In this paper, the well-known Faulkner construction is revisited and adapted to include super case, which gives a bijective correspondence between generalized Jordan (super)pairs faithful Lie (super)algebra (super)modules, under certain constraints (bilinear forms with properties analogous ones of Killing form are required, only finite-dimensional objects considered). We always assume that base...

A molecular phylogenetic analysis with complete species sampling of the family Kyphosidae revealed several discrepancies with the current taxonomy. We thus undertook a complete taxonomic revision of all kyphosid genera, i.e. Kyphosus Lacepède, 1801, and the monotypic Hermosilla Jenkins and Evermann, 1889, Sectator Jordan and Evermann, 1903 and Neoscorpis Smith, 1931. Species delimitation was de...

The large N → ∞ limit of the Exceptional F4, E6 Jordan Matrix Models of Smolin-Ohwashi leads to novel Chern-Simons Membrane Lagrangians which are suitable candidates for a nonperturbative bosonic formulation of M Theory in D = 27 real, complex dimensions, respectively. Freudenthal algebras and triple Freudenthal products permits the construction of a novel E7 × SU(N) invariant Matrix model whos...

A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...

in this paper, using clarke’s generalized directional derivative and di-invexity we introduce new concepts of nonsmooth k-α-di-invex and generalized type i univex functions over cones for a nonsmooth vector optimization problem with cone constraints. we obtain some sufficient optimality conditions and mond-weir type duality results under the foresaid generalized invexity and type i cone-univexi...