T he paradigm that DNA is the central bank of genetic information within the cell, and that portions of the DNA are copied via transcription to RNA, which is subsequently decoded to synthesize protein in a cell, is basically true throughout cellular evolution. However, it is also true that although this is a general blueprint for regulating how genes are expressed, evolution, with its varied se...

Two Bessel sequences are orthogonal if the composition of the synthesis operator of one sequence with the analysis operator of the other sequence is the 0 operator. We characterize when two Bessel sequences are orthogonal when the Bessel sequences have the form of translates of a finite number of functions in L(R). The characterizations are applied to Bessel sequences which have an affine struc...