Crank of a partition

In number theory, the crank of a partition of an integer is a certain integer associated with the partition. The term was first introduced without a definition by Freeman Dyson in a 1944 paper published in Eureka, a journal published by the Mathematics Society of Cambridge University. Dyson then gave a list of properties this yet to be defined quantity should have. George E. Andrews and F.G. Garvan in 1988 discovered a definition for crank satisfying the properties hypothesized for it by Dyson.

Dyson's crank

Let n be a non-negative integer and let p(n) denote the number of partitions of n (p(0) is defined to be 1). Srinivasa Ramanujan in a paper published in 1918 stated and proved the following congruences for the partition function p(n), since known as Ramanujan congruences.

These congruences imply that partitions of numbers of the form 5n + 4 (respectively, of the forms 7n + 5 and 11n + 6 ) can be divided into 5 (respectively, 7 and 11) subclasses of equal size. The then known proofs of these congruences were based on the ideas of generating functions and they did not specify a method for the division of the partitions into subclasses of equal size.

Crank, Merseyside

Coordinates: 53°29′35″N 2°45′00″W / 53.493°N 2.750°W / 53.493; -2.750

Crank is a village near Rainford, Merseyside, England in the Metropolitan Borough of St Helens. Historically part of Lancashire, it is known locally for its ghost stories 'The White Rabbit of Crank' and 'Crank Caverns'.

The village had one public house - The Red Cat, which closed in August 2015.

See also

Crank (surname)

Crank is a surname. Notable people with the surname include:

See also

Unité

Unité is a mobile network operator in Moldova. Working in CDMA, UMTS and LTE standards.

General information

Communication standard: Unité has a license to work in CDMA standard on frequency of 450 MHz as well as in UMTS standard on frequencies of 2100 MHz and 900 MHz.

Numbering resources:
Unité network codes are:

Internationally they have the form:

Network code:
For CDMA standard: 259 03, where 259 — Mobile Country Code (MCC) for Moldova, and 03 — Mobile Network Code (MNC) for Unité network.
For UMTS standard: 259 05, where 259 — Mobile Country Code (MCC) for Moldova, and 05 — Mobile Network Code (MNC) for Unité network.

History

Unité began its activity on March 1, 2007 as CDMA operator. On April 1, 2010 Unité launched its own 3.5G network.

Mobile Internet

Unité offers mobile internet services via CDMA standard under the brand of "Connect" with speeds up to 2.4 Mbit/s and via 3.5G under the brand of "3G Connect" with speeds up to 14.4 Mbit/s

Ownership

Moldtelecom is 100% shareholder of the operator.

Unit of alcohol

Units of alcohol are used in the United Kingdom (UK) as a measure to quantify the actual alcoholic content within a given volume of an alcoholic beverage, in order to provide guidance on total alcohol consumption.

A number of other countries (including Australia, Canada, New Zealand, and the US) use the concept of a "standard drink", the definition of which varies from country to country, for the same purpose. "Standard drinks" were referred to in the first UK guidelines (1984) that published "safe limits" for drinking, but these were replaced by references to "alcohol units" in the 1987 guidelines and the latter term has been used in all subsequent UK guidance.

One unit of alcohol (UK) is defined as 10 millilitres (8 grams) of pure alcohol. Typical drinks (i.e. typical quantities or servings of common alcoholic beverages) may contain 1–3 units of alcohol.

Containers of alcoholic beverages sold directly to UK consumers are normally labelled to indicate the number of units of alcohol in a typical serving of the beverage (optional) and in the full container (can or bottle), as well as information about responsible drinking. Additionally, the advent of smartphones has led to the creation of apps which report the number of units contained in an alcoholic drink.

Military organization

Military organization or military organisation is the structuring of the armed forces of a state so as to offer military capability required by the national defense policy. In some countries paramilitary forces are included in a nation's armed forces, though not considered military. Armed forces that are not a part of military or paramilitary organizations, such as insurgent forces, often mimic military organizations, or use ad hoc structures.

Military organization is hierarchical. The use of formalized ranks in a hierarchical structure came into widespread use with the Roman Army. In modern times, executive control, management and administration of military organization is typically undertaken by the government through a government department within the structure of public administration, often known as a Ministry of Defense, Department of Defense, or Department of War. These in turn manage Armed Services that themselves command combat, combat support and service support formations and units.