title: Alberto Santos-Dumont

text: The conflict continued, and aeroplanes attacked Campo de Marte, in São Paulo, on 23 July. They may have flown over Guarujá, and the sight of planes in combat may have caused deep anguish in Santos-Dumont who, in his nephew's absence, died by suicide at the age of 59. Decree No. 21,668 established three days of mourning. Coroners Roberto Catunda and Angelo Esmolari, who signed his , recorded the death as a heart attack. The chambermaids who found the body reported that he had hanged himself with his tie. According to Henrique Lins de Barros, for a long time it was forbidden to say that he had killed himself and that the idea that he committed suicide due to the military use of the aeroplane would be a legend of the getulista period, as the government sought to mythologise him; the suicide could weaken this. The real cause may have been depression and bipolar disorder. The order of the governor Pedro de Toledo, following Santos-Dumont's death, was: "There will be no investigation, Santos Dumont did not commit suicide". Journalist publicised the cause of death as suicide in 1944.


title: Alberto Santos-Dumont

text: Santos-Dumont left no descendants or suicide note. His body was buried in São João Batista Cemetery, in Rio de Janeiro, on 21 December 1932, during a storm, under the replica of the Icarus de Saint Cloud he had built, after his remains had remained in the São Paulo capital for five months. Physician Walther Haberfield secretly removed his heart during the embalming process and preserved it in formaldehyde. After keeping this a secret for twelve years, he wanted to return it to the Santos-Dumont family, who refused it. The doctor then donated the heart to the Brazilian government after a request from Panair do Brasil. The heart is on display at the Air Force Museum in Campo dos Afonsos, Rio de Janeiro, inside a sphere carried by Icarus, designed by Paulo da Rocha Gomide.


title: Alberto Santos-Dumont

text: On 25 July 1909, Louis Blériot crossed the English Channel, becoming a hero in France. In a letter, Santos-Dumont congratulated Blériot, his friend, with the following words: "This transformation of geography is a victory of air navigation over sea navigation. One day, perhaps, thanks to you, the airplane will cross the Atlantic". Blériot then replied, "I have done nothing but follow and imitate you. Your name to the aviators is a flag. You are our leader." Blériot's last project was named "Santos-Dumont". says that the inventor's influence was both in his aeronautical development and in advocating the public and personal use of aeronautics, whether through lighter or heavier-than-air.


title: Alberto Santos-Dumont

text: During his career, Santos-Dumont's image was printed on products, his Panama hat and collar were copied, his balloons were modelled as toys, and confectioners made cakes shaped like airships. The Aéro-Club de France honoured him with two monuments: the first, in 1910, erected on the Bagatelle Gamefield, where he had flown with the "Oiseau de Proie", and the second, in 1913, in Saint-Cloud, to commemorate the flight of airship No. 6 in 1901. On the unveiling of the Saint-Cloud monument - a statue of Icarus - one of his long-time friends, the cartoonist Georges Goursat (aka "Sem"), wrote the following for the magazine "L'Illustration":


title: Alberto Santos-Dumont

text: On 31 July 1932 state decree No. 10,447 changed the name of the town of Palmira, in Minas Gerais, to Santos-Dumont. Law No. 218, of 4 July 1936, declared 23 October to be "aviator's day," celebrating the historic flight on this date in 1906, "so that this commemoration will always have a worthy civic, sporting, and cultural celebration, especially in schools, emphasizing the initiative of the remarkable Brazilian Santos-Dumont". On 16 October 1936 Rio de Janeiro's first airport was named after him.


title: Alberto Santos-Dumont

text: Law No. 165, dated 5 December 1947, granted him the honorary rank of lieutenant brigadier. Santos-Dumont's birthplace in Cabangu, Minas Gerais, was made into the Cabangu Museum by state decree (MG) No. 5,057, on 18 July 1956. Law No. 3636, of 22 September 1959, made him an honorary air marshal.


title: Alberto Santos-Dumont

text: In 1976, the International Astronomical Union gave Santos-Dumont's name to a lunar crater (27.7°N 4.8°E). He is the only South American to be so honoured. Law 7.243, of 4 November 1984, granted him the title of "Patron of the Brazilian Aeronautics". On 13 October 1997, the then President of the United States, Bill Clinton, visiting Brazil, gave a speech at the Itamaraty Palace, referring to Santos-Dumont as the "father of aviation".


title: Alberto Santos-Dumont

text: On 18 October 2005, the Brazilian Space Agency (AEB) and the Russian Federal Space Agency (Roscosmos) signed an agreement to carry out the Missão Centenário, which took Brazilian astronaut Marcos César Pontes to the International Space Station. The mission is a tribute to the centennial of Santos-Dumont's flight on the 14-bis, on 23 October 1906. The Soyuz TMA-8 spacecraft launched on 30 March 2006, from the Baikonur Launch Centre (Kazakhstan). On 26 July 2006 his name was included in the Steel Book of National Heroes in the Panteão da Pátria, in Brasilia, granting him the status of National Hero.


title: Alberto Santos-Dumont

text: In 1902 the poet composed the song "" in honour of Santos-Dumont's achievements. In 1956, the Brazilian Post Office released a series of stamps commemorating the fiftieth anniversary of the first flight of a heavier-than-air aircraft. In 1973, they released a series of stamps to celebrate Santos-Dumont's centenary. On 23 October 2006, they launched a commemorative stamp for the centenary of the flight of the 14-bis. In the same month, the Brazilian Central Bank issued a coin commemorating Santos-Dumont's invention. He was depicted on the cruzeiro and cruzeiro novo banknotes.


title: Alberto Santos-Dumont

text: In 2012, Cartier produced a series of watches named after Santos-Dumont, celebrating the partnership between him and the brand; as a publicity piece, an award-winning film was made by France's Quad Productions entitled "L'Odyssée de Cartier".


title: Alberto Santos-Dumont

text: In 2015, author Arthur Japin published the historical novel "De gevleugelde" ("O Homem com Asas", in Brazil), about the aviator's life and death, and the extraction of his heart.


title: Alberto Santos-Dumont

text: During the opening ceremony of the 2016 Summer Olympic Games at the Maracanã Stadium, a replica of Santos-Dumont's 14-bis, was built in the stadium and, with the help of steel cables, flew over the runway, "taking off" for a flight over the city of Rio de Janeiro.


title: Alberto Santos-Dumont

text: Santos-Dumont has been portrayed as a character in film, television, and theatre, played by in Marcel Camus' "Les Faucheurs de marguerites" (1974); by in the miniseries Um Só Coração (2004); by Daniel de Oliveira in the short film (2006); by Ricardo Napoleão in ' play "Mais Pesado que o Ar – Santos Dumont" (1996); and by Henri Lalli in the play "Santos-Dumont" (since 2003). Fernanda Montenegro played a transsexual descendant of Santos-Dumont in the soap opera "Zazá" (1997). TV Brasil produced the programme , with a character named Betinho, depicting Santos-Dumont as a child.


title: Alberto Santos-Dumont

text: On 10 November 2019, HBO released the miniseries "Santos-Dumont" across Latin America. The production follows the aviator's steps from childhood in his family's coffee fields Minas Gerais and São Paulo (where the family settled), to the sophisticated salons and aeroclubs in Paris, where Santos-Dumont made his historic flight in the 14-bis in 1906. Actor played the inventor.


title: Alberto Santos-Dumont

text: Santos-Dumont never married and was rather shy, and his sexuality has long been debated, including by his biographers.


title: Alberto Santos-Dumont

text: Researcher Henrique Lins de Barros, from the Brazilian Center for Physics Research, rejects the thesis that the Brazilian inventor was homosexual, arguing that he was just a man concerned with his appearance. According to Barros, "The French refinement sounded like homosexual affectation to American journalists, who described him as effeminate. (...) Hoffman did not understand the customs and values of the time and saw everything with the distorted view that was held at that time in the United States." Also, in his article "Alberto Santos-Dumont: Pioneiro da Aviação," Barros notes that Santos-Dumont had a media-heralded engagement to Edna Powers, daughter of an American millionaire. Cosme Degenar Drumond, writer of "Alberto Santos-Dumont: Novas Revelações," says that in France Santos-Dumont has "a reputation as a conqueror". Santos-Dumont was listed in the list of the "100 VIP homosexuals of Brazil," formulated by anthropologist Luiz Mott, rekindling the discussion about Santos-Dumont's sexuality. Santos-Dumont's family has denied that he was homosexual. Santos-Dumont allegedly had a homo-affective affair with Georges Goursat in 1901.


title: Alberto Santos-Dumont

text: Yolanda Penteado, in her autobiography "Tudo em cor de rosa", says: "(...) I met Alberto Santos-Dumont, a brother of my uncle Henrique. Seu Alberto, as we called him, came every day for dinner and stayed over, saying it was to see the moon come out. In Flamengo the full moon nights were really beautiful. He was a restless person. I thought it was funny that he gave me so much attention. And Aunt Amalia would say: "Alberto, you are getting dizzy dating this girl". Alberto, in fact, used to court me, bring me chocolates, flowers, take me for walks. The people who knew him best said that when he saw me he became electric".


title: Alberto Santos-Dumont

text: In a 1901 letter a friend, Santos Dumont wrote that he was in love with an American woman: "[M]y heart is already very much with her... and I don't know what to do, whether to stop the courtship or to continue."


title: Alberto Santos-Dumont

text: Santos Dumont is traditionally described as having developed multiple sclerosis. However, this diagnosis is disputed by other researchers:


title: Alberto Santos-Dumont

text: Henrique Lins de Barros questions this diagnosis: "I think it difficult to believe in this hypothesis of multiple sclerosis... How could anyone suffering from a degenerative disease like multiple sclerosis ski in Saint Moritz in the 1910s and play tennis in the 1920s, as he did?" Marcos Villares Filho, great-grandnephew of Santos-Dumont, says that he probably had a profound depression. The documentation of the time does not provide a good deal of information to determine that Santos Dumont suffered from multiple sclerosis.


title: Alberto Santos-Dumont

text: The original diagnosis came after consulting a doctor due to symptoms such as dizziness and double vision. Later, this diagnosis was challenged by other doctors, who believed that the aviator was already suffering from psychiatric manifestations. The symptoms reported for the original diagnosis would be only two related to multiple sclerosis.


title: Alberto Santos-Dumont

text: Bipolar disorder is one of the disorders most connected with suicide and Santos Dumont already had precedents in his family, with his mother having taken her own life in 1902 and that the aviator already demonstrated at the end of his life a number of epidemiological risk factors for suicide. It is hard to determine any diagnosis due to the lack of medical documentation.


title: Blastocyst

text: The blastocyst is a structure formed in the early embryonic development of mammals. It possesses an inner cell mass (ICM) also known as the "embryoblast" which subsequently forms the embryo, and an outer layer of trophoblast cells called the trophectoderm. This layer surrounds the inner cell mass and a fluid-filled cavity known as the blastocoel. In the late blastocyst the trophectoderm is known as the trophoblast. The trophoblast gives rise to the chorion and amnion, the two fetal membranes that surround the embryo. The placenta derives from the embryonic chorion (the portion of the chorion that develops villi) and the underlying uterine tissue of the mother. The name "blastocyst" arises from the Greek ' ("a sprout") and ' ("bladder, capsule"). In other animals this is a structure consisting of an undifferentiated ball of cells and is called a blastula.


title: Blastocyst

text: In humans, blastocyst formation begins about five days after fertilization when a fluid-filled cavity opens up in the morula, the early embryonic stage of a ball of 16 cells.


title: Blastocyst

text: The blastocyst has a diameter of about 0.1–0.2 mm and comprises 200–300 cells following rapid cleavage (cell division). About seven days after fertilization, the blastocyst undergoes implantation, embedding into the endometrium of the uterine wall. There it will undergo further developmental processes, including gastrulation. Embedding of the blastocyst into the endometrium requires that it hatches from the zona pellucida, the egg coat that prevents adherence to the fallopian tube as the pre-embryo makes its way to the uterus.


title: Blastocyst

text: The use of blastocysts in "in vitro" fertilization (IVF) involves culturing a fertilized egg for five days before transferring it into the uterus. It can be a more viable method of fertility treatment than traditional IVF. The inner cell mass of blastocysts is the source of embryonic stem cells, which are broadly applicable in stem cell therapies including cell repair, replacement and regeneration. Assisted zona hatching may also be used in IVF, and other fertility treatments.


title: Blastocyst

text: The blastocyst stage occurs between 5 and 9 days after conception. During embryonic development, after fertilization (approximately 5–6 days in the human), the cells of the morula begin to undergo cell differentiation, and the morula changes into the blastocyst. In the uterus the zona pellucida surrounding the blastocyst breaks down, allowing it to implant into the uterine wall. Implantation marks the end of the germinal stage of embryogenesis, and the beginning of gestation.


title: Blastocyst

text: The zygote develops by mitosis, and when it has developed into a compacted ball of 8-16 cells becomes known as the morula. Until this stage in development, all cells (blastomeres) are autonomous and not specified to any particular subsequent functional development. The morula then develops by cavitation to become the blastocyst, or in many other animals the blastula. Cellular differentiation then develops the morula's cells into two types: trophoblast cells that surround the blastocoel and an inner mass of cells (the embryoblast). The inner cell mass consists of embryonic stem cells. The conceptus is then known as the blastocyst.


title: Blastocyst

text: Before cell differentiation takes place there are two transcription factors, Oct-4 and nanog that are uniformly expressed on all of the cells, but both of these transcription factors are turned off in the trophoblast once it has formed. The side of the blastocyst where the inner cell mass forms is called the embryonic pole, and the opposite side is the abembryonic pole. The outer layer of trophoblast cells, resulting from compaction, pumps sodium ions into the blastocyst, which causes water to enter through osmosis and form the internal fluid-filled blastocyst cavity (blastocoel). The blastocoel, trophoblast cells, and inner cell mass are hallmarks of the blastocyst.


title: Blastocyst

text: Implantation is critical to the survival and development of the early human embryo. It establishes a connection between the mother and the early embryo which will continue through the remainder of the pregnancy. Implantation is made possible through structural changes in both the blastocyst and endometrial wall. The zona pellucida surrounding the blastocyst breaches, referred to as hatching. This removes the constraint on the physical size of the embryonic mass and exposes the outer cells of the blastocyst to the interior of the uterus. Furthermore, hormonal changes in the mother, specifically a peak in luteinizing hormone (LH), prepare the endometrium to receive and envelop the blastocyst. The immune system is also modulated to allow for the invasion of the foreign embryonic cells. Once bound to the extracellular matrix of the endometrium, trophoblast cells secrete enzymes and other factors to embed the blastocyst into the uterine wall. The enzymes released degrade the endometrial lining, while autocrine growth factors such as human chorionic gonadotropin (hCG) and insulin-like growth factor (IGF) allow the blastocyst to further invade the endometrium.


title: Blastocyst

text: Implantation in the uterine wall allows for the next step in embryogenesis, gastrulation, which includes the formation of the placenta from trophoblastic cells and differentiation of the inner cell mass into the amniotic sac and epiblast.


title: Blastocyst

text: The blastocoel fluid cavity contains amino acids, growth factors, and other molecules necessary for cellular differentiation.


title: Blastocyst

text: Multiple processes control cell lineage specification in the blastocyst to produce the trophoblast, epiblast, and primitive endoderm. These processes include gene expression, cell signaling, cell-cell contact and positional relationships, and epigenetics.


title: Blastocyst

text: Once the inner cell mass has been established within the blastocyst, it prepares for further specification into the epiblast and primitive endoderm. This process of specification known as cell fate determination is carried out in part by fibroblast growth factor (FGF) signaling which generates a MAP kinase pathway to alter cellular genomes. Further segregation of blastomeres into the trophectoderm and inner cell mass are regulated by the homeodomain protein, Cdx2. This transcription factor represses the expression of Oct4 and Nanog transcription factors in the trophoblast. These genomic alterations allow for the progressive specification of both epiblast and primitive endoderm lineages at the end of the blastocyst phase of development preceding gastrulation. Much of the research conducted on these early embryonic stages is on mouse embryos and specific factors may differ between mammals.


title: Blastocyst

text: During implantation, the trophoblast gives rise to extraembryonic membranes and cell types that will eventually form most of the fetal placenta, the specialized organ through which the embryo obtains maternal nourishment necessary for subsequent exponential growth. The specification of the trophoblast is controlled by the combination of morphological cues arising from cell polarity with differential activity of signaling pathways such as Hippo and Notch, and the restriction to outer cells of lineage specifiers such as CDX2.


title: Blastocyst

text: In the mouse, primordial germ cells are specified from epiblast cells, a process that is accompanied by extensive genome-wide epigenetic reprogramming. Reprogramming involves global DNA demethylation and chromatin reorganization resulting in cellular totipotency. The process of genome-wide demethylation involves the DNA base excision repair pathway.


title: Blastocyst

text: Trophoblasts express integrin on their cell surfaces which allow for adhesion to the extracellular matrix of the uterine wall. This interaction allows for implantation and triggers further specification into the three different cell types, preparing the blastocyst for gastrulation.


title: Blastocyst

text: The level of human chorionic gonadotropin (hCG) secreted by the blastocyst during implantation is the factor measured in a pregnancy test. hCG can be measured in both blood and urine to determine whether a woman is pregnant. More hCG is secreted in a multiple pregnancy. Blood tests of hCG can also be used to check for abnormal pregnancies.


title: Blastocyst

text: In vitro fertilization (IVF) is an alternative to traditional "in vivo" fertilization for fertilizing an egg with sperm and implanting that embryo into a female's womb. For many years the embryo was inserted into the uterus two to three days after fertilization. However at this stage of development it is very difficult to predict which embryos will develop best, and several embryos were typically implanted. Several implanted embryos increased the likelihood of a developing fetus but also led to the development of multiple fetuses. This was a major problem and drawback for using embryos in IVF.


title: Blastocyst

text: The use of blastocysts for human IVF has proved successful. A blastocyst is implanted five to six days after the eggs have been fertilized. After five or six days it is much easier to determine which embryos will result in healthy live births. Knowing which embryos will succeed allows just one blastocyst to be implanted, cutting down dramatically on the health risk and expense of multiple births. Now that the nutrient requirements for embryonic and blastocyst development have been determined, it is much easier to give embryos the correct nutrients to sustain them into the blastocyst phase.


title: Blastocyst

text: Embryo transfer following in vitro fertilization is a procedure in which a catheter is inserted into the vagina, guided through the cervix via ultrasound, and into the uterine cavity where the blastocysts are inserted into the womb.


title: Blastocyst

text: Blastocysts also offer an advantage because they can be used to genetically test the cells to check for genetic problems. There are enough cells in a blastocyst that a few trophectoderm cells can be removed without disturbing the developing blastocyst. These cells can be tested for chromosome aneuploidy using preimplantation genetic screening (PGS), or specific conditions such as cystic fibrosis, often known as preimplantation genetic diagnosis (PGD).


title: Blastocyst

text: In an embryo transfer procedure following an initial ultrasound, a speculum is used to open the walls of the vagina, and using a catheter an embryo is passed through the tube for placement into the womb.


title: Shelby Young

text: Shelby Young is an American actress. She is known for her roles on "American Horror Story", "Days of Our Lives", "The Social Network" and the "Star Wars" franchise.


title: Shelby Young

text: Young always wanted to be an actor. As a child, she loved performing for her friends and family, and performed in pageantry, theater and commercials while living there.


title: Shelby Young

text: As she has grown, her career focus has shifted to voice over and motion capture acting for animation and video.


title: Shelby Young

text: Young's first television role was in 2001 when she played the role of Sue Ann Butler on the Showtime series "Going to California". In 2002, Young played Stephanie in the unaired pilot for "LazyTown". From 2005 to 2008, she had a recurring role as Jennifer on "Everybody" "Hates Chris", and from 2009 to 2011, she recurred on "Days of Our Lives" as Kinsey. Young has also had guest starring roles on the MTV series "Awkward" (2011), "Ghost Whisperer" (2006), and "Freddie" (2006). She then co-starred in the Universal Studios film "Wild Child" (2008). In 2010, Young played the role of KC in the film "The Social Network".


title: Shelby Young

text: In 2011, she had a recurring role as Leah on "", the first season in the anthology series. In addition, Young played the role of Rose in "The Midnight Game", which was released in 2013 by Anchor Bay Entertainment.


title: Shelby Young

text: Young starred in the found-footage horror film "Nightlight"; the film was released in a limited release and through video on demand on March 27, 2015. That same year, she appeared in the film "The House Sitter" opposite Kate Ashfield. She also starred in the horror-thriller film "A Haunting in Cawdor", which was released in the United Kingdom on October 9, 2015, and in the United States in March 2016.


title: Shelby Young

text: As a voice actress, Young is known in the Star Wars galaxy for voicing multiple characters across their animation titles and video games. Her most notable role may be voicing Princess Leia Organa in projects like "", the Disney Channel series "Star Wars Forces of Destiny" and the Disney Plus TV special, "". Young is also known by video game fans for her work as Soph Blazkowicz, whom she brought to life through both voice and movement via MoCap, in "" as one of the first-ever playable female characters in the long-standing franchise. Young's resume includes other AAA franchises such as "Call of Duty", "Battlefield", "Final Fantasy" and "Dead Rising 3", where she voiced and provided MoCap for the lead role of Annie. Young currently recurs as Rayna on Nickelodeon's, "Baby Shark's Big Show!" and she can be heard in the upcoming game "".


title: Shelby Young

text: Young has recently started doing voice impressions on TikTok, YouTube and other social media platforms and has amassed a following of over 4 million users between the platforms.


title: Andrea Meza

text: Alma Andrea Meza Carmona (born 13 August 1994) is a Mexican model and beauty pageant titleholder who was crowned Miss Universe 2020. Since winning the title, she became the third Mexican woman to be crowned Miss Universe. Meza holds the record of the shortest completed reign in Miss Universe history to date.


title: Andrea Meza

text: She had previously been crowned Mexicana Universal 2020 and Miss Mexico 2017, and placed as the first runner-up at Miss World 2017.


title: Andrea Meza

text: Meza was born on 13 August 1994 in Chihuahua City to parents Alma Carmona and Santiago Meza. She grew up in Chihuahua City as the eldest of three daughters, and is of partial Chinese descent. After completing secondary school, Meza enrolled in the Autonomous University of Chihuahua, where she studied software engineering. She graduated with her degree in 2017, and subsequently began working in Mexico as a software engineer in addition to her career as a model.


title: Andrea Meza

text: Meza began her pageantry career in 2016, after she was selected to represent Chihuahua at Miss World Mexico 2016. This was the first edition of the pageant after the Nuestra Belleza México competition lost its license for Miss World. In the pageant, Meza advanced to the top sixteen, then the top ten, and ultimately the top five. After reaching the top five, Meza was one of the two contestants awarded a crown, being crowned as Miss Mexico 2017. Ana Girault, representing Mexico City, was crowned Miss Mexico 2016 and given the opportunity to represent Mexico at Miss World 2016, while Meza was given the opportunity to represent Mexico at Miss World 2017. Also, Meza won the sports challenge at the competition.


title: Andrea Meza

text: As the winner of Miss Mexico 2017, Meza represented Mexico at the 67th edition of Miss World 2017, held on 18 November 2017 at Sanya City Arena in Sanya, China. In the pre-pageant activities, Meza won group sixteen of the Head-to-Head Challenge, which gave her direct entry into the top forty. Additionally, she placed as the fourth runner-up in the talent competition.


title: Andrea Meza

text: During the finals of the competition, Meza advanced from the top forty into the top fifteen, top ten, and top five. After reaching the top five, Julia Morley announced Meza as the first runner-up behind the winner, Manushi Chhillar from India. In addition to her first runner-up finish, Meza was additionally crowned Miss World Americas, placing her within the 2017 Miss World Continental Queens of Beauty.


title: Andrea Meza

text: In 2020, Meza was crowned Mexicana Universal Chihuahua 2020, allowing her to represent Chihuahua at Mexicana Universal 2020. During pre-pageant activities, Meza won six challenges, including the sports challenge. The final was held on 29 November 2020 in Querétaro City. Meza advanced to the top fifteen and top ten, ultimately being crowned Mexicana Universal 2020.


title: Andrea Meza

text: As Mexicana Universal, Meza represented Mexico at the Miss Universe 2020 pageant. The final of the competition was held on May 16, 2021, at the Seminole Hard Rock Hotel & Casino Hollywood in Hollywood, Florida, after being postponed from late 2020 to May 2021 due to the COVID-19 pandemic. Meza advanced from the initial pool of 74 contestants to the top 21, then the top ten, and finally the top five, where she was crowned the winner by the outgoing titleholder Zozibini Tunzi of South Africa. Following her win, she became the third Mexican woman to win the crown, following Lupita Jones in 1991 and Ximena Navarrete in 2010.


title: Andrea Meza

text: With Meza's victory at Miss Universe 2020, this marked Mexico's second consecutive year in the top 3 after Sofía Aragón, Mexicana Universal 2019, finished as the second runner-up at Miss Universe 2019. Meza also surpassed Brook Lee's record of being the oldest to win Miss Universe by winning at the age of 26 years and 276 days.


title: Andrea Meza

text: After winning Miss Universe, Meza was succeeded as Mexicana Universal by Débora Hallal, who was appointed Mexicana Universal 2021.


title: Andrea Meza

text: In her capacity as Miss Universe, Meza traveled to various cities within the United States, South Africa, Puerto Rico, Dominican Republic, The Bahamas, Israel, and her home country of Mexico.


title: Andrea Meza

text: On December 13, 2021, Meza crowned Harnaaz Sandhu of India as her successor, marking the end of the shortest completed reign in Miss Universe history of 211 days.


title: Flocculation

text: Flocculation, in the field of chemistry, is a process by which colloidal particles come out of suspension to sediment under the form of floc or flake, either spontaneously or due to the addition of a clarifying agent. The action differs from precipitation in that, prior to flocculation, colloids are merely suspended, under the form of a stable dispersion (where the internal phase (solid) is dispersed throughout the external phase (fluid) through mechanical agitation) and are not truly dissolved in solution.


title: Flocculation

text: Coagulation and flocculation are important processes in water treatment with coagulation aimed to destabilize and aggregate particles through chemical interactions between the coagulant and colloids, and flocculation to sediment the destabilized particles by causing their aggregation into floc.


title: Flocculation

text: According to the IUPAC definition, flocculation is "a process of contact and adhesion whereby the particles of a dispersion form larger-size clusters". Flocculation


title: Flocculation

text: Basically, coagulation is a process of addition of coagulant to destabilize a stabilized charged particle. Meanwhile, flocculation is a mixing technique that promotes agglomeration and assists in the settling of particles. The most common used coagulant is alum, Al(SO)·14HO.


title: Flocculation

text: During flocculation, gentle mixing accelerates the rate of particle collision, and the destabilized particles are further aggregated and enmeshed into larger precipitates. Flocculation is affected by several parameters, including mixing speeds, mixing intensity, and mixing time. The product of the mixing intensity and mixing time is used to describe flocculation processes.


title: Flocculation

text: The process by which the dosage and choice of flocculant are selected is called a jar test. The equipment used for jar testing consists of one or more beakers, each equipped with a paddle mixer. After the addition of flocculants, rapid mixing takes place, followed by slow mixing and later the sedimentation process. Samples can then be taken from the aqueous phase in each beaker.


title: Flocculation

text: In colloid chemistry, flocculation refers to the process by which fine particulates are caused to clump together into a floc. The floc may then float to the top of the liquid (creaming), settle to the bottom of the liquid (sedimentation), or be readily filtered from the liquid. Flocculation behavior of soil colloids is closely


title: Flocculation

text: related to freshwater quality. High dispersibility of soil colloids not only directly causes turbidity of the surrounding water but it also induces eutrophication due to the adsorption of nutritional substances in rivers


title: Flocculation

text: For emulsions, flocculation describes clustering of individual dispersed droplets together, whereby the individual droplets do not lose their identity. Flocculation is thus the initial step leading to further ageing of the emulsion (droplet coalescence and the ultimate separation of the phases). Flocculation is used in mineral dressing, but can be also used in the design of physical properties of food and pharmaceutical products.


title: Flocculation

text: In a medical laboratory, flocculation is the core principle used in various diagnostic tests, for example the rapid plasma reagin test.


title: Flocculation

text: In civil engineering, and in the earth sciences, flocculation is a condition in which clays, polymers or other small charged particles become attached and form a fragile structure, a floc. In dispersed clay slurries,


title: Flocculation

text: flocculation occurs after mechanical agitation ceases and the dispersed clay platelets spontaneously form flocs because of attractions between negative face charges and positive edge charges.


title: Flocculation

text: Flocculation is used in biotechnology applications in conjunction with microfiltration to improve the efficiency of biological feeds. The addition of synthetic flocculants to the bioreactor can increase the average particle size making microfiltration more efficient. When flocculants are not added, cakes form and accumulate causing low cell viability. Positively charged flocculants work better than negatively charged ones since the cells are generally negatively charged.


title: Flocculation

text: Flocculation is widely employed to measure the progress of curd formation in the initial stages of cheese making to determine how long the curds must set. The reaction involving the rennet micelles are modeled by Smoluchowski kinetics. During the renneting of milk the micelles can approach one another and flocculate, a process that involves hydrolysis of molecules and macropeptides.


title: Flocculation

text: Flocculation is also used during cheese wastewater treatment. Three different coagulants are mainly used:


title: Flocculation

text: In the brewing industry flocculation has a different meaning. It is a very important process in fermentation during the production of beer where cells form macroscopic flocs. These flocs cause the yeast to sediment or rise to the top of a fermentation at the end of the fermentation. Subsequently, the yeast can be collected (cropped) from the top (ale fermentation) or the bottom (lager fermentation) of the fermenter in order to be reused for the next fermentation.


title: Flocculation

text: Yeast flocculation is primarily determined by the calcium concentration, often in the 50-100ppm range. Calcium salts can be added to cause flocculation, or the process can be reversed by removing calcium by adding phosphate to form insolubable calcium phosphate, adding excess sulfate to form insoluble calcium sulfate, or adding EDTA to chelate the calcium ions. While it appears similar to sedimentation in colloidal dispersions, the mechanisms are different.


title: Flocculation

text: Flocculation and sedimentation are widely employed in the purification of drinking water as well as in sewage treatment, storm-water treatment and treatment of industrial wastewater streams. Typical treatment processes consist of grates, coagulation, flocculation, sedimentation, granular filtration and disinfection.


title: Flocculation

text: Deflocculation is the exact opposite of flocculation, also sometimes known as peptization. Sodium silicate (NaSiO) is a typical example. Usually in higher pH ranges in addition to low ionic strength of solutions and domination of monovalent metal cations the colloidal particles can be dispersed.


title: Flocculation

text: The additive that prevents the colloids from forming flocs is called a deflocculant. For deflocculation imparted through electrostatic barriers, the efficacy of a deflocculant can be gauged in terms of zeta potential. According to the Encyclopedic Dictionary of Polymers deflocculation is """a state or condition of a dispersion of a solid in a liquid in which each solid particle remains independent and unassociated with adjacent particles (much like emulsifier). A deflocculated suspension shows zero or very low yield value".


title: Flocculation

text: Deflocculation can be a problem in wastewater treatment plants as it commonly causes sludge settling problems and deterioration of the effluent quality.


title: Hipgnosis

text: Hipgnosis were an English art design group based in London, that specialised in creating album cover artwork for rock musicians and bands. Their commissions included work for Pink Floyd, T. Rex, the Pretty Things, Black Sabbath, UFO, 10cc, Bad Company, Led Zeppelin, AC/DC, Scorpions, The Nice, Paul McCartney & Wings, the Alan Parsons Project, Genesis, Peter Gabriel, Electric Light Orchestra, Rainbow, Styx and Al Stewart.


title: Hipgnosis

text: Hipgnosis consisted primarily of Cambridge natives Storm Thorgerson and Aubrey Powell, and later Peter Christopherson. The group dissolved in 1983, though Thorgerson worked on album designs until his death in 2013. Powell has worked with Paul McCartney and The Who in film and video production, and is the creative director for both Pink Floyd and lead singer David Gilmour. Christopherson went on to produce music videos for many bands and shot some of the earliest promotional photography for the Sex Pistols, but worked primarily as an electronic musician in the bands Throbbing Gristle, Psychic TV and Coil until his death in 2010.


title: Hipgnosis

text: In 1968, Thorgerson and Powell were approached by their friends in Pink Floyd to design the cover for the group's second album, "A Saucerful of Secrets". This led to additional work for EMI, including photos and album covers for the Pretty Things, Free, Toe Fat and the Gods. Being film and art school students, they were able to use the darkroom at the Royal College of Art, but when they completed school, they had to set up their own facilities. They built a small darkroom in Powell's bathroom, but shortly thereafter, in early 1970, rented space and built a studio located at 6 Denmark Street.


title: Hipgnosis

text: When first starting out, Powell and Thorgerson adopted their name from graffiti they found on the door to their apartment. Thorgerson said they liked the word, not only for punning on "hypnosis", but for possessing "a nice sense of contradiction, of an impossible co-existence, from Hip = new, cool, and groovy, and Gnostic, relating to ancient learning."


title: Hipgnosis

text: Hipgnosis gained major international prominence in 1973 with their cover design for Pink Floyd's "The Dark Side of the Moon". The final design was one of several versions prepared for the band to choose from, but according to drummer Nick Mason, the 'prism/pyramid' design was the immediate and unanimous choice. The record itself became one of the biggest-selling and longest-charting albums of all time, and the cover has since been hailed as one of the best of all time (VH1 rated it as No. 4, in 2003). After that, the firm became highly sought-after, and did many covers for high-profile bands and artists such as Led Zeppelin, Genesis, UFO, Black Sabbath, Peter Gabriel, the Alan Parsons Project, and Yes. They also designed the cover for the original UK paperback edition of Douglas Adams' "The Hitchhiker's Guide to the Galaxy" (Adams would describe Thorgerson as "The best album designer in the world"), as well as the original UK hardcover edition of Norman Spinrad's "Bug Jack Barron".


title: Hipgnosis

text: Peter Christopherson joined Hipgnosis as an assistant in 1974, and later became a full partner. The firm employed many assistants and other staff members over the years, including freelance designers and illustrators Richard Evans, George Hardie, and Richard Manning.


title: Hipgnosis

text: Hipgnosis did not have a set fee for designing an album cover but instead asked the artists to "pay what they thought it was worth". According to Thorgerson, this policy only occasionally backfired.


title: Hipgnosis

text: Hipgnosis' approach to album design was strongly photography-oriented, and they pioneered the use of many innovative visual and packaging techniques. In particular, Thorgerson and Powell's surreal, elaborately manipulated photos (utilizing darkroom tricks, multiple exposures, airbrush retouching, and mechanical cut-and-paste techniques) were a film-based forerunner of what would, much later, be called photoshopping. Hipgnosis mainly used Hasselblad medium format cameras for their work, the square film format being especially suited to album cover imagery.


title: Hipgnosis

text: Hipgnosis covers were noted for their quirky humour, such as the cover for the Pink Floyd double-LP compilation "A Nice Pair", which featured an array of visual puns. Such humour once angered Jimmy Page of Led Zeppelin, when Hipgnosis created a visual pun based on " racquet"/" racket" for the album "Houses of the Holy". Hipgnosis almost lost Led Zeppelin as a client as a result.


title: Hipgnosis

text: Another trademark was that many of their cover photos visually related to the album's lyrics, often depicting puns or double meanings of words in the album title. Since both Powell and Thorgerson were film students, they often used models and staged the photos in a highly theatrical manner. Hipgnosis covers rarely featured artists' photos on the outside, and most were in a gatefold cover format to provide ample space for their imagery.


title: Hipgnosis

text: Many of Hipgnosis' covers also featured pen and ink logos and illustrations designed to appear high-tech (often by graphic designer George Hardie), stickers, fancy inner sleeves, and other packaging bonuses. One of the extras created by Hipgnosis was the specially printed inner sleeve for Led Zeppelin's "In Through the Out Door" LP, which was black and white but turned to colour when dampened with water (tying in with the main cover's photographic theme).


title: Myles Munroe

text: Myles Munroe, (20 April 1954 – 9 November 2014) was a Bahamian evangelist and ordained minister avid professor of the Kingdom of God, author, speaker and leadership consultant who founded and led the Bahamas Faith Ministries International (BFMI) and Myles Munroe International (MMI). He was chief executive officer and chairman of the board of the International Third World Leaders Association and president of the International Leadership Training Institute as well as the author of numerous books.


title: Myles Munroe

text: Munroe and his wife died in a plane crash November 9, 2014. Bahamian officials stated their aircraft struck a crane at a ship yard near Grand Bahama International Airport. Munroe and the other passenger were heading to Grand Bahama for a conference.


title: Myles Munroe

text: Born Myles Egbert Munroe in 1954 in Nassau, Bahamas, Munroe grew up poor in a family of eleven children. Raised in the Nassau constituency of Bain Town, he was a lifelong resident of the Commonwealth. Munroe became a Christian during his teenage years, later attending Oral Roberts University (ORU) where he received his Bachelor of Fine Arts, Education, and Theology in 1978 and a Master’s degree in administration from the University of Tulsa in 1980. Munroe was also the recipient of honorary doctoral degrees from various schools of higher education and served as an adjunct professor of the Graduate School of Theology at ORU. He wrote a number of books.


title: Myles Munroe

text: His wife, Ruth Munroe, served as co-pastor with him at BFMI. They got married in 1978. Together, the couple had two children, Myles, Jr. (known as Chairo), and a daughter, Charisa.


title: Myles Munroe

text: Following his graduation from the University of Tulsa, Munroe founded Bahamas Faith Ministries International in the early 1980s.


title: Myles Munroe

text: Munroe and his wife died in a private plane crash during airport approach on 9 November 2014. Bahamian officials stated their aircraft struck a crane at a ship yard near Grand Bahama International Airport. Munroe and the other passengers were en route to Freeport, Grand Bahama for a conference.


title: Myles Munroe

text: Munroe was the author and coauthor of numerous books and Biblical-related study guides as well as a featured speaker on motivational and Bible-study recordings.


title: Infinitesimal

text: In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word "infinitesimal" comes from a 17th-century Modern Latin coinage "infinitesimus", which originally referred to the "infinity-th" item in a sequence.


title: Infinitesimal

text: Infinitesimals do not exist in the standard real number system, but they do exist in other number systems, such as the surreal number system and the hyperreal number system, which can be thought of as the real numbers augmented with both infinitesimal and infinite quantities; the augmentations are the reciprocals of one another.


title: Infinitesimal

text: Infinitesimal numbers were introduced in the development of calculus, in which the derivative was first conceived as a ratio of two infinitesimal quantities. This definition was not rigorously formalized. As calculus developed further, infinitesimals were replaced by limits, which can be calculated using the standard real numbers.


title: Infinitesimal

text: Infinitesimals regained popularity in the 20th century with Abraham Robinson's development of nonstandard analysis and the hyperreal numbers, which, after centuries of controversy, showed that a formal treatment of infinitesimal calculus was possible. Following this, mathematicians developed surreal numbers, a related formalization of infinite and infinitesimal numbers that include both hyperreal cardinal and ordinal numbers, which is the largest ordered field.


title: Infinitesimal

text: The crucial insight for making infinitesimals feasible mathematical entities was that they could still retain certain properties such as angle or slope, even if these entities were infinitely small.


title: Infinitesimal

text: Infinitesimals are a basic ingredient in calculus as developed by Leibniz, including the law of continuity and the transcendental law of homogeneity. In common speech, an infinitesimal object is an object that is smaller than any feasible measurement, but not zero in size—or, so small that it cannot be distinguished from zero by any available means. Hence, when used as an adjective in mathematics, "infinitesimal" means infinitely small, smaller than any standard real number. Infinitesimals are often compared to other infinitesimals of similar size, as in examining the derivative of a function. An infinite number of infinitesimals are summed to calculate an integral.


title: Infinitesimal

text: The concept of infinitesimals was originally introduced around 1670 by either Nicolaus Mercator or Gottfried Wilhelm Leibniz. Archimedes used what eventually came to be known as the method of indivisibles in his work "The Method of Mechanical Theorems" to find areas of regions and volumes of solids. In his formal published treatises, Archimedes solved the same problem using the method of exhaustion. The 15th century saw the work of Nicholas of Cusa, further developed in the 17th century by Johannes Kepler, in particular, the calculation of the area of a circle by representing the latter as an infinite-sided polygon. Simon Stevin's work on the decimal representation of all numbers in the 16th century prepared the ground for the real continuum. Bonaventura Cavalieri's method of indivisibles led to an extension of the results of the classical authors. The method of indivisibles related to geometrical figures as being composed of entities of codimension 1. John Wallis's infinitesimals differed from indivisibles in that he would decompose geometrical figures into infinitely thin building blocks of the same dimension as the figure, preparing the ground for general methods of the integral calculus. He exploited an infinitesimal denoted 1/∞ in area calculations.


title: Infinitesimal

text: The use of infinitesimals by Leibniz relied upon heuristic principles, such as the law of continuity: what succeeds for the finite numbers succeeds also for the infinite numbers and vice versa; and the transcendental law of homogeneity that specifies procedures for replacing expressions involving unassignable quantities, by expressions involving only assignable ones. The 18th century saw routine use of infinitesimals by mathematicians such as Leonhard Euler and Joseph-Louis Lagrange. Augustin-Louis Cauchy exploited infinitesimals both in defining continuity in his "Cours d'Analyse", and in defining an early form of a Dirac delta function. As Cantor and Dedekind were developing more abstract versions of Stevin's continuum, Paul du Bois-Reymond wrote a series of papers on infinitesimal-enriched continua based on growth rates of functions. Du Bois-Reymond's work inspired both Émile Borel and Thoralf Skolem. Borel explicitly linked du Bois-Reymond's work to Cauchy's work on rates of growth of infinitesimals. Skolem developed the first non-standard models of arithmetic in 1934. A mathematical implementation of both the law of continuity and infinitesimals was achieved by Abraham Robinson in 1961, who developed nonstandard analysis based on earlier work by Edwin Hewitt in 1948 and Jerzy Łoś in 1955. The hyperreals implement an infinitesimal-enriched continuum and the transfer principle implements Leibniz's law of continuity. The standard part function implements Fermat's adequality.


title: Infinitesimal

text: The notion of infinitely small quantities was discussed by the Eleatic School. The Greek mathematician Archimedes (c. 287 BC – c. 212 BC), in "The Method of Mechanical Theorems", was the first to propose a logically rigorous definition of infinitesimals. His Archimedean property defines a number "x" as infinite if it satisfies the conditions |"x"|>1, |"x"|>1+1, |"x"|>1+1+1, ..., and infinitesimal if "x"≠0 and a similar set of conditions holds for "x" and the reciprocals of the positive integers. A number system is said to be Archimedean if it contains no infinite or infinitesimal members.


title: Infinitesimal

text: The English mathematician John Wallis introduced the expression 1/∞ in his 1655 book "Treatise on the Conic Sections". The symbol, which denotes the reciprocal, or inverse, of ∞, is the symbolic representation of the mathematical concept of an infinitesimal. In his "Treatise on the Conic Sections", Wallis also discusses the concept of a relationship between the symbolic representation of infinitesimal 1/∞ that he introduced and the concept of infinity for which he introduced the symbol ∞. The concept suggests a thought experiment of adding an infinite number of parallelograms of infinitesimal width to form a finite area. This concept was the predecessor to the modern method of integration used in integral calculus. The conceptual origins of the concept of the infinitesimal 1/∞ can be traced as far back as the Greek philosopher Zeno of Elea, whose Zeno's dichotomy paradox was the first mathematical concept to consider the relationship between a finite interval and an interval approaching that of an infinitesimal-sized interval.


title: Infinitesimal

text: Infinitesimals were the subject of political and religious controversies in 17th century Europe, including a ban on infinitesimals issued by clerics in Rome in 1632.


title: Infinitesimal

text: Prior to the invention of calculus mathematicians were able to calculate tangent lines using Pierre de Fermat's method of adequality and René Descartes' method of normals. There is debate among scholars as to whether the method was infinitesimal or algebraic in nature. When Newton and Leibniz invented the calculus, they made use of infinitesimals, Newton's "fluxions" and Leibniz' "differential". The use of infinitesimals was attacked as incorrect by Bishop Berkeley in his work "The Analyst". Mathematicians, scientists, and engineers continued to use infinitesimals to produce correct results. In the second half of the nineteenth century, the calculus was reformulated by Augustin-Louis Cauchy, Bernard Bolzano, Karl Weierstrass, Cantor, Dedekind, and others using the (ε, δ)-definition of limit and set theory.


title: Infinitesimal

text: While the followers of Cantor, Dedekind, and Weierstrass sought to rid analysis of infinitesimals, and their philosophical allies like Bertrand Russell and Rudolf Carnap declared that infinitesimals are "pseudoconcepts", Hermann Cohen and his Marburg school of neo-Kantianism sought to develop a working logic of infinitesimals. The mathematical study of systems containing infinitesimals continued through the work of Levi-Civita, Giuseppe Veronese, Paul du Bois-Reymond, and others, throughout the late nineteenth and the twentieth centuries, as documented by Philip Ehrlich (2006). In the 20th century, it was found that infinitesimals could serve as a basis for calculus and analysis (see hyperreal numbers).


title: Infinitesimal

text: In extending the real numbers to include infinite and infinitesimal quantities, one typically wishes to be as conservative as possible by not changing any of their elementary properties. This guarantees that as many familiar results as possible are still available. Typically "elementary" means that there is no quantification over sets, but only over elements. This limitation allows statements of the form "for any number x..." For example, the axiom that states "for any number "x", "x" + 0 = "x"" would still apply. The same is true for quantification over several numbers, e.g., "for any numbers "x" and "y", "xy" = "yx"." However, statements of the form "for any "set" "S" of numbers ..." may not carry over. Logic with this limitation on quantification is referred to as first-order logic.


title: Infinitesimal

text: The resulting extended number system cannot agree with the reals on all properties that can be expressed by quantification over sets, because the goal is to construct a non-Archimedean system, and the Archimedean principle can be expressed by quantification over sets. One can conservatively extend any theory including reals, including set theory, to include infinitesimals, just by adding a countably infinite list of axioms that assert that a number is smaller than 1/2, 1/3, 1/4, and so on. Similarly, the completeness property cannot be expected to carry over, because the reals are the unique complete ordered field up to isomorphism.


title: Infinitesimal

text: We can distinguish three levels at which a non-Archimedean number system could have first-order properties compatible with those of the reals:


title: Infinitesimal

text: Systems in category 1, at the weak end of the spectrum, are relatively easy to construct but do not allow a full treatment of classical analysis using infinitesimals in the spirit of Newton and Leibniz. For example, the transcendental functions are defined in terms of infinite limiting processes, and therefore there is typically no way to define them in first-order logic. Increasing the analytic strength of the system by passing to categories 2 and 3, we find that the flavor of the treatment tends to become less constructive, and it becomes more difficult to say anything concrete about the hierarchical structure of infinities and infinitesimals.


title: Infinitesimal

text: An example from category 1 above is the field of Laurent series with a finite number of negative-power terms. For example, the Laurent series consisting only of the constant term 1 is identified with the real number 1, and the series with only the linear term "x" is thought of as the simplest infinitesimal, from which the other infinitesimals are constructed. Dictionary ordering is used, which is equivalent to considering higher powers of "x" as negligible compared to lower powers. David O. Tall refers to this system as the super-reals, not to be confused with the superreal number system of Dales and Woodin. Since a Taylor series evaluated with a Laurent series as its argument is still a Laurent series, the system can be used to do calculus on transcendental functions if they are analytic. These infinitesimals have different first-order properties than the reals because, for example, the basic infinitesimal "x" does not have a square root.


title: Infinitesimal

text: The Levi-Civita field is similar to the Laurent series, but is algebraically closed. For example, the basic infinitesimal x has a square root. This field is rich enough to allow a significant amount of analysis to be done, but its elements can still be represented on a computer in the same sense that real numbers can be represented in floating-point.


title: Infinitesimal

text: Conway's surreal numbers fall into category 2, except that the surreal numbers form a proper class and not a set, They are a system designed to be as rich as possible in different sizes of numbers, but not necessarily for convenience in doing analysis, in the sense that every ordered field is a subfield of the surreal numbers. There is a natural extension of the exponential function to the surreal numbers.


title: Infinitesimal

text: The most widespread technique for handling infinitesimals is the hyperreals, developed by Abraham Robinson in the 1960s. They fall into category 3 above, having been designed that way so all of classical analysis can be carried over from the reals. This property of being able to carry over all relations in a natural way is known as the transfer principle, proved by Jerzy Łoś in 1955. For example, the transcendental function sin has a natural counterpart *sin that takes a hyperreal input and gives a hyperreal output, and similarly the set of natural numbers formula_2 has a natural counterpart formula_3, which contains both finite and infinite integers. A proposition such as formula_4 carries over to the hyperreals as formula_5 .


title: Infinitesimal

text: The superreal number system of Dales and Woodin is a generalization of the hyperreals. It is different from the super-real system defined by David Tall.


title: Infinitesimal

text: In linear algebra, the dual numbers extend the reals by adjoining one infinitesimal, the new element ε with the property ε = 0 (that is, ε is nilpotent). Every dual number has the form "z" = "a" + "b"ε with "a" and "b" being uniquely determined real numbers.


title: Infinitesimal

text: One application of dual numbers is automatic differentiation. This application can be generalized to polynomials in n variables, using the Exterior algebra of an n-dimensional vector space.


title: Infinitesimal

text: Synthetic differential geometry or smooth infinitesimal analysis have roots in category theory. This approach departs from the classical logic used in conventional mathematics by denying the general applicability of the law of excluded middle – i.e., "not" ("a" ≠ "b") does not have to mean "a" = "b". A "nilsquare" or "nilpotent" infinitesimal can then be defined. This is a number "x" where "x" = 0 is true, but "x" = 0 need not be true at the same time. Since the background logic is intuitionistic logic, it is not immediately clear how to classify this system with regard to classes 1, 2, and 3. Intuitionistic analogues of these classes would have to be developed first.


title: Infinitesimal

text: Cauchy used an infinitesimal formula_6 to write down a unit impulse, infinitely tall and narrow Dirac-type delta function formula_7 satisfying formula_8 in a number of articles in 1827, see Laugwitz (1989). Cauchy defined an infinitesimal in 1821 (Cours d'Analyse) in terms of a sequence tending to zero. Namely, such a null sequence becomes an infinitesimal in Cauchy's and Lazare Carnot's terminology.


title: Infinitesimal

text: Modern set-theoretic approaches allow one to define infinitesimals via the ultrapower construction, where a null sequence becomes an infinitesimal in the sense of an equivalence class modulo a relation defined in terms of a suitable ultrafilter. The article by Yamashita (2007) contains bibliography on modern Dirac delta functions in the context of an infinitesimal-enriched continuum provided by the hyperreals.


title: Infinitesimal

text: The method of constructing infinitesimals of the kind used in nonstandard analysis depends on the model and which collection of axioms are used. We consider here systems where infinitesimals can be shown to exist.


title: Infinitesimal

text: In 1936 Maltsev proved the compactness theorem. This theorem is fundamental for the existence of infinitesimals as it proves that it is possible to formalise them. A consequence of this theorem is that if there is a number system in which it is true that for any positive integer "n" there is a positive number "x" such that 0 < "x" < 1/"n", then there exists an extension of that number system in which it is true that there exists a positive number "x" such that for any positive integer "n" we have 0 < "x" < 1/"n". The possibility to switch "for any" and "there exists" is crucial. The first statement is true in the real numbers as given in ZFC set theory : for any positive integer "n" it is possible to find a real number between 1/"n" and zero, but this real number depends on "n". Here, one chooses "n" first, then one finds the corresponding "x". In the second expression, the statement says that there is an "x" (at least one), chosen first, which is between 0 and 1/"n" for any "n". In this case "x" is infinitesimal. This is not true in the real numbers (R) given by ZFC. Nonetheless, the theorem proves that there is a model (a number system) in which this is true. The question is: what is this model? What are its properties? Is there only one such model?


title: Infinitesimal

text: There are in fact many ways to construct such a one-dimensional linearly ordered set of numbers, but fundamentally, there are two different approaches:


title: Infinitesimal

text: In 1960, Abraham Robinson provided an answer following the first approach. The extended set is called the hyperreals and contains numbers less in absolute value than any positive real number. The method may be considered relatively complex but it does prove that infinitesimals exist in the universe of ZFC set theory. The real numbers are called standard numbers and the new non-real hyperreals are called nonstandard.


title: Infinitesimal

text: In 1977 Edward Nelson provided an answer following the second approach. The extended axioms are IST, which stands either for Internal set theory or for the initials of the three extra axioms: Idealization, Standardization, Transfer. In this system, we consider that the language is extended in such a way that we can express facts about infinitesimals. The real numbers are either standard or nonstandard. An infinitesimal is a nonstandard real number that is less, in absolute value, than any positive standard real number.


title: Infinitesimal

text: In 2006 Karel Hrbacek developed an extension of Nelson's approach in which the real numbers are stratified in (infinitely) many levels; i.e., in the coarsest level, there are no infinitesimals nor unlimited numbers. Infinitesimals are at a finer level and there are also infinitesimals with respect to this new level and so on.


title: Infinitesimal

text: Calculus textbooks based on infinitesimals include the classic "Calculus Made Easy" by Silvanus P. Thompson (bearing the motto "What one fool can do another can") and the German text "Mathematik fur Mittlere Technische Fachschulen der Maschinenindustrie" by R. Neuendorff. Pioneering works based on Abraham Robinson's infinitesimals include texts by Stroyan (dating from 1972) and Howard Jerome Keisler (). Students easily relate to the intuitive notion of an infinitesimal difference 1-"0.999...", where "0.999..." differs from its standard meaning as the real number 1, and is reinterpreted as an infinite terminating extended decimal that is strictly less than 1.


title: Infinitesimal

text: Another elementary calculus text that uses the theory of infinitesimals as developed by Robinson is "Infinitesimal Calculus" by Henle and Kleinberg, originally published in 1979. The authors introduce the language of first-order logic, and demonstrate the construction of a first order model of the hyperreal numbers. The text provides an introduction to the basics of integral and differential calculus in one dimension, including sequences and series of functions. In an Appendix, they also treat the extension of their model to the "hyperhyper"reals, and demonstrate some applications for the extended model.


title: Infinitesimal

text: An elementary calculus text based on smooth infinitesial analysis is Bell, John L. (2008). A Primer of Infinitesimal Analysis, 2nd Edition. Cambridge University Press. ISBN 9780521887182.


title: Infinitesimal

text: A more recent calculus text utilizing infinitesimals is Dawson, C. Bryan (2022), Calculus Set Free: Infinitesimals to the Rescue, Oxford University Press. ISBN 9780192895608.


title: Infinitesimal

text: In a related but somewhat different sense, which evolved from the original definition of "infinitesimal" as an infinitely small quantity, the term has also been used to refer to a function tending to zero. More precisely, Loomis and Sternberg's "Advanced Calculus" defines the function class of infinitesimals, formula_9, as a subset of functions formula_10 between normed vector spaces by formula_11, as well as two related classes formula_12 (see Big-O notation) by formula_13, andformula_14.The set inclusions formula_15generally hold. That the inclusions are proper is demonstrated by the real-valued functions of a real variable formula_16, formula_17, and formula_18: formula_19 but formula_20 and formula_21.As an application of these definitions, a mapping formula_22 between normed vector spaces is defined to be differentiable at formula_23 if there is a formula_24 [i.e, a bounded linear map formula_25] such that formula_26in a neighborhood of formula_6. If such a map exists, it is unique; this map is called the "differential" and is denoted by formula_28, coinciding with the traditional notation for the classical (though logically flawed) notion of a differential as an infinitely small "piece" of "F". This definition represents a generalization of the usual definition of differentiability for vector-valued functions of (open subsets of) Euclidean spaces.


title: Infinitesimal

text: Let formula_29 be a probability space and let formula_30. An array formula_31 of random variables is called infinitesimal if for every formula_32, we have:


title: Infinitesimal

text: The notion of infinitesimal array is essential in some central limit theorems and it is easily seen by monotonicity of the expectation operator that any array satisfying Lindeberg's condition is infinitesimal, thus playing an important role in Lindeberg's Central Limit Theorem (a generalization of the central limit theorem).


title: Andrew East

text: Andrew Dean East (born September 17, 1991) is a former American football long snapper. He played college football at Vanderbilt, and has also had multiple stints with various NFL teams, most recently the Washington Redskins.


title: Andrew East

text: East was named a captain of the North Central High School football team in Indianapolis, Indiana. He was a three-year starter on defense and special teams for the 5A division school in the Indianapolis area.


title: Andrew East

text: When East was a sophomore and junior, he started at the linebacker position, posting 110 tackles as a junior. He was named the All-Around-Area linebacker while starting as a long-snapper.


title: Andrew East

text: As a senior, East contributed 64 tackles and seven quarterback sacks as a first-year starter. He also received the Indiana Academic All-State honors award.


title: Andrew East

text: He signed with the Kansas City Chiefs as an undrafted free agent on May 11, 2015. He was released by the Chiefs on August 30, 2015.


title: Andrew East

text: East signed a reserve/future contract with the Seattle Seahawks on January 4, 2016. He was waived on March 24, 2016.


title: Andrew East

text: East was signed by the Oakland Raiders on April 5, 2016. He was waived by the team on August 29, 2016.


title: Andrew East

text: On July 28, 2017, East was signed by the Raiders. He was waived on September 2, 2017. He signed a reserve/future contract with the Raiders on January 19, 2018. He was waived by the Raiders on April 9, 2018.


title: Andrew East

text: On December 15, 2018, East was signed by the Washington Redskins after long snapper Nick Sundberg was placed on injured reserve due to a back injury. He was waived on August 2, 2019.


title: Andrew East

text: East is married to Olympic gymnast and gold medalist Shawn Johnson. East and Johnson were engaged on July 24, 2015, at Wrigley Field during a Chicago Cubs game, and were married on April 16, 2016, in Franklin, Tennessee. The couple live in Nashville, Tennessee. They have two children, a daughter who was born in October 2019 and a son who was born in July 2021.


title: Royal Jordanian

text: Royal Jordanian Airlines (; transliterated: "Al-Malakiyyah al-'Urduniyyah"), formerly known as Alia Royal Jordanian Airlines, is the flag carrier airline of Jordan with its head office in the capital, Amman. The airline operates scheduled international services over four continents from its main base at Queen Alia International Airport, with over 500 flights per week and at least 110 daily departures. It joined the Oneworld airline alliance in 2007.


title: Royal Jordanian

text: The airline was established on 9 December 1963 and started operations on 15 December 1963 after a royal decree by the late King Hussein. It was named "Alia" (or "Aalya") after King Hussein's eldest child, Princess Alia bint Al Hussein of Jordan (born on 13 February 1956). It is a common misconception that the airline was named after the King's third wife, Queen Alia, whom King Hussein did not marry until 1972. The airline was founded with capital from private shareholders but the Jordanian government later took over the company.


title: Royal Jordanian

text: Alia (the Royal Jordanian Airline) started operations with two Handley Page Dart Heralds and a Douglas DC-7 aircraft, serving Kuwait City, Beirut and Cairo from Amman. In 1964, another DC-7 was added and service began to Jeddah. In 1965, Alia initiated service to Rome, its first destination in Europe. The progress made by the airline was threatened by an Israeli air raid during the 1967 Six-Day War when the DC-7 aircraft were destroyed. They were replaced by two Fokker F27 Friendship airliners.


title: Royal Jordanian

text: In 1968, the airline joined the jet age when it introduced the Sud Aviation Caravelle, and expanded the route network to Nicosia, Benghazi, Dhahran and Doha. 1969 saw the addition of service to Munich, Istanbul and Tehran.


title: Royal Jordanian

text: In 1970, Alia phased out the F27s and ordered Boeing 707 aircraft. Frankfurt and Abu Dhabi were added to the network. The 707s were delivered in 1971. In that year, service was initiated to Madrid, Copenhagen and Karachi. During the rest of the decade, Boeing 720s, Boeing 727s, and Boeing 747s were added to the fleet. A catering department was established, and duty-free shops were opened at Amman airport. Services were added to destinations including Bahrain, Dubai, Muscat, Rabat, Geneva, Amsterdam, Baghdad, Bangkok, Vienna, Damascus, New York City, Houston, and Ras al-Khaimah. In 1979, Alia became a founding member of the Arab Airlines Technical Consortium (AATC).


title: Royal Jordanian

text: In the 1980s, Tunis and Tripoli joined the route map, and Alia's IBM computer center was inaugurated. Lockheed L-1011 Tristars, Airbus A310s and Airbus A320s joined the fleet. In 1986, Alia changed its name to Royal Jordanian, when princess Alia was nearing her divorce. The airline's first woman pilot flew one of their aircraft during this decade. Service was added to Belgrade, Chicago, Los Angeles, Miami, Bucharest, Singapore, Riyadh, Kuala Lumpur – in cooperation with MAS, Sana'a, Moscow. Montreal, Delhi, Calcutta and Ankara. This decade also saw the introduction of the Gabriel Automated Ticket System – (GATS).


title: Royal Jordanian

text: The 1990s saw further expansion. Royal Jordanian and nine other Arab air carriers signed up for the Galileo CRS. The IMCS maintenance and engineering system was added, a new Amman city air terminal was opened at the 7th Circle of the Jordanian capital, and services to Rafah started, since then halted. The cities of Toronto, Colombo, Jakarta, Berlin, Mumbai, Milan and Tel Aviv were added to the network. In November 1997, Royal Jordanian became a code-sharing partner with the US carrier Trans World Airlines and moved operations into the TWA Flight Center (Terminal 5) at the John F. Kennedy International Airport in New York.


title: Royal Jordanian

text: In 2000, the U.S. Federal Aviation Administration (FAA) renewed the airline's maintenance and engineering department's license. The duty-free shop was among the services to be privatised. A holding company, RJI, wholly owned by the government, was incorporated as a public limited company in February 2001 to hold all the airlines and associated investments. The airline's name was changed on 5 February 2001 to "Alia – The Royal Jordanian Airlines Company", although travellers still use the popular name of Royal Jordanian.


title: Royal Jordanian

text: The flag carrier's subsidiary Royal Wings operated an Airbus A320-212 aircraft on both scheduled and charter services to destinations in Egypt, Cyprus, and Israel.


title: Royal Jordanian

text: On 20 December 2006, Royal Jordanian announced that they would replace two Airbus A321s with two new units, and order four new Airbus A319s to enter service in early 2008.


title: Royal Jordanian

text: In April 2007, Royal Jordanian became part of Oneworld, thus becoming the first Arab airline to join such a global alliance system. The following month, the airline announced an order for a total of 10 Boeing 787 Dreamliners, for service entry in 2010. This is the first order Royal Jordanian has placed with Boeing.


title: Royal Jordanian

text: Montreal was re-added to the network on 25 May 2007, after the route was cancelled in 1997. Also during May, Royal Jordanian was the sponsor of the World Economic Forum, which was held at the Dead Sea, Jordan.


title: Royal Jordanian

text: On 11 July 2007, Royal Jordanian celebrated thirty years of non-stop service between Amman and New York City, making it the longest-serving Arab airline to this gateway to the U.S. RJ won the "Airline Strategy Award" in the technology category at the sixth annual Airline Strategy Awards on 16 July 2007. On 23 July, RJ saw the introduction of cargo flights, Damascus being the first destination served from Amman, using a Boeing 737.


title: Royal Jordanian

text: Royal Jordanian made its first flight to Budapest, on 28 July, using an Embraer 195. In October, RJ announced the switch of two Embraer 195 jets of its original order to two Embraer 175 jets. Royal Jordanian opened a new lounge at King Hussein International Airport in Aqaba.


title: Royal Jordanian

text: RJ will be the first Middle East airline to provide its passengers with OnAir's in-flight Internet and mobile phone services, including e-mail, SMS and voice calls. Royal Jordanian has upgraded its three Airbus A310s at a cost of over 10 million Jordanian dinars (JOD).


title: Royal Jordanian

text: Royal Jordanian was privatized at the end of 2007, resulting in 71% of its assets being sold. The market capitalization of the company stands at 260 million JOD, and share-trading commenced on 17 December 2007.


title: Royal Jordanian

text: On 24 December 2007, Royal Jordanian confirmed Baku as one of its new destinations for 2008, using an Embraer 195 twice weekly from Amman. In early 2008, however, RJ officials decided against the new route, citing that high fuel prices and a new market were a risk too large to take at that time. Royal Jordanian plans to operate the Amman-Baku route in late 2009 or early 2010. On 22 January 2008, RJ launched flights to Hong Kong via Bangkok, with three flights/week during winter, and five flights/week during summer, making it the airline's first route to China.


title: Royal Jordanian

text: The Airbus A319 entered service on 13 March 2008, making RJ the first Middle East airline to operate three aircraft of the Airbus A320 family. On 17 August 2008, Royal Jordanian opened a new route to Kyiv, using Embraer 195 jets for this twice-weekly service. On 24 August 2008, Royal Jordanian opened its new lounge at Queen Alia International Airport Amman, replacing the "Petra" and "Jerash" lounges. The new lounge is located on the second floor of the South Terminal and is the second-largest airport lounge in the Middle East, being able to handle over 340 passengers.


title: Royal Jordanian

text: The airline recorded an 18% increase in passenger numbers in July 2008. With the airline transporting 278,000 passengers, the seat factor grew by 5% in that month to reach 81%. As part of Royal Jordanian's commitment to its airline alliance Oneworld, an announcement was made at the alliance's 10th birthday celebrations on 3 February 2009 that RJ would paint its new A319 (due for delivery in late March) in a scheme that would be based around the Oneworld name and logo. This is the first special colour scheme Royal Jordanian will have used.


title: Royal Jordanian

text: Royal Jordanian resumed service to Brussels on 1 April 2009, six years after the route was discontinued by the airline, flying twice weekly from Amman with the airline planning to add a further two flights per week later in 2009.


title: Royal Jordanian

text: On 28 March 2010, Royal Jordanian inaugurated regular direct flights to Madinah Munawwarah, Saudi Arabia, with four weekly flights. On the 23 March, Royal Jordanian confirmed that it had ordered two A330-200s and one Embraer 175. Royal Jordanian recommenced operations to Malaysia's capital Kuala Lumpur on June 2, 2010, after it had suspended this route in 2004. Aircraft used on this route is the new Airbus A330-200 and later switched to Boeing 787 Dreamliner.


title: Royal Jordanian

text: In May 2011, Royal Jordanian announced that they will retire the Airbus A310 aircraft in December 2011, and January 2012. Royal Jordanian uses an Airbus A330 and an Airbus A321 for non-stop flights to London (Heathrow Terminal 3).


title: Royal Jordanian

text: In June 2014, Royal Jordanian announced that it had suspended services to Mosul in northern Iraq due to the capture of the airport by the Islamic State.


title: Royal Jordanian

text: The first of Royal Jordanian's Boeing 787 Dreamliner aircraft (267-seat, two-class configuration) entered service in September 2014, initially linking Amman with Jeddah, Saudi Arabia. The 787 Dreamliner is Royal Jordanian's first Boeing aircraft since the 707s and 747s, and replaced the Airbus A340-200s which had reached the end of their lives. The Dreamliners have replaced the Airbus A330-200s as leases on those aircraft have expired. The Dreamliners are generally used on Royal Jordanian's Far East destinations, to London and North America.


title: Royal Jordanian

text: In May 2017, Royal Jordanian announced the appointment of Stefan Pichler, the ex CEO of Air Berlin, Fiji Airways, Jazeera Airways, Virgin Australia and Thomas Cook as the new president and CEO.


title: Royal Jordanian

text: Pichler developed a turnaround plan which helped moving Royal Jordanian back into profitability by the end of 2017. In this context, the airline cancelled the order of the 8th Dreamliner and also withdrew the A330F from its Cargo fleet for similar reasons. The CEO also stated that the strategy of Royal Jordanian would lead to a single type narrow-body fleet, not mentioning whether it will be Airbus, Boeing, Bombardier, or Embraer. In September 2020, Pichler resigned from his duties which were taken over by Chairman Saeed Samih Darwazah.


title: Royal Jordanian

text: , Haddadinco Engineering Company for Contracting is building the new Royal Jordanian head office in Amman. The building was designed by Niels Torp. The new building was completed in late 2011, and RJ employees began work in the building on January 3, 2012. In the 1960s, Alia's head office was in the Mango Building in Amman.


title: Royal Jordanian

text: Royal Jordanian has invested heavily in its crew training facility at its headquarters in Amman. , Royal Jordanian employed 4,394 people, according to the most recent annual report.


title: Royal Jordanian

text: Royal Jordanian began to put into place a new strategy at the end of 2002 which saw the airline concentrate on its neighboring nations, with increased frequencies. In a plan to establish itself as the Middle East's "regional airline" it began to add smaller routes such as Alexandria in Egypt to Aleppo in Syria which the bigger airlines, such as Emirates, would not undertake with the larger aircraft compared to Royal Jordanian's regional jets. As of the end of 2008, the plan had proven successful for the airline, with its main rivals being Middle East Airlines and Egypt Air.


title: Royal Jordanian

text: Since 2008, Royal Jordanian has faced increased competition within the Middle East. The arrival of many new low-cost airlines such as Air Arabia, Jazeera Airways, and flydubai have caused problems for the Jordanian airline. With the arrival of these new airlines, Royal Jordanian has focused upon improving its onboard and ground services in order to retain market share.


title: Royal Jordanian

text: The following information can be found in the 2009, 2013, 2015, 2016, 2017 and 2018 Royal Jordanian Annual Reports.


title: Royal Jordanian

text: From 1963 to 1986, the original livery of Royal Jordanian Airlines consisted of a white fuselage with both red and gold cheatlines.


title: Royal Jordanian

text: In December 1986, the airline changed its name from Alia Royal Jordanian Airlines to simply Royal Jordanian Airlines, which coincided the arrival of Airbus A310 and Airbus A320 airliners. The new livery consisted of a charcoal grey fuselage with the same red and gold cheatlines, similar to the earlier version. The tail consists of a golden crown with a red tip on the charcoal grey coloured aircraft tail.


title: Royal Jordanian

text: Until 2009, Royal Jordanian had never had an aircraft painted in a special colour scheme. It announced at the 10th birthday celebrations in February 2009 of the airline alliance Oneworld that it would paint its new A319 due for delivery in late March in a special scheme, which would be based around the Oneworld name and logo. The aircraft, registration JY-AYP, has its fuselage painted white, with the tailfin and engines in normal Royal Jordanian colours. "A member of Oneworld" in prominent lettering is located at the front of the aircraft, with the usual title "Royal Jordanian" further back.


title: Royal Jordanian

text: In October 2021, Royal Jordanian unveiled "Discover Petra" special livery on one of its Boeing 787 Dreamliners, registered JY-BAH.


title: Royal Jordanian

text: A month later, in November 2021, the airline revealed an Airbus A321, JY-AYV, in its retro "Alia" livery. The aircraft's first flight in the new paint scheme was to London Heathrow.


title: Royal Jordanian

text: Food and drinks served on flights leaving Amman are provided by Dnata. Hot meals will be served on a flight of at least three hours in length. If the flight is shorter than one hour, the cabin crew will provide snacks and drinks throughout, or before, the flight. These flights include those to Tel Aviv, Cairo, Baghdad, Beirut and Aqaba from Amman.


title: Royal Jordanian

text: Interactive games are available in all classes on all flights, as well as news provided by CNN on all flights. On very short flights (from Amman to Tel Aviv, Beirut or Damascus), the AVOD system is turned on but there is only the selection of games, CNN News, the "Flight Show", and the comedy channel. This is due to the flights being less than 45 minutes hence movies/shows would not be complete upon arrival.


title: Royal Jordanian

text: Crown Class seats on Boeing 787s are fully flat beds. Seat pitch is 83 inches on the Dreamliners and 46 inches on the short and medium haul aircraft. In Economy Class, Royal Jordanian offers 32-inch seat pitch on board its Embraer aircraft, whilst it offers 34-inch seat pitch on board its Airbus aircraft. All Royal Jordanian Economy class seats also offer a foot-rest.


title: Royal Jordanian

text: Crown Class passengers can use lounges across the world including all Oneworld member airline lounges. Royal Jordanian operates two lounges: one in Amman, at Queen Alia International Airport, and one at Aqaba, at King Hussein International Airport. In August 2008, Royal Jordanian opened its new lounge, which can handle over 340 passengers. It is located in the South Terminal on the second floor and replaces the previous Jerash and Petra lounges in the airport.


title: Royal Jordanian

text: Royal Club is Royal Jordanian's frequent flyer program. Passengers are awarded miles based on the type, class of flight and destination. Royal Club members can also get miles by traveling on other Oneworld airlines. Card holders of Royal Jordanian's Royal Plus with either Silver, Gold or Platinum can use Oneworld airport services across the world while Gold and Platinum also have lounge access.


title: Royal Jordanian

text: Royal Jordanian has experienced 13 aviation occurrences and six hijackings throughout its history, four of them fatal. The airline's two worst accidents, both involving chartered Boeing 707s, happened in Nigeria in 1973 and Morocco in 1975, and to date are both the deadliest accidents in those countries and the deadliest worldwide involving the 707.


title: Royal Jordanian

text: Since the name of the carrier was changed to Royal Jordanian Airlines in 1986, the only fatal incident was when a hijacker, seeking political asylum, was killed by the on-board security agent on 5 July 2000, on board a Royal Jordanian Airbus A320 flying from Amman to Damascus.


title: Outnumbered (British TV series)

text: Outnumbered is a British sitcom about the Brockman family, starring Hugh Dennis as the father, Claire Skinner as the mother and their three children played by Tyger Drew-Honey, Daniel Roche and Ramona Marquez.


title: Outnumbered (British TV series)

text: There were five series, which aired on BBC One from 2007 to 2014. A Christmas special aired on 26 December 2016. More specials are planned after the success of the 2016 Christmas special.


title: Outnumbered (British TV series)

text: Produced by Hat Trick Productions, "Outnumbered" was written, directed and produced by Andy Hamilton and Guy Jenkin, although parts of the show are semi-improvised. The adult actors learn the scripts, while the children are given last-minute instructions by the writers instead.


title: Outnumbered (British TV series)

text: The programme has received critical acclaim for its semi-improvisational scripting and realistic portrayal of children and family life. Ratings have been average for its time slot, but the series has won a number of awards from the Comedy.co.uk awards, the Royal Television Society, the British Comedy Awards and the Broadcasting Press Guild. Plans for an American adaptation were announced in February 2009, but this has not materialised. The original series began airing in the US on BBC America on 30 July 2011, as well as airing on PBS stations.


title: Outnumbered (British TV series)

text: "Outnumbered" is centred on the Brockmans, a middle-class family living in Chiswick, whose two parents are "outnumbered" by their three somewhat unruly children. The father, Pete (Hugh Dennis), is a history teacher at a dysfunctional inner city school and the mother, Sue (Claire Skinner), is a part-time personal assistant and is four years younger than Pete. The three children are: Jake (Tyger Drew-Honey), the straight man of the family, whose teenage sarcasm and obsession with girls worries his mother, Ben (Daniel Roche), who is hyperactive, a pathological liar, does unusual things (experimenting or as Pete puts it, "roasting insects"), and is always coming up with hypothetical questions like "who would win in a fight between...", and Karen (Ramona Marquez), who asks too many questions, frequently imitates a lot of what she sees on television (reenacting reality shows with her toys) and criticises nearly everything.


title: Outnumbered (British TV series)

text: Other regular characters include Sue's new age sister, Angela Morrison (Samantha Bond), and their elderly father Frank (David Ryall), referred to as "Grandad", who is in the early stages of dementia. He is a silent and deceased character in the 2016 special. The writers also use the popular sitcom device of the unseen character in the form of Veronica, Sue's unreasonably demanding boss in series one. In series two, the device is used again, but in the form of Sue's new boss Tyson, who is revealed to be a conman who absconds in the final episode of the series. Series three introduces Rosalind Ayres as Pete's mum Sandra, referred to as "Gran", on online-gambling addict with a growing hatred for Pete's father, from whom she has separated, though has not divorced as she "couldn't face all the paperwork".


title: Outnumbered (British TV series)

text: Other new characters in Series 3 include Kelly (Anna Skellern), a psychology student on whom Jake has a crush, Angela's new husband Brick (Douglas Hodge), who is an American therapist (later revealed to be abusive towards his children, especially 15-year-old Misty), and his daughter Taylor Jean, who wants to live with her mum. Also introduced is a campaigner against council plans to place speed bumps on the road (Alex MacQueen) who pesters the family.


title: Outnumbered (British TV series)

text: By series 5, the Brockman children have changed considerably. Jake has developed a penchant for engaging with a suspect crowd of friends, and a general teenage cockiness. Ben has doubled in size and strength, but not his maturity. And the pre-teen Karen has become moody, sullen and developed a superiority complex as she heads towards a prestigious secondary school.


title: Outnumbered (British TV series)

text: "Outnumbered" was the first collaboration between Hamilton and Jenkin since "Drop the Dead Donkey" ended in 1998. It was commissioned by BBC controller Lucy Lumsden. The executive producer is Jon Rolph. The 20-minute pilot was given to Lumsden, who then commissioned six episodes. The show is set in Chiswick, West London, and shot on location in Wandsworth. The house used for external shots is in Dempster Road. During the second series, the family receive a final demand for council tax from the fictional "Limebridge Council", sent to the fictional address of 19 Keely Road, London, W4 2CF.


title: Outnumbered (British TV series)

text: The writers use improvisation in order to achieve convincing performances from the child actors. Jenkin added: You rarely get the feeling that children in sitcoms are real. They tend to be the same type of character – the smartarse who says adult things – and they are rooted to the spot, staring at the camera, because they've been told to stand in one place and say the lines. We decided to attempt to do something that hadn't been tried before, bounced some ideas around and we got very keen on this idea of involving improvisation very quickly. The child performers were cast based on how their responses reflected the outlines of the characters they would be playing. Hamilton said in an interview: "I saw about 30 [children], then we whittled it down to the perfect three. Ramona [Marquez]...was in the same class as Guy's twin sons. His wife said to him: 'There's a girl who's got something - you should meet her.'"


title: Outnumbered (British TV series)

text: The fourth series began on 2 September 2011 at 9.00 pm on BBC One. After the series had aired, Tyger Drew-Honey suggested that there would be no fifth series because he and the other child actors were growing out of their roles. BBC Television's Head of Communications, Sam Hodges, reassured fans of the series that "contrary to reports, talks are already under way regarding a new series".


title: Outnumbered (British TV series)

text: The fifth and final series was confirmed by BBC and began to air Wednesday 29 January 2014. The series comprised six episodes.


title: Outnumbered (British TV series)

text: In 2015, Tyger Drew-Honey hinted that the series could return for a Christmas special in 2016. This was officially confirmed by co-creator Andy Hamilton in September 2016.


title: Outnumbered (British TV series)

text: The show initially received a mixed reception, though after the second series reviews gradually shifted towards a fairly positive tone. The "Daily Mirror" found the mundane settings to be similar to the American sitcom "Seinfeld", saying: compared to the ridiculous carry-on of "My Family", it's much more low-key and realistic. In fact it's so low-key, nothing actually happens, which could well be a nod to "Seinfeld" – the touchstone of all great sitcoms. The getting ready for school chaos is like "Supernanny: The Movie" only with nicer children. It's also taken a leaf out of "Curb Your Enthusiasm's" book with large chunks of improvisation – although the strongest language you'll find here is "ponk".


title: Outnumbered (British TV series)

text: Kevin Maher of "The Times" dismissed the programme, saying it was not funny or dramatic enough. He wrote: "Outnumbered" was at its most meretricious. For every exchange between adult and child was hijacked by a crass sitcommy need for "sotto voce" punchlines and knowing winks to the wings. A protracted scene in which 45-year-old dad (Hugh Dennis) was unable to wrestle a live power drill from the hands of 7-year-old son Ben (Daniel Roche), and instead had to, ho-ho, pay him £5 for the privilege, was emblematic of the show's dubious capacity for fake pay-offs.


title: Outnumbered (British TV series)

text: Rod Liddle, writing in "The Sunday Times", praised the show, although he was somewhat surprised: "An exquisitely middle-class, middle-aged domestic situation comedy set in West London – and starring one of those bloody stand-up comics who now festoons every network, it really should be hated before it is even seen. Start liking this sort of programme and you are an ace away from enjoying "Terry and June" and having a house that smells faintly of weak tea, Murray Mints and urine. So, maybe it's just me, but "Outnumbered" is very funny indeed: despite its current bout of self-flagellation, the BBC still knows how to make people laugh. Comedy may be the very last thing the corporation does well."


title: Outnumbered (British TV series)

text: James Walton wrote in "The Daily Telegraph" that the domestic setting and more mundane storylines were a virtue, saying, "All of this feels both carefully observed and suspiciously heartfelt. More unusually, it's not contrived. "Outnumbered" sticks firmly with the mundane, yet manages to be funny about it. It doesn't avoid the sheer dullness involved in family life either – but, happily, depicts it with a winning mixture of exasperation and affection." He did, however, criticise the scheduling of the programme saying, "Despite the very specific London setting, the series (shown in two batches of three, this week and next) will surely appeal to the parents of young children everywhere. As long, that is, as they're not asleep by 10.35pm."


title: Outnumbered (British TV series)

text: In 2008 review in "The Times", Bryan Appleyard described "Outnumbered" as "the best British sitcom in years and among the best ever".


title: Outnumbered (British TV series)

text: The first episode received 4.1 million viewers (25.5% of the audience share) when it began and finished with 2.8 million (19.5%) at the end, which is larger than the average 2.2 million (14%) normally attracted by television shows in its particular time slot. The audience for the second episode fell by half a million viewers, while still being the highest ranking show in its time slot, with 18% of the audience share. However, it maintained a constant audience throughout the first series, with the fourth episode attracting 2.7 million viewers (20% audience share).


title: Outnumbered (British TV series)

text: "Outnumbered" was nominated for the 2008 ""Broadcast" Award" for "Best Comedy Programme", but lost the award to "The Thick of It".


title: Outnumbered (British TV series)

text: The show was given the "British Comedy Guide Editors' Award" in The Comedy.co.uk Awards 2007 and the "Best Returning British TV Sitcom" in The Comedy.co.uk Awards 2008, beating "Peep Show" by six votes.


title: Outnumbered (British TV series)

text: In 2009, it won the Royal Television Society Award for "Scripted Comedy", and two Broadcasting Press Guild Awards in the same year: "Best Comedy/Entertainment" and the "Writer's Award". "Outnumbered" also won three awards at the 2009 British Comedy Awards: Best Sitcom, Best British Comedy and Best Female Newcomer for Ramona Marquez.


title: Outnumbered (British TV series)

text: The show has received four BAFTA TV Award nominations: Best Situation Comedy, the Audience Award, and Best Comedy Performance for Claire Skinner in 2009; and Best Male Performance in a Comedy Role for Hugh Dennis in 2010.


title: Outnumbered (British TV series)

text: At the National Television Awards in 2011, Outnumbered was nominated for Best Comedy but lost out to ITV's "Benidorm". It was nominated again the following year and won.


title: Outnumbered (British TV series)

text: All five series and the three Christmas specials are available on DVD. The first Comic Relief special is available on the Series 2 DVD, the first Sport Relief special is available on the Series 3 DVD and the second Comic Relief special is available on the Series 4 DVD. It has been said that the second Sport Relief special will either be available on the next Christmas Special DVD or the Series 5 DVD (if they will be filmed or if they have been filmed). The DVDs have been published by 2 Entertain.