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In theoretical physics, dimensional regularization is a method introduced by Giambiagi and Bollini [1] as well as – independently and more comprehensively [2] – by 't Hooft and Veltman [3] for regularizing integrals in the evaluation of Feynman diagrams; in other words, assigning values to them that are meromorphic functions of a complex parameter d, the analytic continuation of the number ...
A dimensional data element is similar to a categorical variable in statistics. Typically dimensions in a data warehouse are organized internally into one or more hierarchies. "Date" is a common dimension, with several possible hierarchies: "Days (are grouped into) Months (which are grouped into) Years",
As first explained by Witten, [10] the space of conformal blocks of a two-dimensional CFT can be identified with the quantum Hilbert space of a 2+1 dimensional Chern-Simons theory, which is an example of a topological field theory. This connection has been very fruitful in the theory of the fractional quantum Hall effect.
Two-dimensional gel electrophoresis, abbreviated as 2-DE or 2-D electrophoresis, is a form of gel electrophoresis commonly used to analyze proteins. Mixtures of proteins are separated by two properties in two dimensions on 2D gels. 2-DE was first independently introduced by O'Farrell [ 1 ] and Klose [ 2 ] in 1975.
There is an exponential increase in volume associated with adding extra dimensions to a mathematical space.For example, 10 2 = 100 evenly spaced sample points suffice to sample a unit interval (try to visualize a "1-dimensional" cube) with no more than 10 −2 = 0.01 distance between points; an equivalent sampling of a 10-dimensional unit hypercube with a lattice that has a spacing of 10 −2 ...
A three-dimensional integrated circuit (3D IC) is a MOS (metal-oxide semiconductor) integrated circuit (IC) manufactured by stacking as many as 16 or more ICs and interconnecting them vertically using, for instance, through-silicon vias (TSVs) or Cu-Cu connections, [1] [2] so that they behave as a single device to achieve performance ...
He joined the faculty of MIT in 1997, and was tenured in 2002. [2] At MIT, he is a research affiliate at Blueprint Labs, co-directs MIT’s Shaping the Future of Work Initiative, and heads its Global Economics and Management Group. [2] Johnson has been a research associate at the NBER since 2004, and is an affiliate of BREAD. [2]
A unitary representation on a finite-dimensional inner product space is defined in the same way, except that is required to map into the group of unitary operators. If G is a compact Lie group, every finite-dimensional representation is equivalent to a unitary one. [2]