Differential geometry: a natural tool for describing symmetry operations

Differential geometry: a natural tool for describing symmetry operations.

Differential geometry provides a useful mathematical framework for describing the fundamental concepts in crystallography. The notions of point and associated vector spaces correspond to those of manifold and tangent space at a given point. A space-group operation is a one-to-one map acting on the manifold, whereas a point-group operation is a linear map acting between two tangent spaces of the...

Natural Operations in Differential Geometry

Natural Operations on Differential Forms

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Describing geometry and symmetry of cryo-EM datasets using algebra

Cryo-electron microscopy (cryo-EM) is a microscopy technique used to discover the 3D structure of molecules from very noisy 2D images. This thesis presents two projects that use algebra to describe cryo-EM datasets. In the first part, we obtain an algebraic description of common lines datasets. Common lines are lines of intersection between cryo-EM images in 3D. They are an important ingredient...

The differential transform method for solving the model describing biological species living together

F. Shakeri and M. Dehghan in [13] presented the variational iteration method for solving the model describing biological species living together. Here we suggest the differential transform (DT) method for finding the numerical solution of this problem. To this end, we give some preliminary results of the DT and by proving some theorems, we show that the DT method can be easily applied to mentio...