Next, based on experts' estimation of elementary relations among projects over periods, we derive mathematical formulae for covariances among projects and periods.
The exhaustive presentation of these elementary relations grounds aesthetics as a science.
In the next section we establish elementary relations among the concepts of boundedness, lacunary statistical boundedness and lacunary statistical convergence of sequences of numbers.
Our knowledge of logical laws is more probable than our knowledge of other psychological laws only 'because we experiment, throughout our life, daily and every hour, with these elementary relations between phenomena of consciousness' (1905, 33).
The elementary force displacement relation of each fibril is considered to obey the peeling theory of a tape, although other refined constitutive relations could be invoked for the adhesive constitutive response without any lack of generality.
The following elementary embedding relations hold: l^{p}subset l^{q}, qquad Vert u Vert _{l^{q}}leq Vert u Vert _{l^{p}}, qquad1le ple qle infty, quadmbox{where } Vert u Vert _{l^{infty}}:=max_{ninmathbb{Z}^{m}} vert u_{n} vert.
Clearly, the following elementary embedding relations hold: l^{p}subset l^{q}, quad Vert u Vert _{l^{q}}leq Vert u Vert _{l^{p}}, quad 1 le ple qle infty,text{ where } Vert u Vert _{l^{infty }}:= max _{nin Z^{m}}vert u_{n} vert.
Even the simple, elementary properties and relations of numbers often demand sophisticated mathematical tools.
Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability.
