Order of Saint-Charles

The Order of Saint-Charles (French: Ordre de Saint-Charles) is an order established in Monaco on 15 March 1858.

Award

This order rewards service to the State or Prince. In particular cases, it may be granted to foreigners. It is awarded by the current Grand-Master, Prince Albert II.

Reception

Except for Members of the Princely Family and foreigners, one can only receive the Order first with the rank of Knight. To be awarded the following higher ranks, one must keep the lower rank for a set length of time:

Officer: four years as a Knight

Commander: three years as an Officer

Grand Officer: four years as a Commander

Grand Cross: five years as a Grand Officer

Nominations belong to the Grand-Master. The Chancellor proposes promotions. According to the Prince's orders, the Chancellor proposes the projects of nomination and promotion ordonnances. The grantees must be received in the Order before wearing the decorations. The Grand-Master receives the Grand Crosses, Grand Officers and Commanders. The Chancellor receives the Officers and Knights. One exception : the foreigners will be admitted in the Order, but not received.

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Mexican Imperial Orders

There were three Imperial Orders of the Mexican Empire, created to reward those subjects loyal to the Monarchy during the two periods of the Mexican Empire – the Order of Guadalupe (Spanish: la Orden de Guadalupe), the Order of the Mexican Eagle (Spanish: la Orden del Águila Mexicana), and the Order of Saint Charles (Spanish: la Orden de San Carlos).

All three were abolished after the fall of the Second Mexican Empire and the execution of Maximilian I in 1867. Today, Article 12 of the Constitution of Mexico bans the creation and award of titles of nobility and other hereditary honours. Additionally, Article 37 strips Mexican citizenship from those who accept titles that require allegiance to a foreign government or monarch. Foreign awards that do not require allegiance to a foreign government can be accepted after being approved by the Mexican Congress.

Order of Guadalupe

The Order of Guadalupe (originally: "National Order of Our Lady of Guadalupe") was established by Emperor Agustín I of Mexico in the fall of 1821, although its statutes would not be published until February 1822. It was originally divided into two classes: Grand Cross and Numerary Member. After the death of the Agustin I, the Order fell out of use and remained inactive for 30 years until Antonio López de Santa Anna convinced Pope Pius IX to recognize it in 1854. It fell into disuse again in August of that same year after the successful Ayutla Revolution and the ousting of Santa Anna from government.

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Big O notation

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.

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