The non-commutative geometric construction of A. Connes [1-5] has been successful in giving a geometrical interpretation of the standard model as well as some grand unification models. Our lack of ability to quantize the non-commutative actions forced on us to quantize the classical actions resulting from the non-commutative ones by adopting the usual rules. The symmetries that might be present...

In this paper we present an approach to determine the smallest possible number of neurons in a layer neural network such way that topology input space can be learned sufficiently well. We introduce general procedure based on persistent homology investigate topological invariants manifold which suspect data set. specify required dimensions precisely, assuming there is smooth or near are located....

We present a derivation of the general form of the scalar potential in Yang-Mills theory of a non-commutative space which is a product of a four-dimensional manifold times a discrete set of points. We show that a non-trivial potential without flat directions is obtained after eliminating the auxiliary fields only if constraints are imposed on the mass matrices utilised in the Dirac operator. Th...

We show that the first five of the axioms we had formulated on spectral triples suffice (in a slightly stronger form) to characterize the spectral triples associated to smooth compact manifolds. The algebra, which is assumed to be commutative, is shown to be isomorphic to the algebra of all smooth functions on a unique smooth oriented compact manifold, while the operator is shown to be of Dirac...

Fundamental group of a manifold gives deep effect on its underlying smooth structure. In this paper we introduce new variant the Donaldson invariant in Yang-Mills gauge theory from twisting by Picard four case when fundamental is free abelian. We then generalize it to general groups use framework non commutative geometry. also verify that our distinguishes structures between some homeomorphic m...

We complete the details of a theory outlined by Kontsevich and Soibelman that associates to a semi-algebraic set a certain graded commutative differential algebra of “semi-algebraic differential forms” in a functorial way. This algebra encodes the real homotopy type of the semialgebraic set in the spirit of the DeRham algebra of differential forms on a smooth manifold. Its development is needed...

In this paper, we extend Sasaki metric for tangent bundle of a Riemannian manifold and Sasaki-Mok metric for the frame bundle of a Riemannian manifold [I] to the case of a semi-Riemannian vector bundle over a semi- Riemannian manifold. In fact, if E is a semi-Riemannian vector bundle over a semi-Riemannian manifold M, then by using an arbitrary (linear) connection on E, we can make E, as a...

the objective of this work was to develop a new design of an intake manifold through a 1d simulation. it is quite familiar that a duly designed intake manifold is essential for the optimal performance of an internal combustion engine. air flow inside the intake manifold is one of the important factors, which governs the engine performance and emissions. hence the flow phenomenon inside the inta...

An equivariant Thom isomorphism theorem in operator K-theory is formulated and proven for infinite rank Euclidean vector bundles over finite dimensional Riemannian manifolds. The main ingredient in the argument is the construction of a non-commutative C-algebra associated to a bundle E → M , equipped with a compatible connection ∇, which plays the role of the algebra of functions on the infinit...

the present article serves the purpose of pursuing geometrization of heat flow on volumetrically isothermal manifold by means of rf approach. in this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of riemannian manifold and fundamental properties of thermodynamic systems. by making use of the notions of various curva...