In the present work, two SIR patterns with demography will be considered: classical pattern and a modified linear coefficient of infection transmission. By reformulating each first-order differential systems as system second-order equations, we examine nonlinear dynamics from Jacobi stability perspective through Kosambi–Cartan–Chern (KCC) geometric theory. The intrinsic properties studied by de...

In this note we study Cartan subalgebras of Lie algebras defined over finite fields. We prove that a possible Lie algebra of minimal dimension without Cartan subalgebras is semisimple. Subsequently, we study Cartan subalgebras of gl(n, F ). AMS classification: 17B50

We provide an intrinsic notion of curved cosets for arbitrary Cartan geometries, simplifying the existing construction orbits a given holonomy reduction. To do this, we intrinsically define group, which is shown to coincide precisely with standard definition group geometries in terms associated principal connection. These retain many characteristics their homogeneous counterparts, and they beha...

Analogous to the characterisation of Brownian motion on a Riemannian manifold as development Euclidean space, we construct sub-Riemannian diffusions equinilpotentisable manifolds by developing canonical stochastic process arising lift an associated model space. The notion introduce for uses Cartan connections, which take place Levi-Civita connection in geometry. We first derive general expressi...

In this paper, we review deformation, cohomology and homotopy theories of relative Rota–Baxter ( RB $\mathsf {RB}$ ) Lie algebras, which have attracted quite much interest recently. Using Voronov's higher derived brackets, one can obtain an L ∞ $L_\infty$ -algebra whose Maurer–Cartan elements are algebras. Then using the twisting method, that controls deformations a algebra. Meanwhile, cohomolo...

We present a gauge formulation of the special affine algebra extended to include an antisymmetric tensorial generator belonging tensor representation linear group. then obtain Maxwell modified metric gravity action with cosmological constant term. find field equations theory and show that reduces Einstein-like equation for source added \mu contains contributions from new fields. The reduction R...

An investigation into the Cartan form and nondegeneracy conditions for field-theoretic Lagrangians based on the Cartan equivalence method.

The dualism between classical matter and geometry is extended to include elementary hadronic matter described in quantized form in terms of a gauge theory based on the group SO(4; 1) containing a built-in fundamental length parameter R of geometric origin of the order of a Fermi. Quantized matter at subnuclear distances is described in terms of generalized quantum mechanical wave functions ((rs...