title: Lottery mathematics

text: Using the same principle, the odds of getting a score of 2 and the powerball are formula_30 for the score of 2 multiplied by the probability of one of the remaining four numbers matching the bonus ball, which is . Since formula_31, the probability of obtaining the score of 2 and the bonus ball is formula_32, approximate decimal odds of 1 in 81.2.


title: Lottery mathematics

text: The general formula for formula_13 matching balls in a formula_11 choose formula_12 lottery with one bonus ball from the formula_11 pool of balls is:


title: Lottery mathematics

text: The general formula for formula_13 matching balls in a formula_11 choose formula_12 lottery with zero bonus ball from the formula_11 pool of balls is:


title: Lottery mathematics

text: The general formula for formula_13 matching balls in a formula_11 choose formula_12 lottery with one bonus ball from a separate pool of formula_46 balls is:


title: Lottery mathematics

text: The general formula for formula_13 matching balls in a formula_11 choose formula_12 lottery with no bonus ball from a separate pool of formula_46 balls is:


title: Lottery mathematics

text: It is a hard (and often open) problem to calculate the minimum number of tickets one needs to purchase to guarantee that at least one of these tickets matches at least 2 numbers. In the 5-from-90 lotto, the minimum number of tickets that can guarantee a ticket with at least 2 matches is 100.


title: Lottery mathematics

text: As a discrete probability space, the probability of any particular lottery outcome is atomic, meaning it is greater than zero. Therefore, the probability of any event is the sum of probabilities of the outcomes of the event. This makes it easy to calculate quantities of interest from information theory. For example, the information content of any event is easy to calculate, by the formula


title: Lottery mathematics

text: In particular, the information content of outcome formula_54 of discrete random variable formula_55 is


title: Lottery mathematics

text: For example, winning in the example above is a Bernoulli-distributed random variable formula_55 with a chance of winning ("success") We write formula_58 with formula_59 and formula_60. The information content of winning is


title: Lottery mathematics

text: formula_61shannons or bits of information. (See units of information for further explanation of terminology.) The information content of losing is


title: Lottery mathematics

text: The information entropy of a lottery probability distribution is also easy to calculate as the expected value of the information content.


title: Lottery mathematics

text: Oftentimes the random variable of interest in the lottery is a Bernoulli trial. In this case, the Bernoulli entropy function may be used. Using formula_55 representing winning the 6-of-49 lottery, the Shannon entropy of 6-of-49 above is


title: Blair Waldorf

text: Blair Cornelia Waldorf (married name Bass) is one of the main characters of "Gossip Girl", introduced in the original series of novels and also appearing as the lead in the television adaptation; she also appears in the comic adaptation. Described as "a girl of extremes" by creator Cecily von Ziegesar, she is a New York City socialite and a comical overachiever who possesses both snobbish and sensitive sides. Due to her position as queen bee of Manhattan's social scene, Blair's actions and relations are under constant scrutiny from the mysterious Gossip Girl, a popular blogger.


title: Blair Waldorf

text: Leighton Meester, who portrayed the character in the television drama, has described Blair as being insecure about her social status. At times, this anxiety creates flaws and complexities which contribute to character development. In Meester's view, the true Blair is ultimately a good girl at heart.


title: Blair Waldorf

text: Blair has been compared to vintage film and literary figures, including Becky Sharp and Lizzie Eustace. She is commonly likened to Lila Fowler of Francine Pascal's "Sweet Valley High" series. Meester's portrayal has also drawn comparisons to roles played by Joan Collins and Audrey Hepburn. She is the most critically acclaimed character of the franchise, while the television character has drawn real-life attention surrounding fashion and her love life.


title: Blair Waldorf

text: "Gossip Girl" is a series of novels about socially prominent young adults in New York City. The story primarily follows Blair Waldorf and her best friend Serena van der Woodsen during their years in high school and college. Due to her fame on the Upper East Side, Blair is featured on the website of "Gossip Girl," an anonymous gossip blogger whose posts appear occasionally throughout the story.


title: Blair Waldorf

text: In the first book, Blair is introduced as a privileged, comically vain overachiever. She is described as an alluring brunette, and occasionally models her appearance and demeanor after famous actresses, including Marilyn Monroe and, most often, Audrey Hepburn. In early novels, the character is also written as bulimic.


title: Blair Waldorf

text: Blair is largely motivated by matters surrounding family, romance, and ambition. However, her tendency to overachieve can lead to feelings of paranoia, with dramatic or comical results. In a review for "The New Yorker", Janet Malcolm remarked that Blair's issues made her "both a broader caricature and a more real person" than the other "Gossip Girl" characters. In a 2009 interview, "Gossip Girl" creator Cecily von Ziegesar claimed to identify with Blair the most, stating, "She is so unpredictable and dramatic. Such a bitch, but we understand why she is a bitch and we like her anyway".


title: Blair Waldorf

text: Throughout most of the series' run, Blair grapples with a number of changes within her family. One year prior to the opening novel, Blair's parents divorced after her father ran off with another man. When her mother remarries, and her father leaves the country, Blair has difficulty accepting her stepfather, Cyrus Rose. In addition, her stress over these matters occasionally affects her other relationships. However, Blair ultimately remains close to her father Harold, who she often turns to for comfort. By contrast, she maintains a somewhat tenser relationship with her mother Eleanor. It is also revealed that Blair has struggled with bulimia.


title: Blair Waldorf

text: In the opening novel, Blair learns of an affair between her friend Serena van der Woodsen and her boyfriend Nate. This marks the beginning of the story's primary love triangle, which recurs throughout the series. Blair's romantic life has various effects on her character development. After Nate repeatedly hurts her, she eventually refuses to take him back until she believes in his ability to commit to her. In pursuing Nate, however, Blair herself cheats on her new boyfriend Pete, which results in her losing both of them. She eventually begins to acknowledge her mistakes, with her father's help. She later grows closer to Chuck Bass (which initially occurred in the series' television adaptation), who she'd previously known for years, which leads them to briefly date one another.


title: Blair Waldorf

text: Blair is noted for an over-achieving nature, which often appears in humorous scenes. In a review for "New York" magazine, Emily Nussbaum lauded one of Blair's fantasies, which involves "joining the Peace Corps, getting a killer tan, winning the Nobel Peace Prize, and having dinner with the president, 'who would then write her a recommendation to Yale, and then Yale would fall all over themselves to accept her.' " "The New Yorker" Janet Malcolm remarked that unlike some of her forerunners in film and literature, "Blair already has all the money and position anyone could want. She is pure naked striving, restlessly seeking an object, any object, and never knowing when enough is enough."


title: Blair Waldorf

text: Blair encounters a setback during her interview at Yale by revealing the recent stress in her life, and then kissing her interviewer on the cheek upon dismissal. Her father then makes a donation to the school, though Blair is still wait-listed. In the twelfth book, "I Will Always Love You", it is revealed that she has been admitted to the university.


title: Blair Waldorf

text: In addition to her feelings for Nate, Blair is sometimes said to feel competitive with Serena in other areas, including matters of beauty and popularity. This also leads to an occasional envy on Blair's part. It is unclear how much of Blair's perception of Serena is in line with reality; the narrative describes both characters as "hands down the two hottest girls on the Upper East Side, and maybe all of Manhattan, or even the whole world."


title: Blair Waldorf

text: In 2010, Yen Press began publishing a manga adaptation titled "Gossip Girl: For Your Eyes Only", written and illustrated by HyeKyung Baek. This series adapts notable scenarios from the novel—including the triangle with Nate and Serena—but also features new material.


title: Blair Waldorf

text: After losing her position as queen bee, Blair attempts to regain her former status while adjusting to a less privileged lifestyle. In addition to this series, Blair also appears in a manga adaptation of the novel "Gossip Girl: Psycho Killer", a parody of horror stories.


title: Blair Waldorf

text: In 2007, "Gossip Girl" was adapted for television. According to Cecily von Ziegesar, the television character is largely faithful to the original. Among the aspects to be maintained are her admiration for Audrey Hepburn and her interest in Yale University. However, the series is also noted for its deviations from the source material, including the exclusion of Blair's brother Tyler. The show also explores romances between Blair and multiple male leads, resulting in occasional love triangles. In the fifth season, Blair is revealed to be pregnant with Prince of Monaco, Louis Grimaldi's child. However the child later dies before birth after a car crash Blair and Chuck were in.


title: Blair Waldorf

text: Among fans and the media, Blair's bond with Chuck Bass was commonly known by the portmanteau "Chair", while her relationship with Dan Humphrey was referred to as “Dair”. The nicknames and viewer interest in these relationships were recognized by the show's producers.


title: Blair Waldorf

text: To prepare for the part of Blair, actress Leighton Meester, a natural blonde, dyed her hair brown before auditioning, and also studied the first novel. She has described the character as multi-faceted, labeling her "a little bit of everything which is pretty amazing." Like von Ziegesar, Meester has also claimed to relate to Blair on certain levels. Prior to the show's debut in 2007, the actress stated that, "The only way to play Blair, or any character, and make her human, is to find what she is inside me. And I know I have my insecurities, too." She went on to say that, "The way Blair and I are "not" alike when it comes to insecurities is: "She" pays "so" much attention to hers!" Meester's casting was described by "Yahoo!" as a star-making role which moved her "into the pop culture vanguard," while Cecily von Ziegesar has called her a perfect choice.


title: Blair Waldorf

text: In December 2010, Meester revealed plans to leave the show in 2012. "E! Online" and other outlets speculated that her departure would possibly mark the end of the series.


title: Blair Waldorf

text: In of "Gossip Girl", Blair is introduced as the Upper East Side's beautiful and popular queen bee. She is the daughter of Eleanor Waldorf, a famous fashion designer. She is dating Nate Archibald, and is best friends with Serena van der Woodsen. She also finds a close companion in Nate's best friend and her childhood friend Chuck Bass, who becomes a partner for her schemes. When Serena returns home from boarding school, Blair learns from Nate that he lost his virginity to a drunken Serena over a year ago. Blair retaliates by publicly revealing Serena's connection to a rehab hospital. She then learns that the actual patient is Serena's younger brother, Eric, who had been committed after a suicide attempt. Afterward, a remorseful Blair reconciles with Serena.


title: Blair Waldorf

text: After learning that Nate no longer loves her, Blair sleeps with Chuck, eventually falling for him. This leads to a heated affair and an eventual love triangle. Her inability to choose creates much of the first season's story line. There are brief mentions of Blair's past struggle with bulimia.


title: Blair Waldorf

text: She also begins a brief power struggle with freshman Jenny Humphrey. After she unites with Chuck and Nate in order to save Serena from the scheming Georgina Sparks, Chuck realizes that his feelings for Blair are real and suggests that they spend the summer together in Tuscany. However, he is discouraged by his father at the last minute, and stands Blair up.


title: Blair Waldorf

text: At the launch of the second season, Blair was described by creators as the queen at the center of the "Gossip Girl" chess game. A large portion of her story line in revolves around her love-hate relationship with Chuck Bass, which was labeled "the heart of "GG"" by "People" magazine. While competing with Serena, Blair forms an unexpected friendship with Jenny, who states that they each work for everything they achieve, while Serena often glides through life. During their interviews at Yale University, Blair and Serena apologize for their ill feelings and resume their friendship.


title: Blair Waldorf

text: In the episode "O Brother, Where Bart Thou?", Chuck is devastated by news of his father's death, prompting Blair to offer her support while telling Chuck that she loves him. He initially shuns her advances, but later turns to her for comfort. However, the two stop seeing each other due to Chuck's uncle, Jack Bass, convincing him he has an inability to commit to a relationship. After being rejected by Yale, Blair finds unexpected encouragement from Nate. She is later accepted into New York University, and her competitive relationship with Georgina is eventually renewed.


title: Blair Waldorf

text: As the season ends, Blair crowns Jenny the new queen of Constance Billard School. In the season finale, it is discovered that Blair slept with Chuck's uncle Jack and that Chuck had slept with Vanessa Abrams. Chuck then departs for Europe. He later returns to New York and reconciles with Blair while declaring his love for her, and the two finally begin a committed relationship.


title: Blair Waldorf

text: In the third season, Blair joins Vanessa, Georgina, and Jenny's brother Dan at NYU. Much of her storyline concerns her inability to attain her previous status at her new school. She finds emotional support from her mother, as well as Chuck. However, she and Chuck separate once again when Blair feels that he manipulated her while competing with his uncle (Chuck made a deal with Jack that Blair could sleep with him and in exchange, Chuck gets his hotel back that Jack initially stole to 'destroy Chuck').


title: Blair Waldorf

text: She later transfers to Columbia University, and learns that an emotionally reformed Chuck was responsible for her enrollment. They later team up as part of a role-playing scheme to help Serena's mother and Chuck's adopted mother, Lily. In the season finale, Chuck attempts to propose to Blair, but is interrupted by Dan, who reveals that Chuck had slept with Jenny. Two weeks later, Blair and Serena depart for Paris intending to spend the summer together.


title: Blair Waldorf

text: In Blair and Chuck become competitive once again, but eventually resume their sexual relations before recognizing their love for one another. When the relationship interferes with their business interests, she and Chuck break up once more. Chuck promises he'll wait for her, and both affirm their belief that their love will reunite them in the end.


title: Blair Waldorf

text: Blair then teams up with Dan when the two share common goals. They also end up working together at "W." magazine, where friction develops between the two. On Valentine's Day, she discovers that Chuck has romantic feelings for Raina Thorpe, the daughter of his business rival. Later, she and Dan spend the evening talking on their cell phones while watching "Rosemary's Baby". Blair later quits "W." and is shown asleep with Dan in his Brooklyn flat. Later, upon growing curious of their feelings for one another, Blair and Dan share a kiss before the mid-season hiatus.


title: Blair Waldorf

text: Blair eventually decides that she wants to be with Chuck, but shuns him once again after he tries to humiliate Dan. She is later courted by a prince from Monaco named Louis. During a private confrontation, a drunken Chuck punches a window after he finds out Prince Louis has proposed to Blair, which cuts Blair's face as it shatters. Afterward, Blair chooses to accept a proposal from Louis. Blair later attempts to warn Chuck about potential trouble in his family. She is then abducted by an enemy of the Basses, Raina's father Russell Thorpe. Chuck later rescues Blair and apologizes for his violent actions. Following a night out together, the two have sex before Chuck advises Blair to return to Louis, believing that she will be happier with him. However, the season ends with the revelation that Blair may be pregnant.


title: Blair Waldorf

text: Amidst the fourth season, the romance between Dan and Blair became a polarizing topic among viewers which also drew significant media interest. Jarett Wieselman of the "New York Post" applauded the development, feeling that Blair had "more chemistry" with Dan than with Chuck. "New York" magazine's Chris Rovzar called Blair and Dan's story line "believable", citing their common ground in education and taste. Rovzar further stated, "Since they live in a world where both only seem to have half a dozen real friends (if that), is it so crazy they'd end up together?" An article from "The Huffington Post" declared that "Dan and Blair together are like Harry Burns and Sally Albright reincarnated — the couple was obviously inspired by "When Harry Met Sally..."." It further commented that the couple paralleled Pacey and Joey's relationship from "Dawson's Creek" and concluded that Dan and Blair were "the most inspired storyline and couple of the show". "Entertainment Weekly" stated that Dan and Blair were like stars in an "updated version of "You've Got Mail"". Tierney Bricker of E! ranked all 25 "Gossip Girl" couples placing 'Dair' as the third best couple after Blair and Serena (#1) and 'Chair' (#2).


title: Blair Waldorf

text: Dawn Fallik of "The Wall Street Journal" was less positive, asserting that "both characters have been so Blandified that there's no fun left in the show." A writer for "E! Online"<nowiki>'</nowiki>s Team WWK labeled the Dan/Blair relationship "nomance nonsense".


title: Blair Waldorf

text: With regard to Chuck and Blair, Meester stated, "I can really relate to it—not necessarily because it's this dramatic, tumultuous relationship, but because the way they love each other is very real, and not for the sake of being dramatic. It's actual love. There's nobody for each other but them." Meester also expressed fondness for Dan and Blair, however, stating, "I think they're good for each other in a lot of ways, in a way that Chuck and Blair aren't." Badgley claimed that he thought "Blair [was] Dan's soul mate" but that Blair's soulmate was Chuck “because Blair and Chuck belong with each other, obviously.” He further stated that he thought the Blair and Dan storyline was "the most exciting for Dan as a person".


title: Blair Waldorf

text: Producers initially noticed chemistry between Blair and Dan in the episode "Bad News Blair". According to producer Joshua Safran, the creators planned to revisit their relationship once the timing was right. Safran also stated that the outcome wasn't necessarily decided ahead of time. "One thing we are very conscious of—and I know some fans get upset about this—is we really try to treat the characters as living, breathing, well-rounded individuals. And we're often surprised by where their journeys take them; they open new doors for us all the time," he said.


title: Blair Waldorf

text: Following the of Safran spoke on behalf of the series regarding the scene in which Chuck became violent with Blair.


title: Blair Waldorf

text: In response to these comments, Carina MacKenzie of Zap2it stated, "We're left wondering if Safran missed the part where she went home bleeding because Chuck was using physical intimidation to release his own emotions." While reviewing the episode, Tierney Bricker of Zap2it felt that there were "really no excuses for Chuck Bass anymore." MacKenzie also called the show's explanation "disturbing, particularly given the young, female target demographic of "Gossip Girl" and The CW."


title: Blair Waldorf

text: In a review for the "Los Angeles Times", Judy Berman addressed Safran's description of Blair during the scene. "Considering how terrified Blair looked at the end of their encounter, and how quickly she got out of there, the show is sending a mixed message at best." She went on to state, "We have no right to expect "Gossip Girl" to be a paragon of morality, or even realism, but the idea that true love requires taking a shard of glass to the face is disturbing even in this alternate, soap-opera dimension."


title: Blair Waldorf

text: In the fifth-season premiere, Blair continues to plan her wedding, but begins to encounter problems in her relationship with Louis. It is later revealed that she is pregnant. Blair tells Chuck that the child is Louis', and states that part of her wanted Chuck to be the father. Dan becomes Blair's confidante and is shown to be in love with her, though she remains oblivious to his feelings and states that there is nothing more than friendship between them.


title: Blair Waldorf

text: Though she insists that she is in love with Louis, Blair begins to seek Chuck out as the season progresses. The two eventually declare their love for each other prior to a car accident in her limousine while being chased by paparazzi. Though both recover, Blair suffers a miscarriage from the crash. After the crash Blair decides that she must commit herself to Louis, converting to Catholicism and cutting off any connection with Chuck. At the wedding, Gossip Girl releases a recording of Blair confessing her love for Chuck. Nevertheless, Louis and Blair get married, making Blair a Princess of Monaco, though Louis informs her that they will have a loveless marriage of convenience. She then receives support from Dan, leading them to share a kiss on Valentine's Day. Amidst these developments, Blair grows conflicted between her feelings for Dan and Chuck. After taking steps to end her marriage, she chooses to pursue a relationship with Dan. By the end of the season, however, after a debate about which love is the best, Blair declares that she is still in love with Chuck, and chooses to pursue him.


title: Blair Waldorf

text: In the final season, Blair resumes her romantic relationship with Chuck, while Chuck and his father Bart—who is revealed to be alive in the previous season—become bitter rivals. Blair pursues her career as head of Waldorf Designs, with several mishaps, before staging a successful line. In the penultimate episode, Bart falls to his death while trying to attack Chuck atop a building. Afterward, Blair and Chuck depart together. In the series finale, Blair marries Chuck which results in her not having to testify against him in his father's murder case. Five years later, Blair is shown to be running her mother's successful fashion line and she works with Jenny in a line called "J for Waldorf", and she and Chuck are shown to have a son named Henry.


title: Blair Waldorf

text: While covering the book series, Janet Malcolm of "The New Yorker" labeled the character "an antiheroine of the first rank," and asserted that "the series belongs to awful Blair, who inspires von Ziegesar's highest flights of comic fancy." She also compared Blair to vintage film and literary figures such as Becky Sharp of "Vanity Fair", and Lizzie Eustace of "The Eustace Diamonds". In addition, several critics have likened Blair to the character Lila Fowler of the earlier "Sweet Valley High" series.


title: Blair Waldorf

text: In the 2007 book "Children's Literature and Culture", writer Harry Edwin Eiss chastised the depiction of Blair's bulimia. "If handled properly, the inclusion of her illness could have provided a powerful lesson for young adult readers who worry about their weight and food consumption. Unfortunately, Cecily von Ziegesar, the author of the series, presents a seriously flawed treatment of the problem. In a failed attempt at humor, the writer regards Blair's sickness as just another source of gossip," he said. Emily Nussbaum of "New York" magazine had similar comments, calling the bulimia "more of an icky weakness than a full-fledged pathology." However, she went on to commend Blair as "hilariously self-centered".


title: Blair Waldorf

text: Julie Opipari of "Manga Maniac Cafe" gave the initial "Gossip Girl" manga a negative review, citing displeasure with the characters and plot. However, she acknowledged that this gave her a greater appreciation for Blair in the second volume, noting that Blair "really had to learn how to rough it" after losing her privileged lifestyle. She went on to state that "Blair is one character that is fun to hate on. So imagine my surprise when I actually started to like her by the end of the book".


title: Blair Waldorf

text: The show's breakout character, Blair Waldorf has garnered much media recognition. "Yahoo!" proclaims Blair a member of "television's pantheon of razor-witted, solipsistic high school Alpha females." While commenting on Meester, "New York" magazine's 2008 cover story of the series states, "Her villain-you-want-to-root-for is the most sophisticated performance on the show." In another 2008 article, "People" magazine commented that "Meester has burst out of this ensemble to stardom." "Variety" described her performance as similar to that of "a predatory junior Joan Collins who practically breathes fire out of her pinched, perfectly WASP-ish nostrils." "FHM Online" ranked the actress the "Hottest TV Star" of autumn 2008, stating that as Blair Waldorf, "Leighton Meester has stolen the spotlight with her mind-blowing good looks and amazing performance." "OK!" magazine likened her character to Audrey Hepburn's portrayal of Holly Golightly. The physical similarity was also noted by "USA Today".


title: Blair Waldorf

text: In its 2009 "Hot List", "Rolling Stone" cited Blair as "the reason we love the back-stabby soap most." Regarding the fictional fame of Blair's friend Serena, Tim Stack of "Entertainment Weekly" asserted that "Serena may be the star of the media but Blair is quickly becoming the star of this show." While citing Serena's long-revered allure, "Glamour" and its readers compared the two characters in 2008, with Blair being recognized as more beautiful than Serena. In a review from "The Atlantic", Blair and Serena's friendship was praised as "it offered a relationship whose depth and complexity approached Rory and Paris' [from "Gilmore Girls"]."


title: Blair Waldorf

text: In May 2009, Blair received attention from "Forbes", which interviewed her via the series' writers. "Television Without Pity" listed Meester in their "Golden Globes 2009: Overlooked TV Shows and Performances" article, labeling Blair "so multi-faceted, well-dressed and beautifully played that she elevates this teen soap to something we don't even feel guilty about admitting we love." Meester won the Teen Choice Award for "Choice TV Actress Drama" in 2009, and again in 2010. In 2009, she was voted the "Best Mean Girl" in Zap2it first poll of the best television characters in the 2000s. In February 2012, Zap2it held another poll to determine TV's Most Crushworthy. Blair was elected TV's Most Crushworthy 1% Female over Temperance "Bones" Brennan. The 1 percenters are people that "have everything going for them with their fantastic good looks and their opulent lifestyle". Her relationship with Chuck Bass was included in "TV Guide" list of "The Best TV Couples of All Time" as well as "Entertainment Weekly" "30 Best 'Will They/Won't They?' TV Couples".


title: Blair Waldorf

text: The character's wardrobe—credited to designers Abigail Lorick and Eric Daman—was popular, earning mentions from periodicals such as "InStyle" and "New York", along with recognition from websites. "TV Guide" listed Blair among its "Best Dressed TV Characters of 2007". "Entertainment Weekly" named Blair Waldorf and Chuck Bass the "Most Stylish" characters of 2008. Lifetime television ranks Blair first in its listing of "The Top 10 Best-Dressed TV Characters", while "Glamour" has named her among its best-dressed TV characters of all time. In a "Vanity Fair" interview, costume designers Eric Daman and Meredith Markworth-Pollack named Audrey Hepburn and "Vogue" editor-in-chief Anna Wintour as their inspirations when dressing Meester as Blair. The designers also cited New York socialites Tinsley Mortimer and Arden Wohl as influences. "TV Guide" named her the sixth most fashionable TV character.


title: Hurtcore

text: Hurtcore, a portmanteau of the words "hardcore" and "hurt", is a name given to a particularly extreme form of child pornography, usually involving degrading violence, bodily harm and murder relating to child sexual abuse. The material is usually so extreme, even most pedophiles have been said to be repulsed by this genre of pornography and condemn its topic in most discussions. Eileen Ormsby, Australian writer and author of "The Darkest Web", described hurtcore as "a fetish for people who get aroused by the infliction of pain, or even torture, on another person who is not a willing participant". An additional motivation for the perpetrator, next to their position of power over their victim(s), can be the reaction of their victim(s) to the physical abuse, like crying or screaming of pain. This reaction can stimulate the arousal of the perpetrator even more.


title: Hurtcore

text: Some dark web forums are dedicated to the discussion, and the sharing of images and videos, of hurtcore. In 2013, Vice called Hurt2theCore" "the dark web's most notorious hurtcore site", run by Matthew Graham, who became known as the "King of Hurtcore" and "one of the biggest child pornography and hurtcore distributors in the world".


title: Bose–Einstein statistics

text: In quantum statistics, Bose–Einstein statistics (B–E statistics) describes one of two possible ways in which a collection of non-interacting, indistinguishable particles may occupy a set of available discrete energy states at thermodynamic equilibrium. The aggregation of particles in the same state, which is a characteristic of particles obeying Bose–Einstein statistics, accounts for the cohesive streaming of laser light and the frictionless creeping of superfluid helium. The theory of this behaviour was developed (1924–25) by Satyendra Nath Bose, who recognized that a collection of identical and indistinguishable particles can be distributed in this way. The idea was later adopted and extended by Albert Einstein in collaboration with Bose.


title: Bose–Einstein statistics

text: The Bose–Einstein statistics applies only to the particles not limited to single occupancy of the same state – that is, particles that do not obey the Pauli exclusion principle restrictions. Such particles have integer values of spin and are named bosons. Particles with half-integer spins are called fermions and obey Fermi-Dirac statistics.


title: Bose–Einstein statistics

text: At low temperatures, bosons behave differently from fermions (which obey the Fermi–Dirac statistics) in a way that an unlimited number of them can "condense" into the same energy state. This apparently unusual property also gives rise to the special state of matter – the Bose–Einstein condensate. Fermi–Dirac and Bose–Einstein statistics apply when quantum effects are important and the particles are "indistinguishable". Quantum effects appear if the concentration of particles satisfies


title: Bose–Einstein statistics

text: where is the number of particles, is the volume, and is the quantum concentration, for which the interparticle distance is equal to the thermal de Broglie wavelength, so that the wavefunctions of the particles are barely overlapping.


title: Bose–Einstein statistics

text: Fermi–Dirac statistics applies to fermions (particles that obey the Pauli exclusion principle), and Bose–Einstein statistics applies to bosons. As the quantum concentration depends on temperature, most systems at high temperatures obey the classical (Maxwell–Boltzmann) limit, unless they also have a very high density, as for a white dwarf. Both Fermi–Dirac and Bose–Einstein become Maxwell–Boltzmann statistics at high temperature or at low concentration.


title: Bose–Einstein statistics

text: B–E statistics was introduced for photons in 1924 by Bose and generalized to atoms by Einstein in 1924–25.


title: Bose–Einstein statistics

text: with and where is the occupation number (the number of particles) in state , formula_2 is the degeneracy of energy level , is the energy of the -th state, "μ" is the chemical potential, is the Boltzmann constant, and is absolute temperature.


title: Bose–Einstein statistics

text: The variance of this distribution formula_3 is calculated directly from the expression above for the average number.


title: Bose–Einstein statistics

text: For comparison, the average number of fermions with energy formula_5 given by Fermi–Dirac particle-energy distribution has a similar form:


title: Bose–Einstein statistics

text: As mentioned above, both the Bose–Einstein distribution and the Fermi–Dirac distribution approaches the Maxwell–Boltzmann distribution in the limit of high temperature and low particle density, without the need for any ad hoc assumptions:


title: Bose–Einstein statistics

text: In addition to reducing to the Maxwell–Boltzmann distribution in the limit of high formula_13 and low density, B–E statistics also reduces to Rayleigh–Jeans law distribution for low energy states with <br> formula_14, namely


title: Bose–Einstein statistics

text: Władysław Natanson in 1911 concluded that Planck's law requires indistinguishability of "units of energy", although he did not frame this in terms of Einstein's light quanta.


title: Bose–Einstein statistics

text: While presenting a lecture at the University of Dhaka (in what was then British India and is now Bangladesh) on the theory of radiation and the ultraviolet catastrophe, Satyendra Nath Bose intended to show his students that the contemporary theory was inadequate, because it predicted results not in accordance with experimental results. During this lecture, Bose committed an error in applying the theory, which unexpectedly gave a prediction that agreed with the experiment. The error was a simple mistake—similar to arguing that flipping two fair coins will produce two heads one-third of the time—that would appear obviously wrong to anyone with a basic understanding of statistics (remarkably, this error resembled the famous blunder by d'Alembert known from his "Croix ou Pile" article). However, the results it predicted agreed with experiment, and Bose realized it might not be a mistake after all. For the first time, he took the position that the Maxwell–Boltzmann distribution would not be true for all microscopic particles at all scales. Thus, he studied the probability of finding particles in various states in phase space, where each state is a little patch having phase volume of "h", and the position and momentum of the particles are not kept particularly separate but are considered as one variable.


title: Bose–Einstein statistics

text: Bose adapted this lecture into a short article called "Planck's law and the hypothesis of light quanta" and submitted it to the "Philosophical Magazine". However, the referee's report was negative, and the paper was rejected. Undaunted, he sent the manuscript to Albert Einstein requesting publication in the . Einstein immediately agreed, personally translated the article from English into German (Bose had earlier translated Einstein's article on the general theory of relativity from German to English), and saw to it that it was published. Bose's theory achieved respect when Einstein sent his own paper in support of Bose's to , asking that they be published together. The paper came out in 1924.


title: Bose–Einstein statistics

text: The reason Bose produced accurate results was that since photons are indistinguishable from each other, one cannot treat any two photons having equal quantum numbers (e.g., polarization and momentum vector) as being two distinct identifiable photons. By analogy, if in an alternate universe coins were to behave like photons and other bosons, the probability of producing two heads would indeed be one-third, and so is the probability of getting a head and a tail which equals one-half for the conventional (classical, distinguishable) coins. Bose's "error" leads to what is now called Bose–Einstein statistics.


title: Bose–Einstein statistics

text: Bose and Einstein extended the idea to atoms and this led to the prediction of the existence of phenomena which became known as Bose–Einstein condensate, a dense collection of bosons (which are particles with integer spin, named after Bose), which was demonstrated to exist by experiment in 1995.


title: Bose–Einstein statistics

text: In the microcanonical ensemble, one considers a system with fixed energy, volume, and number of particles. We take a system composed of formula_16 identical bosons, formula_17 of which have energy formula_5 and are distributed over formula_2 levels or states with the same energy formula_5, i.e. formula_2 is the degeneracy associated with energy formula_5 of total energy formula_23. Calculation of the number of arrangements of formula_17 particles distributed among formula_2 states is a problem of combinatorics. Since particles are indistinguishable in the quantum mechanical context here, the number of ways for arranging formula_17 particles in formula_2 boxes (for the formula_28th energy level) would be (see image).


title: Bose–Einstein statistics

text: where formula_30 is the "k"-combination of a set with "m" elements. The total number of arrangements in an ensemble of bosons is simply the product of the binomial coefficients formula_31 above over all the energy levels, i.e.


title: Bose–Einstein statistics

text: The maximum number of arrangements determining the corresponding occupation number formula_17 is obtained by maximizing the entropy, or equivalently, setting formula_34 and taking the subsidiary conditions formula_35 into account (as Lagrange multipliers). The result for formula_36, formula_37, formula_38 is the Bose–Einstein distribution.


title: Bose–Einstein statistics

text: The Bose–Einstein distribution, which applies only to a quantum system of non-interacting bosons, is naturally derived from the grand canonical ensemble without any approximations. In this ensemble, the system is able to exchange energy and exchange particles with a reservoir (temperature "T" and chemical potential "µ" fixed by the reservoir).


title: Bose–Einstein statistics

text: Due to the non-interacting quality, each available single-particle level (with energy level "ϵ") forms a separate thermodynamic system in contact with the reservoir. That is, the number of particles within the overall system "that occupy a given single particle state" form a sub-ensemble that is also grand canonical ensemble; hence, it may be analysed through the construction of a grand partition function.


title: Bose–Einstein statistics

text: Every single-particle state is of a fixed energy, formula_39. As the sub-ensemble associated with a single-particle state varies by the number of particles only, it is clear that the total energy of the sub-ensemble is also directly proportional to the number of particles in the single-particle state; where formula_40 is the number of particles, the total energy of the sub-ensemble will then be formula_41. Beginning with the standard expression for a grand partition function and replacing formula_42 with formula_43, the grand partition function takes the form


title: Bose–Einstein statistics

text: This formula applies to fermionic systems as well as bosonic systems. Fermi–Dirac statistics arises when considering the effect of the Pauli exclusion principle: whilst the number of fermions occupying the same single-particle state can only be either 1 or 0, the number of bosons occupying a single particle state may be any integer. Thus, the grand partition function for bosons can be considered a geometric series and may be evaluated as such:


title: Bose–Einstein statistics

text: Note that the geometric series is convergent only if formula_46, including the case where formula_47. This implies that the chemical potential for the Bose gas must be negative, i.e., formula_48, whereas the Fermi gas is allowed to take both positive and negative values for the chemical potential.


title: Bose–Einstein statistics

text: This result applies for each single-particle level and thus forms the Bose–Einstein distribution for the entire state of the system.


title: Bose–Einstein statistics

text: As a result, for highly occupied states the standard deviation of the particle number of an energy level is very large, slightly larger than the particle number itself: formula_52. This large uncertainty is due to the fact that the probability distribution for the number of bosons in a given energy level is a geometric distribution; somewhat counterintuitively, the most probable value for "N" is always 0. (In contrast, classical particles have instead a Poisson distribution in particle number for a given state, with a much smaller uncertainty of formula_53, and with the most-probable "N" value being near formula_54.)


title: Bose–Einstein statistics

text: It is also possible to derive approximate Bose–Einstein statistics in the canonical ensemble. These derivations are lengthy and only yield the above results in the asymptotic limit of a large number of particles. The reason is that the total number of bosons is fixed in the canonical ensemble. The Bose–Einstein distribution in this case can be derived as in most texts by maximization, but the mathematically best derivation is by the Darwin–Fowler method of mean values as emphasized by Dingle. See also Müller-Kirsten. The fluctuations of the ground state in the condensed region are however markedly different in the canonical and grand-canonical ensembles.


title: Bose–Einstein statistics

text: Suppose we have a number of energy levels, labeled by index formula_55, each level having energy formula_56 and containing a total of formula_57 particles. Suppose each level contains formula_58 distinct sublevels, all of which have the same energy, and which are distinguishable. For example, two particles may have different momenta, in which case they are distinguishable from each other, yet they can still have the same energy.


title: Bose–Einstein statistics

text: formula_58 associated with level formula_55 is called the "degeneracy" of that energy level. Any number of bosons can occupy the same sublevel.


title: Bose–Einstein statistics

text: Let formula_61 be the number of ways of distributing formula_62 particles among the formula_63 sublevels of an energy level. There is only one way of distributing formula_62 particles with one sublevel, therefore formula_65. It is easy to see that there are formula_66 ways of distributing formula_62 particles in two sublevels which we will write as:


title: Bose–Einstein statistics

text: With a little thought (see Notes below) it can be seen that the number of ways of distributing formula_62 particles in three sublevels is


title: Bose–Einstein statistics

text: For example, the population numbers for two particles in three sublevels are 200, 110, 101, 020, 011, or 002 for a total of six which equals 4!/(2!2!). The number of ways that a set of occupation numbers formula_57 can be realized is the product of the ways that each individual energy level can be populated:


title: Bose–Einstein statistics

text: Following the same procedure used in deriving the Maxwell–Boltzmann statistics, we wish to find the set of formula_57 for which "W" is maximised, subject to the constraint that there be a fixed total number of particles, and a fixed total energy. The maxima of formula_79 and formula_80 occur at the same value of formula_57 and, since it is easier to accomplish mathematically, we will maximise the latter function instead. We constrain our solution using Lagrange multipliers forming the function:


title: Bose–Einstein statistics

text: Using the formula_77 approximation and using Stirling's approximation for the factorials formula_84 gives


title: Bose–Einstein statistics

text: Where "K" is the sum of a number of terms which are not functions of the formula_17. Taking the derivative with respect to formula_57, and setting the result to zero and solving for formula_57, yields the Bose–Einstein population numbers:


title: Bose–Einstein statistics

text: By a process similar to that outlined in the Maxwell–Boltzmann statistics article, it can be seen that:


title: Bose–Einstein statistics

text: which, using Boltzmann's famous relationship formula_91 becomes a statement of the second law of thermodynamics at constant volume, and it follows that formula_92 and formula_93 where "S" is the entropy, formula_94 is the chemical potential, "k" is Boltzmann's constant and "T" is the temperature, so that finally:


title: Bose–Einstein statistics

text: Also note that when the particle numbers are not conserved, removing the conservation of particle numbers constraint is equivalent to setting formula_98 and therefore the chemical potential formula_94 to zero. This will be the case for photons and massive particles in mutual equilibrium and the resulting distribution will be the Planck distribution.


title: Bose–Einstein statistics

text: A much simpler way to think of Bose–Einstein distribution function is to consider that n particles are denoted by identical balls and g shells are marked by g-1 line partitions. It is clear that the permutations of these n balls and g − 1 partitions will give different ways of arranging bosons in different energy levels. Say, for 3 (= "n") particles and 3 (= "g") shells, therefore , the arrangement might be |●●|●, or ||●●●, or |●|●● , etc. Hence the number of distinct permutations of objects which have "n" identical items and ("g" − 1) identical items will be:


title: Bose–Einstein statistics

text: See the image for a visual representation of one such distribution of "n" particles in "g" boxes that can be represented as partitions.


title: Bose–Einstein statistics

text: The purpose of these notes is to clarify some aspects of the derivation of the Bose–Einstein (B–E) distribution for beginners. The enumeration of cases (or ways) in the B–E distribution can be recast as follows. Consider a game of dice throwing in which there are formula_62 dice, with each die taking values in the setformula_102, for formula_103. The constraints of the game are that the value of a die formula_55, denoted by formula_105, has to be greater than or equal to the value of die formula_106, denoted by formula_107, in the previous throw, i.e., formula_108. Thus a valid sequence of die throws can be described by an "n"-tuple formula_109, such that formula_108. Let formula_111 denote the set of these valid "n"-tuples:


title: Bose–Einstein statistics

text: Then the quantity formula_61 (defined above as the number of ways to distribute formula_62 particles among the formula_63 sublevels of an energy level) is the cardinality of formula_111, i.e., the number of elements (or valid "n"-tuples) in formula_111. Thus the problem of finding an expression for formula_61 becomes the problem of counting the elements in formula_111.


title: Bose–Einstein statistics

text: Subset formula_123 is obtained by fixing all indices formula_105 to formula_125, except for the last index, formula_126, which is incremented from formula_127 to formula_128. Subset formula_129 is obtained by fixing formula_130, and incrementing formula_131 from formula_132 to formula_128. Due to the constraint formula_134 on the indices in formula_111, the index formula_136 must automatically take values in formula_137. The construction of subsets formula_138 and formula_139 follows in the same manner.


title: Bose–Einstein statistics

text: Each element of formula_122 can be thought of as a multiset of cardinality formula_141; the elements of such multiset are taken from the set formula_142 of cardinality formula_128, and the number of such multisets is the multiset coefficient


title: Bose–Einstein statistics

text: More generally, each element of formula_111 is a multiset of cardinality formula_62 (number of dice) with elements taken from the set formula_147 of cardinality formula_63 (number of possible values of each die), and the number of such multisets, i.e., formula_61is the multiset coefficient


title: Bose–Einstein statistics

text: which is exactly the same as the formula for formula_150, as derived above with the aid of a theorem involving binomial coefficients, namely


title: Bose–Einstein statistics

text: By deleting the index formula_159 (shown in red with double underline) in the subset formula_160 of formula_161, one obtains the set


title: Bose–Einstein statistics

text: In other words, there is a one-to-one correspondence between the subset formula_160 of formula_161 and the set formula_165. We write


title: Bose–Einstein statistics

text: It can then be verified that (8) and (2) give the same result for formula_175, formula_176, formula_177, etc.


title: Bose–Einstein statistics

text: Viewed as a pure probability distribution, the Bose–Einstein distribution has found application in other fields:


title: Cape Colony

text: The Cape Colony (), also known as the Cape of Good Hope, was a British colony in present-day South Africa named after the Cape of Good Hope, which existed from 1795 to 1802, and again from 1806 to 1910, when it united with three other colonies to form the Union of South Africa.


title: Cape Colony

text: The British colony was preceded by an earlier corporate colony that became an original Dutch colony of the same name, which was established in 1652 by the Dutch East India Company (VOC). The Cape was under VOC rule from 1652 to 1795 and under rule of the Napoleonic Batavia Republic from 1803 to 1806. The VOC lost the colony to Great Britain following the 1795 Battle of Muizenberg, but it was acceded to the Batavia Republic following the 1802 Treaty of Amiens. It was re-occupied by the British following the Battle of Blaauwberg in 1806, and British possession affirmed with the Anglo-Dutch Treaty of 1814. The Cape of Good Hope then remained in the British Empire, becoming self-governing in 1872.


title: Cape Colony

text: The colony was coextensive with the later Cape Province, stretching from the Atlantic coast inland and eastward along the southern coast, constituting about half of modern South Africa: the final eastern boundary, after several wars against the Xhosa, stood at the Fish River. In the north, the Orange River, natively known as the (Black River) and subsequently called the Gariep River, served as the boundary for some time, although some land between the river and the southern boundary of Botswana was later added to it. From 1878, the colony also included the enclave of Walvis Bay and the Penguin Islands, both in what is now Namibia.


title: Cape Colony

text: It united with three other colonies to form the Union of South Africa in 1910. It then was renamed the Province of the Cape of Good Hope. South Africa became a sovereign state in 1931 by the Statute of Westminster. In 1961, it became the Republic of South Africa. Following the 1994 creation of the present-day South African provinces, the Cape Province was partitioned into the Eastern Cape, Northern Cape, and Western Cape, with smaller parts in North West province.


title: Cape Colony

text: An expedition of the VOC led by Jan van Riebeeck established a trading post and naval victualing station at the Cape of Good Hope in 1652. Van Riebeeck's objective was to secure a harbour of refuge for VOC ships during the long voyages between Europe and Asia. Within about three decades, the Cape had become home to a large community of , also known as ('free citizens'), former VOC employees who settled in the colonies overseas after completing their service contracts. were mostly married citizens who undertook to spend at least twenty years farming the land within the fledgling colony's borders; in exchange they received tax exempt status and were loaned tools and seeds. Reflecting the multi-national nature of the early trading companies, the VOC granted status to Dutch, Scandinavian and German employees, among others. In 1688 they also sponsored the immigration of nearly two hundred French Huguenot refugees who had fled to the Netherlands upon the Edict of Fontainebleau. There was a degree of cultural assimilation due to Dutch cultural hegemony that included the almost universal adoption of the Dutch language.


title: Cape Colony

text: Many of the colonists who settled directly on the frontier became increasingly independent and localised in their loyalties. Known as "Boers", they migrated westwards beyond the Cape Colony's initial borders and had soon penetrated almost a thousand kilometres inland. Some Boers even adopted a nomadic lifestyle permanently and were denoted as . The VOC colonial period had a number of bitter, genocidal conflicts between the colonists and the Khoe-speaking indigenes, followed by the Xhosa, both of which they perceived as unwanted competitors for prime farmland.


title: Cape Colony

text: VOC traders imported thousands of enslaved people to the Cape of Good Hope from the Dutch East Indies and other parts of Africa. By the end of the eighteenth century the Cape's population swelled to about 26,000 people of European descent and 30,000 enslaved people.


title: Cape Colony

text: In 1795, France occupied the Seven Provinces of the Dutch Republic, the mother country of the Dutch United East India Company. This prompted Great Britain to occupy the Cape Colony in 1795 as a way to better control the seas in order to stop any potential French attempt to reach India. The British sent a fleet of nine warships which anchored at Simon's Town and, following the defeat of the VOC militia at the Battle of Muizenberg, took control of the territory. The United East India Company transferred its territories and claims to the Batavian Republic (the Revolutionary period Dutch state) in 1798, and went bankrupt in 1799. Improving relations between Britain and Napoleonic France, and its vassal state the Batavian Republic, led the British to hand the Cape of Good Hope over to the Batavian Republic in 1803, under the terms of the Treaty of Amiens.


title: Cape Colony

text: In 1806, the Cape, now nominally controlled by the Batavian Republic, was occupied again by the British after their victory in the Battle of Blaauwberg. The temporary peace between the UK and Napoleonic France had crumbled into open hostilities, whilst Napoleon had been strengthening his influence on the Batavian Republic (which Napoleon would subsequently abolish and directly administer later the same year). The British, who set up a colony on 8 January 1806, hoped to keep Napoleon out of the Cape, and to control the Far East trade routes.


title: Cape Colony

text: The Cape Colony at the time of British occupation was three months' sailing distance from London. The White colonial population was small, no more than 25,000 in all, scattered across a territory of 100,000 square miles. Most lived in Cape Town and the surrounding farming districts of the Boland, an area favoured with rich soils, a Mediterranean Climate and reliable rainfall. Cape Town had a population of 16,000 people.


title: Cape Colony

text: In 1814 the Dutch government formally ceded sovereignty over the Cape to the British, under the terms of the Convention of London.


title: Cape Colony

text: The British started to settle the eastern border of the cape colony, with the arrival in Port Elizabeth of the 1820 Settlers. They also began to introduce the first rudimentary rights for the Cape's Black African population and, in 1834, abolished slavery; however, the government proved unable to rein in settler violence against the San, which continued largely unabated as it had during the Dutch period. The resentment that the Boers felt against this social change, as well as the imposition of English language and culture, caused them to trek inland en masse. This was known as the Great Trek, and the migrating Boers settled inland, eventually forming the Boer Republics.


title: Cape Colony

text: British Immigration continued in the Cape, even as many of the Boers continued to trek inland, and the ending of the British East India Company's monopoly on trade led to economic growth.


title: Cape Colony

text: At the same time, the long series of Xhosa Wars fought between the Xhosa people in the east and the government of the Cape Colony as well as Boer settlers finally died down when the Xhosa took part in a mass destruction of their own crops and cattle, in the belief that this would cause their ancestors to wake from the dead. The resulting famine crippled Xhosa country and ushered in a long period of stability on the border.


title: Cape Colony

text: Peace and prosperity led to a desire for political independence. In 1853, the Cape Colony became a British Crown colony with representative government. In 1854, the Cape of Good Hope elected its first parliament, on the basis of the multi-racial Cape Qualified Franchise. Cape residents qualified as voters based on a universal minimum level of property ownership, regardless of race.


title: Cape Colony

text: Executive power remaining completely in the authority of the British governor did not relieve tensions in the colony between its eastern and western sections.


title: Cape Colony

text: In 1872, after a long political battle, the Cape of Good Hope achieved responsible government under its first Prime Minister, John Molteno. Henceforth, an elected Prime Minister and his cabinet had total responsibility for the affairs of the country. A period of strong economic growth and social development ensued, and the eastern-western division was largely laid to rest. The system of multi-racial franchise also began a slow and fragile growth in political inclusiveness, and ethnic tensions subsided. In 1877, the state expanded by annexing Griqualand West and Griqualand East – that is, the Mount Currie district (Kokstad). The emergence of two Boer mini-republics along the Missionary Road resulted in 1885 in the Warren Expedition, sent to annex the republics of Stellaland and Goshen (lands annexed to British Bechuanaland). Major-General Charles Warren annexed the land south of the Molopo River as the colony of British Bechuanaland and proclaimed a protectorate over the land lying to the North of the river. Vryburg, the capital of Stellaland, became capital of British Bechuanaland, while Mafeking (now Mahikeng), although situated south of the protectorate border, became the protectorate's administrative centre. The border between the protectorate and the colony ran along the Molopo and Nossob rivers. In 1895 British Bechuanaland became part of the Cape Colony.


title: Cape Colony

text: However, the discovery of diamonds around Kimberley and gold in the Transvaal led to a return to instability, particularly because they fuelled the rise to power of the ambitious imperialist Cecil Rhodes. On becoming the Cape's Prime Minister in 1890, he instigated a rapid expansion of British influence into the hinterland. In particular, he sought to engineer the conquest of the Transvaal, and although his ill-fated Jameson Raid failed and brought down his government, it led to the Second Boer War and British conquest at the turn of the century. The politics of the colony consequently came to be increasingly dominated by tensions between the British colonists and the Boers. Rhodes also brought in the first formal restrictions on the political rights of the Cape of Good Hope's black African citizens.


title: Cape Colony

text: The Cape of Good Hope remained nominally under British rule until the formation of the Union of South Africa in 1910, when it became the Province of the Cape of Good Hope, better known as the Cape Province.


title: Cape Colony

text: Population Figures for the 1865, 1875, 1891 and 1904 censuses. Groups marked "nd" are Not Distinguished in the censuses for those years.


title: Ritika Singh

text: Ritika Mohan Singh is an Indian actress and former mixed martial artist, who predominantly appears in Tamil films in addition to Hindi Telugu and Malayalam Language films. After competing for India at the 2009 Asian Indoor Games and then participating in the Super Fight League, she played a leading role in Sudha Kongara Prasad's Tamil film "Irudhi Suttru" (also simultaneously shot in Hindi as "Saala Khadoos") alongside R. Madhavan. She won Special Mention at the 63rd National Film Awards for her performance in the film. She received Filmfare Awards thrice for the same role in three languages: Tamil ("Irudhi Suttru"), Hindi ("Saala Khadoos") and Telugu ("Guru").


title: Ritika Singh

text: Singh trained as a kickboxer and as a mixed martial artist since childhood, under the guidance of her father. She appeared in the inaugural season of the Super Fight League and competed as a mixed martial artist.


title: Ritika Singh

text: Ritika Singh began her acting career in 2013, she was spotted by director Sudha Kongara Prasad in an advert for the Super Fight League and she later auditioned to play a leading role in her bilingual film, "Saala Khadoos" (2016), after the makers managed to contact her through the competition's chairman, Raj Kundra. Portraying Madhi, a Marwari girl who grows up in the slums of Chennai, Singh was signed because the makers wanted a professional boxer to act, rather than an actress to act as a boxer. For the Tamil version, "Irudhi Suttru", Singh phonetically learned her part in Tamil by writing down the dialogues in Hindi. Co-produced by the film's lead actor R. Madhavan and Rajkumar Hirani, the film was released in late January 2016. Ritika received rave reviews for her portrayal, with Sify.com stating "she is a marvelous discovery" and "her lip sync, body language and gait is a major highlight for the film". For her performance in "Irudhi Suttru", Ritika won the a Special Mention at the 63rd National Film Awards, and became the first actress, who did not dub for her role, to be recognised at the National Awards. Singh later appeared in Manikandan's "Aandavan Kattalai", which was released in September 2016. His next following was the Telugu movie "Guru" (2017), remake of "Irudhi Suttru". Later, she performed in the horror comedy by P. Vasu's "Shivalinga" (2017) and Telugu movie "Neevevaro" (2018).


title: Ritika Singh

text: In 2020, she played the female protagonist in the film "Oh My Kadavule" with Ashok Selvan and Vani Bhojan.


title: 2016–17 UEFA Europa League

text: The 2016–17 UEFA Europa League was the 46th season of Europe's secondary club football tournament organised by UEFA, and the eighth season since it was renamed from the UEFA Cup to the UEFA Europa League.


title: 2016–17 UEFA Europa League

text: The final was played between Ajax and Manchester United at the Friends Arena in Solna, Sweden. Manchester United beat Ajax 2–0 to win their first title. With this victory, they became the fifth club – after Juventus, Ajax, Bayern Munich and Chelsea – to have won all three major European trophies (European Champion Clubs' Cup/UEFA Champions League, UEFA Cup/UEFA Europa League, and the now-defunct Cup Winners' Cup).


title: 2016–17 UEFA Europa League

text: Manchester United qualified for the 2017–18 UEFA Champions League, and also earned the right to play against the winners of the 2016–17 UEFA Champions League, Real Madrid, in the 2017 UEFA Super Cup.


title: 2016–17 UEFA Europa League

text: As the title holders, Sevilla qualified for the 2016–17 UEFA Champions League. Having won the last three Europa League tournaments, Sevilla were unable to defend their titles as they reached the Champions League knockout stage, where they were eliminated by Leicester City in the round of 16.


title: 2016–17 UEFA Europa League

text: A total of 188 teams from 54 of the 55 UEFA member associations were expected to participate in the 2016–17 UEFA Europa League (the exception being Kosovo, whose participation was not accepted in their first attempt as UEFA members). The association ranking based on the UEFA country coefficients was used to determine the number of participating teams for each association:


title: 2016–17 UEFA Europa League

text: The UEFA Executive Committee approved in December 2014 changes to the rewards given according to the Respect Fair Play ranking, and starting from the 2016–17 season, the three Fair Play berths were no longer allocated to the Europa League.


title: 2016–17 UEFA Europa League

text: For the 2016–17 UEFA Champions League, the associations were allocated places according to their 2015 UEFA country coefficients, which took into account their performance in European competitions from 2010–11 to 2014–15.


title: 2016–17 UEFA Europa League

text: Apart from the allocation based on the country coefficients, associations could have additional teams participating in the Europa League, as noted below:


title: 2016–17 UEFA Europa League

text: In the default access list, Sevilla enter the third qualifying round (as the seventh-placed team of the 2015–16 La Liga). However, since they qualified for the Champions League as the Europa League title holders, the spot which they qualified for in the Europa League third qualifying round is vacated, and the following changes to the default allocation system are made:


title: 2016–17 UEFA Europa League

text: A Europa League place is vacated when a team qualifies for both the Champions League and the Europa League, or qualifies for the Europa League by more than one method. When a place is vacated, it is redistributed within the national association by the following rules (regulations Articles 3.03 and 3.04):


title: 2016–17 UEFA Europa League

text: Notably two teams took part in the competition that were not playing in their national top division, Zürich (2nd tier) and Hibernian (2nd tier).


title: 2016–17 UEFA Europa League

text: The schedule of the competition was as follows (all draws were held at the UEFA headquarters in Nyon, Switzerland, unless stated otherwise).


title: 2016–17 UEFA Europa League

text: Matches in the qualifying, play-off, and knockout rounds could also be played on Tuesdays or Wednesdays instead of the regular Thursdays due to scheduling conflicts.


title: 2016–17 UEFA Europa League

text: In the qualifying rounds and the play-off round, teams were divided into seeded and unseeded teams based on their 2016 UEFA club coefficients, and then drawn into two-legged home-and-away ties. Teams from the same association could not be drawn against each other.


title: 2016–17 UEFA Europa League

text: The draws for the first and second qualifying round were held on 20 June 2016. The first legs were played on 28 and 30 June, and the second legs were played on 5, 6 and 7 July 2016.


title: 2016–17 UEFA Europa League

text: The draw for the third qualifying round was held on 15 July 2016. The first legs were played on 28 July, and the second legs were played on 3 and 4 August 2016.


title: 2016–17 UEFA Europa League

text: The draw for the play-off round was held on 5 August 2016. The first legs were played on 17 and 18 August, and the second legs were played on 25 August 2016.


title: 2016–17 UEFA Europa League

text: The draw for the group stage was held on 26 August 2016, at the Grimaldi Forum in Monaco. The 48 teams were drawn into twelve groups of four, with the restriction that teams from the same association could not be drawn against each other. For the draw, the teams were seeded into four pots based on their 2016 UEFA club coefficients.


title: 2016–17 UEFA Europa League

text: In each group, teams play against each other home-and-away in a round-robin format. The group winners and runners-up advance to the round of 32, where they are joined by the eight third-placed teams of the 2016–17 UEFA Champions League group stage. The matchdays are 15 September, 29 September, 20 October, 3 November, 24 November, and 8 December 2016.


title: 2016–17 UEFA Europa League

text: A total of 21 national associations are represented in the group stage. Astana, Celta Vigo, Dundalk, Hapoel Be'er Sheva, Konyaspor, Mainz 05, Manchester United, Nice, Olympiacos, Osmanlıspor, Sassuolo, Southampton and Zorya Luhansk made their debut appearances in the UEFA Europa League group stage (although Celta Vigo and Olympiacos had appeared in the UEFA Cup group stage and Manchester United and Olympiacos had already competed in the UEFA Europa League knockout phase after a third place in the UEFA Champions League group stage).


title: 2016–17 UEFA Europa League

text: In the knockout phase, teams play against each other over two legs on a home-and-away basis, except for the one-match final. The mechanism of the draws for each round is as follows:


title: 2016–17 UEFA Europa League

text: The draw for the round of 32 was held on 12 December 2016. The first legs were played on 16 February, and the second legs were played on 22 and 23 February 2017.


title: 2016–17 UEFA Europa League

text: The draw for the round of 16 was held on 24 February 2017. The first legs were played on 9 March, and the second legs were played on 16 March 2017.


title: 2016–17 UEFA Europa League

text: The draw for the quarter-finals was held on 17 March 2017. The first legs were played on 13 April, and the second legs were played on 20 April 2017.


title: 2016–17 UEFA Europa League

text: The draw for the semi-finals was held on 21 April 2017. The first legs were played on 3 and 4 May, and the second legs were played on 11 May 2017.


title: 2016–17 UEFA Europa League

text: The final was played on 24 May 2017 at Friends Arena in Solna, Sweden. The "home" team (for administrative purposes) was determined by an additional draw held after the semi-final draw.


title: 2016–17 UEFA Europa League

text: A new UEFA Europa League Player of the Season award was introduced for the 2016–17 season. Votes were cast by coaches of the 48 teams in the group stage, together with 55 journalists selected by the European Sports Media (ESM) group, representing each of UEFA's member associations. The coaches were not allowed to vote for players from their own teams. Jury members selected their top three players, with the first receiving five points, the second three and the third one. The shortlist of the top three players were announced on 4 August 2017. The award winner was announced and presented to during the 2017–18 UEFA Europa League group stage draw in Monaco on 25 August 2017.


Birthright citizenship in the United States is United States citizenship acquired by a person automatically, by operation of law. This takes place in two situations: by virtue of the person's birth within United States territory or because one or both of their parents is (or was) a US citizen. Birthright citizenship contrasts with citizenship acquired in other ways, for example by naturalization.


title: Birthright citizenship in the United States

text: Birthright citizenship is guaranteed to most people born on U.S. territory by the first part of the Citizenship Clause introduced by the Fourteenth Amendment to the United States Constitution (adopted July 9, 1868), which states:


text: The Amendment overrode the Supreme Court decision in "Dred Scott v. Sandford" (1857) that denied US citizenship to African Americans, whether born in the United States or not, and whether a slave or a free person. Pursuant to the Fourteenth Amendment and the Immigration and Nationality Act (INA) a person born within and subject to the jurisdiction of the United States automatically acquires US citizenship, known as "jus soli" ("right of the soil"). This includes the territories of Puerto Rico, the Marianas (Guam and the Northern Mariana Islands), and the U.S. Virgin Islands. The "subject to the jurisdiction thereof" clause excluded Native Americans living under tribal sovereignty, and U.S.-born children of foreign diplomats. Birthright citizenship was later extended to U.S.-born Native American subjects by the Indian Citizenship Act of 1924. Federal law also grants birthright citizenship to children born elsewhere in the world to U.S. citizens (with certain exceptions), known as "jus sanguinis" ("right of blood").


text: Some people oppose the application of birthright citizenship to children of illegal immigrants. Some argue citizenship is not guaranteed by the Fourteenth Amendment to the children of illegal immigrants, but this interpretation has never been endorsed by federal courts. The Pew Hispanic Center estimates that approximately 7.5% of all births in the U.S. (about 300,000 births per year) are to unauthorized immigrants. The Pew Hispanic Center also estimates that there are 4.5 million children born to unauthorized immigrants who received citizenship by birth in the United States, while the Migration Policy Institute estimates that there are 4.1 million children. Both estimates exclude anyone 18 and older who might have benefited. On January 24, 2020, the Trump administration adopted a policy to make it more difficult for pregnant foreign women to come to the US where it is suspected that the purpose is to give birth on US soil and thereby to ensure their children become US citizens, a practice commonly called "birth tourism".


text: Citizenship in the United States is a matter of federal law, governed by the United States Constitution.


text: Since the adoption of the Fourteenth Amendment to the United States Constitution on July 9, 1868, the citizenship of persons born in the United States has been controlled by its Citizenship Clause, which states: "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside."


text: The Fourteenth Amendment applies to incorporated territories, so people born in incorporated territories of the U.S. are automatically U.S. citizens at birth.


text: There are special provisions governing children born in some current and former U.S. territories or possessions, including Puerto Rico, the Panama Canal Zone, the Virgin Islands, Guam, and the Northern Mariana Islands. For example, states that "All persons born in Puerto Rico [between] April 11, 1899, and ... January 13, 1941 ... residing on January 13, 1941, in Puerto Rico ... [and] persons born in Puerto Rico on or after January 13, 1941, ... are citizens of the United States at birth."


text: According to congressional enactment, persons born in American Samoa are American nationals but not U.S. citizens. A 2016 ruling by the D.C. Circuit Court upheld the United States government's position interpretation that American Samoa is not "in the United States" for purposes of the Fourteenth Amendment and thus American Samoans are nationals but not citizens at birth, A 2021 ruling by the 10th Circuit Court similarly upheld the government's position and reversed a lower court ruling that said American Samoan plaintiffs were United States citizens at birth.


text: According to persons born (or found, and of unknown parentage, under the age of 5) in an outlying possession of the U.S. (which is defined by as American Samoa and Swains Island) are U.S. nationals but not citizens, unless otherwise provided in section 1401. The U.S. State Department publication titled "Historical Background to Acquisition by Birth in U.S. Territories and Possessions" explains the complexities of this topic.


text: A child born in U.S. waters or airspace is a U.S. citizen by birth. See 8 FAM 301.1–4 ("Birth in U.S. Internal Waters and Territorial Sea"), 8 FAM 301.1–5 ("What Is Birth in U.S. Airspace?"), and 8 FAM 301.1–6 ("Documenting Birth in U.S. Waters and U.S. Airspace").


text: Under certain circumstances, children may acquire U.S. citizenship from their parents. The Naturalization Act of 1790 provided for birthright citizenship for children born out of U.S. jurisdiction to two citizen parents. The Naturalization Act of 1795, which increased the period of required residence from two to five years, introduced the Declaration of Intention requirement, or "first papers", which created a two-step naturalization process, and omitted the term "natural born". The Act specified that naturalized citizenship was reserved only for "free white person[s]" and changed the requirement in the 1790 Act of "good character" to read "good moral character". The Naturalization Act of 1798 increased the period necessary for immigrants to become naturalized citizens in the United States from 5 to 14 years.


text: In 1855, birthright citizenship was extended to children with citizen fathers and noncitizen mothers. In 1934, it was extended to children with citizen mothers and noncitizen fathers. From 1940 until 1978, a child born abroad who acquired U.S. citizenship at birth but had only one U.S. citizen parent had to fulfill a "retention requirement" of residing, or being physically present, in the United States or its outlying possessions for a certain number of years before reaching a specified age. Otherwise the child would not retain the U.S. citizenship (hence the name "retention requirement"). The retention requirement was changed several times, eliminated in 1978, and subsequently eliminated with retroactive effect in 1994.


text: The following conditions affect children born outside the U.S. and its outlying possessions to married parents (special conditions affect children born out of wedlock: see below):


text: There is an asymmetry in the way citizenship status of children born overseas to unmarried parents, only one of whom is a U.S. citizen, is handled.


text: Title paragraph (c) provides that children born abroad after December 24, 1952, to unmarried American mothers are U.S. citizens, as long as the mother has lived in the U.S. for a continuous period of at least one year at any time prior to the birth.


text: Because of this rule, unusual cases have arisen whereby children have been fathered by American men overseas from non-American women, brought back to the United States as babies without the mother, raised by the American father in the United States, and later held to be deportable as non-citizens in their 20s. The final element has taken an especially significant importance in these circumstances, as once the child has reached 18, the father is forever unable to establish paternity to deem his child a citizen.


text: This distinction between unwed American fathers and American mothers was constructed and reaffirmed by Congress out of concern that a flood of illegitimate Korean and Vietnamese children would later claim American citizenship as a result of their parentage by American servicemen overseas fighting wars in their countries. In many cases, American servicemen passing through in wartime may not have even learned they had fathered a child. In 1998, the Supreme Court upheld the discriminatory provisions of section 1409 in "Miller v. Albright" in a 6–3 decision which held that a woman's ties to a child are biological, but a father's ties to a child are a legally constructed choice. In 2001, the Supreme Court, by 5–4 majority in "Nguyen v. INS", reaffirmed the constitutionality of this gender distinction.


text: According to the Constitution of the United States only natural born citizens (or citizens at the time of the adoption of the Constitution) are eligible to serve as President of the United States or as Vice President. The text of the Constitution does not define what is meant by "natural born": in particular it does not specify whether there is any distinction to be made between persons whose citizenship is based on "jus sanguinis" (parentage) and those whose citizenship is based on "jus soli" (birthplace). As a result, controversies have arisen over the eligibility of a number of candidates for the office.


text: Throughout the history of the United States, the fundamental legal principle governing citizenship has been that birth within the United States grants U.S. citizenship; although enslaved persons and children of enslaved mothers, under the principle of "partus sequitur ventrem", were excluded, as were married women until the middle of the 20th century. The United States did not grant citizenship after the American Civil War to all former slaves until the passage of the Civil Rights Act of 1866, which was subsequently confirmed by the Fourteenth Amendment. American Indian tribal members are not covered specifically by the constitutional guarantee. Those living in tribes on reservations were generally not considered citizens until passage of the Indian Citizenship Act of 1924, although by that time nearly two-thirds of American Indians were already citizens.


text: Birthright citizenship, as with much United States law, has its roots in English common law. "Calvin's Case", 77 Eng. Rep. 377 (1608), was particularly important as it established that, under English common law, "a person's status was vested at birth, and based upon place of birth—a person born within the king's dominion owed allegiance to the sovereign, and in turn, was entitled to the king's protection."


text: This same principle was well-established in the antebellum United States. Justice Joseph Story described the rule in "Inglis v. Trustees of Sailor's Snug Harbor":


text: Justice Story described as exceptions to the rule the children of ambassadors and the children of occupying enemy soldiers.


text: As these exceptions were narrow, the rule was quite generous in scope. As one antebellum American treatise put it:


text: In the 1844 New York case of "Lynch v. Clarke", the court held that the common law rule applied in the United States, and ruled that a child born in United States of a temporary visitor to the country was a natural-born citizen of the United States under this rule.


text: Chancellor James Kent, in his influential Commentaries on American Law, framed the rule in terms similar to what would become the citizenship clause of the Fourteenth Amendment: “Natives,” he said, “are all persons born within the jurisdiction of the United States,” while “[a]n alien,” conversely, “is a person born out of the jurisdiction of the United States.”


text: The Supreme Court thus stated that the rule was "ancient and fundamental", i.e., well-established common law, in 1898: "the Fourteenth Amendment affirms the ancient and fundamental rule of citizenship by birth within the territory, in the allegiance and under the protection of the country, including all children here born of resident aliens, with the exceptions or qualifications (as old as the rule itself) of children of foreign sovereigns or their ministers, or born on foreign public ships, or of enemies within and during a hostile occupation of part of our territory, and with the single additional exception of children of members of the Indian tribes owing direct allegiance to their several tribes." "United States v. Wong Kim Ark", 169 U.S. 649 (1898).


text: The Naturalization Act of 1790 () provided the first rules to be followed by the United States in the granting of national citizenship. While the law did not specifically prevent women from having their own citizenship, the law recognized only the authority of a husband if a woman was married. Under the practice of coverture, the control of the physical body of married woman, as well as rights to her person or property, were the possession of her husband. Her loyalty to her spouse was deemed more significant than any obligation she might have to the state. Judicial rulings on domestic relations held that infants, slaves, and women were unable to participate in public life, because they lacked sufficient judgement and could not control either their own will or property. Since that time, laws concerning immigration and naturalization in the United States have undergone a number of revisions.


text: The Naturalization Act of 1804 specifically confirmed that married women's access to citizenship was tied to their state of marriage. The law stated that widows and children of aliens who had complied with the declaration of intent to become a citizen specified in the Act of 1802, but died prior to being naturalized were entitled to the rights and privileges of citizenship, if they took the necessary oath. Provisions of the Naturalization Act of 1855 specified that a woman married to a native-born citizen or a naturalized alien, or a child born on foreign soil, but to a citizen father, were citizens, as long as they were white.


text: Justice Roger B. Taney in the majority opinion in "Dred Scott v. Sandford" held that African Americans, whether slave or free, had never been and could never become citizens of the United States, as they were excluded by the Constitution. The political scientist Stuart Streichler writes that Taney's decision was based on "a skewed reading of history". Justice Benjamin R. Curtis in his dissent showed that under the Articles of Confederation, free blacks had already been considered citizens in five states and carried that citizenship forward when the Constitution was ratified.


text: The first section of the second article of the Constitution uses the language "a natural-born citizen". It thus assumes that citizenship may be acquired by birth. Undoubtedly, this language of the Constitution was used in reference to that principle of public law, well understood in the history of this country at the time of the adoption of the Constitution, which referred Citizenship to the place of birth. At the Declaration of Independence, and ever since, the received general doctrine has been, in conformity with the common law, that free persons born within either of the colonies, were the subjects of the King; that by the Declaration of independence, and the consequent acquisition of sovereignty by the several States, all such persons ceased to be subjects, and became citizens of the several States ... The Constitution has left to the States the determination what person, born within their respective limits, shall acquire by birth citizenship of the United States ...


text: Justice John McLean, in his dissent, said of Dred Scott himself: “Being born under our Constitution and laws, no naturalization is required, as one of foreign birth, to make him a citizen.”


text: In 1862, Secretary of the Treasury Salmon P. Chase sent a question to Attorney General Edward Bates asking whether or not "colored men" can be citizens of the United States. Attorney General Bates responded on November 29, 1862, with a 27-page opinion concluding, "I conclude that the "free man of color", mentioned in your letter, if born in the "United States", is a citizen of the United States..." [italics in original] In the course of that opinion, Bates commented at some length on the nature of citizenship, and wrote,


text: The Civil Rights Act of 1866 declared: "...all persons born in the United States, and not subject to any foreign power, excluding Indians not taxed, are hereby declared to be citizens of the United States." ("Indians not taxed" referred to Native American tribal members living on reservations.)


text: Representative James F. Wilson of Iowa, upon introducing the citizenship clause of the Act, stated that it was "merely declaratory of what the law now is," and recounted at length the common law history of birthright citizenship. Representative John Bingham of Ohio affirmed that the clause was "simply declaratory of what is written in the Constitution," with specific reference to the "natural-born citizen" qualification for presidential office.


text: Since the adoption of the Fourteenth Amendment to the Constitution on July 9, 1868, citizenship of persons born in the United States has been controlled by its Citizenship Clause, which states: "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside."


text: This act, a companion piece to the Fourteenth Amendment, was approved on July 27, 1868. The law allowed Americans to voluntarily give up their citizenship. Though it did not provide specific requirements to do that, subsequent court cases, such as that of Nellie Grant Sartoris, ruled that marriage to an alien was a voluntary expatriation. Further clarifications from rulings maintained that a married woman could lose her citizenship if she lived abroad with her alien spouse or if her marriage automatically bestowed upon her the nationality of her husband.


text: The Expatriation Act of 1868 led President Ulysses S. Grant to write in 1873, that the United States had "led the way in the overthrow of the feudal doctrine of perpetual allegiance".


text: Edward J. Erler of California State University, San Bernardino, and Brook Thomas of the University of California at Irvine, have argued that this Act was an explicit rejection of birth-right citizenship as the ground for American citizenship, basing that argument on the debate that surrounded the passage of this act. Professor Garrett Epps of the University of Baltimore disagrees: "The Expatriation Act is not, as Erler imagines, 'a necessary companion piece to the citizenship clause.' In fact, there is no relationship at all between the two. The act was written in a different year, by different authors, on a different subject, and in a different Congress, than the Fourteenth Amendment." American courts had long recognized that the rule of perpetual allegiance "does not stand upon the same reason or principle as the common law doctrine of allegiance by birth, and does not follow from the adoption of the latter.", concluding in 1844 that, "A diversity of opinion and of practice on the subject of perpetual allegiance prevailed in the colonies and in the states, under the old Confederation. [...] [I]n the national government, the common law rale of perpetual allegiance did not prevail; while the universal prevalence of the rule of allegiance by birth in all the colonies and states up to [1789], would be a convincing argument that such rule became the national law.


text: In 1873, The Attorney General of the United States published the following legal opinion concerning the Fourteenth Amendment:


text: The word 'jurisdiction' must be understood to mean absolute and complete jurisdiction, such as the United States had over its citizens before the adoption of this amendment. Aliens, among whom are persons born here and naturalized abroad, dwelling or being in this country, are subject to the jurisdiction of the United States only to a limited extent. Political and military rights and duties do not pertain to them.


text: The child born of alien parents in the United States is held to be a citizen thereof, and to be subject to duties with regard to this country which do not attach to the father. The same principle on which such children are held by us to be citizens of the United States, and to be subject to duties to this country, applies to the children of American fathers born without the jurisdiction of the United States, and entitles the country within whose jurisdiction they are born to claim them as citizen and to subject them to duties to it. Such children are born to a double character: the citizenship of the father is that of the child so far as the laws of the country of which the father is a citizen are concerned, and within the jurisdiction of that country; but the child, from the circumstances of his birth, may acquire rights and owes another fealty besides that which attaches to the father.


text: That same year, the trial of Susan B. Anthony resulted in a ruling by Associate Justice of the Supreme Court of the United States Ward Hunt, in the U.S. Circuit Court for the Northern District of New York. He held that neither the Fourteenth Amendment, which prohibited states from abridging the rights and privileges of citizens, nor the Fifteenth Amendment, which granted citizens the right to vote, applied to Anthony, because voting rights and conditions were defined by the state and not the national government. Since denying the vote on the basis of sex was not prohibited by the Fifteenth Amendment and sanctions for violating the second section of the Fourteenth Amendment only defined breaches to male citizens' rights, Hunt determined that a state could define unequal rights to different people.


text: The Expatriation Act of 1907 codified that women married to aliens lost their citizenship upon marriage to a non-citizen. It did not matter if they resided in the United States or abroad and was applied retroactively and without notice. It also prevented immigrant women from being able to obtain their own US nationality, if their spouse was not or could not be naturalized, because he was racially excluded, was an anarchist, or was a practitioner of polygamy. If her husband later was able to acquire US citizenship, a wife automatically gained his new nationality. Women did not have their own nationality papers, instead they were required to provide a copy of their marriage record and husband's proof of citizenship.


text: As soon as women gained the right to vote, they began pressuring Congress to eliminate provisions which automatically reassigned women's citizenship upon their marriage. In 1922, the Cable Act was passed which guaranteed women independent citizenship if their spouse was eligible for naturalization. A wife's nationality was still dependent upon her husband's status and if he was ineligible, or if she lived abroad in her husband's country for two years, or in any foreign nation for five years, her nationality was forfeited. Ineligibility applied to anyone who was neither white nor of African descent. The Act also allowed American-born women who had lost their citizenship by virtue of marriage a means to repatriate, if they returned to the United States. However, to re-enter the United States and apply under a petition for naturalization, required that her return did not exceed the restricted the number of immigrants from each country specified in the Emergency Quota Act of 1921. The same requirement did not apply to foreign wives of American men. Wives and children of male citizens were exempt from restrictive quotas.


text: Under the terms of the Asian Exclusion Act, Asians were not only excluded from naturalizing, but were prohibited from entering the country. It also provided that an American-born woman who lost her citizenship and was married or had been married to an immigrant who was ineligible for US citizenship was considered to have been "born in the country of which [they were] a citizen or subject". In 1923, a Supreme Court ruling, "United States v. Bhagat Singh Thind" retroactively stripped citizenship from Asian men, and combined with the provisions of the Cable Act, automatically deprived their wives of American citizenship as well. Even if she remained in the United States, an American woman's citizenship was automatically revoked if she married a man of Asian descent. If she left the country, she could not be readmitted to the United States. Under terms of the law, American men could petition for their foreign-born wives to lawfully immigrate, but American women were barred from petitioning on behalf of their husbands.


text: The Indian Citizenship Act of 1924 provided "That all noncitizen Indians born within the territorial limits of the United States be, and they are hereby, declared to be citizens of the United States". This same provision (slightly reworded) is contained in present-day law as section 301(b) of the Immigration and Nationality Act of 1965 ().


text: The Equal Nationality Act of 1934 allowed a married woman with children who had been born abroad to transmit her citizenship to her children, provided the mother had resided in the United States before the child was born. The law was not retroactive, thus children born before 1934 had difficulty in proving claims to derivative citizenship from their mother. The maternal derivative citizenship for children born abroad before 1934 was not confirmed until 1989. Previously only fathers were able to transmit derivative citizenship to their offspring. The law had no provisions for derivative nationality if the child(ren) were illegitimate.


text: The Nationality Act of 1936 reaffirmed that a woman who had lost her citizenship through marriage to an alien before September 22, 1922, could regain her citizenship if the marriage had terminated, as long as she took the oath of citizenship. It did not repeal the Cable Act, but the Nationality Act of 1940 repealed sections 1, 2, 3, and 4, as well as amendments from 1930, 1931, and 1934 of the Cable Act. The 1940 law allowed all women who lost their citizenship because of marriage to repatriate without regard to their marital status upon swearing the oath of allegiance. It also specified that derivative citizenship for children born out of wedlock could pass from mother to child, but required that a father legitimize the child declaring paternity before it reached majority.