Virtually everybody working in discrete mathematics is familiar with the generalized triangle of order 2 aka the Fano plane, the smallest projective plane, PG 2,2), or the unique symmetric block design with parameters 2− 7,3,1), and its elementary representation as the geometrical configuration of an equilateral triangle together with its three medians and inscribed circle.
Infima can be presented only by the mental act of an elementary representation, while objects of higher order can be presented by representations (gained by the production of representation; see above 3.3.3) and by other mental acts as well.
(B) Representation of hierarchical grouping of a subset of the species allowing exploring the relation between phylogenetic and genealogical trees (left: a photograph taken during a class in an elementary school; right: schematic representation of the photograph).
(A) Discuss with the students examples of biological and inherited human traits and write some of these examples on the board (left: a photograph taken during a class in an elementary school; right: schematic representation of the photograph).
To further analyze the influence of symmetry properties on the system algebra, we recall some elementary representation theory (see, e.g., Theorem 1.5 of [73]): Proposition 50 Consider a completely reducible complex matrix representation Φ ( g ) of a group G, where k is the degree of Φ.
The color image is decomposed into its R, G and B components, and each component is further decomposed into eight disjoint elementary images depending upon the bit-map representation of the color value at each pixel.
The developed ALD gas surface reaction mechanism, purely based on consecutive and parallel elementary Eley Rideal reaction steps, was incorporated into the computational fluid dynamic representation of the equipment-scale.
Moreover, the size of the elementary cubes of the partition is chosen to allow for the accurate representation of the material properties.
The main idea of Wigner's approach is the supposition that each irreducible (projective) representation of the relevant space-time symmetry group yields the state space of one kind of elementary physical system, where the prime example is an elementary particle which has the more restrictive property of being structureless.
