Symmetry groupIn group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object X is G = Sym(X). For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space.
Density functional theoryDensity-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. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density.
Crystal healingCrystal healing is a pseudoscientific alternative-medicine practice that uses semiprecious stones and crystals such as quartz, agate, amethyst or opal. Adherents of the practice claim that these have healing powers, but there is no scientific basis for this claim. Practitioners of crystal healing believe they can boost low energy, prevent bad energy, release blocked energy, and transform a body's aura.
Energy (esotericism)Proponents and practitioners of various esoteric forms of spirituality and alternative medicine refer to a variety of claimed experiences and phenomena as being due to "energy" or "force" that defy measurement and thus are distinguished from the scientific form of energy. Claims related to energy therapies are most often anecdotal, rather than being based on repeatable empirical evidence. There is no scientific evidence for the existence of such energy, and physics educators criticize the use of the term "energy" to describe ideas in esotericism and sprituality as potentially confusing.
System UIn mathematical logic, System U and System U− are pure type systems, i.e. special forms of a typed lambda calculus with an arbitrary number of sorts, axioms and rules (or dependencies between the sorts). They were both proved inconsistent by Jean-Yves Girard in 1972. This result led to the realization that Martin-Löf's original 1971 type theory was inconsistent as it allowed the same "Type in Type" behaviour that Girard's paradox exploits. System U is defined as a pure type system with three sorts ; two axioms ; and five rules .
