Since Cauchy sequences can also be defined in general topological groups, an alternative to relying on a metric structure for defining completeness and constructing the completion of a space is to use a group structure.

Since the latter is valid over the entire cycle, this gave Clausius the hint that at each stage of the cycle, work and heat would not be equal, but rather their difference would be a state function that would vanish upon completion of the cycle.

Since its completion, the UPWT facility has been the most heavily used NASA wind tunnel.

Since the completion of the initial portion of the interstate highway system, regulations were changed, and portions of toll facilities have been added to the system.

Since the completion of the conversion carried out between 1993 and 1995, Carré des Arts hosts the Graduate School of Arts and visual ( ESAPV ) and regional television TV Borinage Mons ( Tele MB ).

Since the MAPS projects ' completion, the downtown area has seen continued development.

Since completion, the Columbus Lighthouse, which supposedly houses Columbus ' remains, has been a minor tourist attraction.

Since completion of the River Common, various improvements to city infrastructure have been progressing.

Since the completion of the Interstate system and the growth of Nashville, Williamson County has seen tremendous growth.

Since the early 1970s and the completion of Interstate 71, which connects Oldham County to Downtown Louisville and shopping in Eastern Jefferson County, Oldham County has increasingly become suburban in nature, a natural extension of Louisville's wealthy East End as it ran out of large tracts of undeveloped land.

Since its completion in 1995, the AA Highway has allowed Greenup residents to more easily travel to Maysville, Kentucky as well as Northern Kentucky and Cincinnati, Ohio.

Since the completion of the reservoir system, the highest Chattanooga flood stage has been nearly 37 feet, which occurred in 1973.

Since the completion of the Greenbelt, many subdivisions have been built along or near the belt to allow for easy access to I-264 and I-265.

Since completion, several new medical practices have opened there.

Since the completion of Interstate 195 and Interstate 295, which intersect southwest of the circle, much of the traffic that would have passed through the circle now uses the wider, faster freeways.

Since the completion of the Main Street USA project in the 1980s, Conway's downtown has been revitalized with shops and bistros.

Since its completion, the span length has been surpassed by eight other bridges.

Since its completion, the building has won a number of prestigious awards for architecture.

Since the completion of the Trans-Alaska Pipeline System in 1977, the government of the state of Alaska has been reliant on taxes paid by oil producers and shippers.

Since the completion of the present Winchester High School in 1972, with population growth leveling off, town leaders have had more time and funds to devote to maintaining rather than molding Winchester's character.

Since the international terminal's original completion, it has undergone two large expansions.

Since the completion of the Torrão Damn in 1988, situated less than 1 km from the outlet into the Douro river and the town of Entre-os-Rios in the municipality of Marco de Canaveses, the Tâmega has been slowly recovering from the effects of pollution.

Since its completion in 2002, the square has hosted numerous public events, performances and art displays, establishing itself as a prominent landmark in Toronto and one of the city's prime tourist attractions.

Since then, a lull of inactivity that would last three years would come about, and since then Ancient have parted ways with Metal Blade Records due to the completion of their recording contract and the label's " supposed " loss of interest in the black metal genre.

Since 1999, the Confederated Tribes of Warm Springs have been pursuing an off-reservation casino to be sited in Cascade Locks.

Since in the open air, as many engines as needed can be added to a train to overcome a steep gradient, a better solution would have been to have a level tunnel from " New Tye " ( West ) to Cascade Tunnel Station ( West ), with a 2. 6 mile stretch of say 4 % gradient ( 1 in 25 ) on the western approaches from say Windy Point Tunnel.

Since 1968, Frederick Douglass High School has served the communities of Historic Collier Heights, Peyton Forest, Cascade Heights and Center Hill and the city of Atlanta.

Since construction of the Aswan Dam, agriculture in the Nile valley depends on irrigation.

Since Zambia's independence, two dams have been built on the Kafue River: the Kafue Gorge Dam and the Itezhi-Tezhi Dam.

Since a large part of the original railway line is now submerged by the Vajiralongkorn Dam, and the surrounding terrain is mountainous, it would take extensive tunneling to reconnect Thailand with Burma by rail.

Since the opening of the W. Kerr Scott Dam in 1962, the Yadkin River has not flooded in the county.

Since the 1950s, the name commonly refers to the High Dam.

Since the delta no longer receives an annual supply of nutrients and sediments from upstream due to the construction of the Aswan High Dam, the soils of the floodplains have become poorer, and large amounts of fertilizers are now used.

Since it was last full in 1998 the Warragamba Dam catchment area experienced extremely low rainfall, and on 8 February 2007 the lake recorded an all time low of 32. 5 % of capacity, although this had returned to 60 % by late 2008.

Since the construction of the Clyde Dam and the filling of Lake Dunstan in the early 1990s the river confluence was drowned, as was the old town centre.

Since its construction, Seven Oaks Dam has not yet been filled to capacity.

Since 1917, the water level in the lake has been regulated by the United States Bureau of Reclamation ( BOR )' s Link River Dam as part of the Klamath Reclamation Project, to supply irrigation waters to support agriculture in the upper Klamath Basin.

Since 1967, the headwaters of the Feather River at the confluence of its four forks have been submerged under the waters of Lake Oroville, created by the construction of Oroville Dam in 1967.

Since its completion, Oroville Dam has controlled the flow of the Feather River for diversion into the SWP California Aqueduct, which provides a major irrigation water supply to the Central Valley and municipal water to coastal Southern California, and has prevented large amounts of flood damage – more than $ 1. 3 billion between 1987 and 1999 alone.

Since 1929 Loch Treig has been a reservoir, retained behind the Treig Dam, forming part of the Lochaber hydro-electric scheme, which required diversion of the West Highland Railway.

Since the lower dam-known as the Pipehead Dam has been constructed in the 1970s, flooding of the lower Helena River ( in East Guildford and Guildford ) has been substantially reduced.

Since completion in 1952, the Conemaugh River Dam has prevented over $ 2 billion in damage.

Since the rise of tourism on the west coast, the Franklin Dam issue and the creation of the world heritage wilderness area a steady number of small publications concerning the history and features of the region have been produced.

Since 2006, the archaeologists working for the Merowe Dam Archaeological Salvage Project became accused by environmental and human rights activists as well as the representatives of the affected people of facilitating the political legitimatization of the project.

Since Hardap Dam was built in 1962 floods also have taken place in 1972 and twice in 2000 with previous floods ( before the dam was built ) recorded in 1923 and 1934.

Since construction of Googong Dam in 1979, the endangered Macquarie perch has been very occasionally reported in the reservoir, and rarely beyond the first waterfall upstream of Googong Dam, despite the introduction of 57 Macquarie perch in the 1980s.