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Utrecht (ˈjuːtrɛkt , ˈytrɛxt, Utrecht dialect: Utreg ˈytʁɛχ) is the fourth-largest city and a municipality of the Netherlands, capital and most populous city of the province of Utrecht. It is located in the eastern corner of the Randstad conurbation, in the very centre of mainland Netherlands. It has a population of 361,699 as of . Utrecht's ancient city centre features many buildings and structures, several dating as far back as the High Middle Ages. It has been the religious centre of the Netherlands since the 8th century. In 1579, the Union of Utrecht was signed in the city to lay the foundations for the Dutch Republic. Utrecht was the most important city in the Netherlands until the Dutch Golden Age, when it was surpassed by Amsterdam as the country's cultural centre and most populous city. Utrecht is home to Utrecht University, the largest university in the Netherlands, as well as several other institutions of higher education. Due to its central position within the country, it is an important hub for both rail and road transport; it has the busiest train station in the Netherlands, Utrecht Centraal. It has the second-highest number of cultural events in the Netherlands, after Amsterdam. In 2012, Lonely Planet included Utrecht in the top 10 of the world's unsung places. Although there is some evidence of earlier inhabitation in the region of Utrecht, dating back to the Stone Age (app. 2200 BCE) and settling in the Bronze Age (app. 1800–800 BCE), the founding date of the city is usually related to the construction of a Roman fortification (castellum), probably built in around 50 CE. A series of such fortresses were built after the Roman emperor Claudius decided the empire should not expand further north. To consolidate the border, the Limes Germanicus defense line was constructed along the main branch of the river Rhine, which at that time traversed a more northern route (now known as the Kromme Rijn) compared to today's Rhine flow. These fortresses were designed to house a cohort of about 500 Roman soldiers.

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Dutch language

Dutch (Nederlands ˈneːdərlɑnts), also known as Netherlandic or Netherlandish, is a West Germanic language spoken by about 25 million people as a first language and 5 million as a second language. It is the third most widely spoken Germanic language, after its close relatives German and English. Afrikaans is a separate but somewhat mutually intelligible daughter language spoken, to some degree, by at least 16 million people, mainly in South Africa and Namibia, evolving from the Cape Dutch dialects of Southern Africa.

Utrecht (province)

Utrecht (ˈytrɛxt), officially the Province of Utrecht (Provincie Utrecht), is a province of the Netherlands. It is located in the centre of the country, bordering the Eemmeer in the north-east, the province of Gelderland in the east and south-east, the province of South Holland in the west and south-west and the province of North Holland in the north-west and north. The province of Utrecht has a population of 1,353,596 as of November 2019. With a land area of approximately , it is the smallest province in the country.

Utrecht

Covers the expression of the Kirchhoff-Saint Venant energy in a covariant setting and explores equilibrium equations for spherical shells and linear shell theory.

Covers the dimensional reduction of strain energy from 3D to 2D and linear shell theory equilibrium equations.

Covers the expression of the Kirchhoff-St. Venant energy in a covariant setting and the equilibrium equations for spherical shells, among other topics.