Normality concerning exceptional functions

Normality of Vectorial Functions

The most important building blocks of symmetric cryptographic primitives such as the DES or the AES, are vectorial Boolean functions, also called S-boxes. In this paper, we extend the definition of normality for Boolean functions into several new affine invariant properties for vectorial Boolean functions. We compute the probability of occurrence of these properties and present practical algori...

Asymptotic Normality of Scaling Functions

The Gaussian function G(x) = 1 p 21⁄4 e¡x 2=2; which has been a classical choice for multiscale representation, is the solution of the scaling equation G(x) = Z R ®G(®x¡ y)dg(y); x 2 R; with scale ® > 1 and absolutely continuous measure dg(y) = 1 p 21⁄4(®2 ¡ 1) e¡y 2=2(®2¡1)dy: It is known that the sequence of normalized B-splines (Bn); where Bn is the solution of the scaling equation Á(x) = n ...

Some Normality Criteria of Meromorphic Functions

Let f be a nonconstant meromorphic function in the complex plane C. We shall use the standard notations in Nevanlinna’s value distribution theory of meromorphic functions such as T r, f , N r, f , and m r, f see, e.g., 1, 2 . The notation S r, f is defined to be any quantity satisfying S r, f o T r, f as r → ∞ possibly outside a set of E of finite linear measure. Let F be a family of meromorphi...

INCLUSION RELATIONS CONCERNING WEAKLY ALMOST PERIODIC FUNCTIONS AND FUNCTIONS VANISHING AT INFINITY

We consider the space of weakly almost periodic functions on a transformation semigroup (S, X , ?) and show that if X is a locally compact noncompact uniform space, and ? is a separately continuous, separately proper, and equicontinuous action of S on X, then every continuous function on X, vanishing at infinity is weakly almost periodic. We also use a number of diverse examples to show ...

Concerning Rings of Continuous Functions