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The committee's initial report evolved into NFPA 13, Standard for the Installation of Sprinkler Systems, the most widely used fire sprinkler standard. [ 6 ] Around 1904, the NFPA began to expand its membership from affiliates of fire insurance companies to many other organizations and individuals, and also expanded its mission beyond ...
A primitive element, α, of F p n is an element that generates F * p n. Representing the non-zero field elements as powers of α allows multiplication in the field to be performed efficiently. The primitive polynomial for α is the monic polynomial of smallest possible degree with coefficients in F p that has α as a root in F p n (the minimal ...
In fact, if P is an irreducible factor over GF(p) of X q − X, its degree divides n, as its splitting field is contained in GF(p n). Conversely, if P is an irreducible monic polynomial over GF(p) of degree d dividing n, it defines a field extension of degree d, which is contained in GF(p n), and all roots of P belong to GF(p n), and are roots ...
An irreducible polynomial F(x) of degree m over GF(p), where p is prime, is a primitive polynomial if the smallest positive integer n such that F(x) divides x n − 1 is n = p m − 1. A primitive polynomial of degree m has m different roots in GF(p m), which all have order p m − 1, meaning that any of them generates the multiplicative group ...
The association was founded in 1906 as the "Fire Marshals Association of North America," with the purpose of promoting fire safety and prevention tactics. [2] On October 9, 1911, the association, alongside the local insurance organization Western Insurance Union, [2] held the first "Fire Prevention Week" to commemorate the memory of the Great Chicago Fire forty years prior.
The group was studied by number theorists as the group of wild automorphisms of the local field F p ((t)) and by group theorists including D. Johnson (1988) and the name "Nottingham group" refers to his former domicile. This group is a finitely generated pro-p-group, of finite width. For every finite group of order a power of p there is a ...
The 2025 edition of NFL Honors begins at 9 p.m. ET. Coverage begins an hour earlier, starting at 8 p.m. ET, on NFL Network with the red carpet show. NFL Honors awards.
Liquids having a flash point below 22.8 °C (73 °F) and having a boiling point at or above 37.8 °C (100 °F) or having a flash point between 22.8 and 37.8 °C (73 and 100 °F). 4 Will rapidly or completely vaporize at normal atmospheric pressure and temperature, or is readily dispersed in air and will burn readily (e.g., gasoline , acetylene ...