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The formal foundation of TDDFT is the Runge–Gross (RG) theorem (1984) [1] – the time-dependent analogue of the Hohenberg–Kohn (HK) theorem (1964). [2] The RG theorem shows that, for a given initial wavefunction, there is a unique mapping between the time-dependent external potential of a system and its time-dependent density.
Density functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases.
Acyclic models theorem (algebraic topology) Addition theorem (algebraic geometry) Adiabatic theorem ; Ado's theorem (Lie algebra) Akhiezer's theorem (complex analysis) Akra–Bazzi theorem (computer science) Alternate Interior Angles Theorem ; Alternate segment theorem ; Albert–Brauer–Hasse–Noether theorem
Phase 2: Then, missing details were supplemented and blurred contours were clarified using a 3D editing program by referring to textbooks, atlases, [7] and mock-up models by medical illustrators. Phase 3: Further segmentation and data modification will continue in collaboration with clinical researchers until sufficient concept coverage is ...
Gross anatomy (also called topographical anatomy, regional anatomy, or anthropotomy) is the study of anatomical structures that can be seen by the naked eye. [1] Microscopic anatomy is the study of minute anatomical structures assisted with microscopes , which includes histology (the study of the organization of tissues), [ 1 ] and cytology ...
In the interpretation of quantum mechanics, a local hidden-variable theory is a hidden-variable theory that satisfies the principle of locality.These models attempt to account for the probabilistic features of quantum mechanics via the mechanism of underlying, but inaccessible variables, with the additional requirement that distant events be statistically independent.
If H is normal, then H \ G is a group, and the right action of K on this group factors through the right action of H \ HK. It follows that H \ G / K = G / HK. Similarly, if K is normal, then H \ G / K = HK \ G. If H is a normal subgroup of G, then the H-double cosets are in one-to-one correspondence with the left (and right) H-cosets.
Hume's principle or HP says that the number of Fs is equal to the number of Gs if and only if there is a one-to-one correspondence (a bijection) between the Fs and the Gs. HP can be stated formally in systems of second-order logic.