title: Projectile

text: A projectile is an object that is propelled by the application of an external force and then moves freely under the influence of gravity and air resistance. Although any objects in motion through space are projectiles, they are commonly found in warfare and sports (for example, a thrown baseball, kicked football, fired bullet, shot arrow, stone released from catapult).


title: Projectile

text: In ballistics mathematical equations of motion are used to analyze projectile trajectories through launch, flight, and impact.


title: Projectile

text: Blowguns and pneumatic rifles use compressed gases, while most other guns and cannons utilize expanding gases liberated by sudden chemical reactions by propellants like smokeless powder. Light-gas guns use a combination of these mechanisms.


title: Projectile

text: Railguns utilize electromagnetic fields to provide a constant acceleration along the entire length of the device, greatly increasing the muzzle velocity.


title: Projectile

text: Some projectiles provide propulsion during flight by means of a rocket engine or jet engine. In military terminology, a rocket is unguided, while a missile is guided. Note the two meanings of "rocket" (weapon and engine): an ICBM is a guided missile with a rocket engine.


title: Projectile

text: An explosion, whether or not by a weapon, causes the debris to act as multiple high velocity projectiles. An explosive weapon or device may also be designed to produce many high velocity projectiles by the break-up of its casing; these are correctly termed "fragments".


title: Projectile

text: In projectile motion the most important force applied to the ‘projectile’ is the propelling force, in this case the propelling forces are the muscles that act upon the ball to make it move, and the stronger the force applied, the more propelling force, which means the projectile (the ball) will travel farther. See pitching, bowling.


title: Projectile

text: Many projectiles, e.g. shells, may carry an explosive charge or another chemical or biological substance. Aside from explosive payload, a projectile can be designed to cause special damage, e.g. fire (see also early thermal weapons), or poisoning (see also arrow poison).


title: Projectile

text: An object projected at an angle to the horizontal has both the vertical and horizontal components of velocity. The vertical component of the velocity on the y-axis is given as formula_1 while the horizontal component of the velocity is formula_2. There are various calculations for projectiles at a specific angle formula_3:


title: Projectile

text: 1. Time to reach maximum height. It is symbolized as (formula_4), which is the time taken for the projectile to reach the maximum height from the plane of projection. Mathematically, it is given as formula_5 where formula_6 = acceleration due to gravity (app 9.81 m/s²), formula_7 = initial velocity (m/s) and formula_3 = angle made by the projectile with the horizontal axis.


title: Projectile

text: 2. Time of flight (formula_9): this is the total time taken for the projectile to fall back to the same plane from which it was projected. Mathematically it is given as formula_10.


title: Projectile

text: 3. Maximum Height (formula_11): this is the maximum height attained by the projectile OR the maximum displacement on the vertical axis (y-axis) covered by the projectile. It is given as formula_12.


title: Projectile

text: 4. Range (formula_13): The Range of a projectile is the horizontal distance covered (on the x-axis) by the projectile. Mathematically, formula_14. The Range is maximum when angle formula_3 = 45°, i.e. formula_16.


title: Nick Amaro

text: Nicolas Amaro is a fictional character on the NBC police procedural drama "", portrayed by Danny Pino. Amaro is a detective with the Manhattan SVU at the 16th Precinct of the New York City Police Department.


title: Nick Amaro

text: Amaro is of Cuban and Italian descent. His father, Nicolas Amaro Sr. (Armand Assante), was abusive to both his mother and him, and later fled to Miami, Florida. Amaro attributes his firm belief in divorce to watching his mother, Cesaria (Nancy Ticotin), suffer through her marriage. Amaro testifies against his father when Nicolas is accused of beating his new fiancée, Gabriela (Katty Velasquez), but the elder Amaro is acquitted. After the trial, Amaro and his father make a tentative reconciliation.


title: Nick Amaro

text: Amaro is fluent in Spanish and has some knowledge of Latin. He is married at the start of his tenure with SVU, and has a young daughter named Zara (Alison Fernandez). His wife, (Laura Benanti), is stationed overseas for a year, reporting in Iraq, and their marriage is strained by her deployment. In the Season 14 premiere, she reveals to Amaro that she is accepting a job in Washington, D.C., and following an argument, they separate.


title: Nick Amaro

text: Amaro questions if Maria is suffering from PTSD, and expresses his regret that he did not try harder to understand what she was going through. Maria offers to reconcile with Amaro if he moves to California with her and Zara. He ultimately refuses to do so, however.


title: Nick Amaro

text: It is implied throughout Amaro's tenure on the show that he is in a sexual relationship with his partner, Det. Amanda Rollins (Kelli Giddish). In the episode "Reasonable Doubt", he comes out of a shower in Rollins' apartment, implying that they had been intimate. In "Holden's Manifesto", a murder suspect asks them if they are sleeping together; they do not answer the question, and change the subject.


title: Nick Amaro

text: He also has a son with a former girlfriend, Cynthia (Andrea Navedo), named Gil (Jaden Matthew Rodriguez), whom he meets for the first time in the episode "Undercover Blue".


title: Nick Amaro

text: Amaro is an NYPD detective 2nd grade who transfers to the Special Victims Unit after spending time with both the warrants and narcotics squads. Like Fin Tutuola (Ice-T), he had previously worked undercover while in narcotics. Initially, Amaro has a strained relationship with his new partner, Detective Olivia Benson (Mariska Hargitay), mainly because she misses her old partner, Elliot Stabler (Christopher Meloni). Despite their rocky start, however, Amaro and Benson grow to have a mutual respect for each other and work well together. He had an antagonistic relationship with ADA Rafael Barba (Raúl Esparza); Amaro resents Barba, who is also Cuban-American and from a working-class family, for "selling out" by going to Harvard and distancing himself from his cultural roots.


title: Nick Amaro

text: During his early days in SVU, Amaro has a tough time dealing with the horrible crimes he sees every day, and tells Benson he has the urge to physically assault a suspect. She tells him the better solution would be to ensure that the perpetrators never see the light of day again. In the episode "Hunting Ground", Amaro fatally shoots a serial killer who has Benson at gunpoint. It is the first time he has ever killed anyone, and he is badly shaken by the experience.


title: Nick Amaro

text: In the episode "Valentine's Day", he sees his wife go into an apartment of a man he does not know. In "Street Revenge", he follows his wife to see where she goes during the day; he assaults the man he sees her with. She subsequently finds out, and they get into a heated argument in the SVU squad room in front of his colleagues. She tells him that the man he saw her with is a psychiatrist she is seeing because she is trying to adapt back into her old life.


title: Nick Amaro

text: Amaro is clearly rattled by this, and in subsequent episodes, begins suppressing his anger until it explodes during the investigation into madam Delia Wilson (Brooke Smith), when he threatens to shoot Detective Brian Cassidy (Dean Winters) if Cassidy does not tell him for whom he is working undercover. This, along with his erratic behavior, briefly alienates his SVU colleagues; for example, they are reluctant to give him sensitive information regarding the false charges against Captain Donald Cragen (Dann Florek), fearing that he will make matters worse.


title: Nick Amaro

text: In "Twenty-Five Acts", Amaro asks temporary SVU commanding officer Captain Steven Harris (Adam Baldwin) to let him work their rape case solo, telling Benson she needs a partner she can trust. Benson ends up working the case with Rollins.


title: Nick Amaro

text: In the episode "Undercover Blue", Cassidy is put on trial for rape when he is falsely accused by a prostitute working for pimp Bart Ganzel (Peter Jacobson). Amaro is called to the stand by ADA Derek Strauss (Greg Germann), who asks about his undercover work. When Cassidy's lawyer questions him, Amaro is forced to reveal that he had a romantic relationship with the sister of a drug lord he was investigating undercover. Sergeant John Munch (Richard Belzer) then informs him that the NYPD brass is requesting he take a paternity test because the woman is claiming he has a son from the relationship.


title: Nick Amaro

text: He goes to the woman's house to confront her, but is denied by her boyfriend. Later, while watching the boyfriend pick the boy up from school, he witnesses the man use the boy as a carrier during a drug deal. Amaro then meets the boy and tells the woman that her boyfriend is using their son to deal drugs. After Cassidy apologizes to Amaro for what his lawyer did, he helps him bust the boyfriend for drug dealing. The episode concludes with Amaro knocking on the woman's door, and her letting him in to bond with their son, Gil.


title: Nick Amaro

text: Amaro is arrested for assaulting pedophile Simon Wilkes (Joshua Malina), while off duty. He is then charged by the district attorney and placed on leave. The charges are subsequently dropped, but he is demoted and reassigned to the 116th Precinct in Queens as a patrol officer. At Benson's request, he is reinstated to SVU after his by-the-book handling of the arrest of Hollywood starlet Tensley Evans (Stevie Lynn Jones).


title: Nick Amaro

text: In the Season 16 finale, Amaro plans to take the sergeant's exam and move up the ranks. However, Benson tells him that, because of his history of misconduct accusations, the NYPD will never promote him no matter how well he does; angered, Amaro throws his study materials in the garbage but he eventually got over it. Shortly thereafter, Amaro is involved in a courtroom shootout with Johnny Drake (Charles Halford), a brutal sex trafficker and pimp. Amaro shoots Drake dead, while Drake shoots Amaro in the liver and knee.


title: Nick Amaro

text: Amaro survives the shootout and is seen in crutches at the end of the episode, requiring three months of physical therapy. He reveals to Benson that he intends to retire from the NYPD because of his inability to move up the ranks, in addition to his injuries. He plans to move to California, since Maria is now in Los Angeles with Zara, and Cynthia is planning to move to San Diego with Gil. Before Amaro leaves, Benson remarks on how much her life has changed over the years of working with him and they make a promise to each other to stay friends forever.


title: Nick Amaro

text: At the beginning of Season 17, Rollins mentions that Amaro is now living in Los Angeles, undergoing physical therapy for his injuries, and angling for a position with the United States Park Police. In the 500th episode, which aired during the 23rd season, Amaro is now working for a company that specializes in analyzing cold-case DNA with new technologies, which bring him back to Manhattan in order to clear a man who was wrongfully convicted in a 1996 case which involved the sexual assault and fatal strangulation of a teenage girl.


title: Nick Amaro

text: The following are the medals and service awards worn by Detective Amaro, as seen in "Girls Disappeared" and "Producer's Backend".


title: Nick Amaro

text: On June 27, 2011, NBC announced that Kelli Giddish and Danny Pino would be brought on as the new series regulars.


title: Tony DiNozzo and Ziva David

text: Tony DiNozzo and Ziva David are fictional characters from the American police procedural drama "NCIS". Tony, an original character, is portrayed by Michael Weatherly, and Ziva, who first appeared in the third season, is portrayed by Cote de Pablo. Frequently referred to by the portmanteau "Tiva" (for Tony and Ziva), the characters' flirtation and the idea of them eventually beginning a relationship became a subject of interest among viewers, and by 2010, "TV Guide" reported that "many fans have become obsessed with the romantic tension". Focus and media coverage on the pair escalated over the years, particularly after "NCIS" became the most watched television series in America during its tenth season.


title: Tony DiNozzo and Ziva David

text: The characters were initially scripted as having a "cat and mouse" relationship, something that continues into the later seasons. The pairing develops at a slow pace throughout the series and is dealt a number of obstacles. This includes Tony's "commitment phobias", Ziva's trust issues, a series of other love interests, and Ziva being taken captive and presumed dead between seasons 6 and 7 after a serious breakdown in their relationship.


title: Tony DiNozzo and Ziva David

text: In the season 13 finale, Ziva is seemingly killed by a mortar attack arranged by former CIA Agent Trent Kort, and Tony learns that he and Ziva have a daughter, who she named after her sister, Tali. These events drive Tony to leave NCIS to look for answers and to care for their daughter.


title: Tony DiNozzo and Ziva David

text: In the season 16 episode "She", it is revealed that Ziva is in fact alive and had gone into hiding. It is also implied that Ziva may still be working as an investigator in some capacity. A note left for Eleanor Bishop asks that Bishop keep the secret for "the safety of my (Ziva's) family". Ziva then reappears in the season 16 finale, "Daughters", to warn Gibbs he is in danger after he takes down drug dealers. Ziva reveals that she faked her death and went into hiding to protect Tony and Tali after learning that a powerful woman named Sahar with ties to her brother Ari wanted her dead. After eliminating Sahar and her associates, Ziva returns home to Paris to reunite with Tony and Tali in the season 17 episode "In the Wind".


title: Tony DiNozzo and Ziva David

text: Michael Weatherly was cast for the role of Anthony "Tony" DiNozzo in 2003 and appeared in every episode of the show's first 13 seasons. The character is portrayed as "complex": he is a former Baltimore homicide detective with a "heroic spirit" as well as a "total dinosaur in terms of sexual politics".


title: Tony DiNozzo and Ziva David

text: In the second season finale, "NCIS" series regular Caitlin Todd was killed off after Sasha Alexander, her portrayer, decided to permanently leave the show. Shortly afterwards, series creator Donald P. Bellisario voiced intentions to replace Todd with another female lead, whom he stated would be "someone foreign who brings a whole new attitude". He expressed hopes that the new character would be drastically different from Todd, who was "kind of uptight".


title: Tony DiNozzo and Ziva David

text: One aspect Bellisario wanted to change was the way the character would interact with Tony. Though Tony and Kate had a "wonderful dynamic", he ultimately thought that "[she] treated [him] like a big brother" and decided "to bring in a character that causes Tony to have to sit back and not quite be able to handle her".


title: Tony DiNozzo and Ziva David

text: Cote de Pablo, who was one of the last to audition, was set to perform opposite Michael Weatherly to test for chemistry. Weatherly improvised during the audition by brushing her hair back and commenting, "You remind me of Salma Hayek." De Pablo, who was initially upset by the departure from the script, stayed in character and "dismissed him completely". She later said in an interview, "He totally did it with the other [actresses]. One other girl sort of flirted back with him, and she was sort of open. Which is what actors do! They're sort of open. But I got lucky and got the part because I responded the way they felt was right."


title: Tony DiNozzo and Ziva David

text: According to Bellisario, CBS chief executive Leslie Moonves "took one look at her and said, Wow!" Co-executive producer Charles Floyd Johnson commented, "When you get actors who really listen and respond organically in the moment to what they're hearing, sometimes magic happens. They really seemed to get that immediately, and that doesn't always happen."


title: Tony DiNozzo and Ziva David

text: Producers eventually decided to make de Pablo's character, who was given "the arresting name of Ziva David", an Israeli agent. Bellisario had previously discussed possibly scripting her as European or Australian. She is introduced as having a soldier mentality and as "[someone] who was comfortable in her own sexuality and used to working with men on an equal footing".


title: Tony DiNozzo and Ziva David

text: Tony and Ziva first meet in the "Kill Ari" two-part story arc at the beginning of Season 3 during the manhunt for Ari Haswari, Kate's killer and Ziva's half-brother. Michael Weatherly and Cote de Pablo both point to "Under Covers", the eighth episode of that season, as the catalyst for the flirtation between the characters. The episode involves Tony and Ziva being sent undercover as a married couple, an assignment that requires them to simulate sexual relations in order to solidify their cover. De Pablo commented, "Michael and I talked about all of those scenes right before we did them. We had a totally different way of looking at it. In our minds, we thought the characters weren't faking anything. They just got carried away. Then all of the sudden after that, they saw each other in a different light." Weatherly discussed the creation of the "Under Covers" scenario:


title: Tony DiNozzo and Ziva David

text: At the time, Bellisario said that he "kind of [likes] what's going on now" and that it was unlikely that the relationship would be taken further any time in the immediate future. De Pablo agreed, saying, "I would think if the characters get together, the whole mystery would be done. I think it will be a lot more fun to play the tension." She elaborated in another interview, "My character has sort of this understated flirtation with Michael's character, Tony. She gets jealous, but I think she would never admit it or hook up with someone in the workplace. He scares her to death. He is the epitome of the American man and all of the things that come out of his mouth are brutally stupid."


title: Tony DiNozzo and Ziva David

text: Tony is renowned for his juvenile sense of humor and "commitment phobias" while Ziva is characterized as "a tease" early on, a factor that de Pablo enjoyed playing "because [she's] "so" not that in real life". Some aspects of Ziva's personality disturb him, such as the fact that she sleeps with a gun in her hand and snores very loudly. However, as co-workers, they respect each other despite their frequent exchange of sarcastic remarks. Both have had a string of failed romances.


title: Tony DiNozzo and Ziva David

text: Team leader Gibbs (Mark Harmon) resigns in Hiatus (Part II), the third season finale, and appoints Tony as his replacement. During the 2006 summer break, it was reported that Ziva would fall under suspicion of being a spy in the fall premiere, and in the opening episode, "Shalom", she is framed by the Iranian government for the murder of a terrorist in FBI custody and the two agents guarding him. When she initially goes to the Israeli embassy to report their deaths, which she witnessed, Mossad Officer Michael Bashan asks her directly, "Did you or did you not sleep with him?" In response to her confusion, Bashan tells her that he knows that Tony has been visiting her apartment at least once a week for the past three months and that Mossad officers have been spying on her, evidently on orders from her father, Mossad Director Eli David.


title: Tony DiNozzo and Ziva David

text: Throughout the episode, Tony vigorously defends Ziva's innocence to the FBI, as well as berating any agent who dares question her loyalty when her car is found at a bombing in downtown Georgetown. She is eventually cleared of all wrongdoing. Though Ziva never addresses Bashan's accusation and her relationship with Tony is left undefined, there is no overt romantic connection in subsequent episodes.


title: Tony DiNozzo and Ziva David

text: Shortly afterwards, Tony begins dating Jeanne Benoit (Scottie Thompson) and is shown to be on the verge of a serious commitment for the first time within the series. His romance with Jeanne continues to progress throughout the year, and he remains tight-lipped about it when his colleagues notice the change in his behavior. When questioned about the effects this would have on Tony and Ziva's relationship, de Pablo commented, "Am I just being jealous? I don't know. I still love him very much, but I've sort of thrown away that possibility because I think he's really struggling with some immense feelings for somebody else." In an interview with "Chicago Tribune", she clarified that Ziva "does have feelings for DiNozzo," but that she was uncertain that this would be addressed.


title: Tony DiNozzo and Ziva David

text: In the Season 4 finale, "Angel of Death", it is made apparent that Tony and Jeanne's relationship was orchestrated by NCIS Director Jenny Shepard (Lauren Holly) in hopes of catching Jeanne's father, an arms dealer, though Tony had fallen in love while on assignment. Jeanne breaks it off following this revelation, and their storyline is ultimately given closure in the fifth season episode "Internal Affairs".


title: Tony DiNozzo and Ziva David

text: Bellisario stepped down as executive producer in May 2007 after series star Mark Harmon threatened to walk due to alleged "overly long production days", and co-executive producer Charles Floyd Johnson and head writer Shane Brennan took over afterwards.


title: Tony DiNozzo and Ziva David

text: Following the fatal shooting of Director Shepard in the fifth season finale, the NCIS team is disbanded by the new Director Vance: McGee is sent to cyber crimes, Ziva is returned to Israel, and Tony is deployed on an aircraft carrier.


title: Tony DiNozzo and Ziva David

text: Season 6 focuses more on Ziva and Tony, but leaves their relationship undefined. Gibbs manages to have Ziva and McGee transferred back to the team in the premiere, but Tony is still acting as agent afloat on the USS "Seahawk". In the following episode, Ziva accompanies Gibbs onto the "Seahawk" as part of a murder investigation and notices that Tony has pictures of her in a bikini pinned up in his room. After the investigation is closed, his deployment is ended prematurely and he is allowed to return to the team in the conclusion of the episode.


title: Tony DiNozzo and Ziva David

text: As the season progresses, Ziva seems to have become involved with someone while in Israel but refuses to discuss it. In "Nine Lives", after she plans a visit to Israel, Tony looks through her desk and finds a picture of an unidentified man (Merik Tadros). Before she leaves, he tells her to have a good trip ("Nisiya Tova") in Hebrew, demonstrating that he had at least made some effort to learn that phrase. In "Cloak", Ziva disobeys Gibbs' orders to not engage during a war game, attacking the guards to defend Tony. Later they both say that they are "tired of pretending": Tony about the politics in the hunt for the mole within the team, which required the team to withhold information from each other, and Ziva for reasons undisclosed.


title: Tony DiNozzo and Ziva David

text: Producers and writers for "NCIS" were initially divided over how to proceed with Tadros' character. In January 2009, some were suggesting possibly making him a relative of Ziva, an idea Cote de Pablo opposed. It was also proposed that Ziva would "stop toying with [Tony] completely" which would "drive him even more insane". De Pablo relayed, "We're going to play around with the idea that it could possibly be real love, and see how [he] deals with it." In March, executive producer Shane Brennan stated, "You've got what you might want to call a triangle. It's a triangle with very, very pointy ends. Someone's going to get hurt." He continued, "Something tragic will happen to Tony. Something tragic will happen to Ziva as well."


title: Tony DiNozzo and Ziva David

text: This comes to a head when Tadros appeared again portraying Mossad Officer Michael Rivkin in the "Legend" two-part, which also served as a backdoor pilot for the show's spin-off, "". He arrives in the United States during the NCIS team's hunt for members of a terrorist sleeper cell. Working independently, he draws ire from the agency when he kills suspects rather than bringing them in for questioning. Tony begins to doubt Ziva's loyalty to NCIS when she continues to defend Rivkin, and it becomes apparent by the end of Part II that she is involved in a relationship with him as the two are seen lying together in bed in the last few seconds of "Legend Part 2".


title: Tony DiNozzo and Ziva David

text: More details were released in the days preceding the finale. Michael Weatherly disclosed, "The way this season is ending, and what's gonna happen with Ziva and Tony and Rivkin, it's pretty massive and explosive, and it's gonna span four episodes." De Pablo added, "We could not be farther away from kissing. I'm telling you, it's not 'I hate you' [kissing sound] anger; it's 'I want to kill you' anger. Like, 'I want to shoot you in the head, but instead I'm gonna put my gun on your knee' anger….He does something to her that is almost unforgivable. However, the reason he does it is because he truly believes it's going to help her. Little does he know that he almost kills her." When asked how the storyline would affect Tony and Ziva's interactions, Tadros replied, "I think that love can hurt and heal. In this case, we'll have opportunity to see both of those things take place. I don't want to say too much, but... I think it will only make their connection stronger, as they learn a lot more about each other."


title: Tony DiNozzo and Ziva David

text: Viewers speculated that Ziva's romance with Rivkin was "arranged" and something that she was "trapped" in. Tadros responded:


title: Tony DiNozzo and Ziva David

text: Tony confronts a drunken Rivkin at Ziva's apartment in the episode directly prior to the finale. When he attempts to arrest Rivkin for killing the leader of the terrorist cell in Los Angeles and also an ICE agent (which Mossad leader Eli David later reveals was an accident), a fight breaks out between the two men which eventually results in Tony being forced to shoot Rivkin in self-defense due to the fact that Rivkin is about to stab Tony with a piece of glass. Though he had acted in self-defense, Rivkin later succumbs to his injuries and dies with his death having serious repercussions for Tony and Ziva's relationship, and calling into question whether Ziva and Rivkin really loved each other, culminating in Ziva leaving NCIS to resume working for Mossad in the finale, "Aliyah". She is quickly assigned to take Rivkin's place on a mission to take down a terrorist in Somalia. In the closing moments of the episode, she is shown to have been captured and tortured nearly beyond recognition by a terrorist demanding information on NCIS.


title: Tony DiNozzo and Ziva David

text: Brennan reportedly kept the cliffhanger ending a secret from most of the cast, saying that "those pages were only in one copy of the script". Shortly after "Aliyah" aired, it was assured that Ziva "will be back next season. But she'll be a changed woman."


title: Tony DiNozzo and Ziva David

text: During the summer hiatus, de Pablo admitted that she was to a point tired of the producers teasing the pairing and said, "I wish the writers would just make it easy for us and just say, 'You know, go into the elevator and kiss passionately.' Or, [have us say] say, 'I don't like you.'" She added, "But I've always thought that, deep inside, Tony loves Ziva and Ziva loves Tony, but she's almost ashamed of saying it because he's so stupid. In the best of ways. That personal that he comes out with, that frat boy thing -- he's hiding constantly from the truth. It's just a big facade and she sees right through it."


title: Tony DiNozzo and Ziva David

text: In Season 7 premiere "Truth or Consequences", Tony initiates a mission of revenge against the terrorists believed to be responsible for Ziva's (presumed) death, traveling to Somalia along with Gibbs and McGee to avenge her murder. After intentionally allowing himself to be captured and interrogated, he finds that Ziva is actually still alive, having been held hostage the entire time. Upon being brought into the room to talk to him, she is shown to have been severely beaten and very weak as well as unsure of how to react at Tony's presence. Ziva asks why Tony is in Somalia, saying that he should not have come. Tony, under truth serum, first deflects. When Ziva asks again, he replies, "I couldn't live without you, I guess."


title: Tony DiNozzo and Ziva David

text: Eventually, Gibbs kills their captor with a long range head shot, allowing them to return safely to the US. In the following episode, there seems to be a great degree of awkwardness between them, which is ultimately resolved when Ziva confronts Tony in the men's room and thanks him, saying he would "always have her back" before kissing him on the cheek.


title: Tony DiNozzo and Ziva David

text: Though Tony and Ziva's "will they/won't they" tension appeared to progress during the first few episodes of the seventh season, Cote de Pablo had already stated that it would not be resolved in the immediate future. Michael Weatherly opined that putting the two characters together at the time would be "Kryptonite" due to Ziva's assassin background.


title: Tony DiNozzo and Ziva David

text: Ziva resigns from Mossad in the fourth episode of the season, "Good Cop, Bad Cop", and applies to become a full-fledged NCIS agent, effectively becoming the "probie" on the team.


title: Tony DiNozzo and Ziva David

text: In December 2009, "TV Fanatic" announced that "the January 26 episode finds Tony and Ziva hopping a plane to the most romantic city on earth. The city of light, and of love. That's right, Ziva and Tony in Paris! You wouldn't believe it, but as if that weren't enough, their French hotel totally screws up the reservation and the two bad-ass agents end up ... gulp ... sharing a room together." Executive producer Shane Brennan disclosed, "There will be a realization that the spark is still there. It doesn't mean that something is going to be resolved, but it does mean that the journey may have started again. It's a long road back. When you think about what they went through, for them to resolve what happened and come to terms with that, it's a long road back."


title: Tony DiNozzo and Ziva David

text: During the episode, Ziva tells a witness that she and Tony shared a hotel room, and that she took the couch so she wouldn't have to hear Tony whine about his back. Tony in turn tells McGee that he took the couch. Ziva asks him why he lied and he returns the question. There was much speculation on the part of fans about whether the characters might have shared more than was divulged, but Weatherly said in response, "The truth of what happened is probably something that can be discovered inside the episode itself. If you really listen to what they say, I think it is pretty clear what happened: Nothing." He clarified that Tony and Ziva had "a tremendous amount of fun" in Paris and that, "Ziva had more fun with Tony than she thought she was going to have, which maybe shocked her a little bit, because she was so angry at him after he killed her boyfriend last year." Cote de Pablo added, "Michael has his views of what happened in Paris. I have mine. We haven't discussed it. But all I can say is it was good." Shortly afterwards, Glenn Diaz from BuddyTV reported that the cast was divided on whether or not the characters should be allowed to progress beyond "unfulfilled sexual tension".


title: Tony DiNozzo and Ziva David

text: In the following episode "Masquerade", Ziva mentions her time in Somalia, but refuses to give Tony much more than a few terse statements about it, though he was obviously willing to listen to her. In the final episode of Season 7, "Rule Fifty-One", Tony is forced to miss Ziva's citizenship ceremony due to an unexpected assignment from Director Vance, despite his personal promises to her that he would be there.


title: Tony DiNozzo and Ziva David

text: Executive producer Shane Brennan left "NCIS" to focus on the spinoff, "NCIS: Los Angeles", and was replaced by Gary Glasberg in 2011.


title: Tony DiNozzo and Ziva David

text: The series introduced new love interests for both Tony and Ziva in the latter half of Season 8, and in February 2011, Michael Ausiello from TVLine announced that Ziva's boyfriend "Ray arrives in this season's 20th episode and is described as a handsome, charming, intelligent federal agent of Mediterranean or Latin American descent. He has a strong, nice-guy demeanor but—I'm quoting from the casting notice here—'there's a hint of a mystery behind his smile.'" A week later, Glasberg described the character as a "fun, smart, exciting addition", and Michael Weatherly commented, "I think it's going to be interesting. Tony cares about Ziva and wants to make sure she's not mixed up with the wrong kind of guy, so he's going to be watchful and protective of her." After Enrique Murciano was cast for the role of Ray Cruz, Cote de Pablo said, "You never know if you're gonna have chemistry, and since I had no say in the casting, I was sort of waiting to meet this famous Enrique Murciano." She went on to describe his appearance in the show: "There's a lovely scene in which he basically brings his interpretation of 'fancy' candlelight dinner, which takes place by the vending machines at NCIS. It's really funny. There's kissing involved. We kept it light and we kept it fun, and we kept it like two people who are genuinely in to each other and wanting to move things along. It's about what's going on between the lines. These two people are touchy-feely, and that's different for Ziva."


title: Tony DiNozzo and Ziva David

text: The character of Erica Jane "EJ" Barrett (Sarah Jane Morris) was set to be introduced in the episode "One Last Score", which also marked Weatherly's directing debut. Weatherly divulged, "With the appearance of EJ, suddenly there's a renewed spirit that Tony has always had in him – it's what made him to go Africa and rescue Ziva with McGee. [Sometimes] he acts like a goofball because that's what people expect, but in this episode he comes away from that place. We'll see what the audience thinks, but for me, he feels potential and possibility in a way that he hasn't for years. EJ is a mirror, so he sees that hope for himself again." He added, "She's the diametric opposite of Ziva – physically, and in her demeanor, her way of being. She has her eccentricities as well, which makes her adorable to Tony and highly irritating to Ziva."


title: Tony DiNozzo and Ziva David

text: Around the same time, a "major serial killer plot" was launched that would center on "a murdering psychopath" called the Port to Port killer. TVLine reported, "this menace will prove to be "extremely" formidable — so much so that Gibbs will be forced to expand his team."


title: Tony DiNozzo and Ziva David

text: At the end of EJ's first episode, she begins a relationship with Tony. She is a team leader, having accepted the assignment in Rota, Spain that Tony had turned down several years prior. Ray, a CIA agent, first appears in "Two-Faced" after having evidently dated Ziva for several months. Ziva abruptly ends their relationship after learning that he had lied to her directly about his reasoning for being in Washington, D.C. and by omission about his role in the Port to Port killer case.


title: Tony DiNozzo and Ziva David

text: In the episode "Swan Song", former NCIS agent Mike Franks is killed by the Port to Port killer, who is identified as Lieutenant Jonas Cobb, and Ziva turns to Tony for comfort while the team is grieving over his death. She is kidnapped by Cobb in the following episode, the Season 8 finale, and Tony shows great concern. When EJ assures him that they will find Ziva, he replies that "it's just different for some of us".


title: Tony DiNozzo and Ziva David

text: EJ takes an extended leave of absence with the conclusion of the season. Ziva and Ray repair their relationship somewhat, and he gives her an empty ring box as a "promise" before leaving for a long-term assignment. Glasberg commented, "Ziva and Ray are a little open-ended at the moment. There isn't any closure to it. We'll have to see where it leads, but I think he was pretty clear that he has a job to do at the moment, and that's gonna be the primary focus for him." The use of the ring box was criticized by viewers as an "empty gesture".


title: Tony DiNozzo and Ziva David

text: EJ returns for a guest appearance in the Season 9 episode "Housekeeping". After a fallout with Tony, she tells him that Ziva respects him and cares about him. He at first deflects but then says, "Surround yourself with people you would give your own life for." At the end of the show, he and Ziva have a brief discussion about their relationship but are interrupted when Ray calls her. Ray returns after spending several months on his overseas assignment in the following episode and proposes to Ziva, much to her shock.


title: Tony DiNozzo and Ziva David

text: Glasberg said that Tony would not openly oppose the possibility of her getting engaged, explaining, "Tony wants Ziva to be happy. He's protective of her and cares about her and has feelings for her, and, at the end of the day, wants to make sure that she's safe and happy with the direction of her life." Though Ziva accepts Ray's proposal after some hesitation, she confronts him and breaks off the engagement after realizing that he had killed a woman on American soil while attempting to rectify a failure from overseas. Afterwards, Tony comforts her and assures her that she will find someone, though she insists she is content with the fact that marriage and children aren't in her life right now. Tony asks her if she is really happy with her life, and she responds by asking him the same question. When the deceased's husband thanks them for solving the case and mistakes them for a couple, they tell him that they are just good friends, and he advises them to cherish their friendship, as Ziva and Tony look at each other, perhaps with a sense of agreement.


title: Tony DiNozzo and Ziva David

text: In the ninth season finale, "Till Death Do Us Part", a bomb is planted by domestic terrorist Harper Dearing. Tony and Ziva, feeling bad about missing Jimmy and Breena's wedding, try to cheer each other up by joking about how awful weddings are—an exchange that begins to take on meaning when they become wistful about "the vow, the ring, the kiss, the ketubah..." and eloping instead of dealing with all the fuss. Later, when the Navy Yard is seconds from exploding, Ziva refuses to leave the building without Tony. The bomb goes off while they are still in the elevator; Ziva and Tony fall to the ground, with Tony's arm around her waist, and their free hands clasped tightly as the elevator appears to crash.


title: Tony DiNozzo and Ziva David

text: Glasberg stated that the Season 10 premiere would "pick up with them in that elevator" and that there would be "some conversations". When questioned about the framing of the situation, he replied that their time trapped in the elevator would be the "trajectory" for a more in depth look at the relationship later in the tenth season. He added, "The consensus was to do more of that this season, to peel back some layers and find little moments — and [ever since then] we're finding opportunities I think the Tony and Ziva fans will really enjoy."


title: Tony DiNozzo and Ziva David

text: The tenth season was promoted as "Season X", and Michael Weatherly dubbed it the "Year of Tiva", saying, "This is the year. Trust me. This is the year." Cote de Pablo was more apprehensive and said, "I think that is maybe Michael and his wishful thinking. I've had years in which I thought, 'Oh my God, this a Tiva year,' and there have been years he thought were Tiva years…. The truth is, we have yet to find out where that storyline is going to go. I think they're toying around with us like they always do."


title: Tony DiNozzo and Ziva David

text: However, shortly after the season began, "TV Guide" announced, "In a November episode of CBS' "NCIS", the origins of Tony's fascination with cinema will be explained — and strengthen his bond with Ziva." This involved him finding an old camera with photographs of his mother and later showing them to Ziva. Weatherly stated, "She was really the beginning of his love for movies and why that is such a deep, penetrating part of who he is. The last gift she gave him was to turn to the movies as a moral compass." De Pablo divulged, "We end up going deeper with each other than ever before. It's a profound, soft, vulnerable moment."


title: Tony DiNozzo and Ziva David

text: This was followed by "Ziva reminiscing with her partner about her dead sister [Tali]". In "Shell Shock (Part II)", she attempts to purchase tickets to the opera but is unable due to it being sold out. Tony, believing her to be going on a date, badgers her until she admits that she goes to the opera every year on her deceased sister's birthday, as Tali had wanted to be a singer. Unable to obtain tickets for her himself, he makes a CD of opera music and gives it to her to listen to.


title: Tony DiNozzo and Ziva David

text: In the eleventh episode of Season 10 and the first of 2013, "Shabbat Shalom", Ziva's estranged father Eli is killed in a house attack, along with Director Vance's wife Jackie. Glasberg discussed the ramifications that would be shown in the following episode, "Shiva", saying, "There's a part of Ziva that's wounded, and broken, and Tony is there for her — as a friend, and as a coworker ... We end up back in Tony's apartment, and there's some really lovely, emotional stuff that happens." He added, "You'll really see Tony be there for her and support her and emotionally be strong for her. It's all the things I hope that people who enjoy the Tony-Ziva relationship will look for." Throughout the episode, Tony attempts to comfort Ziva, taking her to his apartment as a precaution against the possibility of her being the next target and bringing her long-time Israeli friend Shmeil Pinkhas to stay with them. Near the end of the episode, he comes to see her off as she prepares to fly to Israel for Eli's funeral and assures her in Hebrew that she is not alone.


title: Tony DiNozzo and Ziva David

text: When asked if the dynamic between the characters would continue to progress, de Pablo remarked, "I have a feeling that they're going to want to play with that [relationship] a little bit more and see where that goes. I think they're always testing that relationship and they're always throwing things at it to see how far they can take [it]. It's already a very complex relationship. They're very close; they're very good friends; and they trust each other. So, I think the complexity of it all can go further and I think they're going to explore more." Pauley Perrette, who portrays series regular Abby Sciuto, openly opposed it and said, "I don't want any of our cast members to be in relationships on screen at all. I like things the way they are, so I'm not in [to] that. I'm petitioning against it."


title: Tony DiNozzo and Ziva David

text: "Berlin", set later in the season, features Tony and Ziva departing for Germany to track down Ilan Bodnar, her father's killer, with the help of her Israeli friend Adam Eshel. Before the episode aired, Glasberg disclosed that they would share a slow dance while there, resulting in "a very personal moment of vulnerability where her guard goes down and she lets herself melt into his arms". De Pablo added, "You also see [Tony] as a man Teddy Bear — like, a very sweet but manly man, a guy who's really taking care of a situation and really wants to make it better, a guy who's not looking for the joke or is uncomfortable staring at a woman or reaching out to hold her hand." This is highlighted in the closing scenes as the two of them drive home from the airport, and Ziva explains her animosity towards Orli Elbaz (Marina Sirtis), the new director of Mossad: Elbaz was the reason her parents split up. She tells Tony, "If it were not for Orli, things would be different. I would be a different person." Tony then takes her hand, and Ziva intertwines their fingers together. Tony replies, "Then I should catch her before she leaves, you know, and thank her." As Ziva begins to tell Tony something, the episode ends with a cliffhanger when an unknown vehicle crashes into them, leaving their fates unknown.


title: Tony DiNozzo and Ziva David

text: They both survive the crash, and despite being urged to back off by various other characters, Ziva ultimately kills Bodnar in the following episode. This leads to DOD investigator Richard Parsons (Colin Hanks) initiating a witch hunt against the team and Ziva being aggressively interrogated about her conduct in the aftermath of her father's death. When he accuses her of sleeping with an old friend while in Israel, Tony, who had been viewing the interrogation from the observation room, abruptly ends it and forces Parsons out. When he approaches Ziva about the accusation, she admits that it was a "moment of weakness" because she felt alone. This obviously hurts Tony, and he says, "My Hebrew must not be as good as I thought because I could've sworn when I dropped you off at the airport, I told you you are not alone". Ziva recalls this, and Tony says that they must have different interpretations before walking away. Despite this, he later confronts Parsons, demanding that Ziva be left alone and calling her his best friend.


title: Tony DiNozzo and Ziva David

text: In the following episode, the Season 10 finale, tension exists until Ziva privately tells Tony that she is sorry if she hurt him during the ordeal, that she cares too much about their friendship, and that she does not want things to be awkward between them. He kisses her forehead and assures her that "nothing is awkward between friends".


title: Tony DiNozzo and Ziva David

text: Despite concerns to the contrary, Glasberg denied that Ziva "friend zoned" Tony in the finale. He explained, "It might not satisfy everyone out there, but I think we're getting there — she even reaches up with her hand and puts it very gently, and in a lovely way, on his shoulder before that kiss happens. I think there are gestures being made that have definitely advanced from where we were a year ago." In response to complaints about the pace of the development, he said, "There are a lot of fans who would like to see that story advance much faster than we're doing it, but I firmly believe a little goes a long way and there are ways to tease it and to flirt that are just as significant and just as meaningful." He maintained, "We made "huge" strides. Their relationship "has" evolved, has changed. They're a little more open with each other and a little more emotionally connected, certainly more than where we were at the beginning of the season. [The couple's closeness] may not be the big leap that a lot of people would like it to be, but I also feel like we're enjoying the pace at which this is happening. That's not to say we're not headed in the direction everyone would like to go, but I think we're getting there. It's very complicated when two agents who are working together get into a relationship, and that's something that [Tony and Ziva] would be very conscious of. So I think they would tread lightly, which is why, in theory, we're treading lightly and being very careful about the steps that we take."


title: Tony DiNozzo and Ziva David

text: On July 10, 2013 it was announced that Cote De Pablo would not be returning to her role as Ziva David for the upcoming 11th season. De Pablo stated "I've had 8 great years with NCIS and Ziva David. I have huge respect and affection for Mark, Gary, Michael, David, Rocky, Pauley, Brian, Sean, all of the team and CBS. I look forward to finishing Ziva's story." However it was announced that Cote De Pablo would return for the beginning of season 11 to wrap up Ziva's storyline. Show runner Gary Glasberg stated in an interview with EW that: "The amazing resolution you're going to see is pretty damn heart-wrenching and we're incredibly proud of it," he writes. "Prepare yourselves for a moment in television history. Images that will end up in the archives. I couldn't be happier with how my NCIS family stepped up and did some of the most emotional work we've ever done."


title: Tony DiNozzo and Ziva David

text: On September 24, 2013 the episode "Whiskey Tango Foxtrot" aired and on October 1, 2013 "Past, Present, and Future" aired, opening with the introduction of a new threat: Benham Parsa and also the Brotherhood of Doubt. Tony makes plans to travel to Tel Aviv to meet Ziva, but is forced to postpone them after being ambushed by the Brotherhood at his apartment. Ziva goes missing and Tony asks Eshel to help him find her. Eshel manages to track down Ziva's location but finds she has fled after surviving an attack, leaving behind her Star of David necklace.


title: Tony DiNozzo and Ziva David

text: In the episode, "Past, Present and Future", Tony heads to Israel with Eshel to search for Ziva but although they find no sign of her, they find a list Ziva had made of things she wanted to do in her life. After speaking with one of Ziva's childhood friends and realizing she had lied to them about not being in contact with Ziva, Tony confronts her and she admits that Ziva confessed to killing Ari to her. This devastated her, as she and Ari had planned to marry and she refused to forgive her, reasoning "Why should she have the man that she loves, when she took mine from me?", referring to Ziva's feelings for Tony.


title: Tony DiNozzo and Ziva David

text: Tony persists in finding Ziva using her remaining family contacts, and a few months later he finds her hiding at the very farmhouse where she was born, Ziva having gone to examine herself and her past. Tony offers to help Ziva recover from her past memories, first by helping her bury her list in order to write a new one. Tony and Ziva share their first on-screen kiss as themselves on the tarmac in Tel-Aviv. However, in 2013, showrunner Gary Glasberg told TVLine the characters had shared another smooch in a previous season, but it did not make the cut. The couple previously kissed in season 3, episode 8 Under Covers during a covert operation as married assassins.


title: Tony DiNozzo and Ziva David

text: Despite Tony's efforts to persuade Ziva to return to the United States and NCIS, Ziva instead chooses to stay in Israel, with Tony reluctantly returning to the United States alone after sharing a final kiss with Ziva, although Tony manages to find Ziva's necklace in his jacket pocket.


title: Tony DiNozzo and Ziva David

text: In the season 13 finale "Family First," after learning of Ziva's death in the bombing of her Israel home caused by Trent Kort, the NCIS crew mourn her. Tony is then introduced to his almost two-year-old daughter, Tali. Conflicted, Tony asks Mossad Director Orli Elbaz about Ziva's motivations for not telling him about Tali. Orli tells him that she wanted to, especially as Tali grew but that she feared he would not be pleased, to which Tony tells her "Then she never knew me at all." Later in the episode, Tony finds a picture of him and Ziva in Paris, to which Tali points to each of them, saying "Ima" and "Abba" indicating that she knew who he was, her father. Tony then gives Tali Ziva's necklace as a keepsake of her mother.


title: Tony DiNozzo and Ziva David

text: After killing Kort, Tony and Gibbs have a heart to heart, where DiNozzo informs him that he is moving on from NCIS, with his daughter, his family.


title: Tony DiNozzo and Ziva David

text: Speaking of Ziva's fate, Glasberg stated "Tremendous thought was put into every element of what you saw last night...down to the lines of dialogue, the specific wordage. At the end of the day, I leave it in the hands of our fantastic fans and audience".


title: Tony DiNozzo and Ziva David

text: In the season sixteen episode "She", NCIS reopens a ten-year-old cold case when they find the starving daughter of a woman who has been missing for ten years. While digging into the case files, Special Agents Ellie Bishop and Nick Torres find that Ziva had kept notes on and had been secretly investigating the case after her departure from NCIS. Bishop wants to continue Ziva's investigation and keep it a secret from Gibbs, reasoning that Ziva would have wanted this, despite Torres' protests. While interviewing the girl's father and woman's boyfriend, who confirms that Ziva followed him for months before clearing him, he points them to a backyard building that Ziva had rented for years as a private office to write private journals as she coped with her job and life in America, though it has not been touched since her apparent death. Bishop tells Gibbs about this, who admits he suspected. McGee tries to contact Tony to tell him about Ziva's private office, and is told by his father that Tony and Tali are on their way back to Paris where they are currently living from a recent vacation and are unable to respond to his query.


title: Tony DiNozzo and Ziva David

text: In one of Ziva's journals shown during the episode "She", written during her capture in Somalia, it is revealed that Ziva had written about her feelings for Tony: "My heart saw him as if for the first time and I knew I could not live without him."


title: Tony DiNozzo and Ziva David

text: Despite Gibbs warning her not to get personally involved in the case as it could get her killed like Ziva, Bishop secretly persists in solving the case. After finding the woman alive and arresting her kidnapper, Gibbs forgives Bishop and allows her to fulfill her promise to Ziva to read a vengeful note from the woman's mother that Ziva had intended to read to the kidnapper. However, the kidnapper reveals to her that someone else had already read it to him before she arrived. Realizing that Ziva may in fact be alive, Bishop runs to her private office only to find an unsigned note from Ziva that says, "Eleanor Bishop, for the safety of my family, please keep my secret."


title: Tony DiNozzo and Ziva David

text: In the season sixteen finale, "Daughters", after Gibbs takes down drug dealers responsible for getting Tobias Fornell's daughter Emily hooked on opioids, Ziva makes her first physical appearance (not counting flashbacks) since her departure from the series, "Past, Present, and Future", to warn Gibbs that he is in danger.


title: Tony DiNozzo and Ziva David

text: During the season seventeen premiere, "Out of the Darkness", it is revealed that Ziva faked her death to protect her family from a woman named Sahar who wants to kill her. Sahar was involved in a Hamas splinter group with Ziva's brother Ari, and is seeking revenge for his death. Ziva speaks about her desire to return "home" to Tony and their daughter Tali, who she has been watching from afar during her time hidden. Her separation from her daughter since her fake death has taken its toll on Ziva, who now takes anxiety medication. Bishop worries about Ziva's safety, and is warned by Ziva's landlord Odette that if Tony knows Ziva is alive, he could be in danger as well. After taking down the organization in the second episode, "Into the Light", Ziva prepares to leave, telling Gibbs she has one more thing to do before she puts it all behind her. Before she leaves, Tony calls Gibbs, returning a call Gibbs made earlier. Gibbs assures Ziva that he did not say anything about her because he was not sure if Tony knew and wanted her to tell him. Ziva assures Gibbs that Tony will hear from her.


title: Tony DiNozzo and Ziva David

text: In the 2019 Christmas episode "The North Pole", Ziva and the team come to realize that Sahar is alive, and the woman they took down in the season's second episode posed as Sahar. Ziva reveals to Gibbs that she has in fact had contact with Tony. In a flashback shown directly after faking her death, Ziva tells Adam Eshel she is nervous because she knows Tony will come looking for her. Back to the present moment between her and Gibbs, Ziva discloses that Tony tracked her down and found her in Cairo, which was the last time she held Tali. Ziva states she and Tony have had little contact since, only when needed. The real Sahar (revealed to have posed as Gibbs' new neighbor Sarah) fights with Ziva, vowing to "end her legacy" by tracking down Tali and killing her, while Ziva retorts that Tali is "everything" to her. Sahar is finally killed when Gibbs shoots her in the head with a sniper shot, but Ziva informs Gibbs she did as he suggested when he told her Sahar is “smarter than we thought” and called Tony to tell him to go into hiding. Once at a safe location with Tali, Tony would then contact Ziva so they can reunite.


title: Tony DiNozzo and Ziva David

text: The following episode, "In the Wind", reveals that Sahar's son, Phineas, is missing. Gibbs gets deeply and personally involved, having bonded with Phineas over the first half of the season. Ziva offers to help Gibbs find Phineas, but Gibbs urges her to go to Paris and reunite with Tony and Tali. Ziva then confides in Palmer that she is uneasy that Tony and Tali would be apprehensive about the reunion, having been separated from them for this long and due to the fact that Tony has not contacted her despite her numerous attempts to reach out to him. Later, Tony sends her a video and pictures of Tali, proving they are ready for Ziva to come home. The team rescues Phineas before his kidnapper can take him to his deceased biological father's brother in Libya, and Sloane brings Phineas's foster parents (from whom he was separated by his mother), for a family reunion. Ziva then bids her farewells to the team as Palmer prepares to take her to the airport to reunite with Tony and Tali in Paris.


title: Tony DiNozzo and Ziva David

text: Over the seasons, Tony and Ziva's flirtation attracted much media attention, commentary, and praise. Maureen Ryan of the "Chicago Tribune" wrote that the characters' "love-hate banter gives the show extra zip" during Cote de Pablo's first year on the show. They have been called a "power couple" by "Entertainment Weekly" and "one of TV's hottest couples" by "TV Guide". In May 2009, they were pictured on the cover of "TV Guide Magazine" and described as "TV's hottest love-hate relationship".


title: Tony DiNozzo and Ziva David

text: Fondness for the pairing led to a dislike for some of Tony and Ziva's other love interests on the show; by contrast, EJ, Tony's ex, became well-received after encouraging him to pursue a relationship with Ziva.


title: Tony DiNozzo and Ziva David

text: The pairing's slow progression was discussed by reviewers, and Ariane Lange from BuzzFeed referred to it as "their sexual-tension-ridden not-quite-love affair". Some viewers became frustrated with the show's seeming unwillingness to allow the characters to enter an actual relationship. Ryan expressed sentiment on the matter in 2009: "It's hard not to enjoy the chemistry between investigators Ziva David (Cote de Pablo) and Tony DiNozzo (Michael Weatherly)...It makes me grind my teeth with frustration that TV writers and producers are so averse to putting will-they-or-won't-they couples together." Executive producer Gary Glasberg admitted to feeling pressure from the audience to pair them officially.


title: Tony DiNozzo and Ziva David

text: The couple was not universally accepted among viewers, and a portion of the audience felt that pairing the characters would disrupt the dynamics of the series. Matt Webb Mitovich from TVLine suggested that the dispute among fans over how far "Tiva" should be taken had left producers in a "no win" situation, saying, "Quite honestly, I think "NCIS" and show boss Gary Glasberg face a tremendously difficult juggling act with this (would-be) couple because it "is" TV's most watched program, and like a game of Jenga, you can't be quite sure which slight move could send things toppling. Is "NCIS" No. 1 because it metes out exactly 25 milligrams of romance every third episode, and never a bit more? Is there a fear that going all-in with Tiva will soap up the show too much?"


title: Tony DiNozzo and Ziva David

text: In 2010, Kate Stroup listed Tony and Ziva among "Entertainment Weekly's" "10 'Will They/Won't They' TV Couples", saying, "The chemistry is undeniable." In 2012, they appeared again in the magazine's "30 Best 'Will They/Won't They?' TV Couples". Similarly, the pair was included in BuddyTV's compile of "The Top 12 Will-They-or-Won't-They Couples of 2012" and "TV Guide"'s top 15 "TV Duos Who Should Do It".


title: Seko Fofana

text: Seko Mohamed Fofana (born 7 May 1995) is a professional footballer who plays as a midfielder for Ligue 1 club Lens. Born in France, he plays for the Ivory Coast national team.


title: Seko Fofana

text: Born in Paris, France, Fofana began his youth career at Paris FC when he was nine and stayed there for six years before joining Lorient. After two years at Lorient, he moved to England when he joined Premier League side Manchester City in 2013 and was immediately sent to the development squad.


title: Seko Fofana

text: Fofana began to be a regular in the under-18s in the 2013–14 season, making 20 appearances and scoring 5 goals in the league and playing 7 times scoring twice in the club's UEFA Youth League campaign against CSKA Moscow and Benfica Juniors. During Manchester City's U21 friendly match against HNK Rijeka, he was racially abused by one of the opposition player just before half-time. As a result, players from Manchester City's U21 squad walked off the pitch, prompting the match to be cancelled. After the match, Manager Patrick Vieira praised the action of the players to walk out.


title: Seko Fofana

text: On 27 November 2014, Fofana signed for Championship side Fulham on loan until 31 January 2015. He made his Fulham debut two days later, where he came on as a substitute for Emerson Hyndman in the 63rd minute, in a 2–1 win over Brighton & Hove Albion. His form and performance convinced Fulham to extend the loan spell until the end of the season. He scored his first goal for the club on 21 March 2015 to secure a 2–0 win away to Huddersfield Town. Having established himself under the management of Kit Symons, Fofana went on to make 25 appearances scoring once before returning to his parent club.


title: Seko Fofana

text: After making two appearances for City during their pre-season tour in Australia (playing the second half of a 2–0 win over Adelaide United, and coming on as a late substitute in Manchester City's 1–0 win over Melbourne City), the Premier League club agreed to send Fofana out on loan again to gain further experience. The Frenchman subsequently returned to his native France, to join Bastia on a season-long loan on 29 July 2015. He made his Ligue 1 debut in the opening game of the season 10 days later, on 8 August 2015, playing the full 90 minutes in a 2−1 win at home to Rennes. He then scored his first goal on 12 December 2015, in a 1–1 draw against Troyes, followed up by assisting in the next game on 19 December 2015, in a 2–0 win over Reims. In a 1–0 win over Montpellier on 16 January 2016, Fofana received a straight red card in the 65th minutes. After the match, he was given a four match ban and Fofana, himself, apologised for his action. In total, he made 32 appearances and scoring once for Bastia.


title: Seko Fofana

text: After three years at Manchester City, Fofana joined Serie A side Udinese, signing a five-year deal for worth £2.5 million. In addition, the move included a possible €2 million bonus and Bastia receiving 15% of the total compensation, up to €700K. Fofana made his Udinese debut in the opening game of the season playing 79 minutes before being substituted, in a 4–0 loss against Roma.


title: Seko Fofana

text: On 18 August 2020, Fofana signed a four-year contract with RC Lens. After a string of good performances, he was awarded the Ligue 1 Player of the Month for September 2021. In May 2022, Fofana won the Prix Marc-Vivien Foé as the best African player in France's top flight for the 2021–22 campaign, following a season in which he scored eight goals in 37 appearances.


title: Seko Fofana

text: Fofana was eligible to play for France and Ivory Coast, as his parents come from there. Fofana previously represented France U16, France U17, France U18 and France U19. On 3 April 2017, Fofana chose to represent the Ivory Coast, the country of his parents.


title: Seko Fofana

text: Fofana made his debut for Ivory Coast in a 2–0 2018 FIFA World Cup qualification loss to Morocco on 11 November 2017.


title: Escape from Planet Earth

text: Escape from Planet Earth is a 2013 computer animated comedy-adventure science fiction film produced by Rainmaker Entertainment and distributed by The Weinstein Company in the United States and Entertainment One in Canada, directed by Cal Brunker (in his feature-length directorial debut), with a screenplay which he co-wrote with Bob Barlen, and features an ensemble voice cast that includes Rob Corddry, Brendan Fraser, Sarah Jessica Parker, William Shatner, Jessica Alba, Jane Lynch, Craig Robinson, George Lopez, Sofía Vergara, Steve Zahn, Chris Parnell, Jonathan Morgan Heit, and Ricky Gervais. The film was released on February 15, 2013. "Escape from Planet Earth" received generally negative reviews from critics and grossed over $74 million on a budget of $40 million.


title: Escape from Planet Earth

text: On Planet Baab, reckless astronaut Scorch Supernova works at BASA with his nerdy older brother, Gary. One day, Gary receives a message from the head of BASA, Lena, that Scorch will be sent to the "Dark Planet" (the Baabians' name for Earth) due to an SOS call. Gary opposes the idea, but Scorch accepts without his approval, leading for Gary to quit his job. Gary goes home to his wife, Kira, and his adventure-hungry son, Kip, only to find out that Scorch has already gone to the Dark Planet, via live TV.


title: Escape from Planet Earth

text: Scorch arrives on Earth and finds a 7-Eleven convenience store, where he is ambushed by the US Army, led by General William T. Shanker, and is taken to Area 51. Witnessing this, Kip wants to go rescue Scorch, but Gary discourages him, upsetting Kip. That night, Gary goes to Kip's room to apologize only to find that Kip has escaped. He rushes to BASA with Kira and arrives in time to cancel a launch sequence at the last second and save Kip. Gary, having a change of heart, re-activates the sequence so he himself can rescue Scorch. Gary then arrives at the same 7-Eleven that Scorch arrived at earlier and is shortly captured by Shanker's men, taking him to Area 51 as well.


title: Escape from Planet Earth

text: Gary is taken to Shanker's office where he is quickly removed after he receives an incoming call from Lena, who is revealed to be Shanker's girlfriend, as she has sent him the most powerful energy source in the galaxy, known as "blubonium", via Scorch’s robotic suit, not knowing Shanker only uses her to get the source. Gary is placed in a cell hall where he meets other aliens that were captured: a mouse-like alien named Doc, a cyclops-like alien named Io, and a slug-like alien named Thurman, who tell Gary that various human technology has been invented by them for Shanker to rip off and sell in exchange for their undetermined release from Area 51. Gary reunites with Scorch, but is again annoyed by his behavior. Meanwhile, Lena captures Kira, who stayed at BASA and tried contacting Gary on his rescue mission, while revealing her plan to give Shanker a lifetime supply of blubonium.


title: Escape from Planet Earth

text: The aliens are directed to the base's "peace shield", with Shanker revealing the blubonium, and Gary unintentionally provoking Scorch into stealing and breaking it. Shanker places Scorch into a freezing chamber and orders Gary to fix the blubonium for his brother's release, revealing that he plans to destroy all alien planets with life on them, stemming from an incident which a trio of grey aliens' spaceship (accidentally) killed his father back in 1947. Gary fixes the ray with help from his new friends, but Shanker goes back on his deal and freezes him as well. The other aliens discover Shanker's true intentions when he attempts to destroy Baab with the laser, but it is revealed that Gary rigged the machine to malfunction, destroying itself, and causing Gary, Scorch and other imprisoned Aliens to be released from their icy prisons. The brothers along with their new friends, escape Area 51, and head for Baab after locating Scorch's spaceship.


title: Escape from Planet Earth

text: Meanwhile, back on Baab, Kip frees Kira, who subdues Lena after the latter takes off with a blubonium shipment. US Air Force jets chase the Scorch's ship, but Kip guides him through and manages to evade and destroy the jets. However, Shanker, wearing Scorch's robotic suit, uses a tractor beam to stop the ship in midair. Gary, followed by Scorch, jump out and manage to get the suit off Shanker which causes them all to plummet. While freefalling, Scorch and Gary reconcile before they and Shanker are rescued by the grey aliens, who previously helped Shanker due to their guilt of causing his father’s death but now turn against him after discovering his true agenda. After Gary knocks out Shanker, the grey aliens take him away. Scorch and Gary return to Planet Baab where Gary is reunited with his family. Scorch is greeted as a hero, but gives the credit to his brother. To celebrate his return, Scorch marries his girlfriend, anchorwoman Gabby Babblebrook, with Gary as his best man to Planet Baab. At the start of the film's end credits, a curtain call is used by brief clips of each main character along with the names of their respective voice actors.


title: Escape from Planet Earth

text: The film was in development at The Weinstein Company at least since 2007. The film was first announced in a press release from The Weinstein Company, which announced that the film was in full production and also announced most of the cast.


title: Escape from Planet Earth

text: The film was directed by Cal Brunker, who previously worked as a storyboard artist on the films "Despicable Me", "Horton Hears a Who!" and "". The film was originally set for release on February 14, 2013, but was pushed back to February 15, 2013, due to conflicting schedules.


title: Escape from Planet Earth

text: Writer-director Tony Leech and film producer Brian Inerfeld sued The Weinstein Company, claiming they signed a deal whereby they were to receive at least 20 percent of "Escape"'s adjusted gross profit, which they estimated would be worth close to $50 million in back end participation alone. But the film languished in development, and the plaintiffs claimed that the Weinsteins repeatedly unlocked the script, forcing rewrites at least 17 times, which they say "eviscerated" the movie's budget by keeping 200-plus animators on payroll. With the film pushing its budget, the Weinsteins went outside for fresh capital.


title: Escape from Planet Earth

text: The Weinstein Company entered into a Funding and Security Agreement with JTM whereby the financiers agreed to provide new money and, in return, get 25 percent of the film's gross receipts and 100 percent of all foreign gross receipts. Leech and Inerfeld were upset, alleging that the agreement had mortgaged their own financial upside and said the Weinsteins advised them that if they wanted their past due money, they would have to agree to this arrangement. Instead, Leech and Inerfeld went on the legal attack against TWC even claiming that they were paid $500,000 in hush money to keep the dispute quiet on the verge of the Weinsteins' "The King's Speech" Oscar victory in 2011. As for JTM, the plaintiffs demanded a declaratory judgment that their contractual rights to share in the profits were superior to JTM's security interest in profits from the film.


title: Escape from Planet Earth

text: On February 15, 2013, the same day the film was released, in a document filed in the New York Supreme Court, lawyers for both sides filed a motion of discontinuance in the case, effectively ending it. No details of the settlement were made available but because the motion was filed "with prejudice" both sides would be paying their own legal costs.


title: Escape from Planet Earth

text: "Escape from Planet Earth: Original Motion Picture Soundtrack", the soundtrack of the film was released on February 19, 2013.


title: Escape from Planet Earth

text: "Escape from Planet Earth: Original Score By Aaron Zigman", the soundtrack of the film was scored by Aaron Zigman and performed by the Brussels Philharmonic Orchestra. It was released on February 8, 2013.


title: Escape from Planet Earth

text: Stephen Farber of "The Hollywood Reporter" gave the film a positive review, saying, "The picture has enough entertainment value to tickle its target audience and even offers a few chuckles for accompanying adults. A strong cast and bright – if uninspired – animation help to offset a thin story. Decent box office returns seem likely." Tasha Robinson of "The A.V. Club" gave the film a C, calling it a "Mild-mannered CGI animated film that consists largely of broad conflicts, broadly resolved. It’s unchallenging fun for a younger crowd, but adults might feel like they’re staring down a colorful 24-piece board puzzle, trying to figure out how such a simple activity could be drawn out over 90 minutes." Mack Rawden of "Cinema Blend" gave the film one star out of five, saying, "Every single facet of the film is at best, slightly below average and at worst, downright terrible." Stephen Whitty of the "Newark Star-Ledger" gave the film two and a half stars out of four, saying, "It provides a few smiles, and a decent amount of rainy-day, kiddie entertainment." Neil Genzlinger of "The New York Times" gave the film two and a half stars out of five, saying, "A children’s movie about space-traveling blue beings that has lots of high-flying escapades but fairly low aspirations." Jordan Riefe of the "Boston Phoenix" gave the film two out of four stars, saying, "This might please young kids but torment discerning parents." Michael O'Sullivan of "The Washington Post" gave the film two out of four stars, saying, "Just like its hero and his grounded starship, "Escape From Planet Earth" is, for much of the film, a decidedly earthbound adventure." Vadim Rizov of Time Out gave the film two out of five stars, saying, "The late Douglas Adams summed up Earth as "mostly harmless," a description that also applies to this eminently tolerable animated time-filler."


title: Escape from Planet Earth

text: Alonso Duralde of "The Wrap" gave the film a negative review, saying, "It's a bowl of warm water into which no one has bothered to place a bouillon cube. The kids in the theater with me never mustered a single laugh or gasp of excitement. It's plenty o' nuttin'." Peter Howell of the "Toronto Star" gave the film two and a half stars out of four, saying, "No matter whether you call "Escape from Planet Earth" sincere homage or cynical thievery, it goes down well in its brisk 89 minutes." Gregg Katzman of "IGN" gave the film a 4.5 out of 10, saying, ""Escape From Planet Earth" looks fantastic and is sporting some commendable voice acting, but these qualities can't overcome a stale script and significant lack of laughs. Unless you have a young kid that wants to see it, I just can't recommend this one at all." Sheri Linden of the "Los Angeles Times" gave the film three out of five stars, saying, "It never discovers new worlds, but ""Escape From Planet Earth" is, in its genial way, escape enough." Tom Russo of "The Boston Globe" gave the film two stars out of four, saying, "If "Escape" figures prominently into your February staycation plans, you won't feel like you've thrown your money away, but the kids won't still be buzzing about it when they get back to school, either." Roger Moore of "The Seattle Times" gave the film two out of four stars, saying, "The animation is what sells "Escape from Planet Earth", with rich, textured surfaces – check out the fishnet webbing on Scorch’s spacesuit, the paint worn off the hardware and the perfectly rendered 7-Eleven, where even the Slurpee (product placement in a cartoon?) shimmers like the real thing. But it’s not worth paying 3D prices". Joe Leydon of "Variety" gave the film a positive review, saying, "A lightweight, warp-speed, brightly colored trifle that should delight small children and sporadically amuse their parents."


title: Escape from Planet Earth

text: "Escape from Planet Earth" grossed $57,012,977 in North America, and $17,584,666 in other countries, for a worldwide total of $74,597,643. In North America, the film opened to number four in its first weekend with $15,891,055, behind "A Good Day to Die Hard", "Identity Thief" and "Safe Haven". In its second weekend, the film went up to number three grossing an additional $10,682,037. In its third weekend, the film dropped to number six grossing $6,619,827. In its fourth weekend, the film dropped to number nine grossing $3,218,923.


title: Ə

text: Ə, or ə, also called schwa, is an additional letter of the Latin alphabet. In the International Phonetic Alphabet (IPA), minuscule ə is used to represent the mid central vowel or a schwa.


title: Ə

text: It was invented by Johann Andreas Schmeller for the reduced vowel at the end of some German words and first used in his 1820s works on the Bavarian dialects.


title: Ə

text: It is or was used in several languages around the world, including the Azerbaijani, Gottscheerish, Karay·a and Adyghe languages, and Abenaki language of Quebec, and in the hən̓q̓əmin̓əm̓ dialect of Halkomelem. Both the majuscule and minuscule forms of this letter are based on the form of a turned "e", while the Pan-Nigerian alphabet pairs the same lowercase letter with Ǝ.


title: Ə

text: A superscript minuscule ᵊ is used to modify the preceding consonant to have a mid central vowel release, though it is also commonly used to indicate possible syllabicity of the following sonorant, especially in transcriptions of English. The latter usage is non-standard.


title: Ə

text: In the Azerbaijani alphabet, "Ə" represents the near-open front unrounded vowel, . The letter was used in the 1992 Chechen Latin alphabet proposal where it represented the glottal stop, . It was also used in the Uniform Turkic Alphabet, for example in Janalif for the Tatar language in the 1920s–1930s. Also, in a romanization of Pashto, the letter "Ə" is used to represent . When some Roman orthographies in the Soviet Union were converted to use the Cyrillic script in the 1930s and 1940s, this letter has been adopted verbatim.


title: Ə

text: In the Latin transliteration of Avestan, the corresponding long vowel is written as schwa-macron, Ə̄ ə̄.


title: Ə

text: The schwa has recently also seen increased use in the Italian language, replacing the gendered suffixes of the language, in order to keep words gender neutral. For example, the use of the schwa in the word “tuttə” (all/everyone), as opposed to “tutti” (all/everyone, masculine plural). This usage is controversial, with president of the Accademia della Crusca opposing its use.


title: Ə

text: Since the legacy fixed 8-bit ISO/IEC Turkish encoding contains neither "Ə" nor "ə", "Ä ä" has sometimes been used for the Azerbaijani language instead, as in the Tatar and Turkmen languages.


title: Ə

text: In Windows, the characters can be generated by holding the key and pressing the respective decimal Unicode number, which can be found in the table (e.g. 399, 601), on the number pad preceded by a leading .


title: Ə

text: In OS X with the U.S. Extended keyboard, the letters "Ə ə" are made with followed by or respectively.


title: Rax Roast Beef

text: Rax Roast Beef is a regional U.S. fast food restaurant chain specializing in roast beef sandwiches. The company has been through many iterations, declaring bankruptcy more than once, rising to as many as 504 locations in 38 U.S. states in the 1980s and falling to fewer than 20 locations on more than one occasion. As of 2022, Rax is based in Ironton, Ohio, and has between five and eight (see below) franchisee-owned restaurants still in operation.


title: Rax Roast Beef

text: Rax was originally known as "JAX Roast Beef", founded by Jack Roschman in 1967, in Springfield, Ohio. In 1969, Roschman sold the chain to General Foods, which then changed the name of the restaurants to "RIX Roast Beef". General Foods ran the chain until 1978, when most of the restaurants closed down. The remaining 10 units were franchised units owned by the Restaurant Administration Corporation (RAC), headed by J. Patrick Ross, a franchisee of multiple restaurant chains including Wendy's, Ponderosa Steak House, and Long John Silver's.


title: Rax Roast Beef

text: RAC purchased the remainder of RIX from General Foods, and returned the JAX name to the restaurants. RAC eventually decided to focus on the roast beef business, and began franchising the chain. The JAX restaurants were renamed Rax to be more suitable for trademarking and franchising, with the first Rax-branded franchise restaurant opening in Columbus, Ohio. RAC was renamed Rax Systems Inc., then again to Rax Restaurants Inc. in 1982. By then, Rax had grown to over 221 restaurants in 25 states.


title: Rax Roast Beef

text: In 1981, the chain introduced baked potatoes and salad bars to its menu. By June 1984, the 300th location had opened, in Fort Wayne, Indiana. In 1988, the company decided to reduce the size of its money-losing salad and food bars to help reduce expenses and refocus on sandwiches.


title: Rax Roast Beef

text: At its peak in the 1980s, the Rax chain had grown to 504 locations in 38 states along with an unknown number of restaurants in Guatemala.


title: Rax Roast Beef

text: During this time, Rax began diversifying its core roast beef sales by adding baked potatoes, pizza, and a dinner bar with pasta, Chinese-style food, taco bar, an "endless" salad bar, and a dessert bar. Rax began to transform its restaurants from basic restaurant architecture into designs containing wood elements and solaria, with the intention of becoming the "champagne of fast food". This transformation drove away its core working-class customers, blurred its core business, and caused profits to plunge for Rax as other chains, such as Wendy's, took advantage of Rax's techniques and improved on them.


title: Rax Roast Beef

text: Compounding the decline was a management buyout of the company in 1991 and numerous changes that occurred on the company board. The company attempted to convert under-performing outlets by forming joint ventures with Miami Subs and Red Burrito as they scaled back many of its stand-alone locations to its core markets, particularly in Ohio, Pennsylvania, and West Virginia.


title: Rax Roast Beef

text: By August 1992, the chain had faded into obscurity. That month, a new advertising campaign was formulated with Deutsch Inc. to create a new animated character named Mr. Delicious, a sportcoat-wearing, briefcase-toting divorcee, to attract adult customers. Three months after the Mr. Delicious campaign began, Rax Restaurants Inc. filed for bankruptcy.


title: Rax Roast Beef

text: In 1994, Rax Restaurants Inc. merged with North Carolina-based Franchise Enterprises Inc, renaming the company Heartland Food Systems Inc., and becoming a Hardee's franchisee. Heartland planned to convert all Rax restaurants into Hardee's by 1997. However, by 1996, the difficulty of converting Rax restaurants to Hardee's placed too much pressure on Heartland, and they were forced to once again file for Chapter 11 bankruptcy. As part of a turnaround plan, the company sold the Hardee's units it owned that were not originally Rax stores and changed the company's name back to Rax Restaurants Inc.


title: Rax Roast Beef

text: The company was planning a revival for the Rax concept, including a new, simpler menu, a new store prototype, and a new logo and color scheme. However, in November 1996, Wendy's International made an offer to purchase 37 Rax restaurants, intending to convert most of them to Tim Hortons. This caused a change in strategy, and a buyer was sought for the remaining company-owned restaurants.


title: Rax Roast Beef

text: By December 2005, the brand was owned by Carpediem Management Co., with 51 locations, of which 11 were company-owned and 40 were franchisee-owned. As other fast food chains added kids' meals, Rax created its mascot, Uncle Alligator, who featured in all the kids' meals and toys, always involving some sport or activity (e.g. skateboarding). In 2006, 26 locations remained in Illinois, Indiana, Kentucky, Ohio, Pennsylvania, Virginia, and West Virginia. In December 2007, Rich Donohue, a five-year franchise owner with a restaurant in Ironton, Ohio, purchased the Rax trademark. The new company, From Rax to Rich's Inc., purchased the name to bypass licensing costs, and had plans to open more restaurants in Ohio and Kentucky.


title: Rax Roast Beef

text: The last Rax in Indiana closed in 2011. By February 2015, 15 locations were left in Illinois, Kentucky, and Ohio, and West Virginia. The last Rax in West Virginia closed in 2016 and the number of locations declined to eight by March 2016. Most of the remaining Rax locations are franchisee-owned, with the right to use the Rax name as long as the store is in operation.


title: Rax Roast Beef

text: , a map at the Rax website shows eight locations, six in southern Ohio, and one each in Kentucky and Illinois. However, the locations in Georgetown, Ohio, and West Union, Ohio, listed on the Rax website are no longer open with, respectively, a Little Caesars and a Dairy Queen operating in their old locations. On the website's coupon page, last updated with coupons that will expire 31 December 2022, the coupons themselves list just six locations: Harlan, Kentucky; Joliet, Illinois; Circleville, Ohio; Ironton, Ohio; Lancaster, Ohio; and New Carlisle, Ohio.


title: Support (mathematics)

text: In mathematics, the support of a real-valued function formula_1 is the subset of the function domain containing the elements which are not mapped to zero. If the domain of formula_1 is a topological space, then the support of formula_1 is instead defined as the smallest closed set containing all points not mapped to zero. This concept is used very widely in mathematical analysis.


title: Support (mathematics)

text: Suppose that formula_4 is a real-valued function whose domain is an arbitrary set formula_5 The of formula_6 written formula_7 is the set of points in formula_8 where formula_1 is non-zero:


title: Support (mathematics)

text: The support of formula_1 is the smallest subset of formula_8 with the property that formula_1 is zero on the subset's complement. If formula_14 for all but a finite number of points formula_15 then formula_1 is said to have .


title: Support (mathematics)

text: If the set formula_8 has an additional structure (for example, a topology), then the support of formula_1 is defined in an analogous way as the smallest subset of formula_8 of an appropriate type such that formula_1 vanishes in an appropriate sense on its complement. The notion of support also extends in a natural way to functions taking values in more general sets than formula_21 and to other objects, such as measures or distributions.


title: Support (mathematics)

text: The most common situation occurs when formula_8 is a topological space (such as the real line or formula_23-dimensional Euclidean space) and formula_4 is a continuous real (or complex)-valued function. In this case, the of formula_1, formula_26, or the of formula_1, is defined topologically as the closure (taken in formula_8) of the subset of formula_8 where formula_1 is non-zero that is,


title: Support (mathematics)

text: Since the intersection of closed sets is closed, formula_26 is the intersection of all closed sets that contain the set-theoretic support of formula_33


title: Support (mathematics)

text: then formula_26, the support of formula_1, or the closed support of formula_1, is the closed interval formula_39 since formula_1 is non-zero on the open interval formula_41 and the closure of this set is formula_42


title: Support (mathematics)

text: The notion of closed support is usually applied to continuous functions, but the definition makes sense for arbitrary real or complex-valued functions on a topological space, and some authors do not require that formula_4 (or formula_44) be continuous.


title: Support (mathematics)

text: Functions with ' on a topological space formula_8 are those whose closed support is a compact subset of formula_5 If formula_8 is the real line, or formula_23-dimensional Euclidean space, then a function has compact support if and only if it has ', since a subset of formula_49 is compact if and only if it is closed and bounded.


title: Support (mathematics)

text: For example, the function formula_34 defined above is a continuous function with compact support formula_42 If formula_52 is a smooth function then because formula_1 is identically formula_54 on the open subset formula_55 all of formula_1's partial derivatives of all orders are also identically formula_54 on formula_58


title: Support (mathematics)

text: The condition of compact support is stronger than the condition of vanishing at infinity. For example, the function formula_34 defined by


title: Support (mathematics)

text: Real-valued compactly supported smooth functions on a Euclidean space are called bump functions. Mollifiers are an important special case of bump functions as they can be used in distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution.


title: Support (mathematics)

text: In good cases, functions with compact support are dense in the space of functions that vanish at infinity, but this property requires some technical work to justify in a given example. As an intuition for more complex examples, and in the language of limits, for any formula_64 any function formula_1 on the real line formula_21 that vanishes at infinity can be approximated by choosing an appropriate compact subset formula_67 of formula_21 such that


title: Support (mathematics)

text: for all formula_15 where formula_71 is the indicator function of formula_72 Every continuous function on a compact topological space has compact support since every closed subset of a compact space is indeed compact.


title: Support (mathematics)

text: If formula_8 is a topological measure space with a Borel measure formula_74 (such as formula_75 or a Lebesgue measurable subset of formula_75 equipped with Lebesgue measure), then one typically identifies functions that are equal formula_74-almost everywhere. In that case, the of a measurable function formula_4 written formula_79 is defined to be the smallest closed subset formula_80 of formula_8 such that formula_82 formula_74-almost everywhere outside formula_84 Equivalently, formula_85 is the complement of the largest open set on which formula_82 formula_74-almost everywhere


title: Support (mathematics)

text: The essential support of a function formula_1 depends on the measure formula_74 as well as on formula_6 and it may be strictly smaller than the closed support. For example, if formula_92 is the Dirichlet function that is formula_54 on irrational numbers and formula_94 on rational numbers, and formula_95 is equipped with Lebesgue measure, then the support of formula_1 is the entire interval formula_97 but the essential support of formula_1 is empty, since formula_1 is equal almost everywhere to the zero function.


title: Support (mathematics)

text: In analysis one nearly always wants to use the essential support of a function, rather than its closed support, when the two sets are different, so formula_85 is often written simply as formula_26 and referred to as the support.


title: Support (mathematics)

text: If formula_102 is an arbitrary set containing zero, the concept of support is immediately generalizable to functions formula_103 Support may also be defined for any algebraic structure with identity (such as a group, monoid, or composition algebra), in which the identity element assumes the role of zero. For instance, the family formula_104 of functions from the natural numbers to the integers is the uncountable set of integer sequences. The subfamily formula_105 is the countable set of all integer sequences that have only finitely many nonzero entries.


title: Support (mathematics)

text: Functions of finite support are used in defining algebraic structures such as group rings and free abelian groups.


title: Support (mathematics)

text: In probability theory, the support of a probability distribution can be loosely thought of as the closure of the set of possible values of a random variable having that distribution. There are, however, some subtleties to consider when dealing with general distributions defined on a sigma algebra, rather than on a topological space.


title: Support (mathematics)

text: More formally, if formula_106 is a random variable on formula_107 then the support of formula_8 is the smallest closed set formula_109 such that formula_110


title: Support (mathematics)

text: In practice however, the support of a discrete random variable formula_8 is often defined as the set formula_112 and the support of a continuous random variable formula_8 is defined as the set formula_114 where formula_115 is a probability density function of formula_8 (the set-theoretic support).


title: Support (mathematics)

text: It is possible also to talk about the support of a distribution, such as the Dirac delta function formula_117 on the real line. In that example, we can consider test functions formula_118 which are smooth functions with support not including the point formula_119 Since formula_120 (the distribution formula_121 applied as linear functional to formula_80) is formula_54 for such functions, we can say that the support of formula_121 is formula_125 only. Since measures (including probability measures) on the real line are special cases of distributions, we can also speak of the support of a measure in the same way.


title: Support (mathematics)

text: Suppose that formula_1 is a distribution, and that formula_127 is an open set in Euclidean space such that, for all test functions formula_128 such that the support of formula_128 is contained in formula_130 formula_131 Then formula_1 is said to vanish on formula_133 Now, if formula_1 vanishes on an arbitrary family formula_135 of open sets, then for any test function formula_128 supported in formula_137 a simple argument based on the compactness of the support of formula_128 and a partition of unity shows that formula_139 as well. Hence we can define the of formula_1 as the complement of the largest open set on which formula_1 vanishes. For example, the support of the Dirac delta is formula_142


title: Support (mathematics)

text: In Fourier analysis in particular, it is interesting to study the of a distribution. This has the intuitive interpretation as the set of points at which a distribution .


title: Support (mathematics)

text: For example, the Fourier transform of the Heaviside step function can, up to constant factors, be considered to be formula_143 (a function) at formula_144 While formula_145 is clearly a special point, it is more precise to say that the transform of the distribution has singular support formula_125: it cannot accurately be expressed as a function in relation to test functions with support including formula_119 It be expressed as an application of a Cauchy principal value integral.


title: Support (mathematics)

text: For distributions in several variables, singular supports allow one to define and understand Huygens' principle in terms of mathematical analysis. Singular supports may also be used to understand phenomena special to distribution theory, such as attempts to 'multiply' distributions (squaring the Dirac delta function fails – essentially because the singular supports of the distributions to be multiplied should be disjoint).


title: Support (mathematics)

text: An abstract notion of on a topological space formula_148 suitable for sheaf theory, was defined by Henri Cartan. In extending Poincaré duality to manifolds that are not compact, the 'compact support' idea enters naturally on one side of the duality; see for example Alexander–Spanier cohomology.


title: Support (mathematics)

text: Bredon, "Sheaf Theory" (2nd edition, 1997) gives these definitions. A family formula_149 of closed subsets of formula_8 is a , if it is down-closed and closed under finite union. Its is the union over formula_151 A family of supports that satisfies further that any formula_152 in formula_149 is, with the subspace topology, a paracompact space; and has some formula_154 in formula_149 which is a neighbourhood. If formula_8 is a locally compact space, assumed Hausdorff the family of all compact subsets satisfies the further conditions, making it paracompactifying.


title: Elizabeth Edwards

text: Mary Elizabeth Anania Edwards (July 3, 1949 – December 7, 2010) was an American attorney, author, and health care activist. She was married to John Edwards, the former U.S. Senator from North Carolina who was the 2004 United States Democratic vice-presidential nominee.


title: Elizabeth Edwards

text: Edwards lived a private life until her husband's rise as senator and ultimately unsuccessful vice presidential and presidential campaigns. She was his chief policy advisor during his presidential bid, and was instrumental in pushing him towards more liberal stances on subjects such as universal health care. She was also an advocate for gay marriage and was against the war in Iraq, both topics about which she and her husband disagreed.


title: Elizabeth Edwards

text: In the final years of her life, Edwards publicly dealt with her husband's admission of an extramarital affair and her breast cancer, writing two books and making numerous media appearances. She separated from John Edwards in early 2010. On December 6, 2010, her family announced that her cancer had spread and that her doctors had stated that further treatment would be unproductive. She died the next day.