The Order of the Red Banner (Russian: Орден Крaсного Знамени) was the first Soviet military decoration. The order was established on 16 September 1918, during the Russian Civil War by decree of the All-Russian Central Executive Committee. It was the highest award of Soviet Russia, subsequently the Soviet Union, until the Order of Lenin was established in 1930. Recipients were recognised for extraordinary heroism, dedication, and courage demonstrated on the battlefield. The order was awarded to individuals as well as to military units, cities, ships, political and social organizations, and state enterprises. In later years it was also awarded on the twentieth and again on the thirtieth anniversary of military service without requiring participation in combat.
The Russian Order of the Red Banner was established during the Russian Civil War by decree of the All-Russian Central Executive Committee of September 16, 1918.
The first recipient was Vasily Blyukher on September 28, 1918. The second recipient was Iona Yakir.
In mathematics, big O notation describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann–Landau notation (after Edmund Landau and Paul Bachmann), or asymptotic notation. In computer science, big O notation is used to classify algorithms by how they respond (e.g., in their processing time or working space requirements) to changes in input size. In analytic number theory, it is used to estimate the "error committed" while replacing the asymptotic size, or asymptotic mean size, of an arithmetical function, by the value, or mean value, it takes at a large finite argument. A famous example is the problem of estimating the remainder term in the prime number theorem.
Big O notation characterizes functions according to their growth rates: different functions with the same growth rate may be represented using the same O notation.
Red Banner (Russian: Красное знамя) was a symbol of the USSR associated with the Soviet state flag.
Military units, institutions and organizations (of the Soviet Army, Soviet Navy, MVD Internal Troops, etc.) awarded with the Order of the Red Banner are referred to with the honorific title "of the Red Banner" (Краснознамённый (krasnoznamyonny), e.g. The Red Banner Baltic Fleet or "The Twice Red Banner Alexandrov Soviet Army Choir").
Civilian establishments awarded the Order of the Red Banner of Labour are also sometimes addressed with the "Red-Banner" honorific.
The Transferable Red Banner (Russian: переходящее Красное знамя) was an award for collectives, winners in socialist competitions at various Soviet work places. The term "transferable" means that for a given kind of competition at a given establishment (enterprise, school, institute, clinic, etc.) or category of establishments (e.g., type of industry) there was a single physical copy of the award which was transferred to the next winner in the competition (held annually or quarterly). There were several levels of the award, depending on the level of the socialist competition: all-Union, republican, oblast-wide, industry-wide, enterprise/institution-wide, etc.