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In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two and so of dimension four as a smooth manifold; the theory of algebraic surfaces is much more complicated than that of algebraic curves. Many results were obtained, however, in the Italian school of algebraic geometry, are up to 100 years old. In the case of dimension one varieties are classified by only the topological genus, but dimension two, the difference between the arithmetic genus p a and the geometric genus p g turns to be important because we cannot distinguish birationally only the topological genus. We introduce the irregularity for the classification of them. A summary of the results, follows: Examples of algebraic surfaces include: κ = −∞: the projective plane, quadrics in P3, cubic surfaces, Veronese surface, del Pezzo surfaces, ruled surfaces κ = 0: K3 surfaces, abelian surfaces, Enriques surfaces, hyperelliptic surfaces κ = 1: elliptic surfaces κ = 2: surfaces of general type.

For more examples see the list of algebraic surfaces. The first five examples are in fact birationally equivalent; that is, for example, a cubic surface has a function field isomorphic to that of the projective plane, being the rational functions in two indeterminates. The Cartesian product of two curves provides examples; the birational geometry of algebraic surfaces is rich, because of blowing up, under which a point is replaced by the curve of all limiting tangent directions coming into it. Certain curves may be blown down, but there is a restriction. One of the fundamental theorems for the birational geometry of surfaces is Castelnuovo's theorem; this states that any birational map between algebraic surfaces is given by a finite sequence of blowups and blowdowns. The Nakai criterion says that: A Divisor D on a surface S is ample if and only if D2 > 0 and for all irreducible curve C on S D•C > 0. Ample divisors have a nice property such as it is the pullback of some hyperplane bundle of projective space, whose properties are well known.

Let D be the abelian group consisting of all the divisors on S. Due to the intersection theorem D × D → Z: ↦ X ⋅ Y is viewed as a quadratic form. Let D 0:= D / D 0:= N u m becomes to be a numerical equivalent class group of S and N u m × N u m ↦ Z = ↦ D ⋅ E becomes to be a quadratic form on N u m, where D ¯ is the image of a divisor D on S. For an ample bundle H on S the definition ⊥:=. Leads the Hodge index theorem of the surface version. For D ∈, D ⋅ D < 0, i.e. ⊥ is a negative definite quadratic form. This theorem is proved by using the Riemann-Roch theorem for surfaces. For all the divisor in ⊥ this theorem is true; this theorem is not only the tool for the research of surfaces but used for the proof of the Weil conjecture by Deligne because it is true on the algebraically closed field. Basic results on algebraic surfaces include the Hodge index theorem, the division into five groups of birational equivalence classes called the classification of algebraic surface

The Fars News Agency is a news agency in Iran. While it describes itself as "Iran's leading no independent news agency", it is described by Western news media to be a "semi-official" news agency of the Government of Iran. All its content is free content, Creative Commons licensed. Fars News Agency was founded in 2003. In addition to Persian reporting, the agency provides news in English and Arabic. and Dari. In June 2012, Fars released an interview with Egyptian President Mohamed Morsi in which Morsi is said to have told Fars that he wanted to restore ties with Iran and wanted to "review" the Egypt–Israel Peace Treaty. Morsi disputed the authenticity of the interview. Fars responded by providing. Arabic newscaster Al Arabiya quoted unnamed experts. In September 2012, the agency picked up a story from The Onion, a satirical newspaper, about a supposed survey showing "an overwhelming majority of rural white Americans would rather vote for Iranian President Mahmoud Ahmadinejad than U. S. President Barack Obama in the upcoming U.

S. elections". The Iranian version copied the original word-for-word including a made-up quote from a fictional West Virginia resident who says he would rather go to a baseball game with Ahmadinejad because "he takes national defense and he'd never let some gay protesters tell him how to run his country like Obama does."Fars News Agency apologized for its mistake, but claimed that a majority of Americans would prefer anyone outside of the American political system to President Obama and American statesmen. In April 2013, the agency carried a story claiming a 27-year-old Iranian scientist had invented a time machine that allowed people to see into the future. A few days the story was removed, replaced with a story quoting an Iranian government official that no such device had been registered. In January 2014, Fars posted a series of articles that suggested U. S. security policy was being driven by an "alien/extraterrestrial intelligence agenda" The report said that proof was found in a Federal Security Service report carried out by Edward Snowden.

The report said that the United States government had been secretly run by a "shadow government" of space aliens since 1945. In February 2016, Fars was one of 40 Iranian news agencies that pledged money toward the bounty against Salman Rushdie in regards to The Satanic Verses controversy. Fars promised \$30,000 for the killing of Rushdie. Iranian state News Agency, Fars, an associate of Iran’s Revolutionary Guards Corps, has been blocked by the new sanctions applied by US treasury’s Office; these sanctions started on 25 January 2020. List of Iranian news agencies farsnews.ir english.farsnews.ir

The East End Historic District in Valdosta, Georgia is a 255 acres historic district, listed on the National Register of Historic Places in 2005. The district is northeast of downtown Valdosta and is bounded by North Ashley and E. Ann Sts. East Hill Ave. and the Georgia and Florida Railroad tracks. The district included 470 contributing buildings, a contributing structure, a contributing site, it includes Smith Park. It includes work by local architect Lloyd Greer and it includes Queen Anne and Colonial Revival architecture. Media related to East End Historic District at Wikimedia Commons

A special election for Negros Occidental's 5th district seat in the House of Representatives of the Philippines was on June 2, 2012. The special election was called after incumbent representative Iggy Arroyo died on January 26, 2012. Binalbagan Mayor Alejandro Mirasol defeated Negros Occidental Provincial Board Member Emilio Yulo in the election. Iggy Arroyo, brother-in-law of Pampanga representative and former President Gloria Macapagal-Arroyo, was in his third and final term as representative of Negros Occidental's 5th district when he died on January 26, 2012, in London. A House resolution was filed declaring the seat vacant to pave the way for a special election, although Speaker Feliciano Belmonte, Jr. and Negros Occidental Commission on Elections supervisor Jessie Suarez expressed reservations since the 2013 elections were just more than a year away. Belmonte instead suggested of appointing a caretaker to attend to the projects in the district. Provincial governor Alfredo Marañon, Jr. expressed reservations in continuing with the special election, while Negros Occidental Provincial Board Member Melvin Ibañez had expressed interest in contesting the seat if an election would be held.

On February 29, together with Negros Occidental representatives Alfredo Marañon III, Alfredo Benitez, Mercedes Alvarez and Julio Ledesma IV, filed a House resolution calling for a special election. On March 14, the House of Representatives passed the resolution approving the special election. Possible candidates that were running include Arroyo's sister Marilou Arroyo-Lesaca, Binalbagan Mayor Alejandro Mirasol and Board Member Emilio Yulo III; the next night, the commission scheduled the special election on June 9. Benitez announced that the United Negros Alliance, the province's dominant political party, will decide on who will they nominate for the vacant seat, with Benitez adding that the ruling Liberal Party has yet to state its preference among local politicians. Election lawyer Romulo Macalintal said that the commission would just waste money on the special election, saying that money could have been better spent on basic services in the district; the Parish Pastoral Council for Responsible Voting described the decision of holding the special election as "highly unconscionable" and a "total waste", stating that four months after election day, the filing of candidacies for the 2013 election would have had begun.

The UNA meeting on March 24 ended in a stalemate as Mirasol and Yulo, his nephew, disagreed on how the nomination process will be conducted. There were allegations of "grease money" distributed prior to the convention that led to Yulo calling off the convention. On March 27, Arroyo-Lesaca announced that she will not contest the election, while the UNA would meet anew to decide on who among Mirasol and Ibañez will be their nominee; that week, Ibañez withdrew from the contest in favor of Mirasol. If Mirasol is not nominated by UNA, Grace Ibuna, Arroyo's longtime partner, will run. Other prospective candidates include former board member Enrique Montilla, a nephew of Arroyo-Lesaca, former Isabela mayor Renato Malabor. On a resolution dated March 28, the commission set the election on June 2, with a budget of more than 21 million pesos. In a UNA caucus in Bacolod on April, it was decided that Mirasol would be their nominee for the special election; the governor, vice governor, the five other representatives, all mayors in the 5th district gave their support to Mirasol.

Only Himamaylan Mayor Agustin Ernesto Bascon, not present at the caucus, did not support Mirasol, instead endorsing Yulo. Ibuna will support him. Benitez recruited Mirasol, a member of the Nationalist People's Coalition to the Liberal Party, although he said that the Liberals will support Mirasol though he would not join them. Yulo said; this comes as Yulo gave way to Arroyo in the 2010 election after being talked to by Mirasol. Yulo denied that Benitez was offering him to be included in 1DSWD's nominees in the 2013 party-list election to give way for Mirasol, that he was not interested if he was offered, he admitted that while he won't match the financial resources of UNA and he only has the support of his cousin Mayor Bascon, he is not intimidated. On April 20, Macalintal and fellow lawyer Antonio Carlos Bautista questioned the legality of the special election "because it will be held beyond the period as provided for by law." They argued that since Arroyo died on January 25, that a special election "shall be called and held not earlier than 60 days nor longer than 90 days after the occurrence of the vacancy," the period of time when the election can be held is between March 25 and April 25.

Mirasol defected to the Liberal Party of President Aquino on May 5, along with his vice mayor and councilors, although he remained as a UNA member. As a result, a Liberal in 1988 but joined the NPC after the Liberals disappeared from the province, got the endorsement of President Aquino. Former Las Piñas Representative Cynthia Villar, wife of Nacionalista party president and senator Manny Villar, announced they are supporting Yulo's can

Dunham Bridge is a toll bridge across the River Trent in England. It spans the border between the administrative counties of Nottinghamshire and Lincolnshire to the west and east respectively, it forms part of the A57 road, in the section between the Great North Lincoln. It takes its name from the nearby village of Dunham-on-Trent; until the bridge was built and opened in 1832, the crossing of the river was by Dunham Ferry. In 1814, the fare was reported at half a crown; the bridge was established in the 1830s, under the powers of the Dunham Bridge Act 1830, when a group of local businessmen organised the original four-span, cast-iron construction by the civil engineer, George Leather. The superstructure was rebuilt on its original piers in 1977-79 to trunk road standards. A new toll plaza was opened in 1994 by the Right Honourable Mr. Michael Dennis, doubling the number of lanes through the booths from two to four. During the rebuilding, a temporary bridge was built with single lane usage, controlled with temporary traffic signals.

The tolls were last increased in 2013. Tariffs are regulated by the Department for Transport. Passage is free at all times for pedestrians, motor-cyclists and three-wheeled invalid carriages. On Christmas Day and Boxing Day, passage is free for all traffic. Dunham Bridge has been closed twice due to flooding: once in 2001, the second occasion during the last week of December 2012; the extent of the 2012 flooding, according to staff, was unprecedented. Office of Public Sector Information. "Dunham Bridge Act 1994". 1994 c.4. Retrieved 3 May 2008. List of crossings of the River Trent Dunham Bridge Toll Company

Robert T. Craig is a communication theorist from the University of Colorado, Boulder who received his BA in Speech at the University of Wisconsin–Madison, his MA and PhD in communication from Michigan State University. Craig was on the 1988 founding board of the journal "Research on Language and Social Interaction," a position he continues to hold. From 1991 to 1993 Craig was the founding editor of the International Communication Association journal "Communication Theory", in continuous publication since 1991, he is the editor for the ICA Handbook series. In 2009 Craig was elected as a Lifetime Fellow for the International Communication Association, an organization he was president for in 2004–2005. Craig's work "Communication Theory as a Field" received the Best Article Award from the International Communication Association as well as the Golden Anniversary Monograph Award from the National Communication Association; that work has since been translated into Russian. The theory presented in "Communication Theory as a Field" has become the basis of the book "Theorizing Communication" which Craig co-edited with Heidi Muller, as well as being adopted by several other communication theory textbooks as a new framework for understanding the field of communication theory.

In 1995 Robert T. Craig and Karen Tracy published "Grounded Practical Theory: The case of Intellectual Discussion"! This was an attempt by Craig and Tracy to create a methodological model using discourse analysis which will "guide the development and assessment of normative theories." Craig and Tracy argue that the communication discipline has been dominated by scientific theory, concerned with what is, while normative theories are centrally concerned with what ought to be. This neglect of normative theories "limits the practical usefulness of communication studies."Grounded practical theory is a metatheoretical approach based on Craig's notion of communication as a practical, rather than scientific, discipline. The goal of communication as a practical discipline is to develop normative theories to guide practice. Based on this argument, GPT was developed as a methodologically grounded means of theorizing communication practices. GPT involves reconstructing communicative practices, redescribing those practices in less context-specific terms, identifying implicit principles which guide the practice.

A GPT study begins by looking for troubles or dilemmas endemic to situated interaction and observable in discourse. This constitutes the "grounded" component of the GPT approach. Problems are reconstructed concretely and abstractly and matched with the techniques which participants employ for dealing with those problems; this is an important part of the theorizing process. The ideals and standards shaping the practice and how to manage its problems and techniques constitute the “philosophical level.” This situates the practice both locally and for the purpose of normative critique. A methodological approach, explicitly guided by GPT is action implicative discourse analysis. In 1999 Craig wrote a landmark article "Communication Theory as a Field" which expanded the conversation regarding disciplinary identity in the field of communication. At that time, communication theory textbooks had little to no agreement on how to present the field or what theories to include in their textbooks; this article has since become the foundational framework for four different textbooks to introduce the field of communication.

In this article Craig "proposes a vision for communication theory that takes a huge step toward unifying this rather disparate field and addressing its complexities." To move toward this unifying vision Craig focused on communication theory as a practical discipline and shows how "various traditions of communication theory can be engaged in dialogue on the practice of communication." In this deliberative process theorists would engage in dialog about the "practical implications of communication theories." In the end Craig proposes seven different traditions of Communication Theory and outlines how each one of them would engage the others in dialogue. Craig proposes that these seven suggested traditions of communication theory have emerged through research into communication, each one has their own way of understanding communication; these seven traditions are: Rhetorical: views communication as the practical art of discourse. Semiotic: views communication as the mediation by signs. Phenomenological: communication is the experience of dialogue with others.