The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In simulating the discrete cosine transform, we propose a generalized discrete cosine transform with three parameters, and prove its orthogonality for some new...

In 2003, Araujo and Jarosz showed that every bijective linear map θ : A → B between unital standard operator algebras preserving zero products in two ways is a scalar multiple of an inner automorphism. Later in 2007, Zhao and Hou showed that similar results hold if both A,B are unital standard algebras on Hilbert spaces and θ preserves range or domain orthogonality. In particular, such maps are...

The radial part of the wave function of an electron in a Coulomb potential is the product of a Laguerre polynomial and an exponential with the variable scaled by a factor depending on the degree. This note presents an elementary proof of the orthogonality of wave functions with differing energy levels. It is also shown that this is the only other natural orthogonality for Laguerre polynomials. ...

Generation of supercells with a desirable size and reasonable geometry, such as basis vectors similar length are close to orthogonality, is useful for defect calculations dilute alloy calculations. Identification relations between crystals described using very different lattice parameters beneficial in crystal structure analysis. A computational algorithm, applicable any crystal, described, whi...

Two-dimensional liquid chromatography is often used to reduce the proteomic sample complexity prior to tandem mass spectrometry analysis. The 2D-LC performance depends on the peak capacity in both chromatographic dimensions, and separation orthogonality. The peak capacity and selectivity of many LC modes for peptides is not well known, and mathematical characterization for orthogonality is unde...