text:
Information retrieval

Information retrieval (IR) in computing and information science is the task of identifying and retrieving information system resources that are relevant to an information need. The information need can be specified in the form of a search query. In the case of document retrieval, queries can be based on full-text or other content-based indexing. Information retrieval is the science of searching for information in a document, searching for documents themselves, and also searching for the metadata that describes data, and for databases of texts, images or sounds.

Automated information retrieval systems are used to reduce what has been called information overload. An IR system is a software system that provides access to books, journals and other documents; it also stores and manages those documents. Web search engines are the most visible IR applications.

Overview
An information retrieval process begins when a user enters a query into the system. Queries are formal statements of information needs, for example search strings in web search engines. In information retrieval, a query does not uniquely identify a single object in the collection. Instead, several objects may match the query, perhaps with different degrees of relevance.

An object is an entity that is represented by information in a content collection or database. User queries are matched against the database information. However, as opposed to classical SQL queries of a database, in information retrieval the results returned may or may not match the query, so results are typically ranked. This ranking of results is a key difference of information retrieval searching compared to database searching.

Depending on the application the data objects may be, for example, text documents, images, audio, mind maps or videos. Often the documents themselves are not kept or stored directly in the IR system, but are instead represented in the system by document surrogates or metadata.

Most IR systems compute a numeric score on how well each object in the database matches the query, and rank the objects according to this value. The top ranking objects are then shown to the user. The process may then be iterated if the user wishes to refine the query.

History
The idea of using computers to search for relevant pieces of information was popularized in the article As We May Think by Vannevar Bush in 1945. It would appear that Bush was inspired by patents for a 'statistical machine' – filed by Emanuel Goldberg in the 1920s and 1930s – that searched for documents stored on film. The first description of a computer searching for information was described by Holmstrom in 1948, detailing an early mention of the Univac computer. Automated information retrieval systems were introduced in the 1950s: one even featured in the 1957 romantic comedy, Desk Set. In the 1960s, the first large information retrieval research group was formed by Gerard Salton at Cornell. By the 1970s several different retrieval techniques had been shown to perform well on small text corpora such as the Cranfield collection (several thousand documents). Large-scale retrieval systems, such as the Lockheed Dialog system, came into use early in the 1970s.

In 1992, the US Department of Defense along with the National Institute of Standards and Technology (NIST), cosponsored the Text Retrieval Conference (TREC) as part of the TIPSTER text program. The aim of this was to look into the information retrieval community by supplying the infrastructure that was needed for evaluation of text retrieval methodologies on a very large text collection. This catalyzed research on methods that scale to huge corpora. The introduction of web search engines has boosted the need for very large scale retrieval systems even further.

Applications
Areas where information retrieval techniques are employed include (the entries are in alphabetical order within each category):

General applications

 * Digital libraries
 * Information filtering
 * Recommender systems
 * Media search
 * Blog search
 * Image retrieval
 * 3D retrieval
 * Music retrieval
 * News search
 * Speech retrieval
 * Video retrieval
 * Search engines
 * Site search
 * Desktop search
 * Enterprise search
 * Federated search
 * Mobile search
 * Social search
 * Web search

Domain-specific applications

 * Expert search finding
 * Genomic information retrieval
 * Geographic information retrieval
 * Information retrieval for chemical structures
 * Information retrieval in software engineering
 * Legal information retrieval
 * Vertical search

Other retrieval methods
Methods/Techniques in which information retrieval techniques are employed include:
 * Adversarial information retrieval
 * Automatic summarization
 * Multi-document summarization
 * Compound term processing
 * Cross-lingual retrieval
 * Document classification
 * Spam filtering
 * Question answering

Model types
In order to effectively retrieve relevant documents by IR strategies, the documents are typically transformed into a suitable representation. Each retrieval strategy incorporates a specific model for its document representation purposes. The picture on the right illustrates the relationship of some common models. In the picture, the models are categorized according to two dimensions: the mathematical basis and the properties of the model.

First dimension: mathematical basis

 * Set-theoretic models represent documents as sets of words or phrases. Similarities are usually derived from set-theoretic operations on those sets. Common models are:
 * Standard Boolean model
 * Extended Boolean model
 * Fuzzy retrieval
 * Algebraic models represent documents and queries usually as vectors, matrices, or tuples. The similarity of the query vector and document vector is represented as a scalar value.
 * Vector space model
 * Generalized vector space model
 * (Enhanced) Topic-based Vector Space Model
 * Extended Boolean model
 * Latent semantic indexing a.k.a. latent semantic analysis
 * Probabilistic models treat the process of document retrieval as a probabilistic inference. Similarities are computed as probabilities that a document is relevant for a given query. Probabilistic theorems like Bayes' theorem are often used in these models.
 * Binary Independence Model
 * Probabilistic relevance model on which is based the okapi (BM25) relevance function
 * Uncertain inference
 * Language models
 * Divergence-from-randomness model
 * Latent Dirichlet allocation
 * Feature-based retrieval models view documents as vectors of values of feature functions (or just features) and seek the best way to combine these features into a single relevance score, typically by learning to rank methods. Feature functions are arbitrary functions of document and query, and as such can easily incorporate almost any other retrieval model as just another feature.

Second dimension: properties of the model

 * Models without term-interdependencies treat different terms/words as independent. This fact is usually represented in vector space models by the orthogonality assumption of term vectors or in probabilistic models by an independency assumption for term variables.
 * Models with immanent term interdependencies allow a representation of interdependencies between terms. However the degree of the interdependency between two terms is defined by the model itself. It is usually directly or indirectly derived (e.g. by dimensional reduction) from the co-occurrence of those terms in the whole set of documents.
 * Models with transcendent term interdependencies allow a representation of interdependencies between terms, but they do not allege how the interdependency between two terms is defined. They rely on an external source for the degree of interdependency between two terms. (For example, a human or sophisticated algorithms.)

Performance and correctness measures
The evaluation of an information retrieval system' is the process of assessing how well a system meets the information needs of its users. In general, measurement considers a collection of documents to be searched and a search query. Traditional evaluation metrics, designed for Boolean retrieval or top-k retrieval, include precision and recall. All measures assume a ground truth notion of relevance: every document is known to be either relevant or non-relevant to a particular query. In practice, queries may be ill-posed and there may be different shades of relevance.

Timeline

 * Before the 1900s
 * 1801: Joseph Marie Jacquard invents the Jacquard loom, the first machine to use punched cards to control a sequence of operations.
 * 1880s: Herman Hollerith invents an electro-mechanical data tabulator using punch cards as a machine readable medium.
 * 1890 Hollerith cards, keypunches and tabulators used to process the 1890 US Census data.
 * 1920s-1930s
 * Emanuel Goldberg submits patents for his "Statistical Machine", a document search engine that used photoelectric cells and pattern recognition to search the metadata on rolls of microfilmed documents.
 * 1940s–1950s
 * late 1940s: The US military confronted problems of indexing and retrieval of wartime scientific research documents captured from Germans.
 * 1945: Vannevar Bush's As We May Think appeared in Atlantic Monthly.
 * 1947: Hans Peter Luhn (research engineer at IBM since 1941) began work on a mechanized punch card-based system for searching chemical compounds.
 * 1950s: Growing concern in the US for a "science gap" with the USSR motivated, encouraged funding and provided a backdrop for mechanized literature searching systems (Allen Kent et al.) and the invention of the citation index by Eugene Garfield.
 * 1950: The term "information retrieval" was coined by Calvin Mooers.
 * 1951: Philip Bagley conducted the earliest experiment in computerized document retrieval in a master thesis at MIT.
 * 1955: Allen Kent joined Case Western Reserve University, and eventually became associate director of the Center for Documentation and Communications Research. That same year, Kent and colleagues published a paper in American Documentation describing the precision and recall measures as well as detailing a proposed "framework" for evaluating an IR system which included statistical sampling methods for determining the number of relevant documents not retrieved.
 * 1958: International Conference on Scientific Information Washington DC included consideration of IR systems as a solution to problems identified. See: Proceedings of the International Conference on Scientific Information, 1958 (National Academy of Sciences, Washington, DC, 1959)
 * 1959: Hans Peter Luhn published "Auto-encoding of documents for information retrieval".
 * 1960s:
 * early 1960s: Gerard Salton began work on IR at Harvard, later moved to Cornell.
 * 1960: Melvin Earl Maron and John Lary Kuhns published "On relevance, probabilistic indexing, and information retrieval" in the Journal of the ACM 7(3):216–244, July 1960.
 * 1962:
 * Cyril W. Cleverdon published early findings of the Cranfield studies, developing a model for IR system evaluation. See: Cyril W. Cleverdon, "Report on the Testing and Analysis of an Investigation into the Comparative Efficiency of Indexing Systems". Cranfield Collection of Aeronautics, Cranfield, England, 1962.
 * Kent published Information Analysis and Retrieval.
 * 1963:
 * Weinberg report "Science, Government and Information" gave a full articulation of the idea of a "crisis of scientific information". The report was named after Dr. Alvin Weinberg.
 * Joseph Becker and Robert M. Hayes published text on information retrieval. Becker, Joseph; Hayes, Robert Mayo. Information storage and retrieval: tools, elements, theories. New York, Wiley (1963).
 * 1964:
 * Karen Spärck Jones finished her thesis at Cambridge, Synonymy and Semantic Classification, and continued work on computational linguistics as it applies to IR.
 * The National Bureau of Standards sponsored a symposium titled "Statistical Association Methods for Mechanized Documentation". Several highly significant papers, including G. Salton's first published reference (we believe) to the SMART system.
 * mid-1960s:
 * National Library of Medicine developed MEDLARS Medical Literature Analysis and Retrieval System, the first major machine-readable database and batch-retrieval system.
 * Project Intrex at MIT.
 * 1965: J. C. R. Licklider published Libraries of the Future.
 * 1966: Don Swanson was involved in studies at University of Chicago on Requirements for Future Catalogs.
 * late 1960s: F. Wilfrid Lancaster completed evaluation studies of the MEDLARS system and published the first edition of his text on information retrieval.
 * 1968:
 * Gerard Salton published Automatic Information Organization and Retrieval.
 * John W. Sammon, Jr.'s RADC Tech report "Some Mathematics of Information Storage and Retrieval..." outlined the vector model.
 * 1969: Sammon's "A nonlinear mapping for data structure analysis " (IEEE Transactions on Computers) was the first proposal for visualization interface to an IR system.
 * 1970s
 * early 1970s:
 * First online systems—NLM's AIM-TWX, MEDLINE; Lockheed's Dialog; SDC's ORBIT.
 * Theodor Nelson promoting concept of hypertext, published Computer Lib/Dream Machines.
 * 1971: Nicholas Jardine and Cornelis J. van Rijsbergen published "The use of hierarchic clustering in information retrieval", which articulated the "cluster hypothesis".
 * 1975: Three highly influential publications by Salton fully articulated his vector processing framework and term discrimination model:
 * A Theory of Indexing (Society for Industrial and Applied Mathematics)
 * A Theory of Term Importance in Automatic Text Analysis (JASIS v. 26)
 * A Vector Space Model for Automatic Indexing (CACM 18:11)
 * 1978: The First ACM SIGIR conference.
 * 1979: C. J. van Rijsbergen published Information Retrieval (Butterworths). Heavy emphasis on probabilistic models.
 * 1979: Tamas Doszkocs implemented the CITE natural language user interface for MEDLINE at the National Library of Medicine. The CITE system supported free form query input, ranked output and relevance feedback.
 * 1980s
 * 1980: First international ACM SIGIR conference, joint with British Computer Society IR group in Cambridge.
 * 1982: Nicholas J. Belkin, Robert N. Oddy, and Helen M. Brooks proposed the ASK (Anomalous State of Knowledge) viewpoint for information retrieval. This was an important concept, though their automated analysis tool proved ultimately disappointing.
 * 1983: Salton (and Michael J. McGill) published Introduction to Modern Information Retrieval (McGraw-Hill), with heavy emphasis on vector models.
 * 1985: David Blair and Bill Maron publish: An Evaluation of Retrieval Effectiveness for a Full-Text Document-Retrieval System
 * mid-1980s: Efforts to develop end-user versions of commercial IR systems.
 * 1985–1993: Key papers on and experimental systems for visualization interfaces.
 * Work by Donald B. Crouch, Robert R. Korfhage, Matthew Chalmers, Anselm Spoerri and others.
 * 1989: First World Wide Web proposals by Tim Berners-Lee at CERN.
 * 1990s
 * 1992: First TREC conference.
 * 1997: Publication of Korfhage's Information Storage and Retrieval with emphasis on visualization and multi-reference point systems.
 * 1999: Publication of Ricardo Baeza-Yates and Berthier Ribeiro-Neto's Modern Information Retrieval by Addison Wesley, the first book that attempts to cover all IR.
 * late 1990s: Web search engines implementation of many features formerly found only in experimental IR systems. Search engines become the most common and maybe best instantiation of IR models.

Major conferences

 * SIGIR: Conference on Research and Development in Information Retrieval
 * ECIR: European Conference on Information Retrieval
 * CIKM: Conference on Information and Knowledge Management
 * WWW: International World Wide Web Conference
 * WSDM: Conference on Web Search and Data Mining
 * ICTIR: International Conference on Theory of Information Retrieval

Awards in the field

 * Tony Kent Strix award
 * Gerard Salton Award
 * Karen Spärck Jones Award

title: Information retrieval


text:
List of Italian-language poets

List of poets who wrote in Italian (or Italian dialects).

A

 * Antonio Abati
 * Luigi Alamanni
 * Aleardo Aleardi
 * Dante Alighieri
 * Cecco Angiolieri
 * Gabriele D'Annunzio
 * Ludovico Ariosto
 * Francis of Assisi

B

 * Nanni Balestrini
 * Dario Bellezza
 * Giuseppe Gioacchino Belli (Roman dialect)
 * Attilio Bertolucci
 * Carlo Betocchi
 * Alberta Bigagli
 * Giovanni Boccaccio
 * Maria Alinda Bonacci Brunamonti
 * Carlo Bordini
 * Franco Buffoni
 * Michelangelo Buonarroti
 * Helle Busacca
 * Ignazio Buttitta (Sicilian language)
 * Paolo Buzzi

C

 * Dino Campana
 * Giorgio Caproni
 * Giosuè Carducci
 * Guido Cavalcanti
 * Roberto Carifi
 * Gabriello Chiabrera
 * Compagnetto da Prato

D

 * Cielo d'Alcamo
 * Antonio De Santis (Italian and Larinese dialect)
 * Milo de Angelis
 * Fabrizio De André
 * Eugenio De Signoribus

E

 * Muzi Epifani

F

 * Alba Florio
 * Franco Fortini
 * Ugo Foscolo
 * Erminia Fuà Fusinato

G

 * Alfonso Gatto
 * Giuseppe Giusti
 * Corrado Govoni
 * Guido Gozzano
 * Lionello Grifo
 * Giovanni Battista Guarini
 * Amalia Guglielminetti
 * Margherita Guidacci
 * Guido Guinizzelli

I

 * Gianni Ianuale

L

 * Giacomo da Lentini
 * Jacopo da Leona
 * Giacomo Leopardi
 * Mario Luzi
 * Menotti Lerro
 * Franco Loi

N

 * Giampiero Neri

M

 * Lorenzo il Magnifico (sovereign of Florence)
 * Valerio Magrelli
 * Alessandro Manzoni
 * Filippo Tommaso Marinetti
 * Giambattista Marino
 * Alda Merini
 * Metastasio (Pietro Trapassi)
 * Grazyna Miller
 * Eugenio Montale (Nobel Prize in literature, 1975)
 * Vincenzo Monti
 * Marino Moretti
 * Maurizio Moro

P

 * Elio Pagliarani
 * Aldo Palazzeschi
 * Giuseppe Parini
 * Giovanni Pascoli
 * Pier Paolo Pasolini
 * Nicoletta Pasquale
 * Cesare Pavese
 * Francesco Petrarca (Petrarch)
 * Assunta Pieralli
 * Poliziano (Angelo Ambrogini)
 * Lorenzo Da Ponte
 * Antonio Porta (author)
 * Carlo Porta
 * Antonia Pozzi
 * Ezra Pound (Italian, English, and others)
 * Luigi Pulci (1432–84)

Q

 * Salvatore Quasimodo

R

 * Giovanni Raboni
 * Clemente Rebora
 * Amelia Rosselli
 * Gabriele Rossetti
 * Tiziano Rossi

S

 * Umberto Saba
 * Giulio Salvadori
 * Edoardo Sanguineti
 * Leonardo Sinisgalli
 * Maria Luisa Spaziani

T

 * Rosa Taddei
 * Torquato Tasso
 * Laura Terracina
 * Giovanni Testori
 * Jacopone da Todi
 * Trilussa (Carlo Alberto Salustri) (Roman dialect)
 * Theodor Daubler

U

 * Giuseppe Ungaretti

V

 * Diego Valeri (poet)
 * Emilio Villa

Z

 * Andrea Zanzotto

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: List of Italian-language poets


text:
International Criminal Tribunal for the former Yugoslavia

The International Criminal Tribunal for the former Yugoslavia (ICTY) was a body of the United Nations that was established to prosecute the war crimes that had been committed during the Yugoslav Wars and to try their perpetrators. The tribunal was an ad hoc court located in The Hague, Netherlands.

It was established by Resolution 827 of the United Nations Security Council, which was passed on 25 May 1993. It had jurisdiction over four clusters of crimes committed on the territory of the former Yugoslavia since 1991: grave breaches of the Geneva Conventions, violations of the laws or customs of war, genocide, and crimes against humanity. The maximum sentence that it could impose was life imprisonment. Various countries signed agreements with the United Nations to carry out custodial sentences.

A total of 161 persons were indicted; the final indictments were issued in December 2004, the last of which were confirmed and unsealed in the spring of 2005. The final fugitive, Goran Hadžić, was arrested on 20 July 2011. The final judgment was issued on 29 November 2017 and the institution formally ceased to exist on 31 December 2017.

Residual functions of the ICTY, including the oversight of sentences and consideration of any appeal proceedings initiated since 1 July 2013, are under the jurisdiction of a successor body, the International Residual Mechanism for Criminal Tribunals (IRMCT).

Creation
United Nations Security Council Resolution 808 of 22 February 1993 decided that an "international tribunal shall be established for the prosecution of persons responsible for serious violations of international humanitarian law committed in the territory of the former Yugoslavia since 1991", and called on the Secretary-General to "submit for consideration by the Council ... a report on all aspects of this matter, including specific proposals and where appropriate options ... taking into account suggestions put forward in this regard by Member States".

The Court was originally proposed by German Foreign Minister Klaus Kinkel.

Resolution 827 of 25 May 1993 approved the S/25704 report of the Secretary-General and adopted the Statute of the International Tribunal annexed to it, formally creating the ICTY. It was to have jurisdiction over four clusters of crimes committed on the territory of the former SFR Yugoslavia since 1991:

 * 1) Grave breaches of the Geneva Conventions
 * 2) Violations of the laws or customs of war
 * 3) Genocide
 * 4) Crime against humanity.

The maximum sentence the ICTY could impose for these crimes was life imprisonment.

Implementation
In 1993 the internal infrastructure of the ICTY was built. 17 states had signed an agreement with the ICTY to carry out custodial sentences.

1993–1994: In the first year of its existence, the Tribunal laid the foundations for its existence as a judicial organ. It established the legal framework for its operations by adopting the rules of procedure and evidence, as well as its rules of detention and directive for the assignment of defence counsel. Together, these rules established a legal aid system for the Tribunal. As the ICTY was a part of the United Nations and was the first international court for criminal justice, the development of a juridical infrastructure was considered quite a challenge. However, after the first year, the first ICTY judges had drafted and adopted all the rules for court proceedings.

1994–1995: The ICTY established its offices within the Aegon Insurance Building in The Hague (which was, at the time, still partially in use by Aegon) and detention facilities in Scheveningen in The Hague (the Netherlands). The ICTY hired many staff members and by July 1994, the Office of the Prosecutor had sufficient staff to begin field investigations. By November 1994, the first indictments were presented to the Court and confirmed, and in 1995, the staff numbered over 200 persons from all over the world.

Operation
In 1994 the first indictment was issued against the Bosnian-Serb concentration camp commander Dragan Nikolić. This was followed on 13 February 1995 by two indictments comprising 21 individuals which were issued against a group of 21 Bosnian-Serbs charged with committing atrocities against Muslim and Croat civilian prisoners. While the war in the former Yugoslavia was still raging, the ICTY prosecutors showed that an international court was viable. However, no accused was arrested.

The court confirmed eight indictments against 46 individuals and issued arrest warrants. Bosnian Serb indictee Duško Tadić became the subject of the Tribunal's first trial. Tadić was arrested by German police in Munich in 1994 for his alleged actions in the Prijedor region in Bosnia-Herzegovina (especially his actions in the Omarska, Trnopolje and Keraterm detention camps). He made his first appearance before the ICTY Trial Chamber on 26 April 1995, and pleaded not guilty to all of the charges in the indictment.

1995–1996: Between June 1995 and June 1996, 10 public indictments had been confirmed against a total of 33 individuals. Six of the newly indicted persons were transferred in the Tribunal's detention unit. In addition to Duško Tadic, by June 1996 the tribunal had Tihomir Blaškić, Dražen Erdemović, Zejnil Delalić, Zdravko Mucić, Esad Landžo and Hazim Delić in custody. Erdemović became the first person to enter a guilty plea before the tribunal's court. Between 1995 and 1996, the ICTY dealt with miscellaneous cases involving several detainees, which never reached the trial stage.

Indictees and accomplishments
The Tribunal indicted 161 individuals between 1997 and 2004 and completed proceedings with them as follows:
 * 111 had trials completed by the ICTY:
 * 21 were acquitted by the ICTY:
 * 18 acquittals have stood;
 * 1 was originally acquitted by the ICTY, but convicted on appeal by the IRMCT of one count (and sentenced to time served)
 * 2 were originally acquitted by the ICTY, but following a successful appeal by the prosecution the acquittals were overturned and a retrial is being conducted by the IRMCT; and
 * 90 were convicted and sentenced by the ICTY:
 * 87 were transferred to 14 different states where they served their prison sentences, had sentences that amounted to time spent in detention during trial, or died after conviction:
 * 20 remain imprisoned;
 * 58 completed their sentences;
 * 9 died while completing their sentences or after conviction awaiting transfer
 * 2 were convicted and sentenced, and remain in IRMCT detention awaiting transfer; and
 * 1 was convicted and sentenced, but has filed an appeal to the IRMCT that is being considered
 * 13 had their cases transferred to courts in:
 * Bosnia and Herzegovina (10);
 * Croatia (2); and
 * Serbia (1)
 * 37 had their cases terminated prior to trial completion, because
 * the indictments were withdrawn (20); or
 * the indictees died before or after transfer to the Tribunal (17).

The indictees ranged from common soldiers to generals and police commanders all the way to prime ministers. Slobodan Milošević was the first sitting head of state indicted for war crimes. Other "high level" indictees included Milan Babić, former President of the Republika Srpska Krajina; Ramush Haradinaj, former Prime Minister of Kosovo; Radovan Karadžić, former President of the Republika Srpska; Ratko Mladić, former Commander of the Bosnian Serb Army; and Ante Gotovina (acquitted), former General of the Croatian Army.

The very first hearing at the ICTY was a referral request in the Tadić case on 8 November 1994. Croat Serb General and former President of the Republic of Serbian Krajina Goran Hadžić was the last fugitive wanted by the Tribunal to be arrested on 20 July 2011.

An additional 23 individuals have been the subject of contempt proceedings.

In 2004, the ICTY published a list of five accomplishments "in justice and law":

 * 1) "Spearheading the shift from impunity to accountability", pointing out that, until very recently, it was the only court judging crimes committed as part of the Yugoslav conflict, since prosecutors in the former Yugoslavia were, as a rule, reluctant to prosecute such crimes;
 * 2) "Establishing the facts", highlighting the extensive evidence-gathering and lengthy findings of fact that Tribunal judgments produced;
 * 3) "Bringing justice to thousands of victims and giving them a voice", pointing out the large number of witnesses that had been brought before the Tribunal;
 * 4) "The accomplishments in international law", describing the fleshing out of several international criminal law concepts which had not been ruled on since the Nuremberg Trials;
 * 5) "Strengthening the Rule of Law", referring to the Tribunal's role in promoting the use of international standards in war crimes prosecutions by former Yugoslav republics.

Closure
The United Nations Security Council passed resolutions 1503 in August 2003 and 1534 in March 2004, which both called for the completion of all cases at both the ICTY and its sister tribunal, the International Criminal Tribunal for Rwanda (ICTR) by 2010.

In December 2010, the Security Council adopted Resolution 1966, which established the International Residual Mechanism for Criminal Tribunals (IRMCT), a body intended to gradually assume residual functions from both the ICTY and the ICTR as they wound down their mandate. Resolution 1966 called upon the Tribunal to finish its work by 31 December 2014 to prepare for its closure and the transfer of its responsibilities.

In a Completion Strategy Report issued in May 2011, the ICTY indicated that it aimed to complete all trials by the end of 2012 and complete all appeals by 2015, with the exception of Radovan Karadžić whose trial was expected to end in 2014 and Ratko Mladić and Goran Hadžić, who were still at large at that time and were not arrested until later that year.

The IRMCT's ICTY branch began functioning on 1 July 2013. Per the Transitional Arrangements adopted by the UN Security Council, the ICTY was to conduct and complete all outstanding first-instance trials, including those of Karadžić, Mladić and Hadžić. The ICTY would also conduct and complete all appeal proceedings for which the notice of appeal against the judgement or sentence was filed before 1 July 2013. The IRMCT will handle any appeals for which notice is filed after that date.

The final ICTY trial to be completed in the first instance was that of Ratko Mladić, who was convicted on 22 November 2017. The final case to be considered by the ICTY was an appeal proceeding encompassing six individuals, whose sentences were upheld on 29 November 2017.

Organization
While operating, the Tribunal employed around 900 staff. Its organisational components were Chambers, Registry and the Office of the Prosecutor (OTP).

Prosecutors
The Prosecutor was responsible for investigating crimes, gathering evidence and prosecutions and was head of the Office of the Prosecutor (OTP). The Prosecutor was appointed by the UN Security Council upon nomination by the UN Secretary-General.

The last prosecutor was Serge Brammertz. Previous Prosecutors have been Ramón Escovar Salom of Venezuela (1993–1994), however, he never took up that office, Richard Goldstone of South Africa (1994–1996), Louise Arbour of Canada (1996–1999), and Carla Del Ponte of Switzerland (1999–2007). Richard Goldstone, Louise Arbour and Carla Del Ponte also simultaneously served as the Prosecutor of the International Criminal Tribunal for Rwanda until 2003. Graham Blewitt of Australia served as the Deputy Prosecutor from 1994 until 2004. David Tolbert, the President of the International Center for Transitional Justice, was also appointed Deputy Prosecutor of the ICTY in 2004.

Chambers
Chambers encompassed the judges and their aides. The Tribunal operated three Trial Chambers and one Appeals Chamber. The President of the Tribunal was also the presiding Judge of the Appeals Chamber.

Judges
At the time of the court's dissolution, there were seven permanent judges and one ad hoc judge who served on the Tribunal. A total of 86 judges have been appointed to the Tribunal from 52 United Nations member states. Of those judges, 51 were permanent judges, 36 were ad litem judges, and one was an ad hoc judge. Note that one judge served as both a permanent and ad litem judge, and another served as both a permanent and ad hoc judge.

UN member and observer states could each submit up to two nominees of different nationalities to the UN Secretary-General. The UN Secretary-General submitted this list to the UN Security Council which selected from 28 to 42 nominees and submitted these nominees to the UN General Assembly. The UN General Assembly then elected 14 judges from that list. Judges served for four years and were eligible for re-election. The UN Secretary-General appointed replacements in case of vacancy for the remainder of the term of office concerned.

On 21 October 2015, Judge Carmel Agius of Malta was elected President of the ICTY and Liu Daqun of China was elected Vice-President; they assumed their positions on 17 November 2015. His predecessors were Antonio Cassese of Italy (1993–1997), Gabrielle Kirk McDonald of the United States (1997–1999), Claude Jorda of France (1999–2002), Theodor Meron of the United States (2002–2005), Fausto Pocar of Italy (2005–2008), Patrick Robinson of Jamaica (2008–2011), and Theodor Meron (2011–2015).

Registry
The Registry was responsible for handling the administration of the Tribunal; activities included keeping court records, translating court documents, transporting and accommodating those who appear to testify, operating the Public Information Section, and such general duties as payroll administration, personnel management and procurement. It was also responsible for the Detention Unit for indictees being held during their trial and the Legal Aid program for indictees who cannot pay for their own defence. It was headed by the Registrar, a position occupied over the years by Theo van Boven of the Netherlands (February 1994 to December 1994), Dorothée de Sampayo Garrido-Nijgh of the Netherlands (1995–2000), Hans Holthuis of the Netherlands (2001–2009), and John Hocking of Australia (May 2009 to December 2017).

Detention facilities
Those defendants on trial and those who were denied a provisional release were detained at the United Nations Detention Unit on the premises of the Penitentiary Institution Haaglanden, location Scheveningen in Belgisch Park, a suburb of The Hague, located some 3 km by road from the courthouse. The indicted were housed in private cells which had a toilet, shower, radio, satellite TV, personal computer (without internet access) and other luxuries. They were allowed to phone family and friends daily and could have conjugal visits. There was also a library, a gym and various rooms used for religious observances. The inmates were allowed to cook for themselves. All of the inmates mixed freely and were not segregated on the basis of nationality. As the cells were more akin to a university residence instead of a jail, some had derisively referred to the ICT as the "Hague Hilton". The reason for this luxury relative to other prisons is that the first president of the court wanted to emphasise that the indictees were innocent until proven guilty.

Controversies
Criticisms of the court include:
 * Carla Del Ponte, the chief prosecutor of the tribunal, said in 2021 that the US did not want the ICTY to scrutinise war crimes committed by the Kosovo Liberation Army. According to her, Madeleine Albright, the United States secretary of state at the time, told her to slow down the investigation of Ramush Haradinaj.
 * Michael Mandel, William Blum and others accused the court of having a pro-NATO bias due to its refusal to prosecute NATO officials and politicians for war crimes.
 * On 6 December 2006, the Tribunal at The Hague approved the use of force-feeding of Serbian politician Vojislav Šešelj. They decided it was not "torture, inhuman or degrading treatment if there is a medical necessity to do so... and if the manner in which the detainee is force-fed is not inhuman or degrading".
 * Reducing the indictment charges after the arrest of Ratko Mladić, Croatian officials publicly condemned chief prosecutor Serge Brammertz for his announcement that the former Bosnian Serb General would be tried solely for crimes allegedly committed in Bosnia, not in Croatia.
 * Critics have questioned whether the Tribunal exacerbates tensions rather than promotes reconciliation, as is claimed by Tribunal supporters. Polls show a generally negative reaction to the Tribunal among both Serbs and Croats. A majority of Serbs and Croats have expressed doubts regarding the ICTY's integrity and question the tenability of its legal procedures.
 * 68% of indictees have been Serbs (or Montenegrins), to the extent that a sizeable portion of the Bosnian Serb and Croatian Serb political and military leaderships have been indicted. Many have seen this as reflecting bias, while the Tribunal's defenders have seen this as indicative of the actual proportion of crimes committed. However, Marko Hoare claimed that, aside from Milošević, only Momčilo Perišić (Chief of the General Staff of the Yugoslav Army), who was acquitted, has been indicted from the Serbian military or political top when it comes to wars in Croatia and Bosnia.
 * According to Hoare, a former employee at the ICTY, an investigative team worked on indictments of senior members of the "joint criminal enterprise", including not only Milošević but also Veljko Kadijević, Blagoje Adžić, Borisav Jović, Branko Kostić, Momir Bulatović and others. However, Hoare claims that, due to Carla del Ponte's intervention, these drafts were rejected, and the indictment limited to Milošević alone.
 * There have been allegations of censorship: in July 2011, the Appeals Chamber of ICTY confirmed the judgment of the Trial Chamber which found journalist and former Tribunal's OTP spokesperson Florence Hartmann guilty of contempt of court and fined her €7,000. She disclosed documents of FR Yugoslavia's Supreme Defense Council meetings and criticized the Tribunal for granting confidentiality of some information in them to protect Serbia's 'vital national interests' during Bosnia's lawsuit against the country for genocide in front of the International Court of Justice. Hartmann argued that Serbia was freed of the charge of genocide because ICTY redacted certain information in the Council meetings. Since these documents have in the meantime been made public by the ICTY itself, a group of organizations and individuals, who supported her, said that the Tribunal in this appellate proceedings "imposed a form of censorship aimed to protect the international judges from any form of criticism". (France refused to extradite Hartmann to serve the prison sentence issued against her by the ICTY after she refused to pay the €7,000 fine.)
 * Klaus-Peter Willsch compared the Ante Gotovina verdict, in which the late Croatian president Franjo Tuđman was posthumously found to have been participating in a Joint Criminal Enterprise, with the 897 Cadaver Synod trial in Rome, when Pope Stephen VI had the corpse of Pope Formosus exhumed, put on trial and posthumously convicted.
 * Some sentences have been considered too mild, even within the Tribunal, complained at small sentences of convicted war criminals in comparison with their crimes. In 2010, Veselin Šljivančanin's sentence for his involvement in the Vukovar massacre was cut from 17 to 10 years, which caused outrage in Croatia. Upon hearing that news, Vesna Bosanac, who had been in charge of the Vukovar hospital during the fall of the city, said that the "ICTY is dead" for her: "For crimes that he [Šljivančanin], had committed in Vukovar, notably at Ovčara, he should have been jailed for life. I'm outraged.... The Hague(-based) tribunal has showed again that it is not a just tribunal." Danijel Rehak, the head of Croatian Association of Prisoners in Serbian Concentration Camps, said, "The shock of families whose beloved ones were killed at Ovčara is unimaginable. The court made a crucial mistake by accepting a statement of a JNA officer to whom Šljivančanin was a commander. I cannot understand that". Pavle Strugar's 8-year sentence for shelling of Dubrovnik, a UNESCO World Heritage Site, also caused outrage in Croatia. Judge Kevin Parker (of Australia) was named in a Croatian journal (Nacional) as a main cause of the system's failure for having dismissed the testimonies of numerous witnesses.
 * Some of the defendants, such as Slobodan Milošević, claimed that the Court has no legal authority because it was established by the UN Security Council instead of the UN General Assembly and so had not been created on a broad international basis. The Tribunal was established on the basis of Chapter VII of the United Nations Charter; the relevant portion of which reads "the Security Council can take measures to maintain or restore international peace and security". The legal criticism has been succinctly stated in a memorandum issued by Austrian Professor Hans Köchler, which was submitted to the President of the Security Council in 1999. British Conservative Party MEP Daniel Hannan has called for the court to be abolished, claiming it is anti-democratic and a violation of national sovereignty.
 * The interactive thematic debate on the role of international criminal justice in reconciliation was convened on 10 April 2013 by the President of the General Assembly, Vuk Jeremić, the Minister of Foreign Affairs of Serbia during the resumed part of the GA's 67th Session. The debate was scheduled after the convictions of Ante Gotovina and Mladen Markač for inciting war crimes against Serbs in Croatia were overturned by an ICTY Appeals Panel in November 2012. The ICTY president Theodor Meron announced that all three Hague war crimes courts turned down the invitation of UNGA president to participate in the debate about their work. The President of the General Assembly, Jeremić, described Meron's refusal to participate in this debate as scandalous. He emphasized that he does not shy away from criticizing the ICTY, which has "convicted nobody for inciting crimes committed against Serbs in Croatia.". Jeremić, who served as President of the General Assembly in his capacity as Serbian Foreign Minister, was effectively speaking on behalf of the Serbian government when making such statements and his views do not necessarily reflect those of the UN General Assembly. Tomislav Nikolić, the president of Serbia criticized the ICTY, claiming it did not contribute but hindered reconciliation in the former Yugoslavia. He added that although there is no significant ethnic disproportion among the number of casualties in the Yugoslav wars, the ICTY sentenced Serbs and ethnic Serbs to a combined total of 1150 years in prison while claiming that members of other ethnic groups have been sentenced to a total of 55 years for crimes against Serbs. Vitaly Churkin, the ambassador of Russia to the UN, criticized the work of the ICTY, especially the overturned convictions of Gotovina and Ramush Haradinaj.
 * Regarding the final case on 29 November 2017 proceeding encompassing six Bosnian-Croat individuals, one of whom, Slobodan Praljak, in protest in court drank poison and subsequently died, the Prime Minister of Croatia Andrej Plenković claimed the verdict was "unjust" and Praljak's suicide "speaks of deep moral injustice to the six Croats, from Bosnia and Herzegovina and the Croat people". He criticized the verdict because it did not recognize the assistance and support provided by Croatia to Bosnia and Herzegovina and the collaboration of both armies at a time when the neighbouring state was faced with the "Greater-Serbian aggression" and when its territorial integrity was compromised, as well it alludes to the link between the then leadership of the Republic of Croatia, while in the previous verdict to Bosnian-Serb Ratko Mladić does not recognize the connection with Serbia's state officials at that time.
 * Dutch filmmaker Jos de Putter made a trilogy, The Milosevic Case – Glosses at Trial, for Tegenlicht investigative slot at the VPRO. The main hypothesis of the film is that ICTY prosecution has been struggling and failing to prove any link between Milosevic and the media version of the truth of the bloody break-up of Yugoslavia. The legitimacy of the prosecution methodology in securing the witness accounts and evidence, in general, has been examined by the filmmaker.


text:
ISO 216

ISO 216 is an international standard for paper sizes, used around the world except in North America and parts of Latin America. The standard defines the "A", "B" and "C" series of paper sizes, which includes the A4, the most commonly available paper size worldwide. Two supplementary standards, ISO 217 and ISO 269, define related paper sizes; the ISO 269 "C" series is commonly listed alongside the A and B sizes.

All ISO 216, ISO 217 and ISO 269 paper sizes (except some envelopes) have the same aspect ratio, $√2:1$, within rounding to millimetres. This ratio has the unique property that when cut or folded in half widthways, the halves also have the same aspect ratio. Each ISO paper size is one half of the area of the next larger size in the same series.

History
The oldest known mention of the advantages of basing a paper size on an aspect ratio of $\sqrt{2}$ is found in a letter written on 25 October 1786 by the German scientist Georg Christoph Lichtenberg to Johann Beckmann, both at the University of Göttingen. Early variants of the formats that would become ISO paper sizes A2, A3, B3, B4, and B5 then evolved in France, where they were listed in a 1798 French law on taxation of publications (Loi sur le timbre (Nº 2136)) that was based in part on page sizes.

Searching for a standard system of paper formats on a scientific basis at the Bridge association (Die Brücke), as a replacement for the vast variety of other paper formats that had been used before, in order to make paper stocking and document reproduction cheaper and more efficient, in 1911 Wilhelm Ostwald proposed, over a hundred years after the 1798 French law, a global standard – a world format (Weltformat) – for paper sizes based on the ratio $\sqrt{2}$, referring to the argument advanced by Lichtenberg's 1786 letter, but linking this to the metric system using 1 cm as the width of the base format. Walter Porstmann argued in a long article published in 1918, that a firm basis for the system of paper formats, which deal with surfaces, ought not be the length but the area; that is, linking the system of paper formats to the metric system using the square metre rather than the centimetre, constrained by $\tfrac{x}{y}=\sqrt{2}$ and area $a = x \times y = 1$  square metre, where $x$  is the length of the shorter side and $y$  is the length of the longer side, for the second equation both in metres. Porstmann also argued that formats for containers of paper, such as envelopes, should be 10% larger than the paper format itself.

In 1921, after a long discussion and another intervention by Porstmann, the Standardisation Committee of German Industry (Normenausschuß der deutschen Industrie, or NADI in short), which is the German Institute for Standardisation (Deutsches Institut für Normung, or DIN in short) today, published German standard DI Norm 476 the specification of four series of paper formats with ratio $\sqrt{2}$, with series A as the always preferred formats and basis for the other series. All measures are rounded to the nearest millimetre. A0 has a surface area of 1 m2 up to a rounding error, with a width of 841 mm and height of 1189 mm, so an actual area of 0.999949 m2; A4 is recommended as standard paper size for business, administrative and government correspondence; and A6 for postcards. Series B is based on B0 with width of 1 m, C0 is 917 ×, and D0 771 ×. Series C is the basis for envelope formats.

The DIN paper-format concept was soon introduced as a national standard in many other countries, for example, Belgium (1924), Netherlands (1925), Norway (1926), Switzerland (1929), Sweden (1930), Soviet Union (1934), Hungary (1938), Italy (1939), Finland (1942), Uruguay (1942), Argentina (1943), Brazil (1943), Spain (1947), Austria (1948), Romania (1949), Japan (1951), Denmark (1953), Czechoslovakia (1953), Israel (1954), Portugal (1954), Yugoslavia (1956), India (1957), Poland (1957), United Kingdom (1959), Venezuela (1962), New Zealand (1963), Iceland (1964), Mexico (1965), South Africa (1966), France (1967), Peru (1967), Turkey (1967), Chile (1968), Greece (1970), Zimbabwe (1970), Singapore (1970), Bangladesh (1972), Thailand (1973), Barbados (1973), Australia (1974), Ecuador (1974), Colombia (1975) and Kuwait (1975).

It finally became both an international standard (ISO 216) as well as the official United Nations document format in 1975, and it is today used in almost all countries in the world, with the exception of several countries in the Americas.

In 1977, a large German car manufacturer performed a study of the paper formats found in their incoming mail and concluded that out of 148 examined countries, 88 already used the A series formats.

Advantages
The main advantage of this system is its scaling. Rectangular paper with an aspect ratio of $\sqrt{2}$ has the unique property that, when cut or folded in half midway between its shorter sides, each half has the same $\sqrt{2}$  aspect ratio as the whole sheet before it was divided. Equivalently, if one lays two same-sized sheets of paper with an aspect ratio of $\sqrt{2}$ side by side along their longer side, they form a larger rectangle with the aspect ratio of $\sqrt{2}$  and double the area of each individual sheet.

The ISO system of paper sizes exploits these properties of the $\sqrt{2}$ aspect ratio. In each series of sizes (for example, series A), the largest size is numbered 0 (so in this case A0), and each successive size (A1, A2, etc.) has half the area of the preceding sheet and can be cut by halving the length of the preceding size sheet. The new measurement is rounded down to the nearest millimetre. A folded brochure can be made by using a sheet of the next larger size (for example, an A4 sheet is folded in half to make a brochure with size A5 pages). An office photocopier or printer can be designed to reduce a page from A4 to A5 or to enlarge a page from A4 to A3. Similarly, two sheets of A4 can be scaled down to fit one A4 sheet without excess empty paper.

This system also simplifies calculating the weight of paper. Under ISO 536, paper's grammage is defined as a sheet's mass in grams (g) per area in square metres (unit symbol g/m2; the nonstandard abbreviation "gsm" is also used). One can derive the grammage of other sizes by arithmetic division. A standard A4 sheet made from 80 g/m2 paper weighs 5 g, as it is $1/16$ (four halvings, ignoring rounding) of an A0 page. Thus the weight, and the associated postage rate, can be approximated easily by counting the number of sheets used.

ISO 216 and its related standards were first published between 1975 and 1995:
 * ISO 216:2007, defining the A and B series of paper sizes
 * ISO 269:1985, defining the C series for envelopes
 * ISO 217:2013, defining the RA and SRA series of raw ("untrimmed") paper sizes

A series
Paper in the A series format has an aspect ratio of $√2$ (≈ 1.414, when rounded). A0 is defined so that it has an area of 1 m2 before rounding to the nearest 1 mm. Successive paper sizes in the series (A1, A2, A3, etc.) are defined by halving the area of the preceding paper size and rounding down, so that the long side of A(n + 1) is the same length as the short side of An. Hence, each next size is nearly exactly half the area of the prior size. So, an A1 page can fit two A2 pages inside the same area.

The most used of this series is the size A4, which is 210 x and thus almost exactly 1/16 m2 in area. For comparison, the letter paper size commonly used in North America (8+1/2 x) is about 6 mm (0.24 in) wider and 18 mm (0.71 in) shorter than A4. Then, the size of A5 paper is half of A4, i.e. 148 mm × 210 mm (5.8 in × 8.3 in).

The geometric rationale for using the square root of 2 is to maintain the aspect ratio of each subsequent rectangle after cutting or folding an A-series sheet in half, perpendicular to the larger side. Given a rectangle with a longer side, x, and a shorter side, y, ensuring that its aspect ratio, $x⁄y$, will be the same as that of a rectangle half its size, $y⁄x/2$, which means that $x⁄y = y⁄x/2$, which reduces to $x⁄y = √2$; in other words, an aspect ratio of $1:√2$.

Any $An$ paper can be defined as $An = S × L$, where (measuring in metres)

 * $$\text{A}_n = \begin{cases}

S = \left(\sqrt{\frac{1}{2}}\right)^{n + \frac{1}{2}}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{n - \frac{1}{2}} \end{cases}$$

Therefore

 * $$\text{A0} = \begin{cases}

S = \left(\sqrt{\frac{1}{2}}\right)^{0 + \frac{1}{2}} \approx 0.841\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{0 - \frac{1}{2}} \approx 1.189\,\text{m} \end{cases}$$, $$\text{A1} = \begin{cases} S = \left(\sqrt{\frac{1}{2}}\right)^{1 + \frac{1}{2}} \approx 0.595\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{1 - \frac{1}{2}} \approx 0.841\,\text{m} \end{cases}$$ $$\text{A2} = \begin{cases} S = \left(\sqrt{\frac{1}{2}}\right)^{2 + \frac{1}{2}} \approx 0.420\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{2 - \frac{1}{2}} \approx 0.595\,\text{m} \end{cases}$$ Etc.

B series
The B series is defined in the standard as follows: "A subsidiary series of sizes is obtained by placing the geometrical means between adjacent sizes of the A series in sequence." The use of the geometric mean makes each step in size: B0, A0, B1, A1, B2 ... smaller than the previous one by the same factor. As with the A series, the lengths of the B series have the ratio $√2$, and folding one in half (and rounding down to the nearest millimetre) gives the next in the series. The shorter side of B0 is exactly 1 metre.

There is also an incompatible Japanese B series which the JIS defines to have 1.5 times the area of the corresponding JIS A series (which is identical to the ISO A series). Thus, the lengths of JIS B series paper are $√1.5$ ≈ 1.22 times those of A-series paper. By comparison, the lengths of ISO B series paper are $4√2$ ≈ 1.19 times those of A-series paper.

Any $Bn$ paper (according to the ISO standard) can be defined as $Bn = S × L$, where (measuring in metres)

 * $$\text{B}_n = \begin{cases}

S = \left(\sqrt{\frac{1}{2}}\right)^{n}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{n - 1} \end{cases}$$

Therefore

 * $$\text{B0} = \begin{cases}

S = \left(\sqrt{\frac{1}{2}}\right)^{0} = 1\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{0 - 1} \approx 1.414\,\text{m} \end{cases}$$, $$\text{B1} = \begin{cases} S = \left(\sqrt{\frac{1}{2}}\right)^{1} \approx 0.707\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{1 - 1} = 1\,\text{m} \end{cases}$$ $$\text{B2} = \begin{cases} S = \left(\sqrt{\frac{1}{2}}\right)^{2} = 0.5\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{2 - 1} \approx 0.707\,\text{m} \end{cases}$$ Etc.

C series
The C series formats are geometric means between the B series and A series formats with the same number (e.g. C2 is the geometric mean between B2 and A2). The width to height ratio of C series formats is $√2$ as in the A and B series. A, B, and C series of paper fit together as part of a geometric progression, with ratio of successive side lengths of $8√2$, though there is no size half-way between Bn and A(n − 1): A4, C4, B4, "D4", A3, ...; there is such a D-series in the Swedish extensions to the system. The lengths of ISO C series paper are therefore $8√2$ ≈ 1.09 times those of A-series paper.

The C series formats are used mainly for envelopes. An unfolded A4 page will fit into a C4 envelope. Due to same width to height ratio, if an A4 page is folded in half so that it is A5 in size, it will fit into a C5 envelope (which will be the same size as a C4 envelope folded in half).

Any $Cn$ paper can be defined as $Cn = S × L$, where (measuring in metres)

 * $$\text{C}_n = \begin{cases}

S = \left(\sqrt{\frac{1}{2}}\right)^{n + \frac{1}{4}}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{n - \frac{3}{4}} \end{cases}$$

Therefore

 * $$\text{C0} = \begin{cases}

S = \left(\sqrt{\frac{1}{2}}\right)^{0 + \frac{1}{4}} \approx 0.917\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{0 - \frac{3}{4}} \approx 1.297\,\text{m} \end{cases}$$, $$\text{C1} = \begin{cases} S = \left(\sqrt{\frac{1}{2}}\right)^{1 + \frac{1}{4}} \approx 0.648\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{1 - \frac{3}{4}} \approx 0.917\,\text{m} \end{cases}$$ $$\text{C2} = \begin{cases} S = \left(\sqrt{\frac{1}{2}}\right)^{2 + \frac{1}{4}} \approx 0.458\,\text{m}\\ L = \left(\sqrt{\frac{1}{2}}\right)^{2 - \frac{3}{4}} \approx 0.648\,\text{m} \end{cases}$$ Etc.

Tolerances
The tolerances specified in the standard are:
 * ±1.5 mm for dimensions up to 150 mm,
 * ±2.0 mm for dimensions in the range 150 to 600 mm, and
 * ±3.0 mm for dimensions above 600 mm.

These are related to comparison between series A, B and C.

Application
The ISO 216 formats are organized around the ratio 1:$√2$; two sheets next to each other together have the same ratio, sideways. In scaled photocopying, for example, two A4 sheets reduced to A5 size fit exactly onto one A4 sheet, and an A4 sheet in magnified size onto an A3 sheet; in each case, there is neither waste nor want.

The principal countries not generally using the ISO paper sizes are the United States and Canada, which use North American paper sizes. Although they have also officially adopted the ISO 216 paper format, Mexico, Panama, Peru, Colombia, the Philippines, and Chile also use mostly U.S. paper sizes.

Rectangular sheets of paper with the ratio 1:$√2$ are popular in paper folding, such as origami, where they are sometimes called "A4 rectangles" or "silver rectangles". In other contexts, the term "silver rectangle" can also refer to a rectangle in the proportion 1:(1 + $√2$), known as the silver ratio.

Matching technical pen widths
An adjunct to the ISO paper sizes, particularly the A series, are the technical drawing line widths specified in ISO 128. For example, line type A ("Continuous - thick", used for "visible outlines") has a standard thickness of 0.7 mm on an A0-sized sheet, 0.5 mm on an A1 sheet, and 0.35 mm on A2, A3, or A4.

The matching technical pen widths are 0.13, 0.18, 0.25, 0.35, 0.5, 0.7, 1.0, 1.40, and 2.0 mm, as specified in ISO 9175-1. Colour codes are assigned to each size to facilitate easy recognition by the drafter. Like the paper sizes, these pen widths increase by a factor of $√2$, so that particular pens can be used on particular sizes of paper, and then the next smaller or larger size can be used to continue the drawing after it has been reduced or enlarged, respectively.

 * {| class="wikitable"

!style="text-align:left"| Linewidth (mm) !style="text-align:left"| Colour
 * width="9%" colspan=2| 0.10
 * width="9%" colspan=2| 0.13
 * width="9%" colspan=2| 0.18
 * width="9%" colspan=2| 0.25
 * width="9%" colspan=2| 0.35
 * width="9%" colspan=2| 0.50
 * width="9%" colspan=2| 0.70
 * width="9%" colspan=2| 1.0
 * width="9%" colspan=2| 1.4
 * width="9%" colspan=2| 2.0
 * width="2%" style="background:brown"| ||Maroon
 * width="2%" style="background:darkmagenta"| ||Violet
 * width="2%" style="background:crimson"| ||Red
 * width="2%" style="background:white"| ||White
 * width="2%" style="background:gold"| ||Yellow
 * width="2%" style="background:saddlebrown"| ||Brown
 * width="2%" style="background:steelblue"| ||Blue
 * width="2%" style="background:chocolate"| ||Orange
 * width="2%" style="background:lightseagreen"| ||Green
 * width="2%" style="background:silver"| ||Gray
 * }

The earlier DIN 6775 standard upon which ISO 9175-1 is based also specified a term and symbol for easy identification of pens and drawing templates compatible with the standard, called Micronorm, which may still be found on some technical drafting equipment.

Overformats
DIN 476 provides for formats larger than A0, denoted by a prefix factor. In particular, it lists the formats 2A0 and 4A0, which are twice and four times the size of A0 respectively:

While not formally defined, ISO 216:2007 notes them in the table of Main series of trimmed sizes (ISO A series) as well: "The rarely used sizes [2A0 and 4A0] which follow also belong to this series." 2A0 is also known by other unofficial names like "A00".

title: ISO 216


text:
ISO 3864

ISO 3864 specifies international standards for safety signs and markings in workplaces and public facilities. These labels are graphical, to overcome language barriers. The standard is split into four parts.

Parts
ISO 3864 consists of four parts, that provide more specific and situation specific guidance depending on the application.
 * ISO 3864-1:2011 Part 1: Design principles for safety signs and safety markings
 * ISO 3864-2:2016 Part 2: Design principles for product safety labels
 * ISO 3864-3:2012 Part 3: Design principles for graphical symbols for use in safety signs
 * ISO 3864-4:2011 Part 4: Colorimetric and photometric properties of safety sign materials

Part 1 explains how to layout the components of safety signage, dictate the color scheme and sizing information. Part 2 covers the same concepts as part one, but specifically for labels applied on machinery, vehicles and consumer goods. Part 3 contains guidance for designing new safety symbols. Part 4 specifies the standards for phosphorescent material and colours of a sign, as well as testing to confirm these signs meets required standards.

Colours
These are the colours specified in ISO Standard 3864-4 in RAL colour standard.

In addition, ISO standard 3864-2:2016 lays out the following colours that correspond to levels of risk. This standard adds "Orange" as an incremental colour to the pallette above.

Arrows
ISO 3864-3 defines four types of arrow designs, and specifies what situations each type should be used in.

Safety markings
Part 1 also provides design standards for 'safety markings', which are safety colors combined with a contrasting color in an alternating 45° stripe pattern, intended to increase the visibility of an object, location or safety message.

Signage design
In addition to prescribing colours for safety signage, ISO 3864 also specifies how to layout the elements of the sign: A symbol and optional 'supplemental sign' which contains the supplementary text message.

Multi-message signs
For situations where more than one message needs to be communicated, ISO 3864 also provides guidance for "multiple signs", which consist of two or more symbol and text messages combined into a single sign. Additionally, fire protection and safe condition signs, which mark the location of equipment or exits can be combined with an arrow to indicate the direction to the item depicted on the sign.

Related standards
The corresponding American standard is ANSI Z535. ANSI Z535.1 also explicitly uses multiple levels of hazard, including Yellow (Pantone 109) for 'caution' messages, and Orange (Pantone 151) for stronger 'warning' messages. Like ISO 3864, ANSI Z535 includes multiple sections: ANSI Z535.6-2006 defines an optional accompanying text in one or more languages.

ISO 3864 is extended by ISO 7010, which provides a set of symbols based on the principles and properties specified in ISO 3864.

title: ISO 3864


text:
Talk:Infinite product

This article is probably very non-ideal, but when I needed this material a while ago it was hard to find, and so I figured wikipedia would be a good place to hold it. Please feel free to change it around and make it more encyclopedia-like, even more so than usual. :)

We probably need a little caveat about negative numbers: the log formula won't work without problems in that case. Maybe use a different log which is defined on the negative reals? --AxelBoldt
 * A product of negative coefficients does not converge; it can at most flip. --Yecril (talk) 18:00, 20 December 2008 (UTC)

Inaccurate Statement
"Therefore, the logarithm log an will be defined for all but a finite number of n" neither makes sense nor true as I understand it. One can easily imagine a sequence which converges to 1 that is not finite. one simple example is a(n)= 1+(1/n) where n is an integer. This of course is not limited for a being real, for example think of any oscillating function which dampens to 1. this might have been a simple typo the author made, but i don't understand his/her intention, so i am timid to edit this —Preceding unsigned comment added by 129.49.61.161 (talk) 17:06, 17 August 2010 (UTC)

 * Maybe it is a left-over from careless editing. Some sources allow a finite number of 0 factors and still call the product convergent if the product of the non-zero factors is non-zero.  Probably that is the meaning. I'll try to fix it. McKay (talk) 06:09, 31 March 2011 (UTC)

Why is $$\prod_{k=1}^{\infty} a_k = \lim_{n\rightarrow\infty} \prod_{k=1}^{n} a_k = 0$$ an example of divergence?
The article currently indicates that if the infinite product is zero then that is an example of divergence. Why? I would think that that is an example of convergence, despite that a corresponding sum $$\sum_{k=1}^{\infty} \log(a_k)$$ is not finite. — Q uantling (talk | contribs) 18:35, 30 March 2011 (UTC)

 * It is just a convention. The reason for the convention is that allowing convergence to 0 would admit too many uninteresting series (for example, any sequence {an} with | an| < 1/2), and some desirable properties would disappear. McKay (talk) 06:15, 31 March 2011 (UTC)
 * Perhaps it's worth nothing that following that convention, we also neglect many "interesting" examples. Say $$0<a_1<1$$. Can $$a_k$$ converge to 1, and still result in the product converging to 0? If not, then what is the highest number $$a_k$$ can approach? Forgive me if these are well known and simple problems to solve, it's new territory for me.
 * Why should it be deemed that non-trivially converging-to-0 infinite products are necessarily uninteresting? 2601:647:C900:B6C0:99ED:F4A6:FA90:CDFA (talk) 05:52, 16 December 2022 (UTC)

How does this fit in?
If F(x) can be represented as a product:

 * $$F(x)=\Pi_{n=1}^\infty f_n(x)$$

then define G(x)=1-F(x) and using the series expansion for the natural logarithm: $$\ln(1-G(x))= -\sum_{n=1}^\infty G(x)^n/n $$

 * $$\ln(F(x))=-\sum_{n=1}^\infty G(x)^n/n = \sum_{n=1}^\infty \ln(f_n(x))$$

so that $$f_n(x)=e^{-G(x)^n/n}$$ and

 * $$F(x)=\Pi_{n=1}^\infty\, e^{-\frac{1}{n}(1-F(x))^n}$$

I have checked this on Mathematica for a number of functions, and Mathematica agrees, but I have no idea what the conditions are for this formula to work. Can anyone find a reference for this and put a section into the article? Its a very useful and general expression, and much simpler than the more general Weierstrass development. PAR (talk) 17:45, 13 June 2011 (UTC)

 * Ok, probably after almost 6 years this comment might have been forgotten, but let me explain why I don't think is a good idea to include such observation in the article. What you say is a trivial statement: if $$c \in [-1,1]$$ is a fixed number, then

 * $$\Pi_{n=1}^\infty\, e^{-\frac{c^n}{n}} = \exp(-\sum_{n=1}^\infty c^n/n) = \exp(\log(1-c)) = 1-c. $$

 * Since you are expanding $$\log(1-F(x))$$, you are assuming that $$F(x) \in [-1,1]$$ for every $$x$$, and then you are just applying the above formula point-wise. Note that this is quite different from Weierstrass' formula (if you wish, the problem with your expression is that you write $$F(x)$$ in terms of $$F(x)$$, so that is not very useful, just like is not very useful to say that -for example- $$F(x) = [2 F(x)] * \left[\frac{F(x)}{2}\right]$$). Lucha (talk) 16:10, 28 February 2017 (UTC)

title: Talk:Infinite product


text:
Isaac Abendana

Isaac Abendana (c. 1640–1699) was the younger brother of Jacob Abendana, and became hakam of the Spanish Portuguese Synagogue in London after his brother died.

Abendana moved to England before his brother, in 1662, and taught Hebrew at Cambridge University. He completed an unpublished Latin translation of the Mishnah for the university in 1671.

While he was at Cambridge, Abendana sold Hebrew books to the Bodleian Library of Oxford, and in 1689 he took a teaching position in Magdalen College. In Oxford, he wrote a series of Jewish almanacs for Christians, which he later collected and compiled as the Discourses on the Ecclesiastical and Civil Polity of the Jews (1706). Like his brother, he maintained an extensive correspondence with leading Christian scholars of his time, most notably with the philosopher Ralph Cudworth, master of Christ's College, Cambridge.

title: Isaac Abendana