Homotopy Theory of the Suspensions of the Projective Plane

A diffeomorphism classification of manifolds which are like projective planes

We give a complete diffeomorphism classification of 1-connected closed manifolds M with integral homology H∗(M) ∼= Z ⊕ Z ⊕ Z, provided that dim(M) 6= 4. The integral homology of an oriented closed manifold1 M contains at least two copies of Z (in degree 0 resp. dimM). IfM is simply connected and its homology has minimal size (i.e., H∗(M) ∼= Z⊕Z), then M is a homotopy sphere (i.e., M is homotopy...

Nonlinear Vibration Analysis of the Beam Carrying a Moving Mass Using Modified Homotopy

In the present study, the analysis of nonlinear vibration for a simply-supported flexible beam with a constant velocity carrying a moving mass is studied. The amplitude of vibration assumed high and its deformation rate is assumed slow. Due to the high amplitude of vibrations, stretching is created in mid-plane, resulting in, the nonlinear strain-displacement relations is obtained, Thus, Nonlin...

Vibration Analysis of a Nonlinear Beam Under Axial Force by Homotopy Analysis Method

In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differenti...

Minimal graphs of a torus, a projective plane and spheres and some properties of minimal graphs of homotopy classes

Contractible transformations of graphs consist of contractible gluing and deleting of vertices and edges of graphs. They partition all graphs into the family of homotopy classes. Contractible transformations do not change the Euler characteristic and the homology groups of graphs. In this paper we describe the minimal representatives of some homotopy classes and find the formula for computing t...

L-s-homotopy Classes on the Topological Image of a Projective Plane