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The Thomson problem also plays a role in the study of other physical models including multi-electron bubbles and the surface ordering of liquid metal drops confined in Paul traps. The generalized Thomson problem arises, for example, in determining arrangements of protein subunits that comprise the shells of spherical viruses. The "particles" in ...
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, the Milne-Thomson method is a method for finding a holomorphic function whose real or imaginary part is given. [1] It is named after Louis Melville Milne-Thomson . Introduction
It can be described as the molecular geometry in which one atom in the center connects three other atoms in a plane, known as the trigonal planar molecular geometry. [30] In the Thomson problem, concerning the minimum-energy configuration of charged particles on a sphere, and for the Tammes problem of constructing a spherical code maximizing ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
In the Thomson problem, concerning the minimum-energy configuration of charged particles on a sphere, and for the Tammes problem of constructing a spherical code maximizing the smallest distance among the points, the minimum solution known for = places the points at the vertices of a regular icosahedron, inscribed in a sphere. This ...
In mathematics, specifically algebraic geometry, Donaldson–Thomas theory is the theory of Donaldson–Thomas invariants.Given a compact moduli space of sheaves on a Calabi–Yau threefold, its Donaldson–Thomas invariant is the virtual number of its points, i.e., the integral of the cohomology class 1 against the virtual fundamental class.
In order to reduce a geometric problem to a problem of pure number theory, the proof uses the fact that a regular n-gon is constructible if and only if the cosine (/) is a constructible number—that is, can be written in terms of the four basic arithmetic operations and the extraction of square roots.
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