Functions Defined on General Sets
... • A function f from a set X to a set Y, denoted : → , is a relation from X, the domain, to Y, the co-domain, that satisfies two properties: 1. Every element in X is related to some element in Y 2. No element in X is related to more than one element in Y • For any element ∈ , there is a unique elemen ...
... • A function f from a set X to a set Y, denoted : → , is a relation from X, the domain, to Y, the co-domain, that satisfies two properties: 1. Every element in X is related to some element in Y 2. No element in X is related to more than one element in Y • For any element ∈ , there is a unique elemen ...
Lecture 5: Universal One-Way Function and Computational Number
... Proof of Claim. Given a one-way function f that can be computed in time nc , define the function f 0 by f 0 (a||b) = a||f (b), where |a| = mc and |b| = m for some m ∈ N. (We use || to denote concatenation of strings.) One can easily verify that f 0 can be computed in time n2 , where n is the length ...
... Proof of Claim. Given a one-way function f that can be computed in time nc , define the function f 0 by f 0 (a||b) = a||f (b), where |a| = mc and |b| = m for some m ∈ N. (We use || to denote concatenation of strings.) One can easily verify that f 0 can be computed in time n2 , where n is the length ...
fn (x) = f(x). n2x if 0 ≤ x if 1 n ≤ x 0 if 2 n ≤ x ≤1
... Any positive number is less than some value of 2/n (by A.P.) So for any point in (0,1) the sequence fn(x) converges to zero. The sequence may get pretty big while the point is mapping to places close to the peaks of really tall tents, but eventually it will slide quickly down and then be zero foreve ...
... Any positive number is less than some value of 2/n (by A.P.) So for any point in (0,1) the sequence fn(x) converges to zero. The sequence may get pretty big while the point is mapping to places close to the peaks of really tall tents, but eventually it will slide quickly down and then be zero foreve ...
ON ASYMPTOTIC ERRORS IN DISCRETIZATION OF PROCESSES
... have functional convergence (in the J1 Skorokhod sense) since the processes nY n (X) are always continuous themselves. Note that the laws of all Yt are s-selfdecomposable, or equivalently of “class U,” a class of infinitely divisible distributions introduced by Jurek [5]: see in particular Theorem 2 ...
... have functional convergence (in the J1 Skorokhod sense) since the processes nY n (X) are always continuous themselves. Note that the laws of all Yt are s-selfdecomposable, or equivalently of “class U,” a class of infinitely divisible distributions introduced by Jurek [5]: see in particular Theorem 2 ...
Integral identities and constructions of approximations to
... connected to the construction of functional linear forms in polylogarithmic functions ...
... connected to the construction of functional linear forms in polylogarithmic functions ...
CHAP08 Multiplicative Functions
... whenever m, n are coprime. Functions with this property are called multiplicative functions. Of course there are trivial examples such as the constant functions F(n) = 1 or G(n) = n. Less trivial examples are the number of divisors and the sum of the divisors. It is clear that if F(n) is multiplicat ...
... whenever m, n are coprime. Functions with this property are called multiplicative functions. Of course there are trivial examples such as the constant functions F(n) = 1 or G(n) = n. Less trivial examples are the number of divisors and the sum of the divisors. It is clear that if F(n) is multiplicat ...