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The Yang–Mills existence and mass gap problem is an unsolved problem in mathematical physics and mathematics, and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute, which has offered a prize of US$1,000,000 for its solution. The problem is phrased as follows: [1] Yang–Mills Existence and Mass Gap.
M.V. Goganov and L.V. Kapitanskii have shown that the Cauchy problem for hyperbolic Yang–Mills–Higgs equations in Hamiltonian gauge on 4-dimensional Minkowski space have a unique global solution with no restrictions at the spatial infinity. Furthermore, the solution has the finite propagation speed property.
The earliest extant Chinese illustration of 'Pascal's triangle' is from Yang's book Xiángjiě Jiǔzhāng Suànfǎ (詳解九章算法) [1] of 1261 AD, in which Yang acknowledged that his method of finding square roots and cubic roots using "Yang Hui's Triangle" was invented by mathematician Jia Xian [2] who expounded it around 1100 AD, about 500 years before Pascal.
Yang-Hui He (simplified Chinese: 何杨辉; traditional Chinese: 何楊輝; pinyin: Hé Yáng Huī; born 29 September 1975 [1]) is a mathematical physicist, who is a Fellow at the London Institute, [2] which is based at the Royal Institution of Great Britain, as well as lecturer and former Fellow at Merton College, Oxford.
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
A numerical solution to the heat equation on a pump casing model using the finite element method.. Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variational methods, and numerical analysis); and applied probability.
The first version was proved for the Ising model by T. D. Lee and C. N. Yang (Lee & Yang 1952). Their result was later extended to more general models by several people. Asano in 1970 extended the Lee–Yang theorem to the Heisenberg model and provided a simpler proof using Asano contractions.
Mathematical logic is the study of formal logic within mathematics.Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory).