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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.
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.
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 ...
The fundamental basis for this hypothesis, laid out by Columbia anatomy professor Melvin Moss is that bones do not grow but are grown, [2] thus stressing the ontogenetic primacy of function over form. [3] This is in contrast to the current conventional scientific wisdom that genetic, rather than epigenetic (non-genetic) factors, control such ...
The Foundational Model of Anatomy Ontology (FMA) is a reference ontology for the domain of human anatomy. [1] It is a symbolic representation of the canonical, phenotypic structure of an organism; a spatial-structural ontology of anatomical entities and relations which form the physical organization of an organism at all salient levels of granularity.
The Moore–Aronszajn theorem goes in the other direction; it states that every symmetric, positive definite kernel defines a unique reproducing kernel Hilbert space. The theorem first appeared in Aronszajn's Theory of Reproducing Kernels, although he attributes it to E. H. Moore. Theorem. Suppose K is a symmetric, positive definite kernel on a ...
The scientific model concerned with the origin of the first organisms from organic or inorganic molecules is known as abiogenesis, and the prevailing theory for explaining the early development of the universe is the Big Bang model.
The set of eigenvectors span a Banach space, and, when there is a natural inner product, then the eigenvectors span a Hilbert space, at which point the Riesz representation theorem is applied. Examples of such spaces are the orthogonal polynomials that occur as the solutions to a class of second-order ordinary differential equations.