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  2. List of United States dependent visas - Wikipedia

    en.wikipedia.org/wiki/List_of_United_States...

    K-2 visa - for the children of those admitted under a K-1 visa [1]: 37 K-4 visa - for the children of those admitted under a K-3 visa [1]: 37 L-2 visa - for dependents of those admitted under an L-1 visa. L-2 spouses may work while in the US. Children may not be employed. [1]: 39 M-2 visa - for dependents of those admitted under an M-1 visa ...

  3. Tetrahedral molecular geometry - Wikipedia

    en.wikipedia.org/wiki/Tetrahedral_molecular_geometry

    In a tetrahedral molecular geometry, a central atom is located at the center with four substituents that are located at the corners of a tetrahedron.The bond angles are arccos(− ⁠ 1 / 3 ⁠) = 109.4712206...° ≈ 109.5° when all four substituents are the same, as in methane (CH 4) [1] [2] as well as its heavier analogues.

  4. List of character tables for chemically important 3D point groups

    en.wikipedia.org/wiki/List_of_character_tables...

    These groups are characterized by i) an n-fold proper rotation axis C n; ii) n 2-fold proper rotation axes C 2 normal to C n; iii) a mirror plane σ h normal to C n and containing the C 2 s. The D 1 h group is the same as the C 2 v group in the pyramidal groups section.

  5. Symmetry number - Wikipedia

    en.wikipedia.org/wiki/Symmetry_number

    The symmetry number or symmetry order of an object is the number of different but indistinguishable (or equivalent) arrangements (or views) of the object, that is, it is the order of its symmetry group. The object can be a molecule, crystal lattice, lattice, tiling, or in general any kind of mathematical object that admits symmetries. [1]

  6. Symmetry operation - Wikipedia

    en.wikipedia.org/wiki/Symmetry_operation

    In mathematics, a symmetry operation is a geometric transformation of an object that leaves the object looking the same after it has been carried out. For example, a 1 ⁄ 3 turn rotation of a regular triangle about its center, a reflection of a square across its diagonal, a translation of the Euclidean plane, or a point reflection of a sphere through its center are all symmetry operations.

  7. Character table - Wikipedia

    en.wikipedia.org/wiki/Character_table

    The kernel of a character χ is the set of elements g in G for which χ(g) = χ(1); this is a normal subgroup of G. Each normal subgroup of G is the intersection of the kernels of some of the irreducible characters of G. The number of irreducible representations of G equals the number of conjugacy classes that G has.

  8. Hermann–Mauguin notation - Wikipedia

    en.wikipedia.org/wiki/Hermann–Mauguin_notation

    For example, 2 1 is a 180° (twofold) rotation followed by a translation of ⁠ 1 / 2 ⁠ of the lattice vector. 3 1 is a 120° (threefold) rotation followed by a translation of ⁠ 1 / 3 ⁠ of the lattice vector. The possible screw axes are: 2 1, 3 1, 3 2, 4 1, 4 2, 4 3, 6 1, 6 2, 6 3, 6 4, and 6 5.

  9. Chern–Simons form - Wikipedia

    en.wikipedia.org/wiki/Chern–Simons_form

    where the wedge product is used to define F k. The right-hand side of this equation is proportional to the k -th Chern character of the connection A {\displaystyle \mathbf {A} } . In general, the Chern–Simons p -form is defined for any odd p .