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Plane partition
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Special plane partitions
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Symmetric plane partitions A plane partition π is called symmetric if πi,j = πj,i for all i, j. In other words, a plane partition is symmetric if (i,j,k)∈B(r,s,t) if and only if (j,i,k)∈B(r,s,t) . Plane partitions of this type are symmetric with respect to the plane x = y. Below is an example of a symmetric plane partition and its visualisation.
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Plane partition
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Special plane partitions
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43321332132212111 In 1898, MacMahon formulated his conjecture about the generating function for symmetric plane partitions which are subsets of B(r,r,t) . This conjecture is called The MacMahon conjecture. The generating function is given by Macdonald pointed out that Percy A. MacMahon's conjecture reduces to ∑π∈B(r,r,t)/S2q|π|=∏η∈B(r,r,t)/S21−q|η|(1+ht(η))1−q|η|ht(η) In 1972 Edward A. Bender and Donald E. Knuth conjectured a simple closed form for the generating function for plane partition which have at most r rows and strict decrease along the rows. George Andrews showed that the conjecture of Bender and Knuth and the MacMahon conjecture are equivalent. MacMahon's conjecture was proven almost simultaneously by George Andrews in 1977 and later Ian G. Macdonald presented an alternative proof. When setting q = 1 yields the counting function N2(r,r,t) which is given by N2(r,r,t)=∏i=1r2i+t−12i−1∏1≤i<j≤ri+j+t−1i+j−1 For a proof of the case q = 1 please refer to George Andrews' paper MacMahon's conjecture on symmetric plane partitions.
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Plane partition
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Special plane partitions
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Cyclically symmetric plane partitions π is called cyclically symmetric, if the i-th row of π is conjugate to the i-th column for all i. The i-th row is regarded as an ordinary partition. The conjugate of a partition π is the partition whose diagram is the transpose of partition π . In other words, the plane partition is cyclically symmetric if whenever (i,j,k)∈B(r,s,t) then (k, i, j) and (j, k, i) also belong to B(r,s,t) . Below an example of a cyclically symmetric plane partition and its visualization is given.
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Plane partition
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Special plane partitions
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65543364331643114221311111 Macdonald's conjecture provides a formula for calculating the number of cyclically symmetric plane partitions for a given integer r. This conjecture is called The Macdonald conjecture. The generating function for cyclically symmetric plane partitions which are subsets of B(r,r,r) is given by ∑π∈B(r,r,r)/C3q|π|=∏η∈B(r,r,r)/C31−q|η|(1+ht(η))1−q|η|ht(η) This equation can also be written in another way ∏η∈B(r,r,r)/C31−q|η|(1+ht(η))1−q|η|ht(η)=∏i=1r[1−q3i−11−q3i−2∏j=ir1−q3(r+i+j−1)1−q3(2i+j−1)] In 1979, Andrews proved Macdonald's conjecture for the case q = 1 as the "weak" Macdonald conjecture. Three years later William. H. Mills, David Robbins and Howard Rumsey proved the general case of Macdonald's conjecture in their paper Proof of the Macdonald conjecture. The formula for N3(r,r,r) is given by the "weak" Macdonald conjecture N3(r,r,r)=∏i=1r[3i−13i−2∏j=iri+j+r−12i+j−1] Totally symmetric plane partitions A totally symmetric plane partition π is a plane partition which is symmetric and cyclically symmetric. This means that the diagram is symmetric at all three diagonal planes, or in other words that if (i,j,k)∈B(r,s,t) then all six permutations of (i, j, k) are also in B(r,s,t) . Below an example of a matrix for a totally symmetric plane partition is given. The picture shows the visualisation of the matrix.
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Plane partition
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Special plane partitions
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54431433143213111 Macdonald found the total number of totally symmetric plane partitions that are subsets of B(r,r,r) . The formula is given by N4(r,r,r)=∏η∈B(r,r,r)/S31+ht(η)ht(η) In 1995 John R. Stembridge first proved the formula for N4(r,r,r) and later in 2005 it was proven by George Andrews, Peter Paule, and Carsten Schneider. Around 1983 Andrews and Robbins independently stated an explicit product formula for the orbit-counting generating function for totally symmetric plane partitions. This formula already alluded to in George E. Andrews' paper Totally symmetric plane partitions which was published 1980. The conjecture is called The q-TSPP conjecture and it is given by: Let S3 be the symmetric group. The orbit counting function for totally symmetric plane partitions that fit inside B(r,r,r) is given by the formula ∑π∈B(r,r,r)/S3q|π|=∏η∈B(r,r,r)/S31−q1+ht(η)1−qht(η)=∏1≤i≤j≤k≤r1−qi+j+k−11−qi+j+k−2.
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Plane partition
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Special plane partitions
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This conjecture was proved in 2011 by Christoph Koutschan, Manuel Kauers and Doron Zeilberger.
Self-complementary plane partitions If πi,j+πr−i+1,s−j+1=t for all 1≤i≤r , 1≤j≤s , then the plane partition is called self-complementary. It is necessary that the product r⋅s⋅t is even. Below an example of a self-complementary symmetric plane partition and its visualisation is given.
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Plane partition
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Special plane partitions
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443214222321 Richard P. Stanley conjectured formulas for the total number of self-complementary plane partitions N5(r,s,t) . According to Stanley, Robbins also formulated formulas for the total number of self-complementary plane partitions in a different but equivalent form. The total number of self-complementary plane partitions that are subsets of B(r,s,t) is given by N5(2r,2s,2t)=N1(r,s,t)2 N5(2r+1,2s,2t)=N1(r,s,t)N1(r+1,s,t) N5(2r+1,2s+1,2t)=N1(r+1,s,t)N1(r,s+1,t) It is necessary that the product of r,s and t is even. A proof can be found in the paper Symmetries of Plane Partitions which was written by Stanley. The proof works with Schur functions ssr(x) . Stanley's proof of the ordinary enumeration of self-complementary plane partitions yields the q-analogue by substituting xi=qi for i=1,…,n . This is a special case of Stanley's hook-content formula. The generating function for self-complementary plane partitions is given by sγα(q,q2,…,qn)=qγα(α+1)/2∏i=1α∏j=0γ−11−qi+n−α+j1−qi+j Substituting this formula in for B(2r,2s,2t) for B(2r,2s+1,2t) for B(2r+1,2s,2t+1) supplies the desired q-analogue case.
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Plane partition
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Special plane partitions
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Cyclically symmetric self-complementary plane partitions A plane partition π is called cyclically symmetric self-complementary if it is cyclically symmetric and self-complementary. The figure presents a cyclically symmetric self-complementary plane partition and the according matrix is below.
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Plane partition
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Special plane partitions
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4441332132113 In a private communication with Stanley, Robbins conjectured that the total number of cyclically symmetric self-complementary plane partitions is given by N6(2r,2r,2r) . The total number of cyclically symmetric self-complementary plane partitions is given by N6(2r,2r,2r)=Dr2 Dr is the number of r×r alternating sign matrices. A formula for Dr is given by Dr=∏j=0r−1(3j+1)!(r+j)! Greg Kuperberg proved the formula for N6(r,r,r) in 1994.
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Plane partition
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Special plane partitions
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Totally symmetric self-complementary plane partitions A totally symmetric self-complementary plane partition is a plane partition that is both totally symmetric and self-complementary. For instance, the matrix below is such a plane partition; it is visualised in the accompanying picture.
6665536553316553315331153311311 The formula N7(r,r,r) was conjectured by William H. Mills, Robbins and Howard Rumsey in their work Self-Complementary Totally Symmetric Plane Partitions. The total number of totally symmetric self-complementary plane partitions is given by N7(2r,2r,2r)=Dr Andrews proves this formula in 1994 in his paper Plane Partitions V: The TSSCPP Conjecture.
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Aircraft station
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Aircraft station
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An aircraft station (also aircraft radio station) is – according to Article 1.83 of the International Telecommunication Union's (ITU) ITU Radio Regulations (RR) – defined as "A mobile radio station in the aeronautical mobile service, other than survival craft station, located on board an aircraft".
Each station shall be classified by the service in which it operates permanently or temporarily.
See also Selection of UHF/VHF aircraft stations
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Vikki Abrahams
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Vikki Abrahams
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Vikki Martyne Abrahams is an English–American reproductive immunologist. She is a full professor of obstetrics, gynecology and reproductive sciences at the Yale School of Medicine. Her research focuses on understanding the role of innate immune toll-like receptor and NOD-like receptor family members in placental and maternal-fetal immune responses.
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Vikki Abrahams
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Early life and education
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Abrahams earned her Bachelor of Science degree and PhD from the University College London.
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Vikki Abrahams
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Career
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Abrahams came to the United States for her postdoctoral work at Dartmouth Medical School and Yale University in the field of reproductive immunology before accepting a faculty position in 2004. In her role as an assistant professor of obstetrics and gynecology, Abrahams co-authored a study which found that there was a specific defence mechanism used by the immune system which was imitated by cancer cells in order to fight off the effects of cancer drugs like paclitaxel. She was later awarded a one-year grant of $73,284 from the Lupus Research Alliance for her project titled "Effect of Antiphospholipid Antibodies on Trophoblast Function in Pregnancy." In 2010, Abrahams continued her research into pregnancy complications using a three-year grant from the American Heart Association to advance her work. She also co-authored another study which uncovered how hormone progesterone act to prevent preterm birth.Abrahams research focuses on understanding the role of innate immune toll-like receptor and NOD-like receptor family members in placental and maternal-fetal immune responses. In 2014, she was the senior author on a study exploring whether an anti-malaria drug could be used to treat obstetrical antiphospholipid syndrome. Two years later, she was the recipient of the 2016 Novel Research Grant from the Lupus Research Institute to conduct innovative work in lupus. She used this grant to lead a study identifying how the Zika virus infects the placenta.In 2019, Abrahams was the recipient of the annual American Society for Reproductive Immunology Award as someone "who has made outstanding contributions to the area of reproductive immunology."
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Ethmoid sinus
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Ethmoid sinus
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The ethmoid sinuses or ethmoid air cells of the ethmoid bone are one of the four paired paranasal sinuses. Unlike the other three pairs of paranasal sinuses which consist of one or two large cavities, the ethmoidal sinuses entail a number of small air-filled cavities ("air cells"). The cells are located within the lateral mass (labyrinth) of each ethmoid bone and are variable in both size and number. The cells are grouped into anterior, middle, and posterior groups; the groups differ in their drainage modalities, though all ultimately drain into either the superior or the middle nasal meatus of the lateral wall of the nasal cavity.
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Ethmoid sinus
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Structure
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The ethmoid air cells consist of numerous thin-walled cavities in the ethmoidal labyrinth that represent invaginations of the mucous membrane of the nasal wall into the ethmoid bone. They are situated between the superior parts of the nasal cavities and the orbits, and are separated from these cavities by thin bony lamellae.There are 5-15 air cells in either ethmoid bone in the adult, with a combined volume of 2-3mL.
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Ethmoid sinus
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Structure
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Drainage The anterior ethmoidal cells drain (directly or indirectly) into the middle nasal meatus by way of the ethmoidal infundibulum.
The posterior ethmoidal cells drain directly into the middle nasal meatus.The posterior ethmoidal cells drain directly into the superior nasal meatus at the sphenoethmoidal recess; sometimes, one or more opens into the sphenoidal sinus.
Haller cells Haller cells are infraorbital ethmoidal air cells lateral to the lamina papyracea. These may arise from the anterior or posterior ethmoidal sinuses.
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Ethmoid sinus
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Structure
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Lamellae The ethmoidal labyrinth is divided by multiple obliquely oriented, parallel lamellae. The first lamellae is equivalent to the uncinate process of ethmoid bone, the second corresponds the ethmoid bulla, and the third is the basal lamella, and the fourth is equivalent to the superior nasal concha.The anterior and posterior ethmoid cells are separated by the basal lamella (also known as the ground lamella). It is one of the bony divisions of the ethmoid bone and is mostly contained inside the ethmoid labyrinth. The basal lamella is continuous medially with the bony middle nasal concha. Anteriorly, it vertically inserts into the ethmoid crest; the middle part attaches obliquely into the orbital lamina of ethmoid bone (lamina papyricea) while the posterior part attaches into the orbital lamina horizontally.
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Ethmoid sinus
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Structure
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Innervation The ethmoidal air cells receive sensory innervation from the anterior and the posterior ethmoidal nerve (which are ultimately derived from the ophthalmic branch (CN V1) of the trigeminal nerve (CN V)), and the orbital branches of the pterygopalatine ganglion, which carry the postganglionic parasympathetic nerve fibers for mucous secretion from the facial nerve.
Development The ethmoidal cells (sinuses) and maxillary sinuses are present at birth. At birth, 3-4 air cells are present, with the number increasing to 5-15 by adulthood.
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Ethmoid sinus
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Clinical significance
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Acute ethmoiditis in childhood and ethmoidal carcinoma may spread superiorly causing meningitis and cerebrospinal fluid leakage or it may spread laterally into the orbit causing proptosis and diplopia.
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Momo (software)
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Momo (software)
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Momo (Chinese: 陌陌; pinyin: mò mò) is a free social search and instant messaging mobile app. The app allows users to chat with nearby friends and strangers. Momo provides users with free instant messaging services through Wifi, 3G and 4G. The client software is available for Android, iOS, and Windows Phone.Momo officially began operations in July 2011, and a month later, launched the first version of the app for iOS. Momo filed for a NASDAQ IPO on November 7, 2014 and was listed in December 2014.
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Momo (software)
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History
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Founding and incorporation Tang Yan, Zhang Sichuan, Lei Xiaoliang, Yong Li, and Li Zhiwei co-founded Beijing Momo Technology Co., Ltd. in July 2011.
Prior to founding the company, Tang Yan worked as editor and then editor-in-chief at NetEase. In October 2014, Tang was named by Fortune Magazine as one of its "40 Under 40," a list of the most powerful business elites under the age of 40.
The other co-founders all have prior experience with major Chinese Internet companies. In order to facilitate foreign investments, Momo’s co-founders incorporated a holding company called Momo Technology Company Limited in the British Virgin Islands in November 2011. In July 2014, Momo Technology Company Limited was renamed to Momo Inc. and re-domiciled to the Cayman Islands.
In December 2011, Momo established Momo Technology HK Company Limited (Momo HK) as a wholly owned subsidiary in Hong Kong. In March 2012, Momo HK established Beijing Momo Information Technology Co., Ltd.(Beijing Momo IT), a wholly owned People’s Republic of China subsidiary. In May 2013, Beijing Momo established Chengdu Momo Technology Co., Ltd.(Chengdu Momo), as a wholly owned subsidiary.
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Momo (software)
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History
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Growth In December 2011, Momo announced reaching half a million users. Three months later, the number of Momo users reached 2 million. Momo reached 10 million users on its first anniversary in August 2012. In October 2012, Momo surpassed 15 million users. In 2014, App Annie reported that Momo was the number 2 non-game app of 2013 in terms of revenue.
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Momo (software)
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History
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In February 2014, TechNode reported that Momo had announced reaching 100 million registered users. Momo executives also claimed they had reached 40 million monthly active users (MAU).
According to Momo, in June 2014, total registered users and MAU reached 148 million and 52.4 million respectively.
China Internet Watch reported more conservative estimates. In the months of August and September 2014, Momo had 51.279 and 52.101 million MAU. While Momo’s MAU grew, Wechat and QQ both lost MAU within the same time frame. Momo's prospectus reported 60.2 million MAU in September 2014.
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Momo (software)
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History
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Financing Momo reportedly raised USD 2.5 million in Series A financing. Angel investor, PurpleSky Capital (ZiHui ChuangTou), and Matrix Hong Kong led this round of financing. However, Momo's Form F-1 filed with the SEC reports that USD 5 million was raised in this round of financing. Momo Inc. completed its Series B financing in October 2012. This round of financing was led by two institution investors and received $100 million valuation. China Renaissance Partners acted as the exclusive financial advisor. There was much speculation as to whether or not Chinese e-commerce giant, Alibaba Group, was involved in this round of financing. Momo’s registration statement verifies this claim. In total, Momo raised approximately USD 40 million.
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Momo (software)
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History
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In October 2013, raised USD 45 million in Series C financing. Matrix Hong Kong, Gothic Partners, L.P., PJF Acorn I Trust, Gansett Partners, L.L.C., PH momo investment Ltd., Tenzing Holding 2011 Ltd., Alibaba Investment Limited, and DST Team Fund Limited were all issued and sold Series C preferred shares.
In May 2014, Momo raised USD 211.8 million in Series D financing. Momo sold Series D preferred shares to Sequoia Capital China Investment Holdco II, Ltd., Sequoia Capital China GF Holdco III-A, Ltd., SC China Growth III Co-Investment 2014-A, L.P., Rich Moon Limited, and Tiger Global Eight Holdings.
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Momo (software)
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Product and services
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Momo’s mobile application is available on Android, iOS, and Windows platforms. It enables users to establish and expand their social relationships based on similar locations and interests. Some features of the application include subsections like: Nearby Users, Groups, Message Board, Topics, and Nearby Events. Users can send multimedia instant messages as well as play single and multiplayer games within the app’s platform. Users also make a Facebook-like profile and are encouraged to include as much information as possible. Momo execs claim that this allows their software to create more accurate matches with nearby strangers. Momo is claimed to "sift through the clutter of mobile Internet users to find personalized matches for its users".
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Momo (software)
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Product and services
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Momo offers users paid membership subscriptions. A membership will cost around USD 2 a month, or less if a user commits to a longer term of use. Benefits of a paid membership include: VIP logos, advanced search options, discounts in the emoticon store, higher limits on maximum users in a group, and the ability to see a list of recent visitors to a user’s profile page. As of September 30, 2014, there was 2.3 million paid subscriptions.
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Momo (software)
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Product and services
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Like many other instant messaging services, Momo has integrated mobile games into their platform to monetize off their large user base. Third parties develop games, and revenues from in-game purchases are shared between Momo and the developers.
In August 2014, Momo launched Dao Dian Tong, a marketing tool for local merchants. Through Dao Dian Tong, local businesses and merchants can construct profile pages that allow Momo users to find them with the Momo’s LBS. Members can see the businesses just as they would see other Momo users.
Momo plans to further monetize user traffic by referring users from the Momo platform to e-commerce companies. Alibaba was specifically mentioned in Momo’s Form F-1.
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Momo (software)
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Corporate affairs and cultures
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Anti-plagiarism In December 2012, Momo made an official announcement to accuse Sina Corp of copycatting straight from all the features of Momo Group. However, Sina Corp did not give its formal response.
Statement made by NetEase On December 10, 2014, NetEase released a statement accusing that Tang Yan has professional ethic issues, business ethics issues, and has been detained due to personal affairs by the local police in 2007.
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Momo (software)
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Public opinions
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Hook-ups and homeless dogs On April 27, 2012, Mike Sui, a mixed-race comedian and performer in China, first posted his "12 Beijingers" viral video which attracted nearly 5.17 million hits. In this video, one character mentions Momo, for the first time calling it a magical tool to get laid (Chinese: 约炮神器; pinyin: yuē pào shén qì ). Momo has spent millions of dollars to reverse the image of Momo as a one-night stand app. Momo, through its Weibo account, continues to engage the online community through various campaigns. Momo’s latest online campaign focused on supporting the homeless cats and dogs of China.
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Momo (software)
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Public opinions
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Relationships Although Momo is widely considered as a social media application, there are claims that meetings on Momo resulted in marriage.
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Rectangle
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Rectangle
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In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square. The term "oblong" is occasionally used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as ABCD.
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Rectangle
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Rectangle
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The word rectangle comes from the Latin rectangulus, which is a combination of rectus (as an adjective, right, proper) and angulus (angle).
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Rectangle
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Rectangle
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A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals (therefore only two sides are parallel). It is a special case of an antiparallelogram, and its angles are not right angles and not all equal, though opposite angles are equal. Other geometries, such as spherical, elliptic, and hyperbolic, have so-called rectangles with opposite sides equal in length and equal angles that are not right angles.
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Rectangle
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Rectangle
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Rectangles are involved in many tiling problems, such as tiling the plane by rectangles or tiling a rectangle by polygons.
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Rectangle
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Characterizations
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A convex quadrilateral is a rectangle if and only if it is any one of the following: a parallelogram with at least one right angle a parallelogram with diagonals of equal length a parallelogram ABCD where triangles ABD and DCA are congruent an equiangular quadrilateral a quadrilateral with four right angles a quadrilateral where the two diagonals are equal in length and bisect each other a convex quadrilateral with successive sides a, b, c, d whose area is 14(a+c)(b+d) .: fn.1 a convex quadrilateral with successive sides a, b, c, d whose area is 12(a2+c2)(b2+d2).
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Rectangle
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Classification
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Traditional hierarchy A rectangle is a special case of a parallelogram in which each pair of adjacent sides is perpendicular.
A parallelogram is a special case of a trapezium (known as a trapezoid in North America) in which both pairs of opposite sides are parallel and equal in length.
A trapezium is a convex quadrilateral which has at least one pair of parallel opposite sides.
A convex quadrilateral is Simple: The boundary does not cross itself.
Star-shaped: The whole interior is visible from a single point, without crossing any edge.
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Rectangle
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Classification
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Alternative hierarchy De Villiers defines a rectangle more generally as any quadrilateral with axes of symmetry through each pair of opposite sides. This definition includes both right-angled rectangles and crossed rectangles. Each has an axis of symmetry parallel to and equidistant from a pair of opposite sides, and another which is the perpendicular bisector of those sides, but, in the case of the crossed rectangle, the first axis is not an axis of symmetry for either side that it bisects.
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Rectangle
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Classification
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Quadrilaterals with two axes of symmetry, each through a pair of opposite sides, belong to the larger class of quadrilaterals with at least one axis of symmetry through a pair of opposite sides. These quadrilaterals comprise isosceles trapezia and crossed isosceles trapezia (crossed quadrilaterals with the same vertex arrangement as isosceles trapezia).
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Rectangle
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Properties
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Symmetry A rectangle is cyclic: all corners lie on a single circle.
It is equiangular: all its corner angles are equal (each of 90 degrees).
It is isogonal or vertex-transitive: all corners lie within the same symmetry orbit.
It has two lines of reflectional symmetry and rotational symmetry of order 2 (through 180°).
Rectangle-rhombus duality The dual polygon of a rectangle is a rhombus, as shown in the table below.
The figure formed by joining, in order, the midpoints of the sides of a rectangle is a rhombus and vice versa.
Miscellaneous A rectangle is a rectilinear polygon: its sides meet at right angles.
A rectangle in the plane can be defined by five independent degrees of freedom consisting, for example, of three for position (comprising two of translation and one of rotation), one for shape (aspect ratio), and one for overall size (area).
Two rectangles, neither of which will fit inside the other, are said to be incomparable.
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Rectangle
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Formulae
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If a rectangle has length ℓ and width w it has area A=ℓw it has perimeter P=2ℓ+2w=2(ℓ+w) each diagonal has length d=ℓ2+w2 and when ℓ=w , the rectangle is a square.
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Rectangle
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Theorems
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The isoperimetric theorem for rectangles states that among all rectangles of a given perimeter, the square has the largest area.
The midpoints of the sides of any quadrilateral with perpendicular diagonals form a rectangle.
A parallelogram with equal diagonals is a rectangle.
The Japanese theorem for cyclic quadrilaterals states that the incentres of the four triangles determined by the vertices of a cyclic quadrilateral taken three at a time form a rectangle.
The British flag theorem states that with vertices denoted A, B, C, and D, for any point P on the same plane of a rectangle: (AP)2+(CP)2=(BP)2+(DP)2.
For every convex body C in the plane, we can inscribe a rectangle r in C such that a homothetic copy R of r is circumscribed about C and the positive homothety ratio is at most 2 and 0.5 × Area Area × Area (r)
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Rectangle
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Crossed rectangles
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A crossed quadrilateral (self-intersecting) consists of two opposite sides of a non-self-intersecting quadrilateral along with the two diagonals. Similarly, a crossed rectangle is a crossed quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals. It has the same vertex arrangement as the rectangle. It appears as two identical triangles with a common vertex, but the geometric intersection is not considered a vertex.
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Rectangle
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Crossed rectangles
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A crossed quadrilateral is sometimes likened to a bow tie or butterfly, sometimes called an "angular eight". A three-dimensional rectangular wire frame that is twisted can take the shape of a bow tie.
The interior of a crossed rectangle can have a polygon density of ±1 in each triangle, dependent upon the winding orientation as clockwise or counterclockwise.
A crossed rectangle may be considered equiangular if right and left turns are allowed. As with any crossed quadrilateral, the sum of its interior angles is 720°, allowing for internal angles to appear on the outside and exceed 180°.A rectangle and a crossed rectangle are quadrilaterals with the following properties in common: Opposite sides are equal in length.
The two diagonals are equal in length.
It has two lines of reflectional symmetry and rotational symmetry of order 2 (through 180°).
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Rectangle
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Other rectangles
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In spherical geometry, a spherical rectangle is a figure whose four edges are great circle arcs which meet at equal angles greater than 90°. Opposite arcs are equal in length. The surface of a sphere in Euclidean solid geometry is a non-Euclidean surface in the sense of elliptic geometry. Spherical geometry is the simplest form of elliptic geometry.
In elliptic geometry, an elliptic rectangle is a figure in the elliptic plane whose four edges are elliptic arcs which meet at equal angles greater than 90°. Opposite arcs are equal in length.
In hyperbolic geometry, a hyperbolic rectangle is a figure in the hyperbolic plane whose four edges are hyperbolic arcs which meet at equal angles less than 90°. Opposite arcs are equal in length.
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Rectangle
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Tessellations
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The rectangle is used in many periodic tessellation patterns, in brickwork, for example, these tilings:
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Rectangle
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Squared, perfect, and other tiled rectangles
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A rectangle tiled by squares, rectangles, or triangles is said to be a "squared", "rectangled", or "triangulated" (or "triangled") rectangle respectively. The tiled rectangle is perfect if the tiles are similar and finite in number and no two tiles are the same size. If two such tiles are the same size, the tiling is imperfect. In a perfect (or imperfect) triangled rectangle the triangles must be right triangles. A database of all known perfect rectangles, perfect squares and related shapes can be found at squaring.net. The lowest number of squares need for a perfect tiling of a rectangle is 9 and the lowest number needed for a perfect tilling a square is 21, found in 1978 by computer search.A rectangle has commensurable sides if and only if it is tileable by a finite number of unequal squares. The same is true if the tiles are unequal isosceles right triangles.
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Rectangle
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Squared, perfect, and other tiled rectangles
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The tilings of rectangles by other tiles which have attracted the most attention are those by congruent non-rectangular polyominoes, allowing all rotations and reflections. There are also tilings by congruent polyaboloes.
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Rectangle
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Unicode
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U+25AC ▬ BLACK RECTANGLE U+25AD ▭ WHITE RECTANGLE U+25AE ▮ BLACK VERTICAL RECTANGLE U+25AF ▯ WHITE VERTICAL RECTANGLE
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Hydrochlorothiazide
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Hydrochlorothiazide
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Hydrochlorothiazide, sold under the brand name Hydrodiuril among others, is a diuretic medication used to treat hypertension and swelling due to fluid build-up. Other uses include treating diabetes insipidus and renal tubular acidosis and to decrease the risk of kidney stones in those with a high calcium level in the urine. Hydrochlorothiazide is taken by mouth and may be combined with other blood pressure medications as a single pill to increase effectiveness. Hydrochlorothiazide is a thiazide medication which inhibits reabsorption of sodium and chloride ions from the distal convoluted tubules of the kidneys, causing a natriuresis. This initially increases urine volume and lowers blood volume. It is believed to reduce peripheral vascular resistance.Potential side effects include poor kidney function, electrolyte imbalances, including low blood potassium, and, less commonly, low blood sodium, gout, high blood sugar, and feeling lightheaded with standing.Two companies, Merck & Co. and Ciba Specialty Chemicals, state they discovered the medication which became commercially available in 1959. It is on the World Health Organization's List of Essential Medicines. It is available as a generic drug and is relatively affordable. In 2020, it was the eleventh most commonly prescribed medication in the United States, with more than 41 million prescriptions.
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Hydrochlorothiazide
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Medical uses
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Hydrochlorothiazide is used for the treatment of hypertension, congestive heart failure, symptomatic edema, diabetes insipidus, renal tubular acidosis. It is also used for the prevention of kidney stones in those who have high levels of calcium in their urine.Multiple studies suggest hydrochlorothiazide could be used as initial monotherapy in people with primary hypertension; however, the decision should be weighed against the consequence of long-term adverse metabolic abnormalities. Doses of hydrochlorothiazide of 50 mg or less over four years reduced mortality and development of cardiovascular diseases better than high-dose hydrochlorothiazide (50 mg or more) and beta-blockers. A 2019 review supported equivalence between drug classes for initiating monotherapy in hypertension, although thiazide or thiazide-like diuretics showed better primary effectiveness and safety profiles than angiotensin-converting enzyme inhibitors and non-dihydropyridine calcium channel blockers.Low doses (50 mg or less) of hydrochlorothiazide as first‐line therapy for hypertension were found to reduce total mortality and cardiovascular disease events over a four-year study. Hydrochlorothiazide appears be more effective than chlorthalidone in preventing heart attacks and strokes. Hydrochlorothiazide is less potent but may be more effective than chlorthalidone in reducing blood pressure. More robust studies are required to confirm which drug is superior in reducing cardiovascular events. Side effect profile for both drugs appear similar and are dose dependent.Hydrochlorothiazide is also sometimes used to prevent osteopenia and treat hypoparathyroidism, hypercalciuria, Dent's disease, and Ménière's disease.
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Hydrochlorothiazide
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Medical uses
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A low level of evidence, predominantly from observational studies, suggests that thiazide diuretics have a modest beneficial effect on bone mineral density and are associated with a decreased fracture risk when compared with people not taking thiazides. Thiazides decrease mineral bone loss by promoting calcium retention in the kidney, and by directly stimulating osteoblast differentiation and bone mineral formation.The combination of fixed-dose preparation such as losartan/hydrochlorothiazide has added advantages of a more potent antihypertensive effect with additional antihypertensive efficacy at the dose of 100 mg/25 mg when compared to monotherapy.
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Hydrochlorothiazide
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Adverse effects
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Hypokalemia, or low blood levels of potassium are an occasional side effect. It can be usually prevented by potassium supplements or by combining hydrochlorothiazide with a potassium-sparing diuretic Other disturbances in the levels of serum electrolytes, including hypomagnesemia (low magnesium), hyponatremia (low sodium), and hypercalcemia (high calcium) Hyperuricemia (high levels of uric acid in the blood). All thiazide diuretics including hydrochlorothiazide can inhibit excretion of uric acid by the kidneys, thereby increasing serum concentrations of uric acid. This may increase the incidence of gout in doses of ≥ 25 mg per day and in more susceptible patients such as male gender of <60 years old.
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Hydrochlorothiazide
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Adverse effects
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Hyperglycemia, high blood sugar Hyperlipidemia, high cholesterol and triglycerides Headache Nausea/vomiting Photosensitivity Weight gain PancreatitisPackage inserts contain vague and inconsistent data surrounding the use of thiazide diuretics in patients with allergies to sulfa drugs, with little evidence to support these statements. A retrospective cohort study conducted by Strom et al. concluded that there is an increased risk of an allergic reaction occurring in patients with a predisposition to allergic reactions in general rather than cross reactivity from structural components of the sulfonamide-based drug. Prescribers should examine the evidence carefully and assess each patient individually, paying particular attention to their prior history of sulfonamide hypersensitivity rather than relying on drug monograph information.There is an increased risk of non-melanoma skin cancer. In August 2020, the Australian Therapeutic Goods Administration required the Product Information (PI) and Consumer Medicine Information (CMI) for medicines containing hydrochlorothiazide to be updated to include details about an increased risk of non-melanoma skin cancer. In August 2020, the U.S. Food and Drug Administration (FDA) updated the drug label about an increased risk of non-melanoma skin cancer (basal cell skin cancer or squamous cell skin cancer).
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Hydrochlorothiazide
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Society and culture
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Brand names Hydrochlorothiazide is available as a generic drug under a large number of brand names, including Apo-Hydro, Aquazide, BPZide, Dichlotride, Esidrex, Hydrochlorot, Hydrodiuril, HydroSaluric, Hypothiazid, Microzide, Oretic and many others.To reduce pill burden and in order to reduce side effects, hydrochlorothiazide is often used in fixed-dose combinations with many other classes of antihypertensive drugs such as: ACE inhibitors — e.g. Prinzide or Zestoretic (with lisinopril), Co-Renitec (with enalapril), Capozide (with captopril), Accuretic (with quinapril), Monopril HCT (with fosinopril), Lotensin HCT (with benazepril), etc.
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Hydrochlorothiazide
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Society and culture
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Angiotensin receptor blockers — e.g. Hyzaar (with losartan), Co-Diovan or Diovan HCT (with valsartan), Teveten Plus (with eprosartan), Avalide or CoAprovel (with irbesartan), Atacand HCT or Atacand Plus (with candesartan), etc.
Beta blockers — e.g. Ziac or Lodoz (with bisoprolol), Nebilet Plus or Nebilet HCT (with nebivolol), Dutoprol or Lopressor HCT (with metoprolol), etc.
Direct renin inhibitors — e.g. Co-Rasilez or Tekturna HCT (with aliskiren) Potassium sparing diuretics: Dyazide and Maxzide triamterene Sport Use of hydrochlorothiazide is prohibited by the World Anti-Doping Agency for its ability to mask the use of performance-enhancing drugs.
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Hot stamping
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Hot stamping
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Hot stamping or foil stamping is a printing method of relief printing in which pre-dried ink or foils are transferred to a surface at high temperatures. The method has diversified since its rise to prominence in the 19th century to include a variety of processes. After the 1970s, hot stamping became one of the most important methods of decoration on the surface of plastic products.
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Hot stamping
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Process
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In a hot stamping machine, a die is mounted and heated, with the product to be stamped placed beneath it. A metallized or painted roll-leaf carrier is inserted between the two, and the die presses down through it. The dry paint or foil used is impressed into the surface of the product. The dye-stamping process itself is non-polluting because the materials involved are dry. Pressure and heat cause the relevant sections of the foil to become detached from the carrier material and become bonded with the printing surface.
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Hot stamping
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Tools
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Along with foil stamping machines, among the commonly used tools in hot stamping are dies and foil. Dies may be made of metal or silicone rubber, and they may be shaped directly or cast. They can carry high levels of detail to be transferred to the surface and may be shaped to accommodate irregularities in the surface.
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Hot stamping
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Tools
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Foils are multilayered coatings that transfer to the surface of the product. Non-metallic foils consist of an adherence base, a color layer, and a release layer. Metallic foils replace the color layer with a layer of chrome or vacuum-metallized aluminum. Metallic foil construction has a metal-like sheen and is available in different metal shades such as gold, silver, bronze, and copper. Pigment foil does not have a metallic sheen but may be glossy or matte. Holographic foil paper includes a 3-dimensional image to provide a distinctive appearance to specific areas of a digitally printed application. Printing is often done on leather or paper.
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Hot stamping
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Tools
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Different hot stamping machines serve different purposes, but the most common hot stamping machines are simple up-and-down presses. Three of the most common brands are Kwikprint, Kingsley, and Howard. However, for more industrial applications Kluge and Heidelberg presses are more commonly used.
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Hot stamping
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History
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In the 19th century, hot stamping became a popular method of applying gold tooling or embossing in book printing on leather and paper. The first patent for hot stamping was recorded in Germany by Ernst Oeser in 1892.From the 1950s onward, the method became a popular means of marking plastic . Hot Stamping technology for plastic is used for electric components (TV frames, audio components, refrigerators etc.), cosmetic containers (lipstick, cream, mascara, shampoo bottle etc.), automobile parts (interior and exterior materials).As of 1998, it was one of the most commonly used methods of security printing.Foil stamping can be used to make Radio-frequency identification (RFID) tags, although screen printing is faster and cheaper.
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PAQR6
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PAQR6
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Membrane progesterone receptor delta (mPRδ), or progestin and adipoQ receptor 6 (PAQR6), is a protein that in humans is encoded by the PAQR6 gene.
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Sofía Calero
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Sofía Calero
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Sofía Calero Diaz is a Spanish chemist who is a professor and Vice Dean of the Department of Applied Physics and Science Education at the Eindhoven University of Technology. Her research considers computational modelling of functional materials for applications in renewable energy. She was awarded the Spanish Royal Society of Chemistry Award for Scientific Excellence in 2018.
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Sofía Calero
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Early life and education
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Calero was born in Spain. She attended the Complutense University of Madrid and remained there for her doctoral research, which considered the thermodynamic properties of liquids of complex molecules. She moved to the University of Amsterdam as a Marie Curie Fellow.
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Sofía Calero
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Research and career
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Calero moved to the Pablo de Olavide University (UPO) in 2003, where she was named a Ramon y Cajal Fellow, and established a group who studied nanomaterials for applications in technologies. She was part of the European Cooperation in Science and Technology (COST) action on Computational materials sciences for efficient water splitting with nanocrystals from abundant elements. The programme looked to developed highly efficient energy converting devices (e.g. electrochemical cells for water-splitting). Calero was responsible for the development of Monte Carlo simulations of the project, and contributed to the software RASPA. RASPA is a simulation package that allows the study of adsorption and diffusion in nanoporous systems.Calero moved to the Eindhoven University of Technology in 2020. She was made Vice Dean of the Department of Applied Physics and Science Education. She focuses on the simulation of materials for renewable energies and the development of force field to predict the functional properties of materials.
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Sofía Calero
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Awards and honours
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2005 Marie Curie Award for Excellence 2011 European Research Council Consolidator Award 2018 Spanish Royal Society of Chemistry Award for Scientific Excellence 2020 TU/e Irene Curie Grant
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Sofía Calero
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Selected publications
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David Dubbeldam; Sofía Calero; Donald E. Ellis; Randall Q. Snurr (26 February 2015). "RASPA: molecular simulation software for adsorption and diffusion in flexible nanoporous materials". Molecular Simulation. 42 (2): 81–101. doi:10.1080/08927022.2015.1010082. ISSN 0892-7022. S2CID 53077055. Wikidata Q60395799.
D. Dubbeldam; S. Calero; T. J. H. Vlugt; R. Krishna; T. L. M. Maesen; B. Smit (August 2004). "United Atom Force Field for Alkanes in Nanoporous Materials". The Journal of Physical Chemistry B. 108 (33): 12301–12313. doi:10.1021/JP0376727. ISSN 1520-6106. S2CID 14390433. Wikidata Q59281748.
Sofia Calero; David Dubbeldam; Rajamani Krishna; Berend Smit; Thijs J H Vlugt; Joeri Denayer; Johan A. Martens; Theo L M Maesen (1 September 2004). "Understanding the role of sodium during adsorption: a force field for alkanes in sodium-exchanged faujasites". Journal of the American Chemical Society. 126 (36): 11377–11386. doi:10.1021/JA0476056. ISSN 0002-7863. PMID 15355121. Wikidata Q51618932.
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Interactive video
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Interactive video
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The term interactive video usually refers to a technique used to blend interaction and linear film or video.
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Interactive video
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History
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In 1962, Steve Russell, a student at the Massachusetts Institute of Technology (MIT), created Spacewar!, the world's first interactive computer game.In 1967, the first interactive film, The Cinema Machine, was released. While watching this film, the audience in the cinema theatre would choose one of two scenes during the plot fork. Switching between scenes was done manually by the projectionist.
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Interactive video
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History
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In 1972, Philips introduced the first laser disc (LD). Laser disc technology allowed for playback of any video chapter, making interactive video possible.In 1983, Sega released Astron Belt, the first interactive arcade game on LD. Also released in 1983 was Cinematronics's LD animated Dragon's Lair.
During the 1990s, several interactive Video CD formats were available such as CD-i (Compact Disc-Interactive) and Digital Video Interactive (DVI). Since 2000, the LD format has been superseded by the DVD format.
In 2008, YouTube added an interactive annotation feature to videos. This feature was disabled in 2019.Netflix started releasing interactive animations in 2016.TikTok announces support for interactive effects in 2021.
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Interactive video
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Interactive video
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Interactive video (also known as "IV") is a form of digital video that supports user interaction. Interactive videos provide the viewer the ability to click, on a desktop, or touch on mobile devices within the video for an action to occur. These clickable areas, or "hotspots," can perform an action when clicked or touched. For example, the video may display additional information, jump to a different part of the video or another video, or may change the storyline.
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Interactive video
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"Hotspots" In Video
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One popular use of interactive video technology is to add clickable points or 'hotspots' to the video. These hotspots allow the viewer to learn more about a particular object, product, or person in the video. A hotspot can trigger content to appear within the video such as text, images, videos or additional web content can be set within an iframe.
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Interactive video
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"Customizable" online interactive videos
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Customizable videos allow the user to adjust some variables and then play a video customised to the user's particular preferences. However the user does not actually interact with the video while it is playing. Recent examples of this form of video include: Miss Helga—customizable video ad for Volkswagen Golf created by Crispin Porter + Bogusky and The Barbarian Group.
Ave a Word—customizable video ad for Mini created by Glue London - Silver Cannes Lion 2006.
Electric Feel—customizable music video for the so-titled song by the band MGMT.
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Interactive video
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"Conversational" online interactive videos
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Conversational videos allow the user to interact with a video in a turn-based manner, almost as though the user was having a simple conversation with the characters in the video. Recent examples include: Subservient Chicken - a "conversational" interactive video ad for Burger King created by Crispin Porter + Bogusky and The Barbarian Group Cannes Grand Prix 2005.
A Conversation with Sir Ian - Interactive video interview with Sir Ian McKellen on Shakespeare. Created for the National Theatre by Martin Percy. BAFTA nominee 2007.
A conversation with Shimon Peres the Israeli President, created by interactive media and tech company Eko.
An interactive interview with John Hamm before he hosted the 2013 ESPY Awards, also created by Eko.
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Interactive video
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"Exploratory" online interactive videos
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Exploratory videos allow the user to move through a space or look at an object such as an artwork from multiple angles, almost as though the user was looking at the object in real life. The object or space is depicted using video loops, not still, creating a more "live" feel. Recent examples include: The BT Series - Interactive video exploration of the works of Tracey Emin, Anthony Gormley and Rachel Whiteread. Created for the Tate Gallery by Martin Percy. Webby Nominee 2006 and Honoree 2007.
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Interactive video
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"Exploratory" online interactive videos
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Tate Tracks - Interactive video exploration of various works, allowing the user to listen to music while looking at art. Created for the Tate Gallery by Martin Percy. Part of integrated campaign winning Cannes Gold Lion 2007.
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Interactive video
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Interactive video in early computer games
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The term interactive video or interactive movie sometimes refers to a nowadays uncommon technique used to create computer games or interactive narratives. Instead of 3D computer graphics an interactive image flow is created using premade video clips, often produced by overlaying computer-generated material with 12-inch videodisc images (where the setup is known as "level III" interactive video, to distinguish it from "level I" or videodisc-only, and "level II" requiring specially made videodisc players that support handheld-remote-based interactivity without using an external computer setup). The clips can be animation like in the video game Dragon's Lair or live action video like in the video game Night Trap. Compared to other computer graphics techniques interactive video tends to emphasize the looks and movement of interactive characters instead of interactivity.
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Interactive video
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Interactive video in YouTube
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In 2008 YouTube added Video Annotations as an interactive layer of clickable speech-bubble, text-boxes and spotlights. Users may add interactive annotations to their videos and by that a new trend of interactive videos arose, including choose-your-own-adventure video series, online video games using YouTube videos, spot-the-difference-game videos, animal-dubbing and more.
In 2009 YouTube added a community aspect to its Video Annotations feature by allowing video owners to invite their friends and community to add annotations to their movies.
Around 2010 YouTube released the interactive takeovers, certain channels had the opportunity to integrate an iFrame experience enabling them to include interactive videos. Some of the most successful takeovers were done by brands such as Samsung, Tipp-Ex or Chrome.YouTube discontinued the use of annotations on January 15, 2019.
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Interactive video
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Interactive video in advertising
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In 2014, video marketing platform Innovid was awarded a U.S. patent for interactive video technology.In 2017, the interactive video agency Adways created a specific format called InContent that enables to add interactive ads on a live stream for Roland-Garros.
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Interactive video
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Interactive video art
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Contemporary interactive video artists like Miroslaw Rogala, Greyworld, Raymond Salvatore Harmon, Lee Wells, Camille Utterback, Scott Snibbe, and Alex Horn have extended the form of interactive video through the dialog of gesture and the participatory involvement of both active and passive viewers. Perpetual art machine is a video art portal and interactive video installation that integrates over 1000 international video artists into a single interactive large scale video experience.
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Interactive video
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Interactive video in VJing
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Technically VJing is also about creating a stream of video interactively. this involves the user/operator to mix video clips, runtime plugins, and FX to the music's mood, bpm, and vibe.
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Interactive video
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Interactive video in research
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The human-computer interaction (HCI) research community as well as the multimedia research community have published several works on video interaction tools. A survey is provided in
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Entoglossus
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Entoglossus
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The entoglossus is an elongated bony process in lizards and birds that projects from the body of the hyoid apparatus into the tongue.
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Welding
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Welding
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Welding is a fabrication process that joins materials, usually metals or thermoplastics, by using high heat to melt the parts together and allowing them to cool, causing fusion. Welding is distinct from lower temperature techniques such as brazing and soldering, which do not melt the base metal (parent metal).
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Welding
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Welding
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In addition to melting the base metal, a filler material is typically added to the joint to form a pool of molten material (the weld pool) that cools to form a joint that, based on weld configuration (butt, full penetration, fillet, etc.), can be stronger than the base material. Pressure may also be used in conjunction with heat or by itself to produce a weld. Welding also requires a form of shield to protect the filler metals or melted metals from being contaminated or oxidized.
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Welding
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Welding
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Many different energy sources can be used for welding, including a gas flame (chemical), an electric arc (electrical), a laser, an electron beam, friction, and ultrasound. While often an industrial process, welding may be performed in many different environments, including in open air, under water, and in outer space. Welding is a hazardous undertaking and precautions are required to avoid burns, electric shock, vision damage, inhalation of poisonous gases and fumes, and exposure to intense ultraviolet radiation.
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Welding
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Welding
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Until the end of the 19th century, the only welding process was forge welding, which blacksmiths had used for millennia to join iron and steel by heating and hammering. Arc welding and oxy-fuel welding were among the first processes to develop late in the century, and electric resistance welding followed soon after. Welding technology advanced quickly during the early 20th century as world wars drove the demand for reliable and inexpensive joining methods. Following the wars, several modern welding techniques were developed, including manual methods like shielded metal arc welding, now one of the most popular welding methods, as well as semi-automatic and automatic processes such as gas metal arc welding, submerged arc welding, flux-cored arc welding and electroslag welding. Developments continued with the invention of laser beam welding, electron beam welding, magnetic pulse welding, and friction stir welding in the latter half of the century. Today, as the science continues to advance, robot welding is commonplace in industrial settings, and researchers continue to develop new welding methods and gain greater understanding of weld quality.
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Welding
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Etymology
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The term weld is of English origin, with roots from Scandinavia. It is often confused with the Old English word weald, meaning 'a forested area', but this word eventually morphed into the modern version, wild. The Old English word for welding iron was samod ('to bring together') or samodwellung ('to bring together hot', with hot more relating to red-hot or a swelling rage; in contrast to samodfæst, 'to bind together with rope or fasteners'). The term weld is derived from the Middle English verb well (wæll; plural/present tense: wælle) or welling (wællen), meaning 'to heat' (to the maximum temperature possible); 'to bring to a boil'. The modern word was probably derived from the past-tense participle welled (wællende), with the addition of d for this purpose being common in the Germanic languages of the Angles and Saxons. It was first recorded in English in 1590, from a version of the Christian Bible that was originally translated into English by John Wycliffe in the fourteenth century. The original version, from Isaiah 2:4, reads, "...thei shul bete togidere their swerdes into shares..." (they shall beat together their swords into plowshares), while the 1590 version was changed to, "...thei shullen welle togidere her swerdes in-to scharris..." (they shall weld together their swords into plowshares), suggesting this particular use of the word probably became popular in English sometime between these periods.The word is derived from the Old Swedish word valla, meaning 'to boil'. Sweden was a large exporter of iron during the Middle Ages, and many other European languages used different words but with the same meaning to refer to welding iron, such as the Illyrian (Greek) variti ('to boil'), Turkish kaynamak ('to boil'), Grison (Swiss) bulgir ('to boil'), or the Lettish (Latvian) sawdrit ('to weld or solder', derived from wdrit, 'to boil'). In Swedish, however, the word only referred to joining metals when combined with the word for iron (järn), as in valla järn (literally: 'to boil iron'). The word possibly entered English from the Swedish iron trade, or possibly was imported with the thousands of Viking settlements that arrived in England before and during the Viking Age, as more than half of the most common English words in everyday use are Scandinavian in origin.
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Welding
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History
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The history of joining metals goes back several millennia. The earliest examples of this come from the Bronze and Iron Ages in Europe and the Middle East. The ancient Greek historian Herodotus states in The Histories of the 5th century BC that Glaucus of Chios "was the man who single-handedly invented iron welding". Welding was used in the construction of the Iron pillar of Delhi, erected in Delhi, India about 310 AD and weighing 5.4 metric tons.The Middle Ages brought advances in forge welding, in which blacksmiths pounded heated metal repeatedly until bonding occurred. In 1540, Vannoccio Biringuccio published De la pirotechnia, which includes descriptions of the forging operation. Renaissance craftsmen were skilled in the process, and the industry continued to grow during the following centuries.In 1800, Sir Humphry Davy discovered the short-pulse electrical arc and presented his results in 1801. In 1802, Russian scientist Vasily Petrov created the continuous electric arc, and subsequently published "News of Galvanic-Voltaic Experiments" in 1803, in which he described experiments carried out in 1802. Of great importance in this work was the description of a stable arc discharge and the indication of its possible use for many applications, one being melting metals. In 1808, Davy, who was unaware of Petrov's work, rediscovered the continuous electric arc. In 1881–82 inventors Nikolai Benardos (Russian) and Stanisław Olszewski (Polish) created the first electric arc welding method known as carbon arc welding using carbon electrodes. The advances in arc welding continued with the invention of metal electrodes in the late 1800s by a Russian, Nikolai Slavyanov (1888), and an American, C. L. Coffin (1890). Around 1900, A. P. Strohmenger released a coated metal electrode in Britain, which gave a more stable arc. In 1905, Russian scientist Vladimir Mitkevich proposed using a three-phase electric arc for welding. Alternating current welding was invented by C. J. Holslag in 1919, but did not become popular for another decade.Resistance welding was also developed during the final decades of the 19th century, with the first patents going to Elihu Thomson in 1885, who produced further advances over the next 15 years. Thermite welding was invented in 1893, and around that time another process, oxyfuel welding, became well established. Acetylene was discovered in 1836 by Edmund Davy, but its use was not practical in welding until about 1900, when a suitable torch was developed. At first, oxyfuel welding was one of the more popular welding methods due to its portability and relatively low cost. As the 20th century progressed, however, it fell out of favor for industrial applications. It was largely replaced with arc welding, as advances in metal coverings (known as flux) were made. Flux covering the electrode primarily shields the base material from impurities, but also stabilizes the arc and can add alloying components to the weld metal.
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Welding
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History
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World War I caused a major surge in the use of welding, with the various military powers attempting to determine which of the several new welding processes would be best. The British primarily used arc welding, even constructing a ship, the "Fullagar" with an entirely welded hull.: 142 Arc welding was first applied to aircraft during the war as well, as some German airplane fuselages were constructed using the process. Also noteworthy is the first welded road bridge in the world, the Maurzyce Bridge in Poland (1928).
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Welding
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History
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During the 1920s, significant advances were made in welding technology, including the introduction of automatic welding in 1920, in which electrode wire was fed continuously. Shielding gas became a subject receiving much attention, as scientists attempted to protect welds from the effects of oxygen and nitrogen in the atmosphere. Porosity and brittleness were the primary problems, and the solutions that developed included the use of hydrogen, argon, and helium as welding atmospheres. During the following decade, further advances allowed for the welding of reactive metals like aluminum and magnesium. This in conjunction with developments in automatic welding, alternating current, and fluxes fed a major expansion of arc welding during the 1930s and then during World War II. In 1930, the first all-welded merchant vessel, M/S Carolinian, was launched.
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Welding
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History
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During the middle of the century, many new welding methods were invented. In 1930, Kyle Taylor was responsible for the release of stud welding, which soon became popular in shipbuilding and construction. Submerged arc welding was invented the same year and continues to be popular today. In 1932 a Russian, Konstantin Khrenov eventually implemented the first underwater electric arc welding. Gas tungsten arc welding, after decades of development, was finally perfected in 1941, and gas metal arc welding followed in 1948, allowing for fast welding of non-ferrous materials but requiring expensive shielding gases. Shielded metal arc welding was developed during the 1950s, using a flux-coated consumable electrode, and it quickly became the most popular metal arc welding process. In 1957, the flux-cored arc welding process debuted, in which the self-shielded wire electrode could be used with automatic equipment, resulting in greatly increased welding speeds, and that same year, plasma arc welding was invented by Robert Gage. Electroslag welding was introduced in 1958, and it was followed by its cousin, electrogas welding, in 1961. In 1953, the Soviet scientist N. F. Kazakov proposed the diffusion bonding method.Other recent developments in welding include the 1958 breakthrough of electron beam welding, making deep and narrow welding possible through the concentrated heat source. Following the invention of the laser in 1960, laser beam welding debuted several decades later, and has proved to be especially useful in high-speed, automated welding. Magnetic pulse welding (MPW) has been industrially used since 1967. Friction stir welding was invented in 1991 by Wayne Thomas at The Welding Institute (TWI, UK) and found high-quality applications all over the world. All of these four new processes continue to be quite expensive due to the high cost of the necessary equipment, and this has limited their applications.
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Welding
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Processes
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Gas welding The most common gas welding process is oxyfuel welding, also known as oxyacetylene welding. It is one of the oldest and most versatile welding processes, but in recent years it has become less popular in industrial applications. It is still widely used for welding pipes and tubes, as well as repair work.The equipment is relatively inexpensive and simple, generally employing the combustion of acetylene in oxygen to produce a welding flame temperature of about 3100 °C (5600 °F). The flame, since it is less concentrated than an electric arc, causes slower weld cooling, which can lead to greater residual stresses and weld distortion, though it eases the welding of high alloy steels. A similar process, generally called oxyfuel cutting, is used to cut metals.
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Welding
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Processes
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Arc welding These processes use a welding power supply to create and maintain an electric arc between an electrode and the base material to melt metals at the welding point. They can use either direct current (DC) or alternating current (AC), and consumable or non-consumable electrodes. The welding region is sometimes protected by some type of inert or semi-inert gas, known as a shielding gas, and filler material is sometimes used as well.
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Welding
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Processes
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Arc welding processes One of the most common types of arc welding is shielded metal arc welding (SMAW); it is also known as manual metal arc welding (MMAW) or stick welding. Electric current is used to strike an arc between the base material and consumable electrode rod, which is made of filler material (typical steel) and is covered with a flux that protects the weld area from oxidation and contamination by producing carbon dioxide (CO2) gas during the welding process. The electrode core itself acts as filler material, making a separate filler unnecessary.
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Welding
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Processes
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The process is versatile and can be performed with relatively inexpensive equipment, making it well suited to shop jobs and field work. An operator can become reasonably proficient with a modest amount of training and can achieve mastery with experience. Weld times are rather slow, since the consumable electrodes must be frequently replaced and because slag, the residue from the flux, must be chipped away after welding. Furthermore, the process is generally limited to welding ferrous materials, though special electrodes have made possible the welding of cast iron, stainless steel, aluminum, and other metals.
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Welding
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Processes
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Gas metal arc welding (GMAW), also known as metal inert gas or MIG welding, is a semi-automatic or automatic process that uses a continuous wire feed as an electrode and an inert or semi-inert gas mixture to protect the weld from contamination. Since the electrode is continuous, welding speeds are greater for GMAW than for SMAW.A related process, flux-cored arc welding (FCAW), uses similar equipment but uses wire consisting of a steel electrode surrounding a powder fill material. This cored wire is more expensive than the standard solid wire and can generate fumes and/or slag, but it permits even higher welding speed and greater metal penetration.Gas tungsten arc welding (GTAW), or tungsten inert gas (TIG) welding, is a manual welding process that uses a non-consumable tungsten electrode, an inert or semi-inert gas mixture, and a separate filler material. Especially useful for welding thin materials, this method is characterized by a stable arc and high-quality welds, but it requires significant operator skill and can only be accomplished at relatively low speeds.GTAW can be used on nearly all weldable metals, though it is most often applied to stainless steel and light metals. It is often used when quality welds are extremely important, such as in bicycle, aircraft and naval applications. A related process, plasma arc welding, also uses a tungsten electrode but uses plasma gas to make the arc. The arc is more concentrated than the GTAW arc, making transverse control more critical and thus generally restricting the technique to a mechanized process. Because of its stable current, the method can be used on a wider range of material thicknesses than can the GTAW process and it is much faster. It can be applied to all of the same materials as GTAW except magnesium, and automated welding of stainless steel is one important application of the process. A variation of the process is plasma cutting, an efficient steel cutting process.Submerged arc welding (SAW) is a high-productivity welding method in which the arc is struck beneath a covering layer of flux. This increases arc quality since contaminants in the atmosphere are blocked by the flux. The slag that forms on the weld generally comes off by itself, and combined with the use of a continuous wire feed, the weld deposition rate is high. Working conditions are much improved over other arc welding processes, since the flux hides the arc and almost no smoke is produced. The process is commonly used in industry, especially for large products and in the manufacture of welded pressure vessels. Other arc welding processes include atomic hydrogen welding, electroslag welding (ESW), electrogas welding, and stud arc welding. ESW is a highly productive, single-pass welding process for thicker materials between 1 inch (25 mm) and 12 inches (300 mm) in a vertical or close to vertical position.
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Welding
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Processes
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Arc welding power supplies To supply the electrical power necessary for arc welding processes, a variety of different power supplies can be used. The most common welding power supplies are constant current power supplies and constant voltage power supplies. In arc welding, the length of the arc is directly related to the voltage, and the amount of heat input is related to the current. Constant current power supplies are most often used for manual welding processes such as gas tungsten arc welding and shielded metal arc welding, because they maintain a relatively constant current even as the voltage varies. This is important because in manual welding, it can be difficult to hold the electrode perfectly steady, and as a result, the arc length and thus voltage tend to fluctuate. Constant voltage power supplies hold the voltage constant and vary the current, and as a result, are most often used for automated welding processes such as gas metal arc welding, flux-cored arc welding, and submerged arc welding. In these processes, arc length is kept constant, since any fluctuation in the distance between the wire and the base material is quickly rectified by a large change in current. For example, if the wire and the base material get too close, the current will rapidly increase, which in turn causes the heat to increase and the tip of the wire to melt, returning it to its original separation distance.The type of current used plays an important role in arc welding. Consumable electrode processes such as shielded metal arc welding and gas metal arc welding generally use direct current, but the electrode can be charged either positively or negatively. In welding, the positively charged anode will have a greater heat concentration, and as a result, changing the polarity of the electrode affects weld properties. If the electrode is positively charged, the base metal will be hotter, increasing weld penetration and welding speed. Alternatively, a negatively charged electrode results in more shallow welds. Non-consumable electrode processes, such as gas tungsten arc welding, can use either type of direct current, as well as alternating current. However, with direct current, because the electrode only creates the arc and does not provide filler material, a positively charged electrode causes shallow welds, while a negatively charged electrode makes deeper welds. Alternating current rapidly moves between these two, resulting in medium-penetration welds. One disadvantage of AC, the fact that the arc must be re-ignited after every zero crossings, has been addressed with the invention of special power units that produce a square wave pattern instead of the normal sine wave, making rapid zero crossings possible and minimizing the effects of the problem.
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