title: Pia Mia

text: On May 25, 2017, Pia released the single "I'm a Fan" featuring Jeremih. Pia Mia parted ways with Interscope Records and Wolfpack Entertainment, both divisions of Universal Music Group in late 2017. She stated that she didn't have enough creative freedom under the label and that there were excessive delays with her music. On December 15, she self-released her second EP "The Gift 2", which was preceded by the promotional single, "Off My Feet", released on December 1, 2017.


title: Pia Mia

text: In 2019, Perez made her acting debut, portraying Tristan in the film "After". Correspondingly, she released the single, "Bitter Love", which served as the film's theme song. On June 20, 2019, Perez released "Crybaby" featuring Theron Theron as a promotional single. Following this, she released promotional singles "Feel Up" with American rapper YG on September 5, 2019, and "Don't Get Me Started" with rapper Gunna and producer Carnage on October 2, 2019. All four singles were released under Perez's independent record label Cherry Pie Records.


title: Pia Mia

text: On May 14, 2020, it was announced that Perez had signed to Electric Feel Entertainment and Republic Records. Perez released the single "Princess", her first single released under her new label, on May 15, 2020. In an interview with "Idolator", Perez confirmed the release of the single "Hot", which will feature on her upcoming debut studio album. "Hot" was released on July 24, 2020, later accompanied by a visualizer for the song, released on September 14. A remix of the song featuring Sean Paul and Flo Milli was released on October 27, 2020. A visualizer for the remix version was released on October 30.


title: Pia Mia

text: In 2020, Perez announced that she had written a book titled "The Princess Diaries: Sand, Glitter and Silicone" which will be released chapter by chapter via Wattpad. In September 2020, it was officially announced that Pia Mia had joined the content subscription service OnlyFans.


title: Pia Mia

text: On February 14, 2021, Perez released the song "Miss Me" on SoundCloud. Perez announced that the song's release was independent after parting ways with Republic Records and Electric Feel Entertainment. On October 1, 2021, Perez released the "My Side" EP, which was preceded by the singles "730" and "Only One". The EP is her first since 2017's "The Gift 2". A holiday EP titled "Christmas" was released one month after on November 1, 2021.


title: Ramayana: The Legend of Prince Rama

text: Ramayana: The Legend of Prince Rama is a 1993 Anime film co-produced by Japan and India and produced and directed by Yugo Sako and based on the Indian epic the "Ramayana". The film was directed by Koichi Sasaki and Ram Mohan, with music composed by Vanraj Bhatia.


title: Ramayana: The Legend of Prince Rama

text: In 1983, while working on "The Ramayana Relics" a documentary film about excavations by Dr. B. B. Lal near Allahabad in Uttar Pradesh (India) Yugo Sako came to know about the story of Ramayana. He liked the story of the Ramayana so much that he researched deeper into the topic and went on to read 10 versions of Ramayana in Japanese. After reading the Ramayana he wanted to adapt it into animation as he didn't think a live-action movie could capture the true essence of Ramayana, "Because Ram is God, I felt it was best to depict him in animation, rather than by an actor." TEM Co., Ltd. financed the production and a new production studio Nippon Ramayana Film Co., Ltd. was set up and the principal animation of the film began in 1990 with 450 artists on board. Indian animators guided their Japanese teammates with Indian customs and traditions depicted in the film like how dhotis are worn and how the children receive blessings from their elders.


title: Ramayana: The Legend of Prince Rama

text: "The Indian Express" misinterpreted Yugo Sako's "The Ramayana Relics" documentary and published that he was making a new Ramayana. Soon thereafter, a protest letter based on the misunderstanding from the Vishva Hindu Parishad was received by the Japanese Embassy in Delhi, which said that no foreigners could arbitrarily cinematize Ramayana because it was the great national heritage of India. After the misconceptions were cleared, Yugo Sako proposed the idea of an animated Ramayana to the VHP and the government. He told them that animation was a serious art form in Japan and it would help bring the Ramayana to a wider global audience. The Government agreed initially, but later declined his proposal for a bi-nation collaboration, saying the Ramayana is a very sensitive subject and cannot be portrayed as a cartoon. Also, the fact that the movie was being made at the height of the Ayodhya dispute, added to the controversy and axed the prospects of producing it in India. With no choice and support left, the movie was ultimately produced in Japan with nearly 450 artists from both nations contributing to its creation.


title: Ramayana: The Legend of Prince Rama

text: There are different songs for the Original English Version (sung in Sanskrit) and the Hindi Dub version (sung in Hindi), both are listed below. The lyrics are written by Vasant Dev (Sanskrit) and P.K. Mishra (Hindi).


title: Ramayana: The Legend of Prince Rama

text: The original English version with Sanskrit songs was worked on by teams from both countries and was screened for the first time at 24th International Film Festival of India, New Delhi, January 10–20, 1993. The film was also shown at the 1993 Vancouver International Film Festival.


title: Ramayana: The Legend of Prince Rama

text: The Hindi dub version was released in the late 1990s. Arun Govil, who is popularly known for playing the role of Rama in Ramayan (1987 TV series) voiced Prince Rama in the version. This film was distributed as a work in the 40th Anniversary of the Establishment of the Diplomatic Relations between Japan and India. The film was not released on a large scale as the Ram Janmabhoomi (Birthplace) Movement was at its peak and the movie made into controversy. But later it was released on TV channel Cartoon Network.


title: Ramayana: The Legend of Prince Rama

text: It was released in the United States as "Warrior Prince" or "The Prince of Light: The Legend of Ramayana" by Krishna Shah, further localized English dub with narration by James Earl Jones, prince Rama voiced by Bryan Cranston and additional music by Alan Howarth. That version was released on November 9, 2001.


title: Ramayana: The Legend of Prince Rama

text: It was the opening film of the 2000 Lucca Animation Film Festival in Italy, a highlight of the Cardiff Animation Film Festival in the United Kingdom and won Best Animation Film of the Year at the 2000 Santa Clarita International Film Festival in the United States.


title: Ramayana: The Legend of Prince Rama

text: 2022 will be an important year for both countries as they will mark 70 years of India-Japan relations. On the occasion of 70th Anniversary Year, the remaster of this film will be launched during the 5th edition of Japanese Film Festival in India, along with 10 other films.


title: Ramayana: The Legend of Prince Rama

text: The specific 2022 edition of the original film will be called the Anniversary Edition. This edition of the film will be a 4K Remaster version of the original film with stereo audio and better graphics and visuals as tech use in the original film is old. This will be also the first time that this anime movie will be released theatrically, following with releases in DVDs, Blu-rays and OTT platforms.


title: Ramayana: The Legend of Prince Rama

text: When it was screened at the Vancouver International Film Festival, festival director Alan Franey called the film "Extraordinary", and said "The backgrounds are done in beautiful detail, while the foreground characters are an Indian version of the Disney style, with big dewey eyes."


title: Ramayana: The Legend of Prince Rama

text: The film won "Best Animation Film of the Year" award at the Santa Clarita International Family Film Festival. In 2001, Academy of Motion Picture Arts & Sciences announced a new category, Academy Award for Best Animated Feature. Ramayana was one of nine films that qualified to be nominated.


title: Ramayana: The Legend of Prince Rama

text: Ken Eisner writing in "Variety" in 1993 was critical of the film, saying the film is "Relentlessly paced, pic has no heart" and it is "and is not even great to look at". Robert Koehler reviewed the film again in 2001 for "Variety", also giving it a critical review. He described the film as "A curious fusion of an interesting if simplified literary adaptation with emphatically second-rate animation technique" and said "the blatantly American vocal casting and direction are painfully out of kilter with the 5,000-year-old Indian setting".


title: The 6th Day

text: The 6th Day is a 2000 American science fiction action film directed by Roger Spottiswoode and starring Arnold Schwarzenegger, Tony Goldwyn, Michael Rapaport, and Robert Duvall. In the film, a family man of the future is illegally cloned by accident as part of a vast conspiracy involving a shady billionaire businessman, and is thrust into a struggle to clear his name and protect his family from the conspirators who seek to keep the cloning a secret. The title refers to the Judeo-Christian Genesis creation narrative, where God created mankind on the sixth day. The film was Terry Crews' acting debut.


title: The 6th Day

text: Schwarzenegger received a salary of $25 million for his role in the film. The film received mixed reviews and was a box office failure, earning $96 million worldwide on a budget of $82 million.


title: The 6th Day

text: In the near future, animal cloning has become routine, but human cloning is prohibited by so-called "Sixth Day" laws.


title: The 6th Day

text: Charter pilot Adam Gibson is hired for a snowboarding excursion by Michael Drucker, billionaire owner of cloning corporation Replacement Technologies, who requires him to undergo a seemingly routine drug test. When Adam’s wife informs him that their daughter’s dog has died, he reluctantly visits one of Drucker’s “RePet” cloning stores, while his partner Hank poses as Adam and flies Drucker to the mountains, where they are killed by an assassin, Tripp.


title: The 6th Day

text: Buying a life-size animatronic “SimPal” doll for his daughter instead, Adam returns home to discover a clone of himself with his family. Before he can intervene, Adam is abducted by Marshall, Drucker’s head of security, and his agents Talia, Vincent, and Wiley. Adam escapes, killing Talia and Wiley, and goes to the police but is believed to be an escaped mental patient.


title: The 6th Day

text: Drucker, somehow alive, assures reporters that he does not intend to have the Sixth Day laws repealed. However, he and his chief scientist, Dr. Griffin Weir, have already perfected illegal human cloning, and revive clones of Talia and Wiley. Adam breaks out of the police station and is forced to kill Wiley again, before finding Hank at his apartment, still alive. He brings Hank to his house and contemplates killing his clone, but Marshall and Talia arrive, forcing Adam to pose as his clone to send them away.


title: The 6th Day

text: Returning to his apartment, Hank is again killed by Tripp, who is shot by Adam. A dying Tripp reveals he is an anti-cloning extremist who assassinated Drucker, who was subsequently cloned along with Hank. Marshall and Talia arrive, but Adam escapes in their vehicle after shooting off Talia’s fingers, taking her thumb to bypass the car’s biometric lock. Adam uses the thumb to sneak into Replacement Technologies and confronts Dr. Weir, whose pursuit of cloning is driven by his wife Katherine’s liver cancer; she reveals to her husband that she knows she is the latest in a series of clones he has made in an attempt to cure her.


title: The 6th Day

text: Weir explains that the blood and vision tests Adam underwent scanned his DNA and memories — captured as a “syncording” — in the event he needed to be cloned. He reveals Drucker was secretly cloned after dying years earlier to maintain control of his fortune, as clones have no legal rights. Believing both Adam and Hank were killed alongside Drucker, Weir cloned them to return to their lives and cover up Drucker’s murder and second cloning. Weir gives Adam the syncording proving Drucker has been cloned, warning that he may go after Adam’s clone and family.


title: The 6th Day

text: Adam races to Clara’s school recital, where Talia and Vincent have already abducted his wife and daughter. Coming face-to-face with his own clone, Adam reveals their situation, and agrees to deliver the incriminating syncording to Drucker in exchange for his family. Weir confronts Drucker, who engineered the clones, including Katherine, with shortened lifespans as an insurance policy against betrayal. Drucker kills Weir, promising to resurrect him and Katherine as clones.


title: The 6th Day

text: Sending a decoy helicopter to be destroyed, Adam lands on Drucker’s helipad and wreaks havoc until he is captured. Drucker reveals that Adam is actually the clone, proven by a marking inside his eyelid, but realizes the real Adam has also infiltrated the building. While the original Adam rescues his family, his clone fights off Drucker’s agents. They are finally killed, and a mortally wounded Drucker clones himself again, but the malfunctioning equipment creates a deformed, incomplete body. Adam and his clone escape in the helicopter with his family, destroying the facility and all its syncordings as Drucker falls to his death.


title: The 6th Day

text: The real Adam arranges for his clone to start a new life in Argentina, running a satellite office of their charter business. As a parting gift, the clone gives the family Hank's RePet cat, and the real Adam gives his clone a flying send-off.


title: The 6th Day

text: "The 6th Day" premiered at the Tokyo International Film Festival. It was released theatrically on November 17, 2000.


title: The 6th Day

text: "The 6th Day" was released on VHS and DVD in the United States and Canada on March 27, 2001. The movie was released on video on the following dates:


title: The 6th Day

text: A Blu-ray version was released in the United States and Canada on April 8, 2008. It includes two featurettes but lacks the commentary from the DVD release.


title: The 6th Day

text: The film opened at #4 and grossed $13 million in its opening weekend. It eventually grossed $34 million in North America and $96 million worldwide, while "Variety" reports $116 million.


title: The 6th Day

text: On Rotten Tomatoes the film has an approval rating of 40% based on reviews from 117 critics, with a rating of 5.9/10. The site's consensus reads: "This offering from Arnold Schwarzenegger contains an intriguing, disturbing premise, but the film's execution is too routine and formulaic to make good use of it." On Metacritic the film has a score of 49 out of 100 based on reviews from 30 critics. Audiences polled by CinemaScore gave the film an average grade of "C" on an A+ to F scale.


title: The 6th Day

text: Roger Ebert of the "Chicago Sun-Times" gave "The 6th Day" three out of four stars, remarking that it is not in the same league as "Total Recall" and "", but that it nevertheless qualifies as a serious science fiction film. He also found problems with the cloning as depicted in the film, saying that "[his] problem with both processes is that while the resulting clone ... might know everything I know ... I myself would still be over here in the old container." Kenneth Turan of the "Los Angeles Times" disliked the generic appearance of the film and Schwarzenegger's typecasting as an action hero. He gave the film two out of five stars. Todd McCarthy of Variety called it: "A mostly standard-issue latter-day Arnold Schwarzenegger actioner spiked with a creepily plausible cloning angle."


title: The 6th Day

text: "The 6th Day" earned three Razzie Award nominations for Schwarzenegger: Worst Actor (as the real Adam), Worst Supporting Actor (as the clone of Adam) and Worst Screen Couple (Schwarzenegger as Adam and Schwarzenegger as the clone), but lost all three to "Battlefield Earth". The film was also nominated four times at the 27th Saturn Awards, but lost to "X-Men" for Best Actor and Best Science Fiction Film, "Hollow Man" for Best Special Effects and "How the Grinch Stole Christmas" for Best Make-Up.


title: Priority queue

text: In computer science, a priority queue is an abstract data-type similar to a regular queue or stack data structure in which each element additionally has a "priority" associated with it. In a priority queue, an element with high priority is served before an element with low priority. In some implementations, if two elements have the same priority, they are served according to the order in which they were enqueued; in other implementations ordering of elements with the same priority remains undefined.


title: Priority queue

text: While coders often implement priority queues with heaps, they are conceptually distinct from heaps. A priority queue is a concept like a list or a map; just as a list can be implemented with a linked list or with an array, a priority queue can be implemented with a heap or with a variety of other methods such as an unordered array.


title: Priority queue

text: In addition, "peek" (in this context often called "find-max" or "find-min"), which returns the highest-priority element but does not modify the queue, is very frequently implemented, and nearly always executes in "O"(1) time. This operation and its "O"(1) performance is crucial to many applications of priority queues.


title: Priority queue

text: More advanced implementations may support more complicated operations, such as "pull_lowest_priority_element", inspecting the first few highest- or lowest-priority elements, clearing the queue, clearing subsets of the queue, performing a batch insert, merging two or more queues into one, incrementing priority of any element, etc.


title: Priority queue

text: Stacks and queues can be implemented as particular kinds of priority queues, with the priority determined by the order in which the elements are inserted. In a stack, the priority of each inserted element is monotonically increasing; thus, the last element inserted is always the first retrieved. In a queue, the priority of each inserted element is monotonically decreasing; thus, the first element inserted is always the first retrieved.


title: Priority queue

text: There are a variety of simple, usually inefficient, ways to implement a priority queue. They provide an analogy to help one understand what a priority queue is.


title: Priority queue

text: For instance, one can keep all the elements in an unsorted list ("O"(1) insertion time). Whenever the highest-priority element is requested, search through all elements for the one with the highest priority. ("O"("n") pull time),


title: Priority queue

text: In another case, one can keep all the elements in a priority sorted list ("O"(n) insertion sort time), whenever the highest-priority element is requested, the first one in the list can be returned. ("O"(1) pull time)


title: Priority queue

text: To improve performance, priority queues are typically based on a heap, giving "O"(log "n") performance for inserts and removals, and "O"("n") to build the heap initially from a set of "n" elements. Variants of the basic heap data structure such as pairing heaps or Fibonacci heaps can provide better bounds for some operations.


title: Priority queue

text: Alternatively, when a self-balancing binary search tree is used, insertion and removal also take "O"(log "n") time, although building trees from existing sequences of elements takes "O"("n" log "n") time; this is typical where one might already have access to these data structures, such as with third-party or standard libraries. From a space-complexity standpoint, using self-balancing binary search tree with linked list takes more storage, since it requires to store extra references to other nodes.


title: Priority queue

text: From a computational-complexity standpoint, priority queues are congruent to sorting algorithms. The section on the equivalence of priority queues and sorting algorithms, below, describes how efficient sorting algorithms can create efficient priority queues.


title: Priority queue

text: There are several specialized heap data structures that either supply additional operations or outperform heap-based implementations for specific types of keys, specifically integer keys. Suppose the set of possible keys is {1, 2, ..., C}.


title: Priority queue

text: For applications that do many "peek" operations for every "extract-min" operation, the time complexity for peek actions can be reduced to "O"(1) in all tree and heap implementations by caching the highest priority element after every insertion and removal. For insertion, this adds at most a constant cost, since the newly inserted element is compared only to the previously cached minimum element. For deletion, this at most adds an additional "peek" cost, which is typically cheaper than the deletion cost, so overall time complexity is not significantly impacted.


title: Priority queue

text: Monotone priority queues are specialized queues that are optimized for the case where no item is ever inserted that has a lower priority (in the case of min-heap) than any item previously extracted. This restriction is met by several practical applications of priority queues.


title: Priority queue

text: The semantics of priority queues naturally suggest a sorting method: insert all the elements to be sorted into a priority queue, and sequentially remove them; they will come out in sorted order. This is actually the procedure used by several sorting algorithms, once the layer of abstraction provided by the priority queue is removed. This sorting method is equivalent to the following sorting algorithms:


title: Priority queue

text: We present a general deterministic linear space reduction from priority queues to sorting implying that if we can sort up to "n" keys in "S"("n") time per key, then there is a priority queue supporting "delete" and "insert" in "O"("S"("n")) time and "find-min" in constant time.


title: Priority queue

text: That is, if there is a sorting algorithm which can sort in "O"("S") time per key, where "S" is some function of "n" and word size, then one can use the given procedure to create a priority queue where pulling the highest-priority element is "O"(1) time, and inserting new elements (and deleting elements) is "O"("S") time. For example, if one has an "O"("n" log "n") sort algorithm, one can create a priority queue with "O"(1) pulling and "O"( log "n") insertion.


title: Priority queue

text: The Standard Template Library (STL), and the C++ 1998 standard, specifies std::priority_queue as one of the STL container adaptor class templates. However, it does not specify how two elements with same priority should be served, and indeed, common implementations will not return them according to their order in the queue. It implements a max-priority-queue, and has three parameters: a comparison object for sorting such as a function object (defaults to less<T> if unspecified), the underlying container for storing the data structures (defaults to std::vector<T>), and two iterators to the beginning and end of a sequence. Unlike actual STL containers, it does not allow iteration of its elements (it strictly adheres to its abstract data type definition). STL also has utility functions for manipulating another random-access container as a binary max-heap. The Boost libraries also have an implementation in the library heap.


title: Priority queue

text: .NET's library contains a PriorityQueue class, which implements an array-backed, quaternary min-heap.


title: Priority queue

text: Go's library contains a container/heap module, which implements a min-heap on top of any compatible data structure.


title: Priority queue

text: Priority queuing can be used to manage limited resources such as bandwidth on a transmission line from a network router. In the event of outgoing traffic queuing due to insufficient bandwidth, all other queues can be halted to send the traffic from the highest priority queue upon arrival. This ensures that the prioritized traffic (such as real-time traffic, e.g. an RTP stream of a VoIP connection) is forwarded with the least delay and the least likelihood of being rejected due to a queue reaching its maximum capacity. All other traffic can be handled when the highest priority queue is empty. Another approach used is to send disproportionately more traffic from higher priority queues.


title: Priority queue

text: Many modern protocols for local area networks also include the concept of priority queues at the media access control (MAC) sub-layer to ensure that high-priority applications (such as VoIP or IPTV) experience lower latency than other applications which can be served with best-effort service. Examples include IEEE 802.11e (an amendment to IEEE 802.11 which provides quality of service) and ITU-T G.hn (a standard for high-speed local area network using existing home wiring (power lines, phone lines and coaxial cables).


title: Priority queue

text: Usually a limitation (policer) is set to limit the bandwidth that traffic from the highest priority queue can take, in order to prevent high priority packets from choking off all other traffic. This limit is usually never reached due to high level control instances such as the Cisco Callmanager, which can be programmed to inhibit calls which would exceed the programmed bandwidth limit.


title: Priority queue

text: Another use of a priority queue is to manage the events in a discrete event simulation. The events are added to the queue with their simulation time used as the priority. The execution of the simulation proceeds by repeatedly pulling the top of the queue and executing the event thereon.


title: Priority queue

text: When the graph is stored in the form of adjacency list or matrix, priority queue can be used to extract minimum efficiently when implementing Dijkstra's algorithm, although one also needs the ability to alter the priority of a particular vertex in the priority queue efficiently.


title: Priority queue

text: If instead, a graph is stored as node objects, and priority-node pairs are inserted into a heap, altering the priority of a particular vertex is not necessary if one tracks visited nodes. Once a node is visited, if it comes up in the heap again (having had a lower priority number associated with it earlier), it is popped-off and ignored.


title: Priority queue

text: Huffman coding requires one to repeatedly obtain the two lowest-frequency trees. A priority queue is one method of doing this.


title: Priority queue

text: Best-first search algorithms, like the A* search algorithm, find the shortest path between two vertices or nodes of a weighted graph, trying out the most promising routes first. A priority queue (also known as the "fringe") is used to keep track of unexplored routes; the one for which the estimate (a lower bound in the case of A*) of the total path length is smallest is given highest priority. If memory limitations make best-first search impractical, variants like the SMA* algorithm can be used instead, with a double-ended priority queue to allow removal of low-priority items.


title: Priority queue

text: The Real-time Optimally Adapting Meshes (ROAM) algorithm computes a dynamically changing triangulation of a terrain. It works by splitting triangles where more detail is needed and merging them where less detail is needed. The algorithm assigns each triangle in the terrain a priority, usually related to the error decrease if that triangle would be split. The algorithm uses two priority queues, one for triangles that can be split and another for triangles that can be merged. In each step the triangle from the split queue with the highest priority is split, or the triangle from the merge queue with the lowest priority is merged with its neighbours.


title: Priority queue

text: Using min heap priority queue in Prim's algorithm to find the minimum spanning tree of a connected and undirected graph, one can achieve a good running time. This min heap priority queue uses the min heap data structure which supports operations such as "insert", "minimum", "extract-min", "decrease-key". In this implementation, the weight of the edges is used to decide the priority of the vertices. Lower the weight, higher the priority and higher the weight, lower the priority.


title: Priority queue

text: Parallelization can be used to speed up priority queues, but requires some changes to the priority queue interface. The reason for such changes is that a sequential update usually only has formula_2 or formula_3 cost, and there is no practical gain to parallelize such an operation. One possible change is to allow the concurrent access of multiple processors to the same priority queue. The second possible change is to allow batch operations that work on formula_4 elements, instead of just one element. For example, "extractMin" will remove the first formula_4 elements with the highest priority.


title: Priority queue

text: If the priority queue allows concurrent access, multiple processes can perform operations concurrently on that priority queue. However, this raises two issues. First of all, the definition of the semantics of the individual operations is no longer obvious. For example, if two processes want to extract the element with the highest priority, should they get the same element or different ones? This restricts parallelism on the level of the program using the priority queue. In addition, because multiple processes have access to the same element, this leads to contention.


title: Priority queue

text: The concurrent access to a priority queue can be implemented on a Concurrent Read, Concurrent Write (CRCW) PRAM model. In the following the priority queue is implemented as a skip list. In addition, an atomic synchronization primitive, CAS, is used to make the skip list lock-free. The nodes of the skip list consists of a unique key, a priority, an array of pointers, for each level, to the next nodes and a "delete" mark. The "delete" mark marks if the node is about to be deleted by a process. This ensures that other processes can react to the deletion appropriately.


title: Priority queue

text: If the concurrent access to a priority queue is allowed, conflicts may arise between two processes. For example, a conflict arises if one process is trying to insert a new node, but at the same time another process is about to delete the predecessor of that node. There is a risk that the new node is added to the skip list, yet it is not longer reachable. ()


title: Priority queue

text: For instance, "k_extract-min" deletes the formula_4 smallest elements of the priority queue and returns those.


title: Priority queue

text: In a shared-memory setting, the parallel priority queue can be easily implemented using parallel binary search trees and join-based tree algorithms. In particular, "k_extract-min" corresponds to a "split" on the binary search tree that has formula_3 cost and yields a tree that contains the formula_4 smallest elements. "k_insert" can be applied by a "union" of the original priority queue and the batch of insertions. If the batch is already sorted by the key, "k_insert" has formula_10 cost. Otherwise, we need to first sort the batch, so the cost will be formula_11. Other operations for priority queue can be applied similarly. For instance, "k_decrease-key" can be done by first applying "difference" and then "union", which first deletes the elements and then inserts them back with the updated keys. All these operations are highly parallel, and the theoretical and practical efficiency can be found in related research papers.


title: Priority queue

text: The rest of this section discusses a queue-based algorithm on distributed memory. We assume each processor has its own local memory and a local (sequential) priority queue. The elements of the global (parallel) priority queue are distributed across all processors.


title: Priority queue

text: A "k_insert" operation assigns the elements uniformly random to the processors which insert the elements into their local queues. Note that single elements can still be inserted into the queue. Using this strategy the global smallest elements are in the union of the local smallest elements of every processor with high probability. Thus each processor holds a representative part of the global priority queue.


title: Priority queue

text: This property is used when "k_extract-min" is executed, as the smallest formula_12 elements of each local queue are removed and collected in a result set. The elements in the result set are still associated with their original processor. The number of elements formula_12 that is removed from each local queue depends on formula_4 and the number of processors formula_15.


title: Priority queue

text: By parallel selection the formula_4 smallest elements of the result set are determined. With high probability these are the global formula_4 smallest elements. If not, formula_12 elements are again removed from each local queue and put into the result set. This is done until the global formula_4 smallest elements are in the result set. Now these formula_4 elements can be returned. All other elements of the result set are inserted back into their local queues. The running time of "k_extract-min" is expected formula_21, where formula_22 and formula_23 is the size of the priority queue.


title: Priority queue

text: The priority queue can be further improved by not moving the remaining elements of the result set directly back into the local queues after a "k_extract-min" operation. This saves moving elements back and forth all the time between the result set and the local queues.


title: Priority queue

text: By removing several elements at once a considerable speedup can be reached. But not all algorithms can use this kind of priority queue. Dijkstra's algorithm for example can not work on several nodes at once. The algorithm takes the node with the smallest distance from the priority queue and calculates new distances for all its neighbor nodes. If you would take out formula_4 nodes, working at one node could change the distance of another one of the formula_4 nodes. So using k-element operations destroys the label setting property of Dijkstra's algorithm.


title: Overhead power line

text: An overhead power line is a structure used in electric power transmission and distribution to transmit electrical energy across large distances. It consists of one or more uninsulated electrical cables (commonly multiples of three for three-phase power) suspended by towers or poles.


title: Overhead power line

text: Since most of the insulation is provided by the surrounding air, overhead power lines are generally the least costly method of power transmission for large quantities of electric energy.


title: Overhead power line

text: Towers for support of the lines are made of wood either grown or laminated, steel or aluminum (either lattice structures or tubular poles), concrete, and occasionally reinforced plastics. The bare wire conductors on the line are generally made of aluminum (either plain or reinforced with steel or composite materials such as carbon and glass fiber), though some copper wires are used in medium-voltage distribution and low-voltage connections to customer premises. A major goal of overhead power line design is to maintain adequate clearance between energized conductors and the ground so as to prevent dangerous contact with the line, and to provide reliable support for the conductors, resilience to storms, ice loads, earthquakes and other potential damage causes. Today overhead lines are routinely operated at voltages exceeding 765,000 volts between conductors.


title: Overhead power line

text: Overhead power transmission lines are classified in the electrical power industry by the range of voltages:


title: Overhead power line

text: The overhead transmission line is generally categorized into three classes, depending on the length of the line:


title: Overhead power line

text: This categorization is mainly done for the ease of performance analysis of transmission lines by power engineers.


title: Overhead power line

text: Structures for overhead lines take a variety of shapes depending on the type of line. Structures may be as simple as wood poles directly set in the earth, carrying one or more cross-arm beams to support conductors, or "armless" construction with conductors supported on insulators attached to the side of the pole. Tubular steel poles are typically used in urban areas. High-voltage lines are often carried on lattice-type steel towers or pylons. For remote areas, aluminum towers may be placed by helicopters. Concrete poles have also been used. Poles made of reinforced plastics are also available, but their high cost restricts application.


title: Overhead power line

text: Each structure must be designed for the loads imposed on it by the conductors. The weight of the conductor must be supported, as well as dynamic loads due to wind and ice accumulation, and effects of vibration. Where conductors are in a straight line, towers need only resist the weight since the tension in the conductors approximately balances with no resultant force on the structure. Flexible conductors supported at their ends approximate the form of a catenary, and much of the analysis for construction of transmission lines relies on the properties of this form.


title: Overhead power line

text: A large transmission line project may have several types of towers, with "tangent" ("suspension" or "line" towers, UK) towers intended for most positions and more heavily constructed towers used for turning the line through an angle, dead-ending (terminating) a line, or for important river or road crossings. Depending on the design criteria for a particular line, semi-flexible type structures may rely on the weight of the conductors to be balanced on both sides of each tower. More rigid structures may be intended to remain standing even if one or more conductors is broken. Such structures may be installed at intervals in power lines to limit the scale of cascading tower failures.


title: Overhead power line

text: Foundations for tower structures may be large and costly, particularly if the ground conditions are poor, such as in wetlands. Each structure may be stabilized considerably by the use of guy wires to counteract some of the forces applied by the conductors.


title: Overhead power line

text: Power lines and supporting structures can be a form of visual pollution. In some cases the lines are buried to avoid this, but this "undergrounding" is more expensive and therefore not common.


title: Overhead power line

text: For a single wood utility pole structure, a pole is placed in the ground, then three crossarms extend from this, either staggered or all to one side. The insulators are attached to the crossarms. For an "H"-type wood pole structure, two poles are placed in the ground, then a crossbar is placed on top of these, extending to both sides. The insulators are attached at the ends and in the middle. Lattice tower structures have two common forms. One has a pyramidal base, then a vertical section, where three crossarms extend out, typically staggered. The strain insulators are attached to the crossarms. Another has a pyramidal base, which extends to four support points. On top of this a horizontal truss-like structure is placed.


title: Overhead power line

text: A grounded wire is sometimes strung along the tops of the towers to provide lightning protection. An optical ground wire is a more advanced version with embedded optical fibers for communication. Overhead wire markers can be mounted on the ground wire to meet International Civil Aviation Organization recommendations. Some markers include flashing lamps for night-time warning.


title: Overhead power line

text: A "single-circuit transmission line" carries conductors for only one circuit. For a three-phase system, this implies that each tower supports three conductors.


title: Overhead power line

text: A "double-circuit transmission line" has two circuits. For three-phase systems, each tower supports and insulates six conductors. Single phase AC-power lines as used for traction current have four conductors for two circuits. Usually both circuits operate at the same voltage.


title: Overhead power line

text: In HVDC systems typically two conductors are carried per line, but in rare cases only one pole of the system is carried on a set of towers.


title: Overhead power line

text: In some countries, such as Germany, most power lines with voltages above 100 kV are implemented as double, quadruple or in rare cases even hextuple power line as rights of way are rare. Sometimes all conductors are installed with the erection of the pylons; often some circuits are installed later. A disadvantage of double circuit transmission lines is that maintenance can be difficult, as either work in close proximity of high voltage or switch-off of two circuits is required. In case of failure, both systems can be affected.


title: Overhead power line

text: Insulators must support the conductors and withstand both the normal operating voltage and surges due to switching and lightning. Insulators are broadly classified as either pin-type, which support the conductor above the structure, or suspension type, where the conductor hangs below the structure. The invention of the strain insulator was a critical factor in allowing higher voltages to be used.


title: Overhead power line

text: At the end of the 19th century, the limited electrical strength of telegraph-style pin insulators limited the voltage to no more than 69,000 volts. Up to about 33 kV (69 kV in North America) both types are commonly used. At higher voltages only suspension-type insulators are common for overhead conductors.


title: Overhead power line

text: Insulators are usually made of wet-process porcelain or toughened glass, with increasing use of glass-reinforced polymer insulators. However, with rising voltage levels, polymer insulators (silicone rubber based) are seeing increasing usage. China has already developed polymer insulators having a highest system voltage of 1100 kV and India is currently developing a 1200 kV (highest system voltage) line which will initially be charged with 400 kV to be upgraded to a 1200 kV line.


title: Overhead power line

text: Suspension insulators are made of multiple units, with the number of unit insulator disks increasing at higher voltages. The number of disks is chosen based on line voltage, lightning withstand requirement, altitude, and environmental factors such as fog, pollution, or salt spray. In cases where these conditions are suboptimal, longer insulators must be used. Longer insulators with longer creepage distance for leakage current, are required in these cases. Strain insulators must be strong enough mechanically to support the full weight of the span of conductor, as well as loads due to ice accumulation, and wind.


title: Overhead power line

text: Porcelain insulators may have a semi-conductive glaze finish, so that a small current (a few milliamperes) passes through the insulator. This warms the surface slightly and reduces the effect of fog and dirt accumulation. The semiconducting glaze also ensures a more even distribution of voltage along the length of the chain of insulator units.


title: Overhead power line

text: Polymer insulators by nature have hydrophobic characteristics providing for improved wet performance. Also, studies have shown that the specific creepage distance required in polymer insulators is much lower than that required in porcelain or glass. Additionally, the mass of polymer insulators (especially in higher voltages) is approximately 50% to 30% less than that of a comparative porcelain or glass string. Better pollution and wet performance is leading to the increased use of such insulators.


title: Overhead power line

text: Insulators for very high voltages, exceeding 200 kV, may have grading rings installed at their terminals. This improves the electric field distribution around the insulator and makes it more resistant to flash-over during voltage surges.


title: Overhead power line

text: The most common conductor in use for transmission today is aluminum conductor steel reinforced (ACSR). Also seeing much use is all-aluminum-alloy conductor (AAAC). Aluminum is used because it has about half the weight and lower cost of a comparable resistance copper cable. It does, however, require a larger diameter than copper because of lower specific conductivity. Copper was more popular in the past and is still in use, especially at lower voltages and for grounding.


title: Overhead power line

text: While larger conductors lose less energy because of their lower electrical resistance, they cost more than smaller conductors. An optimization rule called "Kelvin's Law" states that the optimum size of conductor for a line is found when the cost of the energy wasted in a smaller conductor is equal to the annual interest paid on that additional cost of the line construction for a larger conductor. The optimization problem is made more complex by additional factors such as varying annual load, varying cost of installation, and the discrete sizes of cable that are commonly made.


title: Overhead power line

text: Since a conductor is a flexible object with uniform weight per unit length, the shape of a conductor hanging between two towers approximates that of a catenary. The sag of the conductor (vertical distance between the highest and lowest point of the curve) varies depending on the temperature and additional load such as ice cover. A minimum overhead clearance must be maintained for safety. Since the length of the conductor increases with increasing heat produced by the current through it, it is sometimes possible to increase the power handling capacity (uprate) by changing the conductors for a type with a lower coefficient of thermal expansion or a higher allowable operating temperature.


title: Overhead power line

text: Two such conductors that offer reduced thermal sag are known as composite core conductors (ACCR and ACCC conductor). In lieu of steel core strands that are often used to increase overall conductor strength, the ACCC conductor uses a carbon and glass fiber core that offers a coefficient of thermal expansion about 1/10 of that of steel. While the composite core is nonconductive, it is substantially lighter and stronger than steel, which allows the incorporation of 28% more aluminum (using compact trapezoidal-shaped strands) without any diameter or weight penalty. The added aluminum content helps reduce line losses by 25 to 40% compared to other conductors of the same diameter and weight, depending upon electric current. The carbon core conductor's reduced thermal sag allows it to carry up to twice the current ("ampacity") compared to all-aluminum conductor (AAC) or ACSR.


title: Overhead power line

text: The power lines and their surroundings must be maintained by linemen, sometimes assisted by helicopters with pressure washers or circular saws which may work three times faster. However this work often occurs in the dangerous areas of the helicopter height–velocity diagram, and the pilot must be qualified for this "human external cargo" method.


title: Overhead power line

text: For transmission of power across long distances, high voltage transmission is employed. Transmission higher than 132 kV poses the problem of corona discharge, which causes significant power loss and interference with communication circuits. To reduce this corona effect, it is preferable to use more than one conductor per phase, or bundled conductors. In addition to reducing corona, audible and radio noise (and associated electrical losses), bundled conductors also increase the amount of current that can be carried compared to a single conductor of equal aluminum content due to the skin effect (for AC lines).


title: Overhead power line

text: Bundle conductors consist of several parallel cables connected at intervals by spacers, often in a cylindrical configuration. The optimum number of conductors depends on the current rating, but typically higher-voltage lines also have higher current. American Electric Power is building 765 kV lines using six conductors per phase in a bundle. Spacers must resist the forces due to wind, and magnetic forces during a short circuit.


title: Overhead power line

text: Bundled conductors reduce the voltage gradient in the vicinity of the line. This reduces the possibility of corona discharge. At extra high voltage, the electric field gradient at the surface of a single conductor is high enough to ionize air, which wastes power, generates unwanted audible noise and interferes with communication systems. The field surrounding a bundle of conductors is similar to the field that would surround a single, very large conductor—this produces lower gradients which mitigates issues associated with high field strength. The transmission efficiency is improved as loss due to corona effect is countered.


title: Overhead power line

text: Bundled conductors cool themselves more efficiently due to the increased surface area of the conductors, further reducing line losses. When transmitting alternating current, bundle conductors also avoid the reduction in ampacity of a single large conductor due to the skin effect. A bundle conductor also has lower reactance, compared to a single conductor.


title: Overhead power line

text: While wind resistance is higher, wind-induced oscillation can be damped at bundle spacers. The ice and wind loading of bundled conductors will be greater than a single conductor of the same total cross section, and bundled conductors are more difficult to install than single conductors. Aeolian vibration is generally less pronounced on bundled conductors due to the effect of spacers and spacer dampers installed at relatively close intervals along the line.


title: Overhead power line

text: Overhead power lines are often equipped with a ground conductor (shield wire, static wire, or overhead earth wire). The ground conductor is usually grounded (earthed) at the top of the supporting structure, to minimize the likelihood of direct lightning strikes to the phase conductors. It also serves as a parallel path with the earth for fault currents. Very high-voltage transmission lines may have two ground conductors. These are either at the outermost ends of the highest cross beam, at two V-shaped mast points, or at a separate cross arm. Older lines may use surge arresters every few spans in place of a shield wire; this configuration is typically found in the more rural areas of the United States. By protecting the line from lightning, the design of apparatus in substations is simplified due to lower stress on insulation. Shield wires on transmission lines may include optical fibers (optical ground wires/OPGW), used for communication and control of the power system.


title: Overhead power line

text: At some HVDC converter stations, the ground wire is used also as the electrode line to connect to a distant grounding electrode. This allows the HVDC system to use the earth as one conductor. The ground conductor is mounted on small insulators bridged by lightning arrestors above the phase conductors. The insulation prevents electrochemical corrosion of the pylon.


title: Overhead power line

text: Medium-voltage distribution lines may also use one or two shield wires, or may have the grounded conductor strung below the phase conductors to provide some measure of protection against tall vehicles or equipment touching the energized line, as well as to provide a neutral line in Wye wired systems.


title: Overhead power line

text: On some power lines for very high voltages in the former Soviet Union, the ground wire is used for PLC-radio systems and mounted on insulators at the pylons.


title: Overhead power line

text: Overhead insulated cables are rarely used, usually for short distances (less than a kilometer). Insulated cables can be directly fastened to structures without insulating supports. An overhead line with bare conductors insulated by air is typically less costly than a cable with insulated conductors.


title: Overhead power line

text: A more common approach is "covered" line wire. It is treated as bare cable, but often is safer for wildlife, as the insulation on the cables increases the likelihood of a large-wing-span raptor to survive a brush with the lines, and reduces the overall danger of the lines slightly. These types of lines are often seen in the eastern United States and in heavily wooded areas, where tree-line contact is likely. The only pitfall is cost, as insulated wire is often costlier than its bare counterpart. Many utility companies implement covered line wire as jumper material where the wires are often closer to each other on the pole, such as an underground riser/pothead, and on reclosers, cutouts and the like.


title: Overhead power line

text: Because power lines can suffer from aeroelastic flutter and "galloping" oscillations driven by wind, tuned mass dampers are often attached to the line, to change the characteristics of the line's physical oscillations. A common type is the Stockbridge damper.


title: Overhead power line

text: A compact overhead transmission line requires a smaller right of way than a standard overhead powerline. Conductors must not get too close to each other. This can be achieved either by short span lengths and insulating crossbars, or by separating the conductors in the span with insulators. The first type is easier to build as it does not require insulators in the span, which may be difficult to install and to maintain.


title: Overhead power line

text: Compact transmission lines may be designed for voltage upgrade of existing lines to increase the power that can be transmitted on an existing right of way.


title: Overhead power line

text: Low voltage overhead lines may use either bare conductors carried on glass or ceramic insulators or an aerial bundled cable system. The number of conductors may be anywhere between two (most likely a phase and neutral) up to as many as six (three phase conductors, separate neutral and earth plus street lighting supplied by a common switch); a common case is four (three phase and neutral, where the neutral might also serve as a protective earthing conductor).


title: Overhead power line

text: Overhead lines or overhead wires are used to transmit electrical energy to trams, trolleybuses and trains. Overhead lines are designed on the principle of one or more overhead wires situated over rail tracks. Feeder stations at regular intervals along the overhead line supply power from the high-voltage grid. In some cases, low-frequency AC is used, and distributed by a special traction current network.


title: Overhead power line

text: Overhead lines are also occasionally used to supply transmitting antennas, especially for efficient transmission of long, medium and short waves. For this purpose a staggered array line is often used. Along a staggered array line the conductor cables for the supply of the earth net of the transmitting antenna are attached on the exterior of a ring, while the conductor inside the ring, is fastened to insulators leading to the high-voltage standing feeder of the antenna.


title: Overhead power line

text: Use of the area below an overhead line is limited because objects must not come too close to the energized conductors. Overhead lines and structures may shed ice, creating a hazard. Radio reception can be impaired under a power line, due both to shielding of a receiver antenna by the overhead conductors, and by partial discharge at insulators and sharp points of the conductors which creates radio noise.


title: Overhead power line

text: In the area surrounding the overhead lines, it is dangerous to risk interference, e.g. flying kites or balloons, using ladders, or operating machinery.


title: Overhead power line

text: Overhead distribution and transmission lines near airfields are often marked on maps, and the lines themselves marked with conspicuous plastic reflectors, to warn pilots of the presence of conductors.


title: Overhead power line

text: Construction of overhead power lines, especially in wilderness areas, may have significant environmental effects. Environmental studies for such projects may consider the effect of bush clearing, changed migration routes for migratory animals, possible access by predators and humans along transmission corridors, disturbances of fish habitat at stream crossings, and other effects.


title: Overhead power line

text: Linear parks will usually occupy the area under overhead power lines, to provide easy access, and prevent obstacles.


title: Overhead power line

text: General aviation, hang gliding, paragliding, skydiving, balloon, and kite flying must avoid accidental contact with power lines. Nearly every kite product warns users to stay away from power lines. Deaths occur when aircraft crash into power lines. Some power lines are marked with obstruction makers, especially near air strips or over waterways that may support floatplane operations. The placement of power lines sometimes use up sites that would otherwise be used by hang gliders.


title: Overhead power line

text: The first transmission of electrical impulses over an extended distance was demonstrated on July 14, 1729, by the physicist Stephen Gray. The demonstration used damp hemp cords suspended by silk threads (the low resistance of metallic conductors not being appreciated at the time).


title: Overhead power line

text: However the first practical use of overhead lines was in the context of telegraphy. By 1837 experimental commercial telegraph systems ran as far as 20 km (13 miles). Electric power transmission was accomplished in 1882 with the first high-voltage transmission between Munich and Miesbach (60 km). 1891 saw the construction of the first three-phase alternating current overhead line on the occasion of the International Electricity Exhibition in Frankfurt, between Lauffen and Frankfurt.


title: Overhead power line

text: In 1912 the first 110 kV-overhead power line entered service followed by the first 220 kV-overhead power line in 1923. In the 1920s RWE AG built the first overhead line for this voltage and in 1926 built a Rhine crossing with the pylons of Voerde, two masts 138 meters high.


title: Overhead power line

text: In 1953, the first 345 kV line was built by The L.E. Myers Co. and put into service by the Ohio Valley Electric Corporation in the United States. In Germany in 1957 the first 380 kV overhead power line was commissioned (between the transformer station and Rommerskirchen). In the same year the overhead line traversing of the Strait of Messina went into service in Italy, whose pylons served the Elbe crossing 1. This was used as the model for the building of the Elbe crossing 2 in the second half of the 1970s which saw the construction of the highest overhead line pylons of the world. Earlier, in 1952, the first 380 kV line was put into service in Sweden, in 1000 km (625 miles) between the more populated areas in the south and the largest hydroelectric power stations in the north. Starting from 1967 in Russia, and also in the US and Canada, overhead lines for voltage of 765 kV were built. In 1982 overhead power lines were built in Soviet Union between Elektrostal and the power station at Ekibastuz, this was a three-phase alternating current line at 1150 kV (Powerline Ekibastuz-Kokshetau). In 1999, in Japan the first powerline designed for 1000 kV with 2 circuits were built, the Kita-Iwaki Powerline. In 2003 the building of the highest overhead line commenced in China, the Yangtze River Crossing.


title: Overhead power line

text: An overhead power line is one example of a transmission line. At power system frequencies, many useful simplifications can be made for lines of typical lengths. For analysis of power systems, the distributed resistance, series inductance, shunt leakage resistance and shunt capacitance can be replaced with suitable lumped values or simplified networks.


title: Overhead power line

text: A short length of a power line (less than 80 km) can be approximated with a resistance in series with an inductance and ignoring the shunt admittances. This value is not the total impedance of the line, but rather the series impedance per unit length of line. For a longer length of line (80–250 km), a shunt capacitance is added to the model. In this case it is common to distribute half of the total capacitance to each side of the line. As a result, the power line can be represented as a two-port network, such as with ABCD parameters.


title: CS gas

text: The compound 2-chlorobenzalmalononitrile (also called "o"-chlorobenzylidene malononitrile; chemical formula: CHClN), a cyanocarbon, is the defining component of tear gas commonly referred to as CS gas, which is used as a riot control agent.


title: CS gas

text: Exposure causes a burning sensation and tearing of the eyes to the extent that the subject cannot keep their eyes open, and a burning irritation of the mucous membranes of the nose, mouth and throat, resulting in profuse coughing, nasal mucus discharge, disorientation, and difficulty breathing, partially incapacitating the subject. CS gas is an aerosol of a volatile solvent (a substance that dissolves other active substances and that easily evaporates) and 2-chlorobenzalmalononitrile, which is a solid compound at room temperature. CS gas is generally accepted as being non-lethal. It was first synthesized by two Americans, Ben Corson and Roger Stoughton, at Middlebury College in 1928, and the chemical's name is derived from the first letters of the scientists' surnames.


title: CS gas

text: CS was developed and tested secretly at Porton Down in Wiltshire, UK, in the 1950s and 1960s. CS was used first on animals, then subsequently on British Army servicemen volunteers. CS has less effect on animals because they have different tear ducts and, in the case of non-human mammals, their fur inhibits the free entry of the gas.


title: CS gas

text: CS is synthesized by the reaction of 2-chlorobenzaldehyde and malononitrile via the Knoevenagel condensation:


title: CS gas

text: The reaction is catalysed with a weak base like piperidine or pyridine. The production method has not changed since the substance was discovered by Corson and Stoughton. Other bases, solvent free methods and microwave promotion have been suggested to improve the production of the substance.


title: CS gas

text: The physiological properties had been discovered already by the chemists first synthesising the compound in 1928:


title: CS gas

text: "Physiological Properties. Certain of these dinitriles have the effect of sneeze and tear gases. They are harmless when wet but to handle the dry powder is disastrous."


title: CS gas

text: As 2-chlorobenzalmalononitrile is a solid at room temperature, not a gas, a variety of techniques have been used to make this solid usable as an aerosol:


title: CS gas

text: In the Waco Siege in the United States, CS was dissolved in the organic solvent dichloromethane (also known as methylene chloride). The solution was dispersed as an aerosol via explosive force and when the highly volatile dichloromethane evaporated, CS crystals precipitated and formed a fine dispersion in the air.


title: CS gas

text: Many types of tear gas and other riot control agents have been produced with effects ranging from mild tearing of the eyes to immediate vomiting and prostration. CN and CS are the most widely used and known, but around 15 different types of tear gas have been developed worldwide, e.g. adamsite or bromoacetone, CNB, and CNC. CS has become the most popular due to its strong effect. The effect of CS on a person will depend on whether it is packaged as a solution or used as an aerosol. The size of solution droplets and the size of the CS particulates after evaporation are factors determining its effect on the human body.


title: CS gas

text: The chemical reacts with moisture on the skin and in the eyes, causing a burning sensation and the immediate forceful and uncontrollable shutting of the eyes. Effects usually include tears streaming from the eyes, profuse coughing, exceptional nasal discharge that is full of mucus, burning in the eyes, eyelids, nose and throat areas, disorientation, dizziness and restricted breathing. It will also burn the skin where sweaty or sunburned. In highly concentrated doses, it can also induce severe coughing and vomiting. Most of the immediate effects wear off within a few hours (such as exceptional nasal discharge and profuse coughing), although respiratory, gastrointestinal, and oral symptoms may persist for months. Excessive exposure can cause chemical burns resulting in permanent scarring.


title: CS gas

text: Adults exposed to tear gas during the 2020 protests in Portland Oregon (USA) also reported menstrual changes (899; 54.5% of 1650 female respondents). Exposure to tear gas is associated with avoidable healthcare utilization.


title: CS gas

text: People or objects contaminated with CS gas can cause secondary exposure to others, including healthcare professionals and police. In addition, repeated exposure may cause sensitisation.


title: CS gas

text: TRPA1 (Transient Receptor Potential-Ankyrin 1) ion channel expressed on nociceptors (especially trigeminal) has been implicated as the site of action for CS gas in rodent models.


title: CS gas

text: Although described as a non-lethal weapon for crowd control, studies have raised doubts about this classification. CS can cause severe pulmonary damage and can also significantly damage the heart and liver.


title: CS gas

text: On 28 September 2000, Prof. Dr. Uwe Heinrich released a study commissioned by John C. Danforth, of the United States Office of Special Counsel, to investigate the use of CS by the FBI at the Branch Davidians' Mount Carmel compound. He said no human deaths had been reported, but concluded that the lethality of CS used would have been determined mainly by two factors: whether gas masks were used and whether the occupants were trapped in a room. He suggests that if no gas masks were used and the occupants were trapped, then, "there is a distinct possibility that this kind of CS exposure can significantly contribute to or even cause lethal effects".


title: CS gas

text: CS gas can have a clastogenic effect (abnormal chromosome change) on mammalian cells, but no studies have linked it to miscarriages or stillbirths. In Egypt, CS gas was reported to be the cause of death of several protesters in Mohamed Mahmoud Street near Tahrir square during the November 2011 protests. The solvent in which CS is dissolved, methyl isobutyl ketone (MIBK), is classified as harmful by inhalation; irritating to the eyes and respiratory system; and repeated exposure may cause skin dryness or cracking.


title: CS gas

text: CS is used in spray form by many police forces as a temporary incapacitant and to subdue attackers, persons, or civil protestors. Officers who are trained in the use and application of CS spray are routinely exposed to it as part of their training.


title: CS gas

text: Although predominantly used by police it has also been used in criminal attacks in various countries.


title: CS gas

text: Use of CS in war is prohibited under the terms of the Chemical Weapons Convention, signed by most countries in 1993 with all but five other states signing between 1994 and 1997. The reasoning behind the prohibition is pragmatic: use of CS by one combatant could easily trigger retaliation with much more toxic chemical weapons such as nerve agents. Only five countries have not signed the Chemical Weapons Convention and are therefore unhindered by restrictions on the use of CS gas: Angola, Egypt, North Korea, Somalia, and South Sudan.


title: CS gas

text: Domestic police use of CS is legal in many countries, as the Chemical Weapons Convention prohibits only military use.


title: CS gas

text: CS gas was used extensively by Bahrain's police from the start of the Bahraini uprising. The Bahrain Independent Commission of Inquiry concluded that Bahrain's police used a disproportionate amount of CS gas when dispersing protests, and that in some situations, police fired CS gas into private homes in an "unnecessary and indiscriminate" manner. In one particular incident witnessed by Commission investigators, police fired "at least four tear gas canisters (each containing six projectiles) ... from a short range into the kitchen and living room of a home."


title: CS gas

text: According to opposition activists and families of the dead, ten individuals died as a result of CS gas between 25 March 2011 and 17 December 2011. One allegedly died from the impact of the CS gas canister, and the remainder are said to have died from the effects of inhaling the gas. The Bahrain Independent Commission of Inquiry received information that a further three deaths may have been attributable to the use of CS gas. Of these three, one allegedly died from the impact of the canister, and two from the effects of inhaling the gas.


title: CS gas

text: The Canadian Forces exposes basic training candidates to CS gas as part of gas mask training and drills. This training continues in subsequent career stages. Many law enforcement agencies also use CS gas as a riot control device. Since 2008, the SPVM police force in Montreal has increased its use of CS Gas for crowd control, although Police policy is to only use it as a last resort. Several incidents where protesters have been seriously injured by having CS gas fired at them from point-blank range have raised concerns about the methodology and training of Officers in the Montreal Riot Squad, particularly in relation to "Use of Force".


title: CS gas

text: Tear gas is routinely used in Chile by Carabineros, to disrupt civilian protests. During the 2019 uprising the use of expired gas has been reported, prompting Carabineros to say that "they are like yogurt expired 5 days ago, it doesn’t damage people".


title: CS gas

text: CS was first tested in the field by the British army in Cyprus in 1958. At this time it was known by the code name T792.


title: CS gas

text: The Police Tactical Unit of the Hong Kong Police Force used 87 rounds of CS projectiles (both riot gun launched and hand thrown) in Hong Kong on 28 September 2014 against thousands of protesters obstructing major thoroughfares in Hong Kong 2014 Hong Kong protests, also known as the Umbrella Movement.


title: CS gas

text: The CS gas canisters and content used were purchased by the Hong Kong SAR Government from CHEMRING, a British weapons manufacturer. The crowd used umbrellas to fend off the gas, which was often ineffective. Apart from the HK police, CS gas spray is also used by Witness Protection and Firearms Section of Independent Commission Against Corruption (Hong Kong).


title: CS gas

text: From 12 June to 4 August 2019, police used 1000 tear gas canisters. Then, on the single day of 5 August, police fired more than 800 tear gas canisters in their operations throughout almost every district of the city. In one instance, a tear gas canister was deployed indoors, in Kwai Fong station during a march, on 11 August 2019. The police initially denied the incident. In defense, protestors are seen picking up tear gas cans with thick gloves to throw them back or to extinguish them in sealed water containers.


title: CS gas

text: Up to 22 October 2019, over 5000 made-in-China tear gas canisters have been deployed by the Hong Kong Police Force. Canisters marked with dates overdue have been collected in many occasions. It is unpredictable for the potential hazards to the Hong Kong environment and living conditions. Recent massive deaths of fish around Hong Kong seas was also suspected to be one of the consequences. Many birds were found dead in the Chinese University of Hong Kong, after 12 November that the riot police fired over 2000 tear gases towards the campus. A Hong Kong journalist, Chan Yu-hong from the Stand News declared he was diagnosed with chloracne (by a Traditional Chinese physician instead of a physician) after exposure to made-in-China tear gas while covering the 2019 Hong Kong protests.


title: CS gas

text: Iraq successfully developed CS during the 1970s and during the 1980s produced tons of the substance firstly at Salman Pak and later at al-Muthanna.


title: CS gas

text: Blackwater Worldwide, acting as an agent of the United States, deployed CS in the Iraq War from a helicopter hovering over a checkpoint in the Green Zone in Baghdad.


title: CS gas

text: Israel Police forces spray CS gas in riot control situations. It is widely used at demonstrations within the Palestinian Territories and at the Israeli West Bank barrier.


title: CS gas

text: CS tear gas was used in suppression of the mutiny in Makati that was led by Sen. Antonio Trillanes. The tear gas was fired in the building and all the people in the building including reporters were affected.


title: CS gas

text: The Gendarmerie of Bucharest used large quantities of CS gas against civilians during the protests of 10 August 2018 in Bucharest.


title: CS gas

text: Russia developed in the late 1970's a K-51 grenade for riot control and for other tactical operations. The K-51 burns for 16 seconds producing a thick CS smoke. Reportedly used in the Donetsk region of Ukraine in 2015 it has been reported in use again in the 2022 Russian invasion of Ukraine, being dropped by drones.


title: CS gas

text: Tear gas is not commonly used in Spain but it has been used some times to disrupt civilian protests by the Policia Nacional and Mossos d'Esquadra in Catalonia.


title: CS gas

text: The LTTE, also known as Tamil Tigers of Sri Lanka, an insurgent group in Sri Lanka used CS gas against government forces in September 2008. Its use hindered the army's progress but ultimately proved ineffective in preventing the army from overrunning LTTE positions.


title: CS gas

text: Sudanese forces extensively used CS gas during the latest wave of demonstrations began in 2018. The use of CS gas fired through rifles or hand grenades is not exclusive to police forces but is widely used by non-trained militia to suppress protesters movement and to intimidate civilians by firing blindly into neighborhoods and homes. CS gas cannisters are generally used also as a ballistic weapon and aimed at the faces of protesters to cause serious body and head injuries. Some death cases were recorded due to choking on tear gas because of excessive use in confined areas.


title: CS gas

text: CS gas was used extensively in the Bogside area of Derry, Northern Ireland during the "Battle of the Bogside", a two-day riot in August 1969. A total of 1,091 canisters containing 12.5g of CS each, and 14 canisters containing 50 g of CS each, were released in the densely populated residential area. On 30 August the Himsworth Inquiry was set up to investigate the medical effects of its use in Derry. Its conclusions, viewed in the political context of the time, still pointed towards the necessity of further testing of CS gas before being used as a riot control agent. During the rioting in Belfast, the following year, known as the Falls Curfew, the Army fired up to 1,600 canisters into the densely populated Falls Road area. It was also used in Lenadoon on 9 July 1972 on the breakdown of the IRA ceasefire. Not long after, the British Army and Royal Ulster Constabulary ceased using CS in Northern Ireland.


title: CS gas

text: CS gas has not been routinely deployed on the British mainland. It has seen use in rare cases. The first use of CS gas on the UK mainland that was not part of military training was carried out in 1944 during a hostage siege at a north London address. Soldiers were asked to throw CS grenades through the skylight in hope of bringing the incident to a speedy conclusion, but the hostage-taker had brought his civilian-issue gas mask with him, negating the effect. The siege of Trough Gate 1973 in Oldham was the second non-military use of CS gas on the UK mainland. During a four-hour standoff, Frank Alan Stockton shot at police but was flushed from his home with CS gas and police dogs.


title: CS gas

text: During the 1980 assault on the Iranian Embassy, SAS soldiers used CS gas contained within stun grenades to incapacitate the militants who had kept the building under siege for six days. All but one of the remaining hostages were saved and all but one of the hostage-takers were killed, with the other being taken into custody.


title: CS gas

text: Following the 2011 England riots, there was consideration given to making CS gas, water cannon and other riot control measures available to police for use in the event of serious disorder. The British Armed Forces use CS gas annually to test their chemical, biological, radiological and nuclear defense (CBRN) equipment. During initial training they introduce recruits to CS gas by placing them in a small enclosed space known as a Confidence Test Facility (CTF) and igniting chemical tablets to induce CS production. After recruits have carried out their CBRN drills, they must remove their respirators so that they are exposed to the CS for up to 20 seconds to experience its effects and become confident their respirators work.


title: CS gas

text: CS incapacitant spray had been used routinely by the British police since its introduction in 1996. It was issued as an item of equipment to police officers for protection and to assist in dealing with violent incidents. British police recruits are typically exposed to CS aerosol, in a controlled environment, as part of their basic training. A six-month trial by sixteen police forces in England began on 1 March 1996. CS spray was used in the UK more than 10,000 times in the period between its introduction in 1996 and September 1998. Forces began replacing CS spray with Captor or PAVA spray, due to its non-flammable nature. This allowed use in conjunction with Tasers, which have been rolled out more widely. As a result, CS spray is now redundant – with Captor or PAVA used by all forces.


title: CS gas

text: The CS spray used by police forces was in the form of a hand-held aerosol canister containing a 5% solution of CS dissolved in methyl isobutyl ketone and propelled by pressurized nitrogen. The CS spray used by UK police was generally more concentrated than that used by American police forces (5% vs 1%). The liquid stream is directed where the user points the canister, being accurate up to 4 metres. Police are also trained in helping the incapacitated person recover once successfully restrained. Under Section 5 of the Firearms Act, CS and other incapacitant sprays are classed as prohibited weapons, making it unlawful for a member of the public to possess them.


title: CS gas

text: On 16 March 1996, a Gambian asylum seeker, Ibrahima Sey, was taken to Ilford Police Station in east London. Whilst incapacitating Sey, who was suffering from excited delirium, police sprayed him with CS spray and held him on the ground for approximately 15 minutes, and he subsequently died. In 1999, the mental health charity MIND called for a suspension of the use of CS spray on mentally ill people until it was proved to be safe. In February 2006, Dan Ford, from Wareham in Dorset, received permanent scarring to his face after being sprayed with CS during an arrest by police. Ford was subsequently advised by doctors to stay out of sunlight for at least 12 months. After the incident, his cousin, Donna Lewis, was quoted as saying, "To look at him, it was like looking at a melting man, with liquid oozing from his face."


title: CS gas

text: CS is used by many police forces within the United States. It was used by Federal Bureau of Investigation law enforcement officials in the 1993 Waco Siege. Riot police in Pittsburgh, Pennsylvania in September 2009 used CS gas and riot control techniques to disperse assemblies in the vicinity of the 2009 G-20 Pittsburgh summit. Tear gas was used in at least 100 cities during the 2020 protests that took place in the U.S. In Portland, Oregon alone, tear gas was used more than 100 times in a two-week period and there were at least two nights in which it was used more than twenty times.


title: CS gas

text: In Berkeley, California during the events in the People's Park on 21 May 1969, a midday memorial was held for student James Rector, a non-protester shot and killed by police, at Sproul Plaza on the university campus. In his honor, several thousand people peacefully assembled to listen to speakers remembering his life. National Guard troops surrounded Sproul Plaza, donned their gas masks, and pointed their bayonets inward, while helicopters dropped CS gas directly on the trapped crowd. No escape was possible, and the gas caused acute respiratory distress, disorientation, temporary blindness and vomiting. Many people, including children and the elderly, were injured during the ensuing panic. The gas was so intense that breezes carried it into Cowell Memorial Hospital, endangering patients, interrupting operations and incapacitating nurses. Students at nearby Jefferson and Franklin elementary schools were also affected.


title: CS gas

text: Members of the United States armed forces are exposed to CS during initial training, and during training refresher courses or equipment maintenance exercises, using CS tablets that are melted on a hotplate. This is to demonstrate the importance of properly wearing a military gas mask or protective mask, as the agent's presence quickly reveals an improper fit or seal of the mask's rubber gaskets against the face. Following exposure while wearing a mask, recruits are ordered to remove the masks and endure exposure in the room. These exercises also encourage confidence in the ability of the equipment to protect the wearer from such chemical attacks. Such an event is a requirement for graduation from United States Army Basic Training, Air Force Basic Military Training, Navy Basic Training, and Marine Corps recruit training. CS gas in the form of grenades is also used extensively in the United States Marine Corps and United States Army in some service schools. CS gas is used during the final field exercise of the Scout Sniper Basic Course to simulate being compromised. In addition, it is used during the escape-and-evasion exercise ("Trail of Tears"), the last event before graduation from the course. Navy Corpsmen participating in Field Medic training in order to serve with the Marines must go through their second CS gas exercise before finally arriving at their unit. It is also used during several events in the Marine Corps Basic Reconnaissance Course (BRC) including some rucksack runs and escape-and-evasion exercises. While students going through the course are given the opportunity to bring and wear a gas mask for the event, usually none are worn because once donned, gas masks could not be removed until the end of the exercise. This could last anywhere from 3–12 hours and would make running 25 km (15 miles) while wearing of gear virtually impossible.


title: CS gas

text: It has been reported that thousands of tons of CS gas were used by the U.S. forces in Vietnam to bring Viet Cong into the open. It was also used by the North Vietnamese forces in some battles like Hue in 1968 or during the Easter Offensive in 1972.


title: CS gas

text: CS gas has been and is still routinely used by Greek riot police (MAT) in order to quell student and labour protests, as well as riots.


title: CS gas

text: CS was used to quell a protest in Lusaka, Zambia in July 1997 and the 1999 WTO riots in Seattle. Amnesty International reported that it had been manufactured by the UK company Pains-Wessex. Subsequently, Amnesty called for an export ban when the receiving regime is either not fully trained in the use of CS, or had shown usage "contrary to the manufacturer’s instructions".


title: CS gas

text: In September 2000, the "Guardian" newspaper revealed how a UK company, HPP, used legal loopholes to export CS to a private security company in Rwanda, in breach of United Nations sanctions. The "Guardian" also reported that CS was used by the Hutu militia in Rwanda to flush Tutsis out of buildings before hacking them to death.


title: CS gas

text: CS has been used by the government in South Africa; by Israel against Palestinians and Israelis; by the South Korean government in Seoul, and during the Balkan conflicts by Serbia. In Malta it was used by police between 1981 and 1987 to the detriment of Nationalist Party Supporters.


title: CS gas

text: CS tear gas was used at the G8 protests in Genoa, Italy and Quebec City, Canada during the FTAA anti-globalization demonstrations during the Quebec City Summit of the Americas.


title: CS gas

text: The Malaysia Federal Reserve Unit has also been known to use CS tear gas against its citizens who rallied for clean and fair elections under what were called Bersih rallies in 2011 and 2012.


title: CS gas

text: The Canadian, Norwegian, Dutch, and Australian Defence Forces train their personnel with CS gas in a manner similar to that of the US, as it is a basic part of CBRN (Chemical, Biological, Radiological, Nuclear) training. Gas is released by burning tablets, usually in a building reserved for this purpose (a "gas hut"). In the training, the person enters the building unprotected and must fit and clear the gas mask before leaving. Other drills such as drinking and under-mask decontamination are also practiced. Some Norwegian units are exposed to CS gas while engaged in mental and physical activity such as addressing the officer in command by stating name, rank, and troop before doing 30 push-ups.


title: CS gas

text: In Australia, prison officers used CS gas against five teenage boys in Darwin's Don Dale Juvenile Detention Centre in August 2014.


title: Barry Evans (actor)

text: Barry Joseph Evans (18 June 1943 – 9 February 1997) was an English actor best known for his appearances in British sitcoms such as "Doctor in the House" and "Mind Your Language".


title: Barry Evans (actor)

text: Born in Guildford, Surrey, and orphaned as a baby, Evans was educated at the orphanage boarding schools run by the Shaftesbury Homes, first at Fortescue House School in Twickenham in a Dr Barnardo's Home, and then at Bisley Boys' School in Bisley, Surrey. His acting ability was recognised at an early age and he often played the leading roles in school plays. He briefly lived in Yalding before moving to London. Evans attended the Italia Conti Academy and later won a John Gielgud Scholarship to study at the Central School of Speech and Drama.


title: Barry Evans (actor)

text: One of his first film credits was the lead role in Clive Donner's film "Here We Go Round the Mulberry Bush" (1968) where he was cast as Jamie McGregor, a teenager who finds it difficult to lose his virginity. "Photoplay" magazine called Evans a "bright and exciting new actor", and "The Sunday Telegraph" described his screen debut as "brilliant".


title: Barry Evans (actor)

text: "Here We Go Round the Mulberry Bush" represented a breakthrough in a number of technical features: the script, the photography and the filming techniques. Jamie McGregor speaks his thoughts out loud. The soundtrack mainly contained songs performed by The Spencer Davis Group and Traffic. The film was listed to compete at the 1968 Cannes Film Festival, but the Festival was cancelled that year. The film saw the beginning of a long-lasting friendship between Barry Evans and the director, Clive Donner, whom Evans regarded as one of his best friends. He worked with Donner again in 1969 in the historical epic "Alfred the Great".


title: Barry Evans (actor)

text: In 1969, Evans appeared alongside Roddy McDowall in an episode of the series "Journey to the Unknown" entitled "The Killing Bottle", as a man planning to murder his brother for the inheritance.


title: Barry Evans (actor)

text: His first significant television role was in the sitcom "Doctor in the House" (1969–70), based on Richard Gordon's series of novels, which had already been turned into a feature film series. Evans starred as the young student doctor Michael Upton, to whom Evans felt he bore no similarities. Following the show's success he starred in the sequel to the series, "Doctor at Large" (1971). Evans enjoyed working with his fellow actors George Layton, Geoffrey Davies, Robin Nedwell and Richard O'Sullivan, and he later described these as the best years of his life. Work on the "Doctor" series was extremely intense and left him no time to take on other roles; he therefore declined to appear in the later sequels. However, in a 1977 interview he stated that he had been "incredibly stupid" to turn the series down.


title: Barry Evans (actor)

text: In 1971, Evans played the character of Eli Frome in Pete Walker's low-budget thriller "Die Screaming, Marianne", alongside Susan George. In 1976, he had the lead role in Stanley Long's sex comedy "Adventures of a Taxi Driver". Unlike in "Here We Go Round the Mulberry Bush", in which the viewer partakes in Jamie's thoughts, Evans's character breaks the fourth wall throughout the film. Although the film was successful, Evans decided not to appear in the sequels, but he starred in the similarly themed "Under the Doctor" the same year.


title: Barry Evans (actor)

text: Evans also did some theatre work, but this did not prove financially worthwhile, and he spent several spells claiming benefits. He wrote to London Weekend Television, "and told them ... I was still alive". This led to what became his best-known comedy role, as Jeremy Brown in the ITV sitcom "Mind Your Language" (1977–79, 1986), which was a humorous look at an evening class tutor teaching English to foreign students. The series was written by TV scriptwriter Vince Powell, and was adapted for American TV as "What a Country!" in 1986. In the same year it was briefly revived in Britain for a further 13 episodes.


title: Barry Evans (actor)

text: In 1982–83, Evans played Dick Emery's trusted assistant Robin Bright in the comedy thriller series "Legacy of Murder".


title: Barry Evans (actor)

text: By the latter half of the 1980s, Evans's youthful appearance was working against him and he found it difficult to obtain mature acting roles in keeping with his age. His last role was as Bazzard in the 1993 film adaptation of "The Mystery of Edwin Drood". By the mid–1990s, Evans was working as a minicab driver in Leicestershire.


title: Barry Evans (actor)

text: In February 1997, police discovered Evans' body in his living room after going to the house to tell him that they had recovered his stolen car, which had been reported missing the day before. The cause of his death has never been confirmed. The coroner found a blow to Evans's head and also found high levels of alcohol in his system. A short will was found on a table next to his body and a spilt packet of aspirin tablets, bearing a pre-decimalisation price tag, indicating that the pack was at least 26 years old, was found on the floor, although the coroner concluded that he had not taken any of them. An open verdict was eventually given. An 18-year-old man was arrested but later released without charge due to insufficient evidence.


title: Barry Evans (actor)

text: A blue plaque commemorating Evans, erected by The Heritage Foundation, is situated at 8 Buckland Crescent in Belsize Park, north west London. He lived at this address from 1960 until the early 1980s. A memorial charity lunch in aid of Barnardo's was held in honour of Evans and "Mind Your Language" writer Vince Powell at the Marriot Hotel near Marble Arch in central London.


title: Biosphere reserves of India

text: Twelve of the eighteen biosphere reserves are a part of the World Network of Biosphere Reserves, based on the UNESCO Man and the Biosphere (MAB) Programme list.


title: Biosphere reserves of India

text: The following is a list of potential sites for Biosphere Reserves as selected by Ministry of Forests and Environment:


title: Differential geometry

text: Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries.


title: Differential geometry

text: Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structure. For example, in Riemannian geometry distances and angles are specified, in symplectic geometry volumes may be computed, in conformal geometry only angles are specified, and in gauge theory certain fields are given over the space. Differential geometry is closely related to, and is sometimes taken to include, differential topology, which concerns itself with properties of differentiable manifolds which do not rely on any additional geometric structure (see that article for more discussion on the distinction between the two subjects). Differential geometry is also related to the geometric aspects of the theory of differential equations, otherwise known as geometric analysis.


title: Differential geometry

text: Differential geometry finds applications throughout mathematics and the natural sciences. Most prominently the language of differential geometry was used by Albert Einstein in his theory of general relativity, and subsequently by physicists in the development of quantum field theory and the standard model of particle physics. Outside of physics, differential geometry finds applications in chemistry, economics, engineering, control theory, computer graphics and computer vision, and recently in machine learning.


title: Differential geometry

text: The history and development of differential geometry as a subject begins at least as far back as classical antiquity. It is intimately linked to the development of geometry more generally, of the notion of space and shape, and of topology, especially the study of manifolds. In this section we focus primarily on the history of the application of infinitesimal methods to geometry, and later to the ideas of tangent spaces, and eventually the development of the modern formalism of the subject in terms of tensors and tensor fields.


title: Differential geometry

text: The study of differential geometry, or at least the study of the geometry of smooth shapes, can be traced back at least to classical antiquity. In particular, much was known about the geometry of the Earth, a spherical geometry, in the time of the ancient Greek mathematicians. Famously, Eratosthenes calculated the circumference of the Earth around 200 BC, and around 150 AD Ptolemy in his "Geography" introduced the stereographic projection for the purposes of mapping the shape of the Earth. Implicitly throughout this time principles that form the foundation of differential geometry and calculus were used in geodesy, although in a much simplified form. Namely, as far back as Euclid's "Elements" it was understood that a straight line could be defined by its property of providing the shortest distance between two points, and applying this same principle to the surface of the Earth leads to the conclusion that great circles, which are only locally similar to straight lines in a flat plane, provide the shortest path between two points on the Earth's surface. Indeed the measurements of distance along such geodesic paths by Eratosthenes and others can be considered a rudimentary measure of arclength of curves, a concept which did not see a rigorous definition in terms of calculus until the 1600s.


title: Differential geometry

text: Around this time there were only minimal overt applications of the theory of infinitesimals to the study of geometry, a precursor to the modern calculus-based study of the subject. In Euclid's "Elements" the notion of tangency of a line to a circle is discussed, and Archimedes applied the method of exhaustion to compute the areas of smooth shapes such as the circle, and the volumes of smooth three-dimensional solids such as the sphere, cones, and cylinders.


title: Differential geometry

text: There was little development in the theory of differential geometry between antiquity and the beginning of the Renaissance. Before the development of calculus by Newton and Leibniz, the most significant development in the understanding of differential geometry came from Gerardus Mercator's development of the Mercator projection as a way of mapping the Earth. Mercator had an understanding of the advantages and pitfalls of his map design, and in particular was aware of the conformal nature of his projection, as well as the difference between "praga", the lines of shortest distance on the Earth, and the "directio", the straight line paths on his map. Mercator noted that the praga were "oblique curvatur" in this projection. This fact reflects the lack of a metric-preserving map of the Earth's surface onto a flat plane, a consequence of the later Theorema Egregium of Gauss.