Since j [equivalent to] 1 (mod 2), the number of such automorphisms
y is 4 x 4 = 16.
In the mixing procedure, they use the torus automorphism
technique  to scramble all secret image pixels, and then the mixed secret image is embedded into the cover image pixel by pixel.
Hou, Characterizations of nest algebra automorphisms
, Chinese Ann.
algebra, we need to know about partial automorphisms
of a [C.
is an automorphism
of H, and the mapping b [right arrow] b * is an embedding of B in Aut H.
of the q-oscillator algebra and basic orthogonal polynomials, Phys.
Mathematicians and scientists discuss such matters as rigid abelian groups and the probabilistic method, looking for indecomposable right bounded complexes, kernel modules of cotorsion pairs, upper cardinal bounds for absolute structures, subgroups of totally projective primary abelian groups and direct sums of cyclic groups, generic endomorphisms of homogeneous structures, special pairs and automorphisms
of centerless groups, and some results on the algebraic entropy.
If Q is a medial quasigroup, then there exist an Abelian group <Q, +, -, 0>, its commuting automorphisms
[phi] and [psi], and an element c [member of] Q such that
Paper topics include growth functions on varieties, groups of units in group rings; representation theory of Lie algebras; Jordan, alternative, and Leibniz algebras; graded identities; automorphisms
of trees; and partial actions.
Suppose that [sigma], [tau] are automorphisms
a] [member of] Aut(B), the set of all automorphisms
Let n now be arbitrary and let K(z, [omega]) be a positive definite kernel in the ball which remains invariant under all holomorphic automorphisms
of the ball and which is the reproducing kernel of a Hilbert space HK of analytic functions in the ball.