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Let V be a representation of a group G; or more generally, let V be a vector space with a set of linear endomorphisms acting on it. In general, a vector space acted on by a set of linear endomorphisms is said to be simple (or irreducible) if the only invariant subspaces for those operators are zero and the vector space itself; a semisimple representation then is a direct sum of simple ...
In mathematics, the first symbol is mainly used in Anglophone countries to represent the mathematical operation of division and is called an obelus. [3] In editing texts, the second symbol, also called a dagger mark † is used to indicate erroneous or dubious content; [ 4 ] [ 5 ] or as a reference mark or footnote indicator. [ 6 ]
There are various ways of approaching the subject, each of which focuses on a slightly different flavor of Chern class. The original approach to Chern classes was via algebraic topology: the Chern classes arise via homotopy theory which provides a mapping associated with a vector bundle to a classifying space (an infinite Grassmannian in this case).
Equivalence class: given an equivalence relation, [] often denotes the equivalence class of the element x. 3. Integral part : if x is a real number , [ x ] {\displaystyle [x]} often denotes the integral part or truncation of x , that is, the integer obtained by removing all digits after the decimal mark .
Intentional homicide is defined by the United Nations Office on Drugs and Crime (UNODC) in its Global Study on Homicide report [3] thus: . Within the broad range of violent deaths, the core element of intentional homicide is the complete liability of the direct perpetrator, which thus excludes killings directly related to war or conflicts, self-inflicted death (suicide), killings due to legal ...
In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag).This is the steady gain in speed caused exclusively by gravitational attraction.
The vast majority of stars are found along the main sequence with blue Class O stars found at the top left of the chart while red Class M stars fall to the bottom right. Certain stars like Deneb and Betelgeuse are found above and to the right of the main sequence, more luminous or cooler than their equivalents on the main sequence.
Defence expenditure was pegged at US$70.12 billion for fiscal year 2022–23 and, increased 9.8% than previous fiscal year. [ 290 ] [ 291 ] India is the world's second-largest arms importer; between 2016 and 2020, it accounted for 9.5% of the total global arms imports. [ 292 ]