  This article is devoted to applications of projection operators to simulate
phenomenological properties of the molecular-genetic code system. Oblique
projection operators are under consideration, which are connected with matrix
representations of the genetic coding system in forms of the Rademacher and
Hadamard matrices. Evidences are shown that sums of such projectors give
abilities for adequate simulations of ensembles of inherited biological
phenomena including ensembles of biological cycles, morphogenetic ensembles of
phyllotaxis patterns, mirror-symmetric patterns, etc. For such modeling, the
author proposes multidimensional vector spaces, whose subspaces are under a
selective control (or coding) by means of a set of matrix operators on base of
genetic projectors. Development of genetic biomechanics is discussed. The
author proposes and describes special systems of multidimensional numbers under
names united-hypercomplex numbers, which attracted his attention when he
studied genetic systems and genetic matrices. New rules of long nucleotide
sequences are described on the base of the proposed notion of tetra-groups of
equivalent oligonucleotides. Described results can be used for developing
algebraic biology, bio-technical applications and some other fields of science
and technology.
