O I A
... Suppose now that iρk and kρj . Let α ik ,α kj ∈ A with α ik ( i, k ) ≠ 0 , α kj ( k , j ) ≠ 0 . Then α = Dα α ik D k α kj D j belongs to A and α (i , j ) ≠ 0 , and thus iρj , proving the transitivity of ρ . Claim 2. The incidence algebra A( ρ ) coincides with A . The inclusion A ⊆ A( ρ ) is obvious. ...
... Suppose now that iρk and kρj . Let α ik ,α kj ∈ A with α ik ( i, k ) ≠ 0 , α kj ( k , j ) ≠ 0 . Then α = Dα α ik D k α kj D j belongs to A and α (i , j ) ≠ 0 , and thus iρj , proving the transitivity of ρ . Claim 2. The incidence algebra A( ρ ) coincides with A . The inclusion A ⊆ A( ρ ) is obvious. ...
Pascal`s triangle and other number triangles in Clifford Analysis
... is true in some generalization of the Pascal matrices which contain also integer powers of x. Such generalized Pascal matrix has the form P(x) = exH . Notice that for x = 0, x = 1 and x = −1, the generalized Pascal matrix reduces to the identity matrix, P and P−1 , respectively. In fact, from Theore ...
... is true in some generalization of the Pascal matrices which contain also integer powers of x. Such generalized Pascal matrix has the form P(x) = exH . Notice that for x = 0, x = 1 and x = −1, the generalized Pascal matrix reduces to the identity matrix, P and P−1 , respectively. In fact, from Theore ...
V.Andreev, N.Maksimenko, O.Deryuzhkova, Polarizability of the
... II. – 400 p.]. Current density j of Dirac particles with the help of Gordon decomposition can be represented as follows: ...
... II. – 400 p.]. Current density j of Dirac particles with the help of Gordon decomposition can be represented as follows: ...
