We study the compression performance of the quincunx discrete wavelet transform (DWT) and we compare it with the dyadic DWT in terms of ratedistortion. The 2D non-separable quincunx wavelet filters are designed by making use of the ‘transformations of variables’ technique of Tay & Kingsbury starting from the 1D biorthogonal (9,7)-taps filters. The applied transformation functions are respective...

We study the compression performance of the quincunx discrete wavelet transform (DWT) and we compare it with the dyadic DWT in terms of PSNR and bit rate. The 2D non-separable quincunx wavelet filters are designed by making use of the ‘transformations of variables’ technique of Tay & Kingsbury starting from the 1D biorthogonal (9,7)-taps filters. The applied transformation functions are respect...

Abstract In this paper, two new estimators $$ E_{2^{k-1},0}^{(1)}(f) E 2 k - 1 , 0 ( ) f </mml...

It is known that q-orthogonal polynomials play an important role in the field of q-series and special functions. While studying Dyson’s “favorite” identity Rogers–Ramanujan type, Andrews pointed out classical orthogonal also have surprising applications world q. By introducing Chebyshev third fourth kinds into Bailey pairs, derived a family type identities results related to mock theta function...

We study generating functions for the number of involutions of length n avoiding (or containing exactly once) 132 and avoiding (or containing exactly once) an arbitrary permutation τ of length k. In several interesting cases these generating functions depend only on k and can be expressed via Chebyshev polynomials of the second kind. In particular, we show that involutions of length n avoiding ...

A partition π of the set [n] = {1, 2, . . . , n} is a collection {B1, B2, . . . , Bk} of nonempty disjoint subsets of [n] (called blocks) whose union equals [n]. In this paper, we find an explicit formula for the generating function for the number of partitions of [n] with exactly k blocks according to the number of peaks (valleys) in terms of Chebyshev polynomials of the second kind. Furthermo...

given function f imperative to have certain smoothness or continuity properties. Particular attention is paid to error estimate of the developed AQS, where it shows the acquired AQS scheme is obtained in the class of functions C[−1, 1] which converges to the exact very fast by increasing the knot points. The first and second kind of Chebyshev polynomials are used in the conjecture. Several nume...

In this paper, a Chebyshev polynomial approximation for the solution of second-order partial differential equations with two variables and variable coefficients is given. Also, Chebyshev matrix is introduced. This method is based on taking the truncated Chebyshev expansions of the functions in the partial differential equations. Hence, the result matrix equation can be solved and approximate va...