The Crossing Number of a Graph on a Compact 2-Manifold

Fractal Dimension of Graphs of Typical Continuous Functions on Manifolds

If M is a compact Riemannian manifold then we show that for typical continuous function defined on M, the upper box dimension of  graph(f) is as big as possible and the lower box dimension of graph(f) is as small as possible.  

On images of continuous functions from a compact manifold to Euclidean space

Soil and Rock Slope Stability Analysis based on Numerical Manifold Method and Graph Theory

Limit equilibrium method, strength reduction method and Finite Difference Methods are the most prevalently used methods for soil and rock slope stability analysis. However, it can be mention that those have some limitations in practical application. In the Limit equilibrium method, the constitutive model cannot be considered and many assumptions are needed between slices of soil and rock. The s...

Matchings in Graphs on Non-orientable Surfaces

P.W. Kasteleyn stated that the number of perfect matchings in a graph embedding on a surface of genus g is given by a linear combination of 4 Pfafans of modi ed adjacencymatrices of the graph, but didn't actually give the matrices or the linear combination. We generalize this to enumerating the perfect matchings of a graph embedding on an arbitrary compact boundaryless 2-manifold S with a linea...

آموزش منیفلد با استفاده از تشکیل گراف منیفلدِ مبتنی بر بازنمایی تنک

In this paper, a sparse representation based manifold learning method is proposed. The construction of the graph manifold in high dimensional space is the most important step of the manifold learning methods that is divided into local and gobal groups. The proposed graph manifold extracts local and global features, simultanstly. After construction the sparse representation based graph manifold,...