In this paper, the intuitionistic fuzzy counterparts of collineations defined in classical projective planes are planes. The properties plane left invariant under characterized depending on base point, line, membership degrees, and non-membership degrees plane.

We prove that a Poisson structure on projective toric variety which is invariant by the torus action and whose symplectic leaves are orbits not exact. This deduced from geometric criterion for non-exactness of structures with finite number leaves.

LetX be a smooth projective geometrically connected curve over a finite field with function field K. Let G be a connected semisimple group scheme over X . Under certain hypothesis we prove the equality of two numbers associated with G. The first is an arithmetic invariant, its Tamagawa number. The second, is a geometric invariant, the number of connected components of the moduli stack of G-tors...

By superimposing a group structure on a sequence of projective probability spaces of Lebesgue measure preserving (l.m.p.) automorphisms of unit interval, the paper extends the Daniel-Kolmogorov consistency theorem that enables the construction of a measurable group structure with invariant Haar probability measure on an uncountably large projective limit space. The projective limit group is the...

let $mathcal{x}$ be a class of $r$-modules‎. ‎in this paper‎, ‎we investigate ;$mathcal{x}$-injective (projective) and dg-$mathcal{x}$-injective (projective) complexes which are generalizations of injective (projective) and dg-injecti‎‎ve (projective) complexes‎. ‎we prove that some known results can be extended to the class of ;$mathcal{x}$-injective (projective) and dg-$mathcal{x}$-injective ...

We give a general procedure to construct algebro-geometric Feynman rules, that is, characters of the Connes–Kreimer Hopf algebra of Feynman graphs that factor through a Grothendieck ring of immersed conical varieties, via the class of the complement of the affine graph hypersurface. In particular, this maps to the usual Grothendieck ring of varieties, defining motivic Feynman rules. We also con...

This paper presents a general framework for the computation of projective invariants of arbitrary degree of freedom (dof) trihedral polyhedra. We show that high dof. figures can be broken down into sets of connected four dof. polyhedra, for which known invariants exist. Although the more general shapes do not possess projective properties as a whole (when viewed by a single camera), each subpar...