based on the randic suggestion of the resolution of a structure into shape, size, and function an index representing structure-catabolic fate relationships of amino acids is constructed. the index obtained by multiplying three factors; (nb2 + nr), nc and m; representing shape, size and function respectively, where nb2 = number of double bonds, nr = number of rings, nc = number of carbon atoms, ...

let $mathcal m$ be a factor von neumann algebra. it is shown that every nonlinear $*$-lie higher derivation$d={phi_{n}}_{ninmathbb{n}}$ on $mathcal m$ is additive. in particular, if $mathcal m$ is infinite type $i$factor, a concrete characterization of $d$ is given.

Let $(M^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the Sasakian space form$widetilde{M}(c)$. We show that if the shape operator $A$ of $M$ isrecurrent then it is parallel. Moreover, we show that $M$is locally a product of two constant $phi-$sectional curvaturespaces.

the decomposition $gamma=bh$ of a group $gamma$ into a subset $b$ and a subgroup $h$ of $gamma$ induces, under general conditions, a group-like structure for $b$, known as a gyrogroup. the famous concrete realization of a gyrogroup, which motivated the emergence of gyrogroups into the mainstream, is the space of all relativistically admissible velocities along with a binary operation given by t...

We consider the unit tangent sphere bundle of Riemannian manifold ( M, g ) with g-natural metric G̃ and we equip it to an almost contact B-metric structure. Considering this structure, we show that there is a direct correlation between the Riemannian curvature tensor of ( M, g ) and local symmetry property of G̃. More precisely, we prove that the flatness of metric g is necessary and sufficien...

Let $mathcal M$ be a factor von Neumann algebra. It is shown that every nonlinear $*$-Lie higher derivation$D={phi_{n}}_{ninmathbb{N}}$ on $mathcal M$ is additive. In particular, if $mathcal M$ is infinite type $I$factor, a concrete characterization of $D$ is given.