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This theorem has since been extended to the time-dependent domain to develop time-dependent density functional theory (TDDFT), which can be used to describe excited states. The second HK theorem defines an energy functional for the system and proves that the ground-state electron density minimizes this energy functional.
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.
The gross anatomy of a muscle is the most important indicator of its role in the body. One particularly important aspect of gross anatomy of muscles is pennation or lack thereof. In most muscles, all the fibers are oriented in the same direction, running in a line from the origin to the insertion.
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 Planck relation [1] [2] [3] (referred to as Planck's energy–frequency relation, [4] the Planck–Einstein relation, [5] Planck equation, [6] and Planck formula, [7] though the latter might also refer to Planck's law [8] [9]) is a fundamental equation in quantum mechanics which states that the energy E of a photon, known as photon energy, is proportional to its frequency ν: =.
The initial concepts that led to the Virtual Physiological Human initiative came from the IUPS Physiome Project.The project was started in 1997 and represented the first worldwide effort to define the physiome through the development of databases and models which facilitated the understanding of the integrative function of cells, organs, and organisms. [7]
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 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.