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Walsh Diagram of an HAH molecule. Walsh diagrams, often called angular coordinate diagrams or correlation diagrams, are representations of calculated orbital binding energies of a molecule versus a distortion coordinate (bond angles), used for making quick predictions about the geometries of small molecules.
Protein folding problem: Is it possible to predict the secondary, tertiary and quaternary structure of a polypeptide sequence based solely on the sequence and environmental information? Inverse protein-folding problem: Is it possible to design a polypeptide sequence which will adopt a given structure under certain environmental conditions?
In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere.It is a subgroup of the orthogonal group O(3), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices.
[8] [5] The first edition of his best known book, College Geometry, a university-level textbook in synthetic geometry, was published in 1925. [9] In 1935 he published the solid geometry textbook Modern Pure Solid Geometry [10] and became a full professor at the University of Oklahoma. He continued teaching there until his retirement in 1951.
In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this context, the partitioning is called simply a dissection (of one polytope into another).
The known solution of the Thomson problem, with one a triangular bipyramid The Thomson problem concerns the minimum energy configuration of charged particles on a sphere. A triangular bipyramid is a known solution in the case of five electrons, placing vertices of a triangular bipyramid within a sphere . [ 18 ]
In mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers.In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves.
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