In this paper we review the definition of the invariants “bar codes” and “Jordan cells” of real and angle valued tame maps as proposed in [1] and [4] and prove the homotopy invariance of the sums ]Bc r + ]Bo r−1 and of the set of Jordan cells. Here Bc r resp. Bo r denote the sets of closed resp. open bar codes in dimension r. In addition we provide calculation of some familiar topological invar...

Complex shapes - such as the surface of the human brain - may be represented and analyzed in frequency space by means of a spherical harmonics transformation. A key step of the processing chain is introducing a suitable parametrization of the triangular mesh representing the brain surface. This problem corresponds to mapping a surface of topological genus zero on a unit sphere. An algorithm is ...

Albert algebras and other Jordan algebras are constructed over curves of genus zero and one, using a generalization of the Tits process and the first Tits construction due to Achhammer.

J. Freudenberger*, R. Jordan*, M. Bossert*, and S. Shavgulidze** * University of Ulm, Dep. of Information Technology Albert-Einstein-Allee 43, D-89081 Ulm, Germany Email: jfreuden,jordan,[email protected] ** Georgian Technical University, Dep. of Digital Communication Theory Kostava str. 77, Tbilisi 380075, Georgia Email: sergo [email protected] Abstract: In this paper we investigate s...

Semispecial quasi-Jordan algebras (also called Jordan dialgebras) are defined by the polynomial identities a(bc) = a(cb), (ba)a = (ba)a, (b, a, c) = 2(b, a, c)a. These identities are satisfied by the product ab = a a b + b ` a in an associative dialgebra. We use computer algebra to show that every identity for this product in degree ≤ 7 is a consequence of the three identities in degree ≤ 4, bu...

collagen, which is widely distributed in pluricellular animals, is one of the most fundamental constituents of the extracellular matrix, and plays mechanically or physiologically important roles in their bodies. in this study, the biochemical and physical characteristics of pepsin-solubilized collagen from the mantle of yesso scallop (ympc), a by-product of processing, was determined. electroph...