A complete algorithm to design 4-band orthogonal wavelets with beautiful structure from 2-band orthogonal wavelets is presented. For more smoothness, the conception of transfer vanishing moment is introduced by transplanting the requirements of vanishing moment from the 4-band wavelets to the 2-band ones. Consequently, the design of 4-band orthogonal wavelets with P vanishing moments and beautiful structure from 2-band ones with P transfer vanishing moments is completed.
Let D be the unit disk in the complex plane with the weighted measure $d\mu _\beta \left( z \right) = \frac{{\beta + 1}}{\pi }\left( {1 - \left| z \right|^2 } \right)^\beta dm\left( z \right)\left( {\beta > - 1} \right)$ . Then $L^2 \left( {D, d\mu _\beta \left( z \right)} \right) = \oplus _{k = 0}^\infty \left( {A_k^\beta \oplus \bar A_k^\beta } \right)$ is the orthogonal direct sum decomposition. In this paper, we define the Hankel and Toeplitz type operators, and study the boundedness, compactness and Sp-criteria for them.
The Hankel transform is an important transform. In this paper, westudy the wavelets associated with the Hankel transform, thendefine the Weyl transform of the wavelets. We give criteria of itsboundedness and compactness on the Lp-spaces.
The key operation in Elliptic Curve Cryptosystems(ECC) is point scalar multiplication. Making use of Frobenius endomorphism, Muller and Smart proposed two efficient algorithms for point scalar multiplications over even or odd finite fields respectively. This paper reduces the corresponding multiplier by modulo Υk-1 +…+Υ+ 1 and improves the above algorithms. Implementation of our Algorithm 1 in Maple for a given elliptic curve shows that it is at least as twice fast as binary method. By setting up a precomputation table, Algorithm 2, an improved version of Algorithm 1, is proposed. Since the time for the precomputation table can be considered free, Algorithm 2 is about (3/2) log2 q - 1 times faster than binary method for an elliptic curve over
