a unital $c^*$ -- algebra $mathcal a,$ endowed withthe lie product $[x,y]=xy- yx$ on $mathcal a,$ is called a lie$c^*$ -- algebra. let $mathcal a$ be a lie $c^*$ -- algebra and$g,h:mathcal a to mathcal a$ be $bbb c$ -- linear mappings. a$bbb c$ -- linear mapping $f:mathcal a to mathcal a$ is calleda lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

Three-flavor neutrino oscillations in matter can be described by three effective masses $\widetilde{m}^{}_i$ (for $i = 1, 2, 3$) and the mixing matrix $V^{}_{\alpha i}$ $\alpha e, \mu, \tau$ 3$). When parameter $a \equiv 2\sqrt{2} G^{}_{\rm F} N^{}_e E$ is taken as an independent variable, a complete set of first-order ordinary differential equations for $\widetilde{m}^2_i$ $|V^{}_{\alpha i}|^2...

We study symplectic structures on characteristically nilpotent Lie algebras (CNLAs) by computing the cohomology space H(g, k) for certain Lie algebras g. Among these Lie algebras are filiform CNLAs of dimension n ≤ 14. It turns out that there are many examples of CNLAs which admit a symplectic structure. A generalization of a sympletic structure is an affine structure on a Lie algebra.

Abstract Complete hom-Lie superalgebras are considered and some equivalent conditions for a superalgebra to be complete established. In particular, the relation between decomposition completeness is described. Moreover, that linear space of $$\alpha ^{s}$$ α s -derivati...

The chromosomal location of Ti alpha was determined by hybridization of a radiolabeled cDNA for the alpha chain of human T cell receptor with 12 human X mouse cell hybrid DNAs cleaved with BamHI. Seven hybrids contained human Ti alpha, while the remaining five lacked it. Only human chromosome 14 matched the distribution of human Ti alpha signal across the mapping panel. Hybrids segregating a ch...

The fact that the optimum proportion flocculation ratio is different when determined by the alpha (Dean and Webb) and beta (Ramon) procedures is pointed out. It is demonstrated that this difference is a consequence of the difference in the two methods, and that the two optima, though they may in certain cases lie near together, can never coincide. A new ratio (the epsilon ratio), intermediate b...

The notion of strongly Lie zero-product preserving maps on normed algebras as a generalization of Lie zero-product preserving maps are dened. We give a necessary and sufficient condition from which a linear map between normed algebras to be strongly Lie zero-product preserving. Also some hereditary properties of strongly Lie zero-product preserving maps are presented. Finally the second dual of...

Models of all the gradings on the exceptional simple Lie algebras induced by Jordan subgroups of their groups of automorphisms are provided.