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FORM has been the essential tool to calculate the higher-order QCD beta function. The mathematical structure of multiple zeta values has been researched with dedicated FORM programs. [2] The software package FormCalc which is widely used in the physics community to calculate Feynman diagrams is built on top of FORM.
The moduli space must not only be Kähler, but also the Kähler form must lift to integral cohomology. Such manifolds are called Hodge manifolds . The first example appeared in the 1979 article "Spontaneous Symmetry Breaking and Higgs Effect in Supergravity Without Cosmological Constant" [ 4 ] and the general statement appeared 3 years later in ...
The real projective space P n is a moduli space that parametrizes the space of lines in R n+1 which pass through the origin. Similarly, complex projective space is the space of all complex lines in C n+1 passing through the origin.
A modular form f that vanishes at q = 0 (equivalently, a 0 = 0, also paraphrased as z = i∞) is called a cusp form (Spitzenform in German). The smallest n such that a n ≠ 0 is the order of the zero of f at i∞. A modular unit is a modular function whose poles and zeroes are confined to the cusps. [5]
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2] The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of ...
For the ring R = Z[√−5], both the module R and its submodule M generated by 2 and 1 + √−5 are indecomposable. While R is not isomorphic to M , R ⊕ R is isomorphic to M ⊕ M ; thus the images of the M summands give indecomposable submodules L 1 , L 2 < R ⊕ R which give a different decomposition of R ⊕ R .
In physics, a fifth force refers to a hypothetical fundamental interaction (also known as fundamental force) beyond the four known interactions in nature: gravitational, electromagnetic, strong nuclear, and weak nuclear forces. Some speculative theories have proposed a fifth force to explain various anomalous observations that do not fit ...
Illustration of uniform compression. The bulk modulus (or or ) of a substance is a measure of the resistance of a substance to bulk compression.It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.