Corollary 3 Sample Clauses

Corollary 3. 3.14 If one replaces the assumption in Theorem 3.3.13 on Xxx’s knowl- edge about S by H∞(S|Z = z) ≥ t log |S|, an A-code results with parameters PI ≤ 2—[(t—1) log |S|+log |B|], PS ≤ (ϵ · |B| + 1) 2—( t−2 1 log |S|+ 1 log |B|).

Corollary 3. 1.6. If X is a cubic surface and # H1(Gk, Pic X) is even, then X satisfies the Xxxxx principle.

Corollary 3. 20.There exists a black-box quantum polynomial-time(n+ 1)- stage quantum algorithm such that for any adaptive adversary against the multi-round Fiat-Shamir transformed versionFS[Π]of a(2n+1)-round PCIPΠ, makingqqueries to a uniformly random functionHwith appropriate domain and range equalC, and for anyx ◦ ∈X: Pr x=x ◦ ∧v=accept: (x, v)→ ⟨S A,V⟩ (2q+n+ 1) 2n H FS x ≥ n! Pr x=x ◦ ∧V H (x,π) : (x,π)→A H −ϵ ◦ . n! where the additive error termϵ x◦ is equal to |C| when summed over allx ◦.

Corollary 3. 2.7. If the set of primes T is good for a Shintani set D, then ζR,T (b, D, U, 0) ∈ Z. We define a Z-valued measure ν(b, D) on up by ν(b, D, U ) ∶= ζR,T (b, D, U, 0), (3.3) ⊆ for U up compact open.

Corollary 3. .2.6 If σˆVIX(K, T ) denotes the implied volatility of a VIX call or put option with strike K, we see that σˆ x : lim σˆ VIX exT H− 1 T |x| ( 0 ) (3.23) VIX( ) = T→0 VIX( 0 , ) = q2J 2VIX2x