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Possible Answers:
DUAL.
Last seen on: Daily Crossword Club Crossword Thursday, 6 July 2023
Random information on the term “Twinned”:
A sister city or a twin town relationship is a form of legal or social agreement between two geographically and politically distinct localities for the purpose of promoting cultural and commercial ties.
While there are early examples of international links between municipalities akin to what are known as sister cities or twin towns today dating back to the 9th century, the modern concept was first established and adopted worldwide during World War II.
The modern concept of town twinning has its roots in the Second World War. More specifically, it was inspired by the bombing of Coventry on 14 November 1940, known as the Coventry Blitz. First conceived by the then Mayor of Coventry, Alfred Robert Grindlay, culminating in his renowned telegram to the people of Stalingrad (now Volgograd) in 1942, the idea emerged as a way of establishing solidarity links between cities in allied countries that went through similar devastating events. The comradeship between the two cities continued, when again in response to the Battle of Stalingrad, 830 women in Coventry – led by the subsequent Mayor Emily Smith – had their names embroidered on a tablecloth along with the words “Little help is better than big sympathy” and sent it, along with money (each donated six pence), to the people of Stalingrad. The tablecloth can now be seen at the Panorama Museum of the Battle of Stalingrad. The twinning between Coventry and Stalingrad was formalised in 1944 and, after the end of the war, similar links were established to foster friendship and understanding among former foes as an act of peace and reconciliation, with new twinnings between Coventry and German cities: Kiel as early as in 1947 and Dresden in 1956. In 1957, Coventry was officially twinned with Belgrade, however, the link actually dates back to 1953 when the Yugoslav Ambassador visited Coventry and offered a gift of timber from his native country for use in the new Civic Theatre, which when finished was named The Belgrade Theatre.
Random information on the term “DUAL”:
In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual of A is A itself. For example, Desargues’ theorem is self-dual in this sense under the standard duality in projective geometry.
In mathematical contexts, duality has numerous meanings. It has been described as “a very pervasive and important concept in (modern) mathematics” and “an important general theme that has manifestations in almost every area of mathematics”.
Many mathematical dualities between objects of two types correspond to pairings, bilinear functions from an object of one type and another object of the second type to some family of scalars. For instance, linear algebra duality corresponds in this way to bilinear maps from pairs of vector spaces to scalars, the duality between distributions and the associated test functions corresponds to the pairing in which one integrates a distribution against a test function, and Poincaré duality corresponds similarly to intersection number, viewed as a pairing between submanifolds of a given manifold.