title: Kaavalan

text: Bhoomi joins the same class where Meera studies, as he has previously discontinued his education. Meera does not like Bhoomi following her as a bodyguard, and plans to divert him. Meera calls Bhoomi over his mobile phone from a private number and introduces herself as "Ammukutty". Initially, Bhoomi hates the mobile call as it will disturb him, but later develops a liking towards Ammukutty and slowly love blossoms for Bhoomi without knowing that it is Meera herself. He saves Meera from an attack from Muthuramalingam's rival. At one point, Meera too feels herself develop liking towards Bhoomi and expresses her desire to meet him in person without revealing her identity. Due to circumstances, they are not able to accomplish this, and she decides to elope with Bhoomi for which he agrees.


title: Kaavalan

text: However, Muthuramalingam learns that Bhoomi and Meera are going to run away and sends his men to stop him. Bhoomi thrashes them up easily but Muthuramalingam thrashes Bhoomi. Meera overhears her father's plans and decides to save Bhoomi by lying that he is in love with some other girl and has planned to elope with her. Muthuramalingam spares Bhoomi, believing that Meera is not his lover, but sends his men to the railway station to find out Bhoomi's lover. He also instructs that Bhoomi should be killed if there is no one in the railway station. In a desperate attempt to save Bhoomi, Meera comes up with a plan and requests Madhu to go to the railway station and pretend to be Ammukutty, so that Muthuramalingam's men will spare Bhoomi believing Madhu to be his lover.


title: Kaavalan

text: Meera also gives a mobile phone to Madhu and informs to give it to Bhoomi when she meets him (as Bhoomi's phone is broken) so that she can reveal the truth to Bhoomi. Madhu agrees and leaves to the station. At the station, Bhoomi gets surprised seeing Madhu in the station and believes that it is Madhu, who was pretending as Ammukutty so far and hugs her. Muthuramalingam's men see this and leave the place, believing that Meera is not Bhoomi's lover. Suddenly, Madhu gets a call in the mobile given by Meera. Madhu understands that the call is from Meera and she wants to speak to Bhoomi. However, Madhu throws away the phone from train, following which it is revealed that Madhu also likes Bhoomi, and she decides to marry him by betraying Meera.


title: Kaavalan

text: 10 years later: Bhoomi is now a high-ranking I.F.S. officer, who returns to Muthuramalingam's village for a short vacation before leaving to Australia, along with his son Sidharth. Muthuramalingam's condition is ill and Madhu had died a few years back due to some medical ailments, but she has written all the truth in a diary and gives it to Sidharth to read it after her death. Sidharth has learnt all the truth. Madhu has also mentioned in the diary that this truth should never be disclosed to Bhoomi. Meera stays with her father, and Bhoomi gets shocked to know that Meera still remains unmarried.


title: Kaavalan

text: When Bhoomi and Sidharth are about to return home, Sidharth asks Meera to come with them and expresses his wish to call her as his mother. Bhoomi berates Sidharth for his suggestion and apologises to Meera and Muthuramalingam, but Muthuramalingam also insists Meera to leave with Bhoomi. Bhoomi, Meera and Sidharth leave together from the village. Just the before the train starts, Sidharth throws the diary containing the truth in a dust bin and comes back, but Bhoomi takes back the diary from the dust bin, without Sidharth's knowledge. Upon reading the diary, Bhoomi is shocked knowing it was Meera who loved him in the name of Ammukutty and wholeheartedly accepts Meera.


title: Kaavalan

text: The film was initially referred to as "Kaavalkaaran", which literally means "bodyguard" in Tamil. After rumours of the title being changed to "Kaaval Kaadhal", the film was officially confirmed to be titled "Kaavalan" in August 2010. The reason for the name confusion and its eventual permanent change was due to complications in obtaining the rights to the title of "Kaavalkaaran" from M. G. Ramachandran's producers. They refused to sell the title to Vijay, leading to the rechristening of the title to "Kaavalan".


title: Kaavalan

text: With the announcement of the remake, Siddique had finalised Vijay to play the lead role, reminiscent of their previous venture "Friends" (2001), which was also a remake of Siddique's own Malayalam film. Asin was signed up to pair with Vijay for the third time after their previous pairings in "Sivakasi" (2005) and "Pokkiri" (2007), also giving Asin a comeback in Tamil cinema after her last appearance in "Dasavathaaram" (2008). This also marks Vijay’s comeback to romance genre after 6 years; the last time he appeared in a romantic film was Sachein. Vadivelu, Rajkiran, and Roja Selvamani were also signed up as supporting characters.


title: Kaavalan

text: The film's principal shoot began in April at Kumbakonam. An incident occurred on set in April, where Asin, her father, and her makeup assistants fainted in their caravan after being exposed to a gas leak. They were treated in hospital the same day and were eventually discharged. The second shoot schedule occurred in Vellore. Vijay and Asin, along with director Siddique and the rest of crew filmed at the Vellore Institute of Technology. A song was shot at Kuala Lumpur, Malaysia.


title: Kaavalan

text: The soundtrack album is composed by Vidyasagar, collaborating with Vijay for the 8th time, after "Coimbatore Mappillai", "Nilaave Vaa", "Thirumalai", "Ghilli", "Madhurey", "Aathi" and "Kuruvi". The soundtrack consists of five tracks, with lyrics written by Yugabharathi, Pa. Vijay, Viveka and Kabilan. The audio launch was held on 8 December 2010.


title: Kaavalan

text: Behindwoods gave the album a rating of 3/5, and stated that it is fresh and youthful. Sify gave the album, rating 4 out of 5, and stated "The album is youthful, and make sure it is an instant hit." MusicAloud.com rated the album 8 out of 10, stating "After a completely subdued soundtrack for "Mandhira Punnagai", he creates another out-and-out commercial score in "Kaavalan". A sureshot musical hit for Vijay!" Rediff rated the album 2.5 out of 5, stating that ""Kaavalan" would be a throwback to the star's earlier, romance-heavy movies, notably "Friends". It looks like Vidhyasagar has followed the same mission directive. It's a relief to see less of hero-overtones and more soft numbers."


title: Kaavalan

text: The trailer was released worldwide on 16 December in Northern California, marking the first time a Vijay film trailer was launched outside India.


title: Kaavalan

text: Due to the failure of "Sura" (2010), theatre owners faced huge losses, and asked Vijay to compensate 35% of the loss amount. However, Vijay did not give any response. A week before the film's release, Tamil Nadu Theatre Owners Association, had announced that they will not give any other co-operation to "Kaavalan", and the actor's other future projects. As a result, two shows were cancelled on the opening day, 14 January 2011, and went ahead with matinee shows.


title: Kaavalan

text: Moreover, it was rumoured that significant industry stakeholders from Dravida Munnetra Kazhagam pressurised exhibitors to stall the film's release, since "Aadukalam", which was distributed by Sun Pictures, was slated to release in January 2011, and also majority of the theatres were controlled by the party supremos. In order to have a smooth release, Vijay sought help from J. Jayalalithaa, from All India Anna Dravida Munnetra Kazhagam, which was the opposition party at that time, as a result the film opened to 450 screens, on 15 January 2011.


title: Kaavalan

text: Originally slated to release on 17 December 2010, "Kaavalan" was released on 15 January 2011. The film was selected at the 14th Shanghai International Film Festival in the panorama section. SIFF issued an invitation to Vijay as guest of honour. The film was later dubbed in Hindi as "Main Hoon Bodyguard". And It Was Dubbed In Bhojpuri As "Hamar Angrakshak".


title: Kaavalan

text: Kaavalan released over 600 screens. Kaavalan released to generally positive reviews from critics. The film collected 6.5 crore in Chennai at its opening day. By the end of six weeks it had grossed around at the worldwide box office. The film grossed 75,000 in the United Kingdom The movie managed to complete a 100-day run in 2 theatres in Tamil Nadu


title: Kaavalan

text: Behindwoods.com rated the film 4 out of 5 stars and called it "a relatable love story shot in a cute and simple manner, rich with emotions, and a smooth narration". The reporter noted good chemistry between Vijay and Asin. Asin's performance was described as convincing. Oneindia commented, "Vijay's performance as extraordinary and describing "Kaavalan" is a family entertainer with an extraordinary script". Pavithra Srinivasan of Rediff.com praised Vadivelu and Vijay's comedic performances, but criticised the Tamil version of the film, for being edited in such a way that scenes either lacked resolution or coherence, and some character dialogue was delivered "without continuity". "Ananda Vikatan" rated the film 42 out of 100. A critic from Rediff.com, while giving the film 3.5 out of 5 stars, credited Vijay for "shedding his action/political persona" and "choosing a script that focuses on comedy and emotions".


title: Kaavalan

text: The Times of India rated the film 3/5 and says "'Kaavalan' is vintage Vijay on display and is proof that if he keeps away from superhero mannerisms and sticks to the vision of the director". Sify.com described the film as "super fun" and a "perfect Pongal family entertainer" and rated it 4.5/5. The reviewer particularly praised Vijay's performance, observing that the film works "purely on his star charisma and larger-than-life image" and that "he carries the film on his shoulders and is one good reason to watch the film".


title: DICOM

text: Digital Imaging and Communications in Medicine (DICOM) is the standard for the communication and management of medical imaging information and related data. DICOM is most commonly used for storing and transmitting medical images enabling the integration of medical imaging devices such as scanners, servers, workstations, printers, network hardware, and picture archiving and communication systems (PACS) from multiple manufacturers. It has been widely adopted by hospitals and is making inroads into smaller applications such as dentists' and doctors' offices.


title: DICOM

text: DICOM files can be exchanged between two entities that are capable of receiving image and patient data in DICOM format. The different devices come with DICOM Conformance Statements which state which DICOM classes they support. The standard includes a file format definition and a network communications protocol that uses TCP/IP to communicate between systems.


title: DICOM

text: The National Electrical Manufacturers Association (NEMA) holds the copyright to the published standard which was developed by the DICOM Standards Committee, whose members are also partly members of NEMA. It is also known as NEMA standard PS3, and as ISO standard 12052:2017 "Health informatics – Digital imaging and communication in medicine (DICOM) including workflow and data management".


title: DICOM

text: DICOM is used worldwide to store, exchange, and transmit medical images. DICOM has been central to the development of modern


title: DICOM

text: radiological imaging: DICOM incorporates standards for imaging modalities such as radiography, ultrasonography, computed tomography (CT), magnetic resonance imaging (MRI), and radiation therapy. DICOM includes protocols for image exchange (e.g., via portable media such as DVDs), image compression, 3-D visualization, image presentation, and results reporting.


title: DICOM

text: DICOM is a standard developed by American College of Radiology (ACR) and National Electrical Manufacturers Association (NEMA).


title: DICOM

text: In the beginning of the 1980s, it was very difficult for anyone other than manufacturers of computed tomography or magnetic resonance imaging devices to decode the images that the machines generated. Radiologists and medical physicists wanted to use the images for dose-planning for radiation therapy. ACR and NEMA joined forces and formed a standard committee in 1983. Their first standard, ACR/NEMA 300, entitled "Digital Imaging and Communications", was released in 1985. Very soon after its release, it became clear that improvements were needed. The text was vague and had internal contradictions.


title: DICOM

text: In 1988 the second version was released. This version gained more acceptance among vendors. The image transmission was specified as over a dedicated 2 pair cable (EIA-485). The first demonstration of ACR/NEMA V2.0 interconnectivity technology was held at Georgetown University, May 21–23, 1990. Six companies participated in this event, DeJarnette Research Systems, General Electric Medical Systems, Merge Technologies, Siemens Medical Systems, Vortech (acquired by Kodak that same year) and 3M. Commercial equipment supporting ACR/NEMA 2.0 was presented at the annual meeting of the Radiological Society of North America (RSNA) in 1990 by these same vendors. Many soon realized that the second version also needed improvement. Several extensions to ACR/NEMA 2.0 were created, like Papyrus (developed by the University Hospital of Geneva, Switzerland) and SPI (Standard Product Interconnect), driven by Siemens Medical Systems and Philips Medical Systems.


title: DICOM

text: The first large-scale deployment of ACR/NEMA technology was made in 1992 by the US Army and Air Force, as part of the MDIS (Medical Diagnostic Imaging Support) program based at Ft. Detrick, Maryland. Loral Aerospace and Siemens Medical Systems led a consortium of companies in deploying the first US military PACS (Picture Archiving and Communications System) at all major Army and Air Force medical treatment facilities and teleradiology nodes at a large number of US military clinics. DeJarnette Research Systems and Merge Technologies provided the modality gateway interfaces from third party imaging modalities to the Siemens SPI network. The Veterans Administration and the Navy also purchased systems from this contract.


title: DICOM

text: In 1993 the third version of the standard was released. Its name was then changed to "Digital Imaging and Communications in Medicine", abbreviated DICOM. New service classes were defined, network support added and the Conformance Statement was introduced. Initially the DICOM standard was referred to as "DICOM 3.0" to distinguish it from its predecessors. DICOM has been constantly updated and extended since 1993, with the intent that changes are backward compatible, except in rare cases where the earlier specification was incorrect or ambiguous. Officially there is no "version" of the standard except the current standard, hence the "3.0" version number is no longer used. There are no "minor" versions to the standard (e.g., no such thing as "DICOM 3.1") and there are no current plans to develop a new, incompatible, version of the standard (i.e., no "DICOM 4.0"). The standard should be referenced without specification of the date of release of a particular published edition, except when specific conformance requirements are invoked that depend on a retired feature that is no longer documented in the current standard.


title: DICOM

text: While the DICOM standard has achieved a near universal level of acceptance among medical imaging equipment vendors and healthcare IT organizations, the standard has its limitations. DICOM is a standard directed at addressing technical interoperability issues in medical imaging. It is not a framework or architecture for achieving a useful clinical workflow. The Integrating the Healthcare Enterprise (IHE) initiative layered on top of DICOM (and HL-7) defines profiles to select features from these standards to implement transactions for specific medical imaging interoperability use cases.


title: DICOM

text: Though always Internet compatible and based on transport over TCP, over time there has been an increasing need to support port 80 HTTP transport to make use easier within the web browser. Most recently, a family of DICOM RESTful web services have been defined to allow mobile device friendly access to DICOM objects and services, which include WADO-RS, STOW-RS and QIDO-RS, which together constitute the DICOMweb initiative.


title: DICOM

text: There are some derivations from the DICOM standard into other application areas. These include DICONDE ("Digital Imaging and Communication in Nondestructive Evaluation") that was established in 2004 as a way for nondestructive testing manufacturers and users to share image data, and DICOS ("Digital Imaging and Communication in Security") that was established in 2009 to be used for image sharing in airport security.


title: DICOM

text: DICOM groups information into data sets. For example, a file of a chest x-ray image may contain the patient ID within the file, so that the image can never be separated from this information by mistake. This is similar to the way that image formats such as JPEG can also have embedded tags to identify and otherwise describe the image.


title: DICOM

text: A DICOM data object consists of a number of attributes, including items such as name, ID, etc., and also one special attribute containing the image pixel data (i.e. logically, the main object has no "header" as such, being merely a list of attributes, including the pixel data). A single DICOM object can have only one attribute containing pixel data. For many modalities, this corresponds to a single image. However, the attribute may contain multiple "frames", allowing storage of cine loops or other multi-frame data. Another example is NM data, where an NM image, by definition, is a multi-dimensional multi-frame image. In these cases, three- or four-dimensional data can be encapsulated in a single DICOM object. Pixel data can be compressed using a variety of standards, including JPEG, lossless JPEG, JPEG 2000, and run-length encoding (RLE). LZW (zip) compression can be used for the whole data set (not just the pixel data), but this has rarely been implemented.


title: DICOM

text: DICOM uses three different data element encoding schemes. With explicit value representation (VR) data elements, for VRs that are not OB, OW, OF, SQ, UT, or UN, the format for each data element is: GROUP (2 bytes) ELEMENT (2 bytes) VR (2 bytes) LengthInByte (2 bytes) Data (variable length). For the other explicit data elements or implicit data elements, see section 7.1 of Part 5 of the DICOM Standard.


title: DICOM

text: The same basic format is used for all applications, including network and file usage, but when written to a file, usually a true "header" (containing copies of a few key attributes and details of the application that wrote it) is added.


title: DICOM

text: To promote identical grayscale image display on different monitors and consistent hard-copy images from various printers, the DICOM committee developed a lookup table to display digitally assigned pixel values. To use the DICOM grayscale standard display function (GSDF), images must be viewed (or printed) on devices that have this lookup curve or on devices that have been calibrated to the GSDF curve.


title: DICOM

text: In addition to a value representation, each attribute also has a "value multiplicity" to indicate the number of data elements contained in the attribute. For character string value representations, if more than one data element is being encoded, the successive data elements are separated by the backslash character "\".


title: DICOM

text: DICOM consists of services, most of which involve transmission of data over a network. The file format for offline media is a later addition to the standard.


title: DICOM

text: The DICOM Store service is used to send images or other persistent objects (structured reports, etc.) to a picture archiving and communication system (PACS) or workstation.


title: DICOM

text: The DICOM storage commitment service is used to confirm that an image has been permanently stored by a device (either on redundant disks or on backup media, e.g. burnt to a CD). The Service Class User (SCU: similar to a client), a modality or workstation, etc., uses the confirmation from the Service Class Provider (SCP: similar to a server), an archive station for instance, to make sure that it is safe to delete the images locally.


title: DICOM

text: This enables a workstation to find lists of images or other such objects and then retrieve them from a picture archiving and communication system.


title: DICOM

text: The DICOM modality worklist service provides a list of imaging procedures that have been scheduled for performance by an image acquisition device (sometimes referred to as a modality system). The items in the worklist include relevant details about the subject of the procedure (patient ID, name, sex, and age), the type of procedure (equipment type, procedure description, procedure code) and the procedure order (referring physician, accession number, reason for exam). An image acquisition device, such as a CT scanner, queries a service provider, such as a RIS, to get this information which is then presented to the system operator and is used by the imaging device to populate details in the image metadata.


title: DICOM

text: Prior to the use of the DICOM modality worklist service, the scanner operator was required to manually enter all the relevant details. Manual entry is slower and introduces the risk of misspelled patient names, and other data entry errors.


title: DICOM

text: A complementary service to modality worklist, this enables the modality to send a report about a performed examination including data about the images acquired, beginning time, end time, and duration of a study, dose delivered, etc.


title: DICOM

text: It helps give the radiology department a more precise handle on resource (acquisition station) use. Also known as MPPS, this service allows a modality to better coordinate with image storage servers by giving the server a list of objects to send before or while actually sending such objects.


title: DICOM

text: The DICOM print service is used to send images to a DICOM printer, normally to print an "X-Ray" film. There is a standard calibration (defined in DICOM Part 14) to help ensure consistency between various display devices, including hard copy printout.


title: DICOM

text: The format for offline media files is specified in Part 10 of the DICOM Standard. Such files are sometimes referred to as "Part 10 files".


title: DICOM

text: DICOM restricts the filenames on DICOM media to 8 characters (some systems wrongly use 8.3, but this does not conform to the standard). No information must be extracted from these names (PS3.10 Section 6.2.3.2). This is a common source of problems with media created by developers who did not read the specifications carefully. This is a historical requirement to maintain compatibility with older existing systems. It also mandates the presence of a media directory, the DICOMDIR file, which provides index and summary information for all the DICOM files on the media. The DICOMDIR information provides substantially greater information about each file than any filename could, so there is less need for meaningful file names.


title: DICOM

text: DICOM files typically have a .dcm file extension if they are not part of a DICOM media (which requires them to be without extension).


title: DICOM

text: There is also an ongoing media exchange test and "connectathon" process for CD media and network operation that is organized by the IHE organization.


title: DICOM

text: The core application of the DICOM standard is to capture, store and distribute medical images. The standard also provides services related to imaging such as managing imaging procedure worklists, printing images on film or digital media like DVDs, reporting procedure status like completion of an imaging acquisition, confirming successful archiving of images, encrypting datasets, removing patient identifying information from datasets, organizing layouts of images for review, saving image manipulations and annotations, calibrating image displays, encoding ECGs, encoding CAD results, encoding structured measurement data, and storing acquisition protocols.


title: DICOM

text: The DICOM information object definitions encode the data produced by a wide variety of imaging device types, including, CT (computed tomography), MRI (magnetic resonance imaging), ultrasound, X-ray, fluoroscopy, angiography, mammography, breast tomosynthesis, PET (positron emission tomography), SPECT (single-photon emission computed tomography), Endoscopy, microscopy, nd whole slide imaging, OCT (optical coherence tomography).


title: DICOM

text: DICOM is also implemented by devices associated with images or imaging workflow including, PACS (picture archiving and communication systems), image viewers and display stations, CAD (computer-aided detection/diagnosis systems), 3D visualization systems, clinical analysis applications, image printers, Film scanners, media burners (that export DICOM files onto CDs, DVDs, etc.), media importers (that import DICOM files from CDs, DVDs, USBs, etc.), RIS (radiology information systems), VNA (vendor-neutral archives), EMR (electronic medical record) systems, and radiology reporting systems


title: DICOM

text: Many fields of medicine have a dedicated Working Group within DICOM, and DICOM is applicable to any field of medicine in which imaging is prevalent, including:, radiology, cardiology, oncology, nuclear medicine, radiotherapy, neurology, orthopedics, obstetrics, gynecology, ophthalmology, dentistry, maxillofacial surgery, dermatology, pathology, clinical trials, veterinary medicine, and medical/clinical photography


title: DICOM

text: DICOM have reserved the following TCP and UDP port numbers by the Internet Assigned Numbers Authority (IANA): 104 well-known port for DICOM over Transmission Control Protocol (TCP) or User Datagram Protocol (UDP). Since 104 is in the reserved subset, many operating systems require special privileges to use it;


title: DICOM

text: According to a paper presented at an international symposium in 2008, the DICOM standard has problems related to data entry. "A major disadvantage of the DICOM Standard is the possibility for entering probably too many optional fields. This disadvantage is mostly showing in inconsistency of filling all the fields with the data. Some image objects are often incomplete because some fields are left blank and some are filled with incorrect data."


title: DICOM

text: DVTk is an Open Source project for testing, validating and diagnosing communication protocols and scenarios in medical environments. It supports DICOM, HL7 and IHE integration profiles.


title: DICOM

text: Health Level 7 is a non-profit organization involved in the development of international healthcare informatics interoperability standards. HL7 and DICOM manage a joint Working Group to harmonize areas where the two standards overlap and address imaging integration in the electronic medical record.


title: DICOM

text: Integrating the Healthcare Enterprise (IHE) is an industry sponsored non-profit organization that profiles the use of standards to address specific healthcare use cases. DICOM is incorporated in a variety of imaging related IHE profiles.


title: DICOM

text: Systematized Nomenclature of Medicine (SNOMED) is a systematic, computer-processable collection of medical terms, in human and veterinary medicine, to provide codes, terms, synonyms and definitions which cover anatomy, diseases, findings, procedures, microorganisms, substances, etc. DICOM data makes use of SNOMED to encode relevant concepts.


title: DICOM

text: The DICOM standard is used in a wide variety of resources (IHE, HL7 ... a) that are related to images.


title: Comac

text: The Commercial Aircraft Corporation of China, Ltd. (COMAC, ) is a Chinese state-owned aerospace manufacturer established on 11 May 2008 in Shanghai. The headquarters are in Pudong, Shanghai. The company has a registered capital of RMB 19 billion ( as of May 2008). The corporation is a designer and constructor of large passenger aircraft with capacities of over 150 passengers.


title: Comac

text: The first jet to be marketed is the ARJ21 developed by China Aviation Industry Corporation I, which will be followed by the C919, which made its maiden flight in 2017 and has attracted interest from Chinese airlines. The C919, which can seat up to 168 passengers, is meant to compete in the market for single-aisle jets.


title: Comac

text: COMAC, Commercial Aircraft Corporation of China, was established on 11 May 2008 in Shanghai. It was established jointly by Aviation Industry Corporation of China, Aluminum Corporation of China, Baosteel Group Corporation, Sinochem Group, Shanghai Guosheng Corporation Limited, and State-owned Assets Supervision and Administration Commission.


title: Comac

text: In January 2021, the United States government named COMAC as a company "owned or controlled" by the People's Liberation Army and thereby prohibited any American company or individual from investing in it.


title: Comac

text: For all models sold beginning with the Comac C919, COMAC's naming system for commercial airliners has taken the form of 9X9.


title: Comac

text: On 24 March 2011, Comac and the Canadian company Bombardier Inc. signed a framework agreement for a long-term strategic cooperation on commercial aircraft.


title: Comac

text: In May 2017, Bombardier and Comac began holding talks about an investment into Bombardier's passenger jet business.


title: Comac

text: On 23 September 2015, Boeing announced plans to build a Boeing 737 completion and finishing plant in China. The facility will be used to paint exteriors and install interiors into airframes built in the United States. The joint-venture plant will be located in Zhoushan, Zhejiang.


title: Comac

text: In June 2011 COMAC and Irish low-cost airline Ryanair signed an agreement to cooperate on the development of the C919, a 200-seat narrow-body commercial jet which will compete with the Boeing 737 and Airbus A320.


title: Comac

text: China-Russia Commercial Aircraft International Co. Ltd. (CRAIC), a joint venture company invested by COMAC and Russia's United Aircraft Corporation (UAC) responsible for the development of a wide-body commercial jet, was established in Shanghai on 22 May 2017. Research and development for the new plane will be conducted in Moscow, and it will be assembled in Shanghai.


title: Ben Folds Five

text: Ben Folds Five is an American alternative rock trio formed in 1993 in Chapel Hill, North Carolina. The group comprises Ben Folds (lead vocals, piano), Robert Sledge (bass guitar, backing vocals) and Darren Jessee (drums, backing vocals). The group achieved success in the alternative, indie and pop music scenes. Their single "Brick" from the second album, "Whatever and Ever Amen" (1997), gained airplay on many mainstream radio stations.


title: Ben Folds Five

text: During their first seven years, the band released three studio records, a compilation of B-sides and outtakes, and eight singles. They also contributed to a number of soundtracks and compilations. Ben Folds Five disbanded in October 2000. They reunited in 2011, and released their fourth album, "The Sound of the Life of the Mind", in 2012.


title: Ben Folds Five

text: Ben Folds Five was formed in 1993 in Chapel Hill by Ben Folds. They were a trio in spite of their name, and the primary motivation behind the name, apart from the band's well-known use of humor, was simple preference, according to Ben: "I think it sounds better than Ben Folds Three." Folds once described their music as "punk rock for sissies," a reaction to the angst prevalent in '90s rock.


title: Ben Folds Five

text: Their first radio single was "Underground" from their self-titled debut album, released in 1995 on Caroline Records. The band's biggest success was the single "Brick" from their second album, "Whatever and Ever Amen," released in 1997. It was followed by the more somber and jazz-based 1999 album, "The Unauthorized Biography of Reinhold Messner". The group contributed an outtake from the "Reinhold Messner" sessions, titled "Leather Jacket", to the 1999 benefit album, "".


title: Ben Folds Five

text: The band's final released recording was a cover of Steely Dan's "Barrytown" for the "Me, Myself & Irene" soundtrack. The band had begun work on a fourth studio album, but following the worldwide tour in support of "The Unauthorized Biography of Reinhold Messner", the band "amicably" broke up in October 2000. Tracks from the sessions later emerged in solo projects.


title: Ben Folds Five

text: Folds went on to pursue a successful solo career, releasing "Rockin' the Suburbs" in 2001, "Songs for Silverman" in 2005, "Way to Normal" in 2008, "Lonely Avenue" in collaboration with novelist Nick Hornby in 2010, and "So There" in collaboration with the chamber group yMusic in 2015. He produced and arranged actor William Shatner's second album, "Has Been", as well as co-wrote the majority of the songs with Shatner. Folds also contributed songs to the soundtracks for the animated movies "Hoodwinked!" and "Over the Hedge".


title: Ben Folds Five

text: Darren Jessee formed the acclaimed indie band Hotel Lights, with his songs featured in television and film. Jessee released five studio albums for Bar/None Records including "Hotel Lights" in 2006, "Firecracker People" in 2008, "Girl Graffiti" in 2011, "Get Your Hand in My Hand" in 2016, and his first solo album, "The Jane, Room 217" in 2018.


title: Ben Folds Five

text: Robert Sledge played with International Orange until the group disbanded in 2005. He is currently the bass player in the three-piece Chapel Hill, NC band Surrender Human with Matt McMichaels from the Mayflies USA.


title: Ben Folds Five

text: Ben Folds Five made a one-off concert appearance in September 2008 at the UNC Memorial Hall in Chapel Hill as part of the MySpace "Front to Back" series, in which artists play an entire album live. The band played its then-final album, "The Unauthorized Biography of Reinhold Messner", and were briefly joined on stage by Ben's father, Dean Folds, who read a transcript of his voice mail message that is used in the album song "Your Most Valuable Possession", encoring with some of the songs from their first two albums".


title: Ben Folds Five

text: In 2011, Ben Folds Five reunited to record three tracks for Ben Folds' "". They made their first live appearance for four years as one of the headliners of the 2012 Mountain Jam festival. They made further appearances at that year's 2012 Bonnaroo and Summerfest festivals.


title: Ben Folds Five

text: The band's fourth studio album, "The Sound of the Life of the Mind" was released in September 2012, supported by the single "Do It Anyway", with a video featuring Anna Kendrick, Rob Corddry, Chris Hardwick and the cast of "Fraggle Rock". and a tour of the US, UK, and Ireland.


title: Ben Folds Five

text: In June 2013, the trio released their first live album, titled "Live". During that year Ben Folds Five toured with the Barenaked Ladies and Guster, before entering a hiatus.


title: Sheaf (mathematics)

text: In mathematics, a sheaf is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open sets of a topological space and defined locally with regard to them. For example, for each open set, the data could be the ring of continuous functions defined on that open set. Such data is well behaved in that it can be restricted to smaller open sets, and also the data assigned to an open set is equivalent to all collections of compatible data assigned to collections of smaller open sets covering the original open set (intuitively, every piece of data is the sum of its parts).


title: Sheaf (mathematics)

text: Sheaves are understood conceptually as general and abstract objects. Their correct definition is rather technical. They are specifically defined as sheaves of sets or as sheaves of rings, for example, depending on the type of data assigned to the open sets.


title: Sheaf (mathematics)

text: There are also maps (or morphisms) from one sheaf to another; sheaves (of a specific type, such as sheaves of abelian groups) with their morphisms on a fixed topological space form a category. On the other hand, to each continuous map there is associated both a direct image functor, taking sheaves and their morphisms on the domain to sheaves and morphisms on the codomain, and an inverse image functor operating in the opposite direction. These functors, and certain variants of them, are essential parts of sheaf theory.


title: Sheaf (mathematics)

text: Due to their general nature and versatility, sheaves have several applications in topology and especially in algebraic and differential geometry. First, geometric structures such as that of a differentiable manifold or a scheme can be expressed in terms of a sheaf of rings on the space. In such contexts, several geometric constructions such as vector bundles or divisors are naturally specified in terms of sheaves. Second, sheaves provide the framework for a very general cohomology theory, which encompasses also the "usual" topological cohomology theories such as singular cohomology. Especially in algebraic geometry and the theory of complex manifolds, sheaf cohomology provides a powerful link between topological and geometric properties of spaces. Sheaves also provide the basis for the theory of "D"-modules, which provide applications to the theory of differential equations. In addition, generalisations of sheaves to more general settings than topological spaces, such as Grothendieck topology, have provided applications to mathematical logic and to number theory.


title: Sheaf (mathematics)

text: In many mathematical branches, several structures defined on a topological space formula_1 (e.g., a differentiable manifold) can be naturally "localised" or "restricted" to open subsets formula_2: typical examples include continuous real-valued or complex-valued functions, formula_3-times differentiable (real-valued or complex-valued) functions, bounded real-valued functions, vector fields, and sections of any vector bundle on the space. The ability to restrict data to smaller open subsets gives rise to the concept of presheaves. Roughly speaking, sheaves are then those presheaves, where local data can be glued to global data.


title: Sheaf (mathematics)

text: Let formula_1 be a topological space. A "presheaf of sets" formula_5 on formula_1 consists of the following data:


title: Sheaf (mathematics)

text: Informally, the second axiom says it doesn't matter whether we restrict to "W" in one step or restrict first to "V", then to "W". A concise functorial reformulation of this definition is given further below.


title: Sheaf (mathematics)

text: Many examples of presheaves come from different classes of functions: to any "formula_7", one can assign the set formula_29 of continuous real-valued functions on "formula_7". The restriction maps are then just given by restricting a continuous function on "formula_7" to a smaller open subset "formula_32", which again is a continuous function. The two presheaf axioms are immediately checked, thereby giving an example of a presheaf. This can be extended to a sheaf of holomorphic functions formula_33 and a sheaf of smooth functions formula_34.


title: Sheaf (mathematics)

text: Another common class of examples is assigning to formula_7 the set of constant real-valued functions on formula_7. This presheaf is called the "constant presheaf" associated to formula_37 and is denoted formula_38.


title: Sheaf (mathematics)

text: Given a presheaf, a natural question to ask is to what extent its sections over an open set "formula_7" are specified by their restrictions to smaller open sets formula_40 of an open cover formula_41 of "formula_7". A "sheaf" is a presheaf that satisfies both of the following two additional axioms:


title: Sheaf (mathematics)

text: The section "formula_59" whose existence is guaranteed by axiom 2 is called the "gluing", "concatenation", or "collation" of the sections "s". By axiom 1 it is unique. Sections "formula_60" and "formula_61" satisfying the agreement precondition of axiom 2 are often called "compatible"; thus axioms 1 and 2 together state that "any collection of pairwise compatible sections can be uniquely glued together". A "separated presheaf", or "monopresheaf", is a presheaf satisfying axiom 1.


title: Sheaf (mathematics)

text: The presheaf consisting of continuous functions mentioned above is a sheaf. This assertion reduces to checking that, given continuous functions formula_62 which agree on the intersections formula_63, there is a unique continuous function formula_64 whose restriction equals the formula_65. By contrast, the constant presheaf is usually "not" a sheaf as it fails to satisfy the locality axiom on the empty set (this is explained in more detail at constant sheaf).


title: Sheaf (mathematics)

text: Presheaves and sheaves are typically denoted by capital letters, formula_5 being particularly common, presumably for the French word for sheaf, "faisceau". Use of calligraphic letters such as formula_67 is also common.


title: Sheaf (mathematics)

text: It can be shown that to specify a sheaf, it is enough to specify its restriction to the open sets of a basis for the topology of the underlying space. Moreover, it can also be shown that it is enough to verify the sheaf axioms above relative to the open sets of a covering. This observation is used to construct another example which is crucial in algebraic geometry, namely quasi-coherent sheaves. Here the topological space in question is the spectrum of a commutative ring formula_68, whose points are the prime ideals formula_69 in formula_68. The open sets formula_71 form a basis for the Zariski topology on this space. Given an formula_68-module formula_73, there is a sheaf, denoted by formula_74 on the Spec formula_68, that satisfies


title: Sheaf (mathematics)

text: Any continuous map formula_79 of topological spaces determines a sheaf formula_80 on formula_1 by setting


title: Sheaf (mathematics)

text: Any such formula_59 is commonly called a section of "formula_78", and this example is the reason why the elements in formula_9 are generally called sections. This construction is especially important when formula_78 is the projection of a fiber bundle onto its base space. For example, the sheaves of smooth functions are the sheaves of sections of the trivial bundle. Another example: the sheaf of sections of


title: Sheaf (mathematics)

text: is the sheaf which assigns to any "formula_7" the set of branches of the complex logarithm on "formula_7".


title: Sheaf (mathematics)

text: Given a point formula_90 and an abelian group formula_91, the skyscraper sheaf formula_92 is defined as follows: if formula_7 is an open set containing formula_90, then formula_95. If formula_7 does not contain formula_90, then formula_98, the trivial group. The restriction maps are either the identity on formula_91, if both open sets contain formula_90, or the zero map otherwise.


title: Sheaf (mathematics)

text: On an formula_3-dimensional formula_102-manifold formula_73, there are a number of important sheaves, such as the sheaf of formula_104-times continuously differentiable functions formula_105 (with formula_106). Its sections on some open formula_7 are the formula_108-functions formula_109. For formula_110, this sheaf is called the "structure sheaf" and is denoted formula_111. The nonzero formula_102 functions also form a sheaf, denoted formula_113. Differential forms (of degree formula_69) also form a sheaf formula_115. In all these examples, the restriction morphisms are given by restricting functions or forms.


title: Sheaf (mathematics)

text: The assignment sending formula_7 to the compactly supported functions on formula_7 is not a sheaf, since there is, in general, no way to preserve this property by passing to a smaller open subset. Instead, this forms a cosheaf, a dual concept where the restriction maps go in the opposite direction than with sheaves. However, taking the dual of these vector spaces does give a sheaf, the sheaf of distributions.


title: Sheaf (mathematics)

text: In addition to the constant presheaf mentioned above, which is usually not a sheaf, there are further examples of presheaves that are not sheaves:


title: Sheaf (mathematics)

text: One of the historical motivations for sheaves have come from studying complex manifolds, complex analytic geometry, and scheme theory from algebraic geometry. This is because in all of the previous cases, we consider a topological space formula_1 together with a structure sheaf formula_144 giving it the structure of a complex manifold, complex analytic space, or scheme. This perspective of equipping a topological space with a sheaf is essential to the theory of locally ringed spaces (see below).


title: Sheaf (mathematics)

text: One of the main historical motivations for introducing sheaves was constructing a device which keeps track of holomorphic functions on complex manifolds. For example, on a compact complex manifold formula_1 (like complex projective space or the vanishing locus of a homogeneous polynomial), the "only" holomorphic functionsformula_146are the constant functions. This means there could exist two compact complex manifolds formula_147 which are not isomorphic, but nevertheless their ring of global holomorphic functions, denoted formula_148, are isomorphic. Contrast this with smooth manifolds where every manifold formula_73 can be embedded inside some formula_150, hence its ring of smooth functions formula_151 comes from restricting the smooth functions from formula_152. Another complexity when considering the ring of holomorphic functions on a complex manifold formula_1 is given a small enough open set formula_2, the holomorphic functions will be isomorphic to formula_155. Sheaves are a direct tool for dealing with this complexity since they make it possible to keep track of the holomorphic structure on the underlying topological space of formula_1 on arbitrary open subsets formula_2. This means as formula_7 becomes more complex topologically, the ring formula_159 can be expressed from gluing the formula_160. Note that sometimes this sheaf is denoted formula_161 or just formula_144, or even formula_163 when we want to emphasize the space the structure sheaf is associated to.


title: Sheaf (mathematics)

text: Another common example of sheaves can be constructed by considering a complex submanifold formula_164. There is an associated sheaf formula_165 which takes an open subset formula_2 and gives the ring of holomorphic functions on formula_167. This kind of formalism was found to be extremely powerful and motivates a lot of homological algebra such as sheaf cohomology since an intersection theory can be built using these kinds of sheaves from the Serre intersection formula.


title: Sheaf (mathematics)

text: Morphisms of sheaves are, roughly speaking, analogous to functions between them. In contrast to a function between sets, which have no additional structure, morphisms of sheaves are those functions which preserve the structure inherent in the sheaves. This idea is made precise in the following definition.


title: Sheaf (mathematics)

text: Let formula_5 and formula_169 be two sheaves on formula_1. A "morphism" formula_171 consists of a morphism formula_172 for each open set formula_7 of formula_1, subject to the condition that this morphism is compatible with restrictions. In other words, for every open subset formula_32 of an open set formula_7, the following diagram is commutative.


title: Sheaf (mathematics)

text: Indeed, given an (formula_3-times continuously differentiable) function formula_181 (with formula_7 in formula_178 open), the restriction (to a smaller open subset formula_32) of its derivative equals the derivative of formula_185.


title: Sheaf (mathematics)

text: With this notion of morphism, sheaves on a fixed topological space formula_1 form a category. The general categorical notions of mono-, epi- and isomorphisms can therefore be applied to sheaves. A sheaf morphism formula_187 is an isomorphism (resp. monomorphism) if and only if each formula_188 is a bijection (resp. injective map). Moreover, a morphism of sheaves formula_187 is an isomorphism if and only if there exists an open cover formula_190 such that formula_191 are isomorphisms of sheaves for all formula_192. This statement, which also holds for monomorphisms, but does not hold for presheaves, is another instance of the idea that sheaves are of a local nature.


title: Sheaf (mathematics)

text: The corresponding statements do not hold for epimorphisms (of sheaves), and their failure is measured by sheaf cohomology.


title: Sheaf (mathematics)

text: The "stalk" formula_193 of a sheaf formula_67 captures the properties of a sheaf "around" a point formula_195, generalizing the germs of functions.


title: Sheaf (mathematics)

text: Here, "around" means that, conceptually speaking, one looks at smaller and smaller neighborhoods of the point. Of course, no single neighborhood will be small enough, which requires considering a limit of some sort. More precisely, the stalk is defined by


title: Sheaf (mathematics)

text: the direct limit being over all open subsets of formula_1 containing the given point formula_90. In other words, an element of the stalk is given by a section over some open neighborhood of formula_90, and two such sections are considered equivalent if their restrictions agree on a smaller neighborhood.


title: Sheaf (mathematics)

text: The natural morphism formula_200 takes a section formula_90 in formula_9 to its "germ" at formula_90. This generalises the usual definition of a germ.


title: Sheaf (mathematics)

text: In many situations, knowing the stalks of a sheaf is enough to control the sheaf itself. For example, whether or not a morphism of sheaves is a monomorphism, epimorphism, or isomorphism can be tested on the stalks. In this sense, a sheaf is determined by its stalks, which are a local data. By contrast, the "global" information present in a sheaf, i.e., the "global sections", i.e., the sections formula_204 on the whole space formula_1, typically carry less information. For example, for a compact complex manifold formula_1, the global sections of the sheaf of holomorphic functions are just formula_207, since any holomorphic function


title: Sheaf (mathematics)

text: It is frequently useful to take the data contained in a presheaf and to express it as a sheaf. It turns out that there is a best possible way to do this. It takes a presheaf formula_5 and produces a new sheaf formula_210 called the "sheafification" or "sheaf associated to the presheaf" formula_5. For example, the sheafification of the constant presheaf (see above) is called the "constant sheaf". Despite its name, its sections are "locally" constant functions.


title: Sheaf (mathematics)

text: The sheaf formula_210 can be constructed using the étalé space of formula_5, namely as the sheaf of sections of the map


title: Sheaf (mathematics)

text: Another construction of the sheaf formula_210 proceeds by means of a functor formula_216 from presheaves to presheaves that gradually improves the properties of a presheaf: for any presheaf formula_5, formula_218 is a separated presheaf, and for any separated presheaf formula_5, formula_218 is a sheaf. The associated sheaf formula_210 is given by formula_222.


title: Sheaf (mathematics)

text: The idea that the sheaf formula_210 is the best possible approximation to formula_5 by a sheaf is made precise using the following universal property: there is a natural morphism of presheaves formula_225 so that for any sheaf formula_169 and any morphism of presheaves formula_227, there is a unique morphism of sheaves formula_228 such that formula_229. In fact formula_230 is the left adjoint functor to the inclusion functor (or forgetful functor) from the category of sheaves to the category of presheaves, and formula_231 is the unit of the adjunction. In this way, the category of sheaves turns into a Giraud subcategory of presheaves. This categorical situation is the reason why the sheafification functor appears in constructing cokernels of sheaf morphisms or tensor products of sheaves, but not for kernels, say.


title: Sheaf (mathematics)

text: If formula_232 is a subsheaf of a sheaf formula_5 of abelian groups, then the quotient sheaf formula_234 is the sheaf associated to the presheaf formula_235; in other words, the quotient sheaf fits into an exact sequence of sheaves of abelian groups;


title: Sheaf (mathematics)

text: Let formula_237 be sheaves of abelian groups. The set formula_238 of morphisms of sheaves from formula_5 to formula_169 forms an abelian group (by the abelian group structure of formula_169). The sheaf hom of formula_5 and formula_169, denoted by,


title: Sheaf (mathematics)

text: is the sheaf of abelian groups formula_245 where formula_246 is the sheaf on formula_7 given by formula_248 (note sheafification is not needed here). The direct sum of formula_5 and formula_169 is the sheaf given by formula_251, and the tensor product of formula_5 and formula_169 is the sheaf associated to the presheaf formula_254.


title: Sheaf (mathematics)

text: All of these operations extend to sheaves of modules over a sheaf of rings formula_255; the above is the special case when formula_255 is the constant sheaf formula_257.


title: Sheaf (mathematics)

text: Since the data of a (pre-)sheaf depends on the open subsets of the base space, sheaves on different topological spaces are unrelated to each other in the sense that there are no morphisms between them. However, given a continuous map formula_258 between two topological spaces, pushforward and pullback relate sheaves on formula_1 to those on formula_260 and vice versa.


title: Sheaf (mathematics)

text: The pushforward (also known as direct image) of a sheaf formula_67 on formula_1 is the sheaf defined by


title: Sheaf (mathematics)

text: Here formula_32 is an open subset of formula_260, so that its preimage is open in formula_1 by the continuity of formula_78.


title: Sheaf (mathematics)

text: where formula_270 is the inclusion, and formula_91 is regarded as a sheaf on the singleton (by formula_272.


title: Sheaf (mathematics)

text: For a map between locally compact spaces, the direct image with compact support is a subsheaf of the direct image. By definition, formula_273 consists of those formula_274 whose support is proper map over formula_32. If formula_78 is proper itself, then formula_277, but in general they disagree.


title: Sheaf (mathematics)

text: The pullback or inverse image goes the other way: it produces a sheaf on formula_1, denoted formula_279 out of a sheaf formula_280 on formula_260. If formula_78 is the inclusion of an open subset, then the inverse image is just a restriction, i.e., it is given by formula_283 for an open formula_7 in formula_1. A sheaf formula_5 (on some space formula_1) is called locally constant if formula_288 by some open subsets formula_40 such that the restriction of formula_5 to all these open subsets is constant. One a wide range of topological spaces formula_1, such sheaves are equivalent to representations of the fundamental group formula_292.


title: Sheaf (mathematics)

text: For general maps formula_78, the definition of formula_279 is more involved; it is detailed at inverse image functor. The stalk is an essential special case of the pullback in view of a natural identification, where formula_231 is as above:


title: Sheaf (mathematics)

text: For the inclusion formula_298 of an open subset, the extension by zero of a sheaf of abelian groups on formula_7 is defined as


title: Sheaf (mathematics)

text: For a sheaf formula_280 on formula_1, this construction is in a sense complementary to formula_305, where formula_231 is the inclusion of the complement of formula_7:


title: Sheaf (mathematics)

text: These functors are therefore useful in reducing sheaf-theoretic questions on formula_1 to ones on the strata of a stratification, i.e., a decomposition of formula_1 into smaller, locally closed subsets.


title: Sheaf (mathematics)

text: In addition to (pre-)sheaves as introduced above, where formula_317 is merely a set, it is in many cases important to keep track of additional structure on these sections. For example, the sections of the sheaf of continuous functions naturally form a real vector space, and restriction is a linear map between these vector spaces.


title: Sheaf (mathematics)

text: Presheaves with values in an arbitrary category formula_318 are defined by first considering the category of open sets on formula_1 to be the posetal category formula_320 whose objects are the open sets of formula_1 and whose morphisms are inclusions. Then a formula_318-valued presheaf on formula_1 is the same as a contravariant functor from formula_320 to formula_318. Morphisms in this category of functors, also known as natural transformations, are the same as the morphisms defined above, as can be seen by unraveling the definitions.


title: Sheaf (mathematics)

text: If the target category formula_318 admits all limits, a formula_318-valued presheaf is a sheaf if the following diagram is an equalizer for every open cover


title: Sheaf (mathematics)

text: If formula_318 is an abelian category, this condition can also be rephrased by requiring that there is an exact sequence


title: Sheaf (mathematics)

text: A particular case of this sheaf condition occurs for formula_7 being the empty set, and the index set formula_337 also being empty. In this case, the sheaf condition requires formula_338 to be the terminal object in formula_318.


title: Sheaf (mathematics)

text: In several geometrical disciplines, including algebraic geometry and differential geometry, the spaces come along with a natural sheaf of rings, often called the structure sheaf and denoted by formula_163. Such a pair formula_341 is called a "ringed space". Many types of spaces can be defined as certain types of ringed spaces. Commonly, all the stalks formula_342 of the structure sheaf are local rings, in which case the pair is called a "locally ringed space".


title: Sheaf (mathematics)

text: For example, an formula_3-dimensional formula_102 manifold formula_73 is a locally ringed space whose structure sheaf consists of formula_102-functions on the open subsets of formula_73. The property of being a "locally" ringed space translates into the fact that such a function, which is nonzero at a point formula_90, is also non-zero on a sufficiently small open neighborhood of formula_90. Some authors actually "define" real (or complex) manifolds to be locally ringed spaces that are locally isomorphic to the pair consisting of an open subset of formula_150 (resp. formula_351) together with the sheaf of formula_102 (resp. holomorphic) functions. Similarly, schemes, the foundational notion of spaces in algebraic geometry, are locally ringed spaces that are locally isomorphic to the spectrum of a ring.


title: Sheaf (mathematics)

text: Given a ringed space, a "sheaf of modules" is a sheaf formula_353 such that on every open set formula_7 of formula_1, formula_356 is an formula_357-module and for every inclusion of open sets formula_358, the restriction map formula_359 is compatible with the restriction map formula_360: the restriction of "fs" is the restriction of formula_78 times that of formula_59 for any formula_78 in formula_364 and formula_59 in formula_356.


title: Sheaf (mathematics)

text: Most important geometric objects are sheaves of modules. For example, there is a one-to-one correspondence between vector bundles and locally free sheaves of formula_163-modules. This paradigm applies to real vector bundles, complex vector bundles, or vector bundles in algebraic geometry (where formula_368 consists of smooth functions, holomorphic functions, or regular functions, respectively). Sheaves of solutions to differential equations are formula_369-modules, that is, modules over the sheaf of differential operators. On any topological space, modules over the constant sheaf formula_257 are the same as sheaves of abelian groups in the sense above.


title: Sheaf (mathematics)

text: There is a different inverse image functor for sheaves of modules over sheaves of rings. This functor is usually denoted formula_371 and it is distinct from formula_372. See inverse image functor.


title: Sheaf (mathematics)

text: Finiteness conditions for module over commutative rings give rise to similar finiteness conditions for sheaves of modules: formula_353 is called "finitely generated" (resp. "finitely presented") if, for every point formula_90 of formula_1, there exists an open neighborhood formula_7 of formula_90, a natural number formula_3 (possibly depending on formula_7), and a surjective morphism of sheaves formula_380 (respectively, in addition a natural number formula_381, and an exact sequence formula_382.) Paralleling the notion of a coherent module, formula_353 is called a "coherent sheaf" if it is of finite type and if, for every open set formula_7 and every morphism of sheaves formula_385 (not necessarily surjective), the kernel of formula_386 is of finite type. formula_163 is "coherent" if it is coherent as a module over itself. Like for modules, coherence is in general a strictly stronger condition than finite presentation. The Oka coherence theorem states that the sheaf of holomorphic functions on a complex manifold is coherent.


title: Sheaf (mathematics)

text: In the examples above it was noted that some sheaves occur naturally as sheaves of sections. In fact, all sheaves of sets can be represented as sheaves of sections of a topological space called the "étalé space", from the French word étalé , meaning roughly "spread out". If formula_388 is a sheaf over formula_1, then the étalé space of formula_5 is a topological space formula_391 together with a local homeomorphism formula_392 such that the sheaf of sections formula_393 of formula_394 is formula_5. The space "formula_391" is usually very strange, and even if the sheaf "formula_5" arises from a natural topological situation, "formula_391" may not have any clear topological interpretation. For example, if "formula_5" is the sheaf of sections of a continuous function formula_400, then formula_401 if and only if formula_78 is a local homeomorphism.


title: Sheaf (mathematics)

text: The étalé space "formula_391" is constructed from the stalks of "formula_5" over "formula_1". As a set, it is their disjoint union and "formula_394" is the obvious map that takes the value formula_90 on the stalk of formula_5 over formula_409. The topology of "formula_391" is defined as follows. For each element formula_19 and each formula_412, we get a germ of formula_59 at formula_90, denoted formula_415 or formula_416. These germs determine points of "formula_391". For any formula_7 and formula_19, the union of these points (for all formula_412) is declared to be open in "formula_391". Notice that each stalk has the discrete topology as subspace topology. Two morphisms between sheaves determine a continuous map of the corresponding étalé spaces that is compatible with the projection maps (in the sense that every germ is mapped to a germ over the same point). This makes the construction into a functor.


title: Sheaf (mathematics)

text: The construction above determines an equivalence of categories between the category of sheaves of sets on "formula_1" and the category of étalé spaces over "formula_1". The construction of an étalé space can also be applied to a presheaf, in which case the sheaf of sections of the étalé space recovers the sheaf associated to the given presheaf.


title: Sheaf (mathematics)

text: This construction makes all sheaves into representable functors on certain categories of topological spaces. As above, let "formula_5" be a sheaf on "formula_1", let "formula_391" be its étalé space, and let formula_427 be the natural projection. Consider the overcategory formula_428 of topological spaces over formula_1, that is, the category of topological spaces together with fixed continuous maps to formula_1. Every object of this category is a continuous map formula_79, and a morphism from formula_432 to formula_433 is a continuous map formula_434 that commutes with the two maps to formula_1. There is a functorformula_436sending an object formula_79 to formula_438. For example, if formula_439 is the inclusion of an open subset, thenformula_440and for the inclusion of a point formula_441, thenformula_442is the stalk of formula_5 at formula_90. There is a natural isomorphismformula_445,which shows that formula_392 (for the étalé space) represents the functor formula_447.


title: Sheaf (mathematics)

text: "formula_391" is constructed so that the projection map "formula_394" is a covering map. In algebraic geometry, the natural analog of a covering map is called an étale morphism. Despite its similarity to "étalé", the word étale has a different meaning in French. It is possible to turn formula_391 into a scheme and "formula_394" into a morphism of schemes in such a way that "formula_394" retains the same universal property, but "formula_394" is "not" in general an étale morphism because it is not quasi-finite. It is, however, formally étale.


title: Sheaf (mathematics)

text: The definition of sheaves by étalé spaces is older than the definition given earlier in the article. It is still common in some areas of mathematics such as mathematical analysis.


title: Sheaf (mathematics)

text: In contexts, where the open set formula_7 is fixed, and the sheaf is regarded as a variable, the set formula_9 is also often denoted formula_456


title: Sheaf (mathematics)

text: As was noted above, this functor does not preserve epimorphisms. Instead, an epimorphism of sheaves formula_457 is a map with the following property: for any section formula_458 there is a covering formula_41 where formula_460 of open subsets, such that the restriction formula_461 are in the image of formula_462. However, formula_463 itself need not be in the image of formula_317. A concrete example of this phenomenon is the exponential map


title: Sheaf (mathematics)

text: between the sheaf of holomorphic functions and non-zero holomorphic functions. This map is an epimorphism, which amounts to saying that any non-zero holomorphic function formula_463 (on some open subset in formula_207, say), admits a complex logarithm "locally", i.e., after restricting formula_463 to appropriate open subsets. However, formula_463 need not have a logarithm globally.


title: Sheaf (mathematics)

text: Sheaf cohomology captures this phenomenon. More precisely, for an exact sequence of sheaves of abelian groups


title: Sheaf (mathematics)

text: (i.e., an epimorphism formula_471 whose kernel is formula_472), there is a long exact sequenceformula_473By means of this sequence, the first cohomology group formula_474 is a measure for the non-surjectivity of the map between sections of formula_475 and formula_476.


title: Sheaf (mathematics)

text: There are several different ways of constructing sheaf cohomology. introduced them by defining sheaf cohomology as the derived functor of formula_447. This method is theoretically satisfactory, but, being based on injective resolutions, of little use in concrete computations. Godement resolutions are another general, but practically inaccessible approach.


title: Sheaf (mathematics)

text: Especially in the context of sheaves on manifolds, sheaf cohomology can often be computed using resolutions by soft sheaves, fine sheaves, and flabby sheaves (also known as flasque sheaves from the French "flasque" meaning flabby). For example, a partition of unity argument shows that the sheaf of smooth functions on a manifold is soft. The higher cohomology groups formula_478 for formula_479 vanish for soft sheaves, which gives a way of computing cohomology of other sheaves. For example, the de Rham complex is a resolution of the constant sheaf formula_480 on any smooth manifold, so the sheaf cohomology of formula_480 is equal to its de Rham cohomology.


title: Sheaf (mathematics)

text: A different approach is by Čech cohomology. Čech cohomology was the first cohomology theory developed for sheaves and it is well-suited to concrete calculations, such as computing the coherent sheaf cohomology of complex projective space formula_482. It relates sections on open subsets of the space to cohomology classes on the space. In most cases, Čech cohomology computes the same cohomology groups as the derived functor cohomology. However, for some pathological spaces, Čech cohomology will give the correct formula_483 but incorrect higher cohomology groups. To get around this, Jean-Louis Verdier developed hypercoverings. Hypercoverings not only give the correct higher cohomology groups but also allow the open subsets mentioned above to be replaced by certain morphisms from another space. This flexibility is necessary in some applications, such as the construction of Pierre Deligne's mixed Hodge structures.


title: Sheaf (mathematics)

text: Many other coherent sheaf cohomology groups are found using an embedding formula_484 of a space formula_1 into a space with known cohomology, such as formula_482, or some weighted projective space. In this way, the known sheaf cohomology groups on these ambient spaces can be related to the sheaves formula_487, giving formula_488. For example, computing the coherent sheaf cohomology of projective plane curves is easily found. One big theorem in this space is the Hodge decomposition found using a spectral sequence associated to sheaf cohomology groups, proved by Deligne. Essentially, the formula_489-page with termsformula_490the sheaf cohomology of a smooth projective variety formula_1, degenerates, meaning formula_492. This gives the canonical Hodge structure on the cohomology groups formula_493. It was later found these cohomology groups can be easily explicitly computed using Griffiths residues. See Jacobian ideal. These kinds of theorems lead to one of the deepest theorems about the cohomology of algebraic varieties, the decomposition theorem, paving the path for Mixed Hodge modules.


title: Sheaf (mathematics)

text: Another clean approach to the computation of some cohomology groups is the Borel–Bott–Weil theorem, which identifies the cohomology groups of some line bundles on flag manifolds with irreducible representations of Lie groups. This theorem can be used, for example, to easily compute the cohomology groups of all line bundles on projective space and grassmann manifolds.


title: Sheaf (mathematics)

text: In many cases there is a duality theory for sheaves that generalizes Poincaré duality. See Grothendieck duality and Verdier duality.


title: Sheaf (mathematics)

text: The derived category of the category of sheaves of, say, abelian groups on some space "X", denoted here as formula_494, is the conceptual haven for sheaf cohomology, by virtue of the following relation:


title: Sheaf (mathematics)

text: The adjunction between formula_372, which is the left adjoint of formula_497 (already on the level of sheaves of abelian groups) gives rise to an adjunction


title: Sheaf (mathematics)

text: where formula_500 is the derived functor. This latter functor encompasses the notion of sheaf cohomology since formula_501 for formula_502.


title: Sheaf (mathematics)

text: Like formula_497, the direct image with compact support formula_504 can also be derived. By virtue of the following isomorphism formula_505 parametrizes the cohomology with compact support of the fibers of formula_78:


title: Sheaf (mathematics)

text: Unlike all the functors considered above, the twisted (or exceptional) inverse image functor formula_509 is in general only defined on the level of derived categories, i.e., the functor is not obtained as the derived functor of some functor between abelian categories. If formula_502 and "X" is a smooth orientable manifold of dimension "n", then


title: Sheaf (mathematics)

text: This computation, and the compatibility of the functors with duality (see Verdier duality) can be used to obtain a high-brow explanation of Poincaré duality. In the context of quasi-coherent sheaves on schemes, there is a similar duality known as coherent duality.


title: Sheaf (mathematics)

text: Perverse sheaves are certain objects in formula_494, i.e., complexes of sheaves (but not in general sheaves proper). They are an important tool to study the geometry of singularities.


title: Sheaf (mathematics)

text: Another important application of derived categories of sheaves is with the derived category of coherent sheaves on a scheme formula_1 denoted formula_514. This was used by Grothendieck in his development of intersection theory using derived categories and K-theory, that the intersection product of subschemes formula_515 is represented in K-theory asformula_516where formula_517 are coherent sheaves defined by the formula_163-modules given by their structure sheaves.


title: Sheaf (mathematics)

text: André Weil's Weil conjectures stated that there was a cohomology theory for algebraic varieties over finite fields that would give an analogue of the Riemann hypothesis. The cohomology of a complex manifold can be defined as the sheaf cohomology of the locally constant sheaf formula_519 in the Euclidean topology, which suggests defining a Weil cohomology theory in positive characteristic as the sheaf cohomology of a constant sheaf. But the only classical topology on such a variety is the Zariski topology, and the Zariski topology has very few open sets, so few that the cohomology of any Zariski-constant sheaf on an irreducible variety vanishes (except in degree zero). Alexandre Grothendieck solved this problem by introducing Grothendieck topologies, which axiomatize the notion of "covering". Grothendieck's insight was that the definition of a sheaf depends only on the open sets of a topological space, not on the individual points. Once he had axiomatized the notion of covering, open sets could be replaced by other objects. A presheaf takes each one of these objects to data, just as before, and a sheaf is a presheaf that satisfies the gluing axiom with respect to our new notion of covering. This allowed Grothendieck to define étale cohomology and ℓ-adic cohomology, which eventually were used to prove the Weil conjectures.


title: Sheaf (mathematics)

text: A category with a Grothendieck topology is called a "site". A category of sheaves on a site is called a "topos" or a "Grothendieck topos". The notion of a topos was later abstracted by William Lawvere and Miles Tierney to define an elementary topos, which has connections to mathematical logic.


title: Sheaf (mathematics)

text: The first origins of sheaf theory are hard to pin down – they may be co-extensive with the idea of analytic continuation. It took about 15 years for a recognisable, free-standing theory of sheaves to emerge from the foundational work on cohomology.


title: Sheaf (mathematics)

text: At this point sheaves had become a mainstream part of mathematics, with use by no means restricted to algebraic topology. It was later discovered that the logic in categories of sheaves is intuitionistic logic (this observation is now often referred to as Kripke–Joyal semantics, but probably should be attributed to a number of authors).


title: The Good Doctor (2011 film)

text: The Good Doctor is a 2011 American thriller film directed by Lance Daly, and starring Orlando Bloom as the eponymous "good doctor".


title: The Good Doctor (2011 film)

text: British medical student Martin E. Blake transfers to a Southern California hospital to start his residency. Outwardly charming, Martin is in reality a narcissist who longs to wield power over others. This attitude quickly alienates him from the nurses, whom he perceives as not respecting him to the extent he deserves. After Martin fails to endear himself to his first few patients and ends up on thin ice with his superiors, 18-year-old Diane Nixon comes in suffering from a kidney infection, which Martin treats. Diane and her family hail Martin as a hero, inflating his self-esteem. As Diane's health begins to improve, Martin begins tampering with her medications and intentionally botching her treatment while maintaining the illusion that he is doing everything within his power to nurse her back to health. Ultimately, he goes too far and accidentally kills Diane when he falls asleep during the night while watching her, after she becomes in critical condition.


title: The Good Doctor (2011 film)

text: An orderly, Jimmy, discovers a diary in which Diane has recorded sexual fantasies about Martin. Recognizing that even the implication of an improper doctor-patient relationship could potentially damage Martin's career, Jimmy uses the diary to blackmail Martin into providing him with narcotics. When Jimmy reveals that he intends to never hand over the diary, Martin laces the drugs with potassium cyanide and kills Jimmy, then breaks into his locker and steals the diary.


title: The Good Doctor (2011 film)

text: During the course of the criminal investigation in Jimmy's death, Martin is questioned by a police detective who comes to visit him at his home. Martin panics during the questioning, eventually locking himself in the bathroom and attempting to flush the diary down the toilet. When the toilet clogs, Martin climbs out the window and goes to the ocean, where he contemplates suicide. Instead, he sneaks back into his apartment and puts the diary in the garbage. With no evidence to implicate Martin in Jimmy's death, the detective leaves.


title: The Good Doctor (2011 film)

text: An unspecified amount of time later, Martin returns to his duties at the hospital, assuring a young patient, "I'm getting better all the time."


title: The Good Doctor (2011 film)

text: "The Good Doctor" premiered at the 2011 Tribeca Film Festival and was released on DVD and Blu-ray on December 18, 2012.


title: The Good Doctor (2011 film)

text: Rotten Tomatoes reports that 66% of 29 surveyed critics gave the film a positive review; the average rating was 6.2/10. On Metacritic, the film has a 52/100 rating based on ten reviews, indicating "mixed or average reviews." Ronnie Scheib of "Variety" wrote, "Black comedy lurks just below the suspenseful surface, with more than a hint of "Lolita"-esque absurdity." Sura Wood of "The Hollywood Reporter" called it "a tense, psychosexual film" with a script that takes too few risks and does not explore Blake's origins satisfactorily.


title: Atari Lynx

text: The Atari Lynx is a hybrid 8/16-bit fourth generation handheld game console released by Atari Corporation in September 1989 in North America and 1990 in Europe and Japan. It was the first handheld game console with a color liquid-crystal display. Powered by a 16 MHz 65C02 8-bit CPU and a custom 16-bit blitter, the Lynx was more advanced than Nintendo's monochrome Game Boy, released two months earlier. It also competed with Sega's Game Gear and NEC's TurboExpress, released the following year.


title: Atari Lynx

text: The system was developed at Epyx by former two former designers of the Amiga personal computers. The project was called the Handy Game or simply Handy. In 1991, Atari replaced the Lynx with a smaller model internally referred to as the Lynx II. Atari published a total of 73 games before the Lynx was discontinued in 1995 in preparation for the launch of the Atari Jaguar.


title: Atari Lynx

text: The Lynx system was originally developed by Epyx as the Handy Game. In 1986, two former Amiga designers, R. J. Mical and Dave Needle, had been asked by a former manager at Amiga, David Morse, to design a portable gaming system. Morse now worked at Epyx, a game software company with a recent string of hit games. Morse's son had asked him if he could make a portable gaming system, prompting a meeting with Mical and Needle to discuss the idea. Morse convinced Mical and Needle and they were hired by Epyx to be a part of the design team. Planning and design of the console began in 1986 and was completed in 1987. Epyx first showed the Handy system at the Winter Consumer Electronics Show (CES) in January 1989. Facing financial difficulties, Epyx sought partners. Nintendo, Sega, and other companies declined, but Atari and Epyx eventually agreed that Atari would handle production and marketing, and Epyx would handle software development. Epyx declared bankruptcy by the end of the year, so Atari essentially owned the entire project. Both Atari and others had to purchase Amigas from Atari arch-rival Commodore in order to develop Lynx software.


title: Atari Lynx

text: The Handy was designed to run games from the cartridge format, and the game data must be copied from ROM to RAM before it can be used. Thus, less RAM is then available and each game's initial loading is slow. There are trace remnants of a cassette tape interface physically capable of being programmed to read a tape. Lynx developers have noted that "there is still reference of the tape and some hardware addresses" and an updated vintage Epyx manual describes the bare existence of what could be utilized for tape support. A 2009 retrospective interview with Mical clarifies that there is no truth to some early reports claiming that games were loaded from tape, and elaborates, "We did think about hard disk a little."


title: Atari Lynx

text: Atari changed the internal speaker and removed the thumb stick on the control pad. At Summer 1989 CES, Atari's press demonstration included the "Portable Color Entertainment System", which was changed to "Lynx" when distributed to resellers, initially retailing in the US at .


title: Atari Lynx

text: Its launch was successful. Atari reported that it had sold 90% of the 50,000 units shipped in the launch month in the U.S. with a limited launch in New York. US sales in 1990 were approximately 500,000 units according to the Associated Press. In late 1991, it was reported that Atari sales estimates were about 800,000, which Atari claimed was within its expected projections. Lifetime sales by 1995 amount to fewer than 7 million units when combined with the Game Gear. In comparison, 16 million Game Boy units were sold by 1995 because of its ruggedness, half price, much longer battery life, bundling with the smash hit "Tetris", and superior game library.


title: Atari Lynx

text: As with the console units, the game cartridge design evolved over the first year of the console's release. The first generation of cartridges are flat, and designed to be stackable for ease of storage. However, this design proved to be very difficult to remove from the console and was replaced by a second design. This style, called "tabbed" or "ridged", adds two small tabs on the underside to aid in removal. The original flat style cartridges can be stacked on top of the newer cartridges, but the newer cartridges can not be easily stacked on each other, nor were they stored easily. Thus a third style, the "curved lip" style was produced, and all official and third-party cartridges during the console's lifespan were released (or re-released) using this style.


title: Atari Lynx

text: In May 1991, Sega launched its Game Gear portable gaming handheld with a color screen. In comparison to the Lynx it had shorter battery life (3–4 hours as opposed to 4-5 for the Lynx), but it is slightly smaller, has significantly more games, and cost $30 less than the Lynx at launch.


title: Atari Lynx

text: Retailers such as Game and Toys "R" Us continued to sell the Lynx well into the mid-1990s on the back of the Atari Jaguar launch, helped by magazines such as "Ultimate Future Games" which continued to cover the Lynx alongside the new generation of 32-bit and 64-bit consoles.


title: Atari Lynx

text: During 1990, the Lynx had moderate sales. In July 1991, Atari introduced the Lynx II with a new marketing campaign, new packaging, slightly improved hardware, better battery life, and a new sleeker look. The new system (referred to within Atari as the "Lynx II") features rubber hand grips and a clearer backlit color screen with a power save option (which turn off the LCD panel's backlighting). It replaced the monaural headphone jack of the original Lynx with one wired for stereo. The new packaging made the Lynx available without any accessories, dropping the price to . Although sales improved, Nintendo still dominated the handheld market.


title: Atari Lynx

text: In 1993, Atari started shifting its focus away from the Lynx in order to prepare for the launch of the Jaguar; a few games were released during that time, including "Battlezone 2000". Support for the Lynx was formally discontinued in 1995.


title: Atari Lynx

text: After the respective launches of the Sega Saturn and Sony PlayStation caused the commercial failure of the Jaguar, Atari ceased all game development and hardware manufacturing by early 1996 and would later merge with JTS, Inc. on July 30 of that year.


title: Atari Lynx

text: The Atari Lynx's features include being the first color handheld, with a backlit display, a switchable right- and left-handed (upside down) configuration, and the ability to network with up to 15 other units via its Comlynx system (though most games network eight or fewer players). Comlynx was originally developed to run over infrared links, codenamed RedEye. This was changed to a cable-based networking system before the final release. According to Peter Engelbrite, when players walked through the beam, the link would be interrupted. The maximum stable connection allowed was eight players. Engelbrite also developed the first recordable eight-player co-op game, and the only eight-player game for the Atari Lynx, "Todd's Adventures in Slime World", using the Comlynx system. Each Lynx needs a copy of the game, and one cable can connect two machines. The cables can be connected into a chain.


title: Atari Lynx

text: The Lynx was cited as the "first gaming console with hardware support for zooming and distortion of sprites". Featuring a 4096 color palette and integrated math and graphics co-processors (including a blitter unit), its pseudo-3D color graphics display was said to be the key defining feature in the system's competition against Nintendo's monochromatic Game Boy. The fast pseudo-3D graphics features were made possible on a minimal hardware system by co-designer Dave Needle having "invented the technique for planar expansion/shrinking capability" and using stretched, textured, triangles instead of full polygons.


title: Atari Lynx

text: Lynx was reviewed in 1990 in "Dragon", which gave it 5 out of 5 stars. The review states that the Lynx "throws the Game Boy into the prehistoric age", and praises the built-in object scaling capabilities, the multiplayer feature of the ComLynx cable, and the strong set of launch games.


title: Atari Lynx

text: Telegames released several games in the late 1990s, including a port of "Raiden" and a platformer called "Fat Bobby" in 1997, and an action sports game called "Hyperdrome" in 1999.


title: Atari Lynx

text: On March 13, 1998, nearly three years after the Lynx's discontinuation, JTS Corporation sold all of the Atari assets to Hasbro Interactive for $5 million. On May 14, 1999, Hasbro, which held on to those properties until selling Hasbro Interactive to Infogrames in 2001, released into the public domain all rights to the Jaguar, opening up the platform for anyone to publish software on without Hasbro's interference. Internet theories say that the Lynx's rights may have been released to the public at the same time as the Jaguar, but this is clearly disputed. Nevertheless, since discontinuation, the Lynx, like the Jaguar, has continued to receive support from a grassroots community which would go on to produce many successful homebrew games such as "T-Tris" (the first Lynx game with a save-game feature), "Alpine Games", and "Zaku".


title: Atari Lynx

text: In 2008, Atari was honored at the 59th Annual Technology & Engineering Emmy Awards for pioneering the development of handheld games with the Lynx.


title: John Pankow

text: John Pankow (born April 28, 1954) is an American actor. He began his career on-stage in New York, in numerous Off-Broadway and Broadway plays including Peter Shaffer's "Amadeus", John Patrick Shanley's "Italian American Reconciliation," and Brian Friel's "Aristocrats." After a starring role in William Friedkin's "To Live and Die in L.A.," he began appearing regularly in film and on television, playing Ira Buchman for all eight seasons of "Mad About You" and later Merc Lapidus on "Episodes."


title: John Pankow

text: Pankow was born in St. Louis, Missouri, to a Catholic family of German and Irish descent, the sixth of nine siblings. His elder brother is trombonist/composer James Pankow, a founding member of the rock group Chicago. Pankow grew up in Park Ridge, Illinois, and attended Maine South High School and Northeastern Illinois University.


title: John Pankow

text: He left the university in his junior year after he attended a performance of David Mamet's "The American Buffalo" at the St. Nicholas Theater. Inspired by the play, he enrolled in the theater's two-year theatrical training program in order to concentrate solely on acting.


title: John Pankow

text: While visiting a friend in New York City, Pankow auditioned for, and won, a role in an episode of PBS' "Great Performances" entitled "Life on the Mississippi". He went on to perform in several Off-Broadway productions including "Aristocrats", "Italian American Reconciliation", and the New York Shakespeare Festival's "The Tempest, Two Gentlemen of Verona" and "Henry VIII". He subsequently made it to Broadway with "Serious Money", "The Iceman Cometh", and as Wolfgang Amadeus Mozart in "Amadeus", replacing Tim Curry in the role and subsequently replacing him for a touring production.


title: John Pankow

text: After minor supporting roles in "The Hunger" and "," he had his first starring role on-screen in "To Live and Die in L.A." as rookie Secret Service agent John Vukovich, starring opposite William Petersen and Willem Dafoe. Pankow was cast after director William Friedkin deliberately sought out young, relatively-unknown stage actors for the project. After casting fellow Chicagoan Petersen, the old friend reached out to Pankow, who brought him to Friedkin who cast him on the spot.


title: John Pankow

text: He subsequently appeared for eight seasons as Ira Buchman on the NBC sitcom "Mad About You," where he was nominated for four Screen Actors Guild Awards for Outstanding Performance by an Ensemble in a Comedy Series. He was a series regular on the Showtime/BBC series "Episodes", playing American television executive Merc Lapidus. He has since appeared in numerous films and television series.


title: John Pankow

text: Pankow has been married to actress Kristine Sutherland since 1986, and they have one daughter together. He resides in New York City.


title: Languages of Scotland

text: The languages of Scotland are the languages spoken or once spoken in Scotland. Each of the numerous languages spoken in Scotland during its recorded linguistic history falls into either the Germanic or Celtic language families. The classification of the Pictish language was once controversial, but it is now generally considered a Celtic language. Today, the main language spoken in Scotland is English, while Scots and Scottish Gaelic are minority languages. The dialect of English spoken in Scotland is referred to as Scottish English.


title: Languages of Scotland

text: The Celtic languages of Scotland can be divided into two groups: Goidelic (or Gaelic) and Brittonic (or Brythonic). Pictish is usually seen as a Brittonic language but this is not universally accepted. They are known collectively as the Insular Celtic languages.


title: Languages of Scotland

text: The Goidelic language currently spoken in Scotland is Scottish Gaelic. It is widely spoken in the Outer Hebrides, and also in parts of the Inner Hebrides and Scottish Highlands, and by some people in other areas of Scotland. It was formerly spoken over a far wider area than today, even in the recent past, as evidenced by placenames. Galwegian Gaelic is the extinct dialect of Scottish Gaelic formerly spoken in southwest Scotland. It was spoken by the independent kings of Galloway in their time, and by the people of Galloway and Carrick until the early modern period. It was also once spoken in Annandale and Strathnith.


title: Languages of Scotland

text: Scottish Gaelic, along with modern Manx and Irish, is descended from Middle Irish, a derivative of Old Irish, which is descended in turn from Primitive Irish, the oldest known form of the Goidelic languages. Primitive Irish is known only from fragments, mostly personal names, inscribed on stone in the Ogham alphabet in Ireland and western Britain up to about the 6th century AD.


title: Languages of Scotland

text: Goidelic languages were once the most prominent by far among the Scottish population, but are now mainly restricted to the West. The Beurla-reagaird is a Gaelic-based cant of the Scottish travelling community related to the Shelta of Ireland.


title: Languages of Scotland

text: The majority of the vocabulary of modern Scottish Gaelic is native Celtic. There are a large number of borrowings from Latin, ("muinntir", "Didòmhnaich"), ancient Greek, especially in the religious domain ("eaglais", "Bìoball" from ἐκκλησία "ekklesia" and βίβλος "biblos"), Norse ("eilean", "sgeir"), Hebrew ("Sàbaid", "Aba"), French ("seòmar") and Lowland Scots ("aidh", "bramar").


title: Languages of Scotland

text: In common with other Indo-European languages, the neologisms which are coined for modern concepts are typically based on Greek or Latin, although written in Gaelic orthography; "television", for instance, becomes "telebhisean" and "computer" becomes "coimpiùtar". Although native speakers frequently use an English word for which there is a perfectly good Gaelic equivalent, they will, without thinking, simply adopt the English word and use it, applying the rules of Gaelic grammar, as the situation requires. With verbs, for instance, they will simply add the verbal suffix ("-eadh", or, in Lewis, -"igeadh", as in, ""Tha mi a' watcheadh" (Lewis, ""watchigeadh"") "an telly"" (I am watching the television), rather than ""Tha mi a' coimhead air an telebhisean"". This tendency was remarked upon by the minister who compiled the account covering the parish of Stornoway in the "New Statistical Account of Scotland", published over 170 years ago. It has even gone so far as the verb "Backdatigeadh". However, as Gaelic medium education grows in popularity, a newer generation of literate Gaels is becoming more familiar with modern Gaelic vocabulary.


title: Languages of Scotland

text: The influence of Scottish Gaelic can be seen particularly in surnames (notably Mac- names, where the "mac" means "Son of...") and toponymy. The surname influence is not restricted to Mac- names: several colours give rise to common Scottish surnames: "bàn" (Bain – white), "ruadh" (Roy – red), "dubh" (Dow – black), "donn" (Dunn – brown), "buidhe" (Bowie – yellow), and Gille- (meaning lad or servant) gives rise to names such as Gilmour and Gillies. Common place name elements from Gaelic in Scotland include "baile" (Bal-, a town) e.g. Balerno, "cille" (Kil-, an old church) e.g. Kilmarnock, "inbhir" (Inver-, Inner-, meaning a confluence) e.g. Inverness, Innerleithen, "ceann" (Kin-, meaning a head or top of something) e.g. Kintyre, Kinross, and "dun" (meaning a fort) e.g. Dundee and Dunfermline.


title: Languages of Scotland

text: None of the Brittonic languages of Scotland survive to the modern day, though they have been reconstructed to a degree.


title: Languages of Scotland

text: The ancestral Common Brittonic language was probably spoken in southern Scotland in Roman times and earlier. It was certainly spoken there by the early medieval era, and Brittonic-speaking kingdoms such as Strathclyde, Rheged, and Gododdin, part of the Hen Ogledd ("Old North"), emerged in what is now Scotland. Eventually Brittonic evolved into a variety known as Cumbric, which survived in southwestern Scotland until around the 11th century.


title: Languages of Scotland

text: The main legacy of these languages has been Scotland's toponymy, e.g. names such as Aberdeen, Tranent and Ochiltree.


title: Languages of Scotland

text: There are also many Brittonic influences on Scottish Gaelic. Scottish Gaelic contains a number of apparently P-Celtic loanwords, but as Q-Celtic has a far greater overlap with P-Celtic than with English in terms of vocabulary, it is not always possible to disentangle P- and Q-Celtic words. However some common words, such as "monadh" ≡ Welsh "mynydd", Cumbric *"monidh", are particularly evident. Often the Brittonic influence on Scots Gaelic is indicated by comparing with the Irish Gaelic usage which is not likely to have been influenced so much by Brittonic. In particular, the word "srath" (anglicised as "Strath") is a native Goidelic word, but its usage appears to have been modified by its Brittonic cognate "ystrad", whose meaning is slightly different.


title: Languages of Scotland

text: The Pictish language is generally understood to be an Insular Celtic language. At its height, it may have been spoken from Shetland down to Fife, but it was pushed back as Scots and Anglo-Saxons invaded Northern Britain, each with their own language. Pritennic may have been a precursor of Pictish.


title: Languages of Scotland

text: Two West Germanic languages in the Anglic group are spoken in Scotland today; Scots, and Scottish English, a dialect of the English language. The Norn language, a North Germanic language, is now extinct.


title: Languages of Scotland

text: The Northumbrian dialect of the Old English language was spoken in the Anglian Kingdom of Northumbria from the Humber estuary to the Firth of Forth. The Viking invasions of the 9th century forced the dialect to split in two and in the north it began to evolve into Scots.