n) time. The generalization of the result in dimenan immediate application to 2-d orthogonal segment intersection ...
Chapter 5 Common Functions and their Properties
... Since two values of x result from a given value of y, the inverse function is multivalued. This tells us that a function may be single-valued but its inverse may be multivalued or vice-versa. In many applications, only the positive square root would be of interest, so if the negative square root is ...
... Since two values of x result from a given value of y, the inverse function is multivalued. This tells us that a function may be single-valued but its inverse may be multivalued or vice-versa. In many applications, only the positive square root would be of interest, so if the negative square root is ...
2.4 Points on modular curves parameterize elliptic curves with extra
... 1/N ∈ Λτ . Third, let Qτ be the point of order N in Eτ defined by τ /N , and consider the basis (Pτ , Qτ ) for E[N ]. Let E be an elliptic curve over C. Theorem 2.4.5 below asserts that the non-cuspidal points on X0 (N ) correspond to isomorphism classes of pairs (E, C) where C is a cyclic subgroup ...
... 1/N ∈ Λτ . Third, let Qτ be the point of order N in Eτ defined by τ /N , and consider the basis (Pτ , Qτ ) for E[N ]. Let E be an elliptic curve over C. Theorem 2.4.5 below asserts that the non-cuspidal points on X0 (N ) correspond to isomorphism classes of pairs (E, C) where C is a cyclic subgroup ...
Note on Nakayama`s Lemma For Compact Λ
... X/IX is finite then X is actually a torsion Λ module. This is immediate from the structure theorem for Λ modules that we have in this case. This result does not, however, extend to other pro-p groups in general. We first note that the concept of a torsion module is only useful when Λ has no zero div ...
... X/IX is finite then X is actually a torsion Λ module. This is immediate from the structure theorem for Λ modules that we have in this case. This result does not, however, extend to other pro-p groups in general. We first note that the concept of a torsion module is only useful when Λ has no zero div ...