Home New Trends in Information and Communications Technology Applications Conference paper Audio Compression Using Transform Coding with LZW and Double Shift Coding Zainab J. Ahmed & Loay E. George Conference paper First Online: 11 January 2022 126 Accesses Part of the Communications in Computer and Information Science book series (CCIS,volume 1511) Abstract The need for audio compression is still a vital issue, because of its significance in reducing the data size of one of the most common digital media that is exchanged between distant parties. In this paper, the efficiencies of two audio compression modules were investigated; the first module is based on discrete cosine transform and the second module is based on discrete wavelet tr

In this paper, we proved that if R is a prime ring, U be a nonzero Lie ideal of R , d be a nonzero (?,?)-derivation of R. Then if Ua?Z(R) (or aU?Z(R)) for a?R, then either or U is commutative Also, we assumed that Uis a ring to prove that: (i) If Ua?Z(R) (or aU?Z(R)) for a?R, then either a=0 or U is commutative. (ii) If ad(U)=0 (or d(U)a=0) for a?R, then either a=0 or U is commutative. (iii) If d is a homomorphism on U such that ad(U) ?Z(R)(or d(U)a?Z(R), then a=0 or U is commutative.

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