Experimental observation of Majorana fermion matter gives a new impetus to the understanding of the Lorentz symmetry and its extension, the geometrical properties of the ambient space-time structure, matter–antimatter symmetry and some new ways to understand the baryo–genesis problem in cosmology. Based on the primordial Majorana fermion matter assumption, we discuss a possibility to solve the ...

The jet formalism for Classical Field theories is extended to the setting of Lie algebroids. We define the analog of the concept of jet of a section of a bundle and we study some of the geometric structures of the jet manifold. When a Lagrangian function is given, we find the equations of motion in terms of a Cartan form canonically associated to the Lagrangian. The Hamiltonian formalism is als...

We extend the Nambu bracket to 1-forms. Following the Poisson-Lie case, we define Nambu-Lie groups as Lie groups endowed with a multiplica-tive Nambu structure. A Lie group G with a Nambu structure P is a Nambu-Lie group iff P = 0 at the unit, and the Nambu bracket of left (right) invariant forms is left (right) invariant. We define a corresponding notion of a Nambu-Lie algebra. We give several...

The Escherichia coli aer regulatory region contains a single promoter that is recognized by RNA polymerase containing the flagellar sigma factor, sigma(28). Expression from this promoter is dependent on direct activation by the cyclic AMP receptor protein, which binds to a target centred 49.5 base pairs upstream from the transcript start. Activator-dependent transcription from the aer promoter ...

Good and Hughes [9] introduced the notion of bi-ideal and Steinfeld [11, 12] introduced the notion of quasi-ideal. Sioson [10] studied some properties of quasi-ideals of ternary semigroups. In [1], Dixit and Dewan studied about the quasi-ideals and bi-ideals of ternary semigroups. Quasi-ideals are generalization of right ideals, lateral ideals, and left ideals whereas bi-ideals are generalizati...

Let $A$ be a Noetherian ring, $I$ be an ideal of $A$ and $sigma$ be a semi-prime operation, different from the identity map on the set of all ideals of $A$. Results of Essan proved that the sets of associated prime ideals of $sigma(I^n)$, which denoted by $Ass(A/sigma(I^n))$, stabilize to $A_{sigma}(I)$. We give some properties of the sets $S^{sigma}_{n}(I)=Ass(A/sigma(I^n))setminus A_{sigma}(I...

let $g$ be a simple graph‎, ‎and $g^{sigma}$‎ ‎be an oriented graph of $g$ with the orientation ‎$sigma$ and skew-adjacency matrix $s(g^{sigma})$‎. ‎the $k-$th skew spectral‎ ‎moment of $g^{sigma}$‎, ‎denoted by‎ ‎$t_k(g^{sigma})$‎, ‎is defined as $sum_{i=1}^{n}( ‎‎‎lambda_{i})^{k}$‎, ‎where $lambda_{1}‎, ‎lambda_{2},cdots‎, ‎lambda_{n}$ are the eigenvalues of $g^{sigma}$‎. ‎suppose‎ ‎$g^{sigma...

We consider topological solitons in the CP sigma models in two space dimensions. In particular, we study “kinks”, which are independent of one coordinate up to a rotation of the target space, and “chains”, which are periodic in one coordinate up to a rotation of the target space. Kinks and chains both exhibit constituents, similar to monopoles and calorons in SU(n) Yang-Mills-Higgs and Yang-Mil...