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Cambridge Assessment English

Cambridge Assessment English or Cambridge English develops and produces Cambridge English Qualifications and the International English Language Testing System (IELTS). The organisation contributed to the development of the Common European Framework of Reference for Languages (CEFR), the standard used around the world to benchmark language skills, and its qualifications and tests are aligned with CEFR levels.

Cambridge Assessment English is part of Cambridge Assessment, a non-teaching department of the University of Cambridge which merged with Cambridge University Press to form Cambridge University Press & Assessment in August 2021.

Current Cambridge English qualifications/exams

Each Cambridge English Qualifications focuses on a level of the Common European Framework of Reference (CEFR).

Schools
These English qualifications are to help school-age children and young people improve their English language skills.

General and higher education
These qualifications are designed for adult learners. A2 Key, B1 Preliminary and B2 First have the same exam format (e.g. number of papers, number of questions, time allowance) as the schools' versions of these qualifications, but use different topics and content suited to adult learners.

Business
These qualifications are designed for adult learners learning English for use in a business context.

Multilevel tests
Multilevel tests are used to find out which English learning programme or exam is right for a student. These cover multiple levels of the CEFR in one test.

Cambridge Exams Publishing, a joint venture with Cambridge University Press, produces Cambridge-branded IELTS resources and materials to help learners prepare and practise for their tests.

Teaching
Qualifications and courses for teachers of all levels of experience.

Discontinued exams
In alphabetical order:

 * BULATS discontinued on 6 December 2019.
 * Cambridge English: Financial (ICFE) discontinued in December 2016.
 * Cambridge English: Legal (ILEC) discontinued in December 2016.
 * CELS (Certificates in English Language Skills) modular qualifications for English language learners.
 * Certificates in ESOL Skills for Life (SfL) (UK only) discontinued in June 2017.
 * DTE(E)LLS (Diploma in Teaching English (ESOL) in the Lifelong Learning Sector) and ADTE(E)LLS (Additional Diploma in Teaching English (ESOL) in the Lifelong Learning Sector): these qualifications for English language teachers in the UK were discontinued in September 2012. CELTA is a recommended alternative for those wanting an English teaching qualification for teaching in the UK.
 * IDLTM (International Diploma in Language Teaching Management) discontinued in June 2016.
 * PTLLS (Preparing to Teach in the Lifelong Learning Sector) discontinued in November 2012.
 * Young Learner (YL) Extension to CELTA discontinued in December 2016.
 * TKT: KAL and TKT: Practical discontinued in December 2016.

Partnerships and acquisitions
In the 1980s Cambridge Assessment English, the British Council and IDP Education formed the international IELTS partnership which delivers the IELTS tests.

In 2010 Cambridge Assessment English and the English Language Institute Testing and Certificate Division of the University of Michigan agreed to form a not-for-profit collaboration known as CaMLA (Cambridge Michigan Language Assessments). Cambridge Assessment English owns 65% of the venture.

Since 2011 Cambridge Exams Publishing, a partnership between Cambridge Assessment English and the English Language Teaching (ELT) business of Cambridge University Press, develops official Cambridge preparation materials for Cambridge English and IELTS exams.

In 2013 Cambridge Assessment English formed a joint venture with the Box Hill Institute to deliver the Occupational English Test, known as OET.

In 2019 Cambridge Assessment English acquired English Language (ELiT), an artificial intelligence developed off technology from the University of Cambridge, to support new English language assessment products.

Alignment with the Common European Framework of Reference for Languages (CEFR)
Cambridge Assessment English was involved in the early development of the Common European Framework of Reference for Languages (CEFR) and all Cambridge English qualifications and tests are aligned with the levels described by the CEFR. Each Cambridge English Qualification targets specific CEFR levels but the exam also contains test material at the adjacent levels. For example, B2 First is aimed at B2, but there are also test items that cover B1 and C1. This allows for inferences to be drawn about candidates' abilities if they are a level below or above the one targeted. Candidates are encouraged to take the exam most suitable to their needs and level of ability.

Research
The Cambridge English EFL Evaluation Unit was established in 1989 and was the first dedicated research unit of its kind. This unit is now called the Research and Validation Group and is the largest dedicated research team of any English language assessment body. Research is published in the Studies in Language Testing (SiLT) series.

Awards
In 2015, Cambridge Assessment English was awarded the Queen's Award for Enterprise in the 'international trade' category.

Cambridge University's examination board (UCLES)
The first Cambridge English exam was produced in 1913 by UCLES (University of Cambridge Local Examinations Syndicate). UCLES had been set up in 1858 to provide exams to students who were not members of a university.

There was a growing concern in Britain with standards of school education and the transition from secondary to tertiary-level education. A number of schools "petitioned the Universities of Oxford and Cambridge [to provide] means of comparing achievements of pupils across schools." The secondary education sector was still voluntary in nature. Without support from the state, it was logical to seek help from universities that were long established and widely admired. The University of Oxford and University of Cambridge, in particular, were "regarded as viable sources of supervision."

UCLES was invited to set exams and inspect schools with the aim of raising educational standards. The University of Oxford also created its own examination board: the University of Oxford Delegacy of Local Examinations (UODLE). UODLE and its partner, the Association of Recognised English Language Schools, merged with UCLES in 1995.

The first UCLES examinations took place on 14 December 1858. The exams were designed to test for university selection and were taken by 370 candidates in British schools, churches and village halls. Candidates were required to "satisfy the examiners" in the analysis and parsing of a Shakespeare text; reading aloud; dictation; and composition (on either the recently deceased Duke of Wellington; a well-known book or a letter of application).

Female candidates were accepted by UCLES on a trial basis in 1864 and on a permanent basis from 1867. Cambridge University itself did not examine female students until 1882 and it was not until 1948 that women were allowed to graduate as full members of the university.

In the mid to late 19th century, UCLES exams were taken by candidates based overseas – in Trinidad and Tobago (from 1863), South Africa (from 1869), Guyana and New Zealand (from 1874), Jamaica (from 1882) and Malaysia (from 1891). Many of these candidates were children of officers of the British colonial service and exams were not yet designed for non-native speakers of English.

The first Cambridge English exam
In 1913 UCLES created the first exam for non-native speakers of English – the Certificate of Proficiency in English (CPE – now known as C2 Proficiency). This may have been prompted by the development of English exams "for foreigners" by other universities.

CPE was originally a qualification for teachers: "the Certificate of Proficiency in English is designed for Foreign Students who desire satisfactory proof of their knowledge of the language with a view to teaching it in foreign schools." The exam was only available for candidates aged 20 or over.

In 1913 the exam could be taken in Cambridge or London, for a fee of £3 (approximately £293 in 2012 prices ). The exam lasted 12 hours and included:

 * 1) Translation from English into French or German: 2 hours
 * 2) Translation from French or German into English, and English Grammar: 2.5 hours
 * 3) English Essay: 2 hours
 * 4) English Literature: 3 hours
 * 5) English Phonetics: 1.5 hours
 * 6) Oral test: dictation (30 minutes); reading aloud and conversation (30 minutes)

The main influence behind the design of the exam was the grammar-translation teaching approach, which aims to establish reading knowledge (rather than the ability to communicate in the language). In 1913, the first requirement for CPE candidates was to translate texts. Translation remained prominent in foreign language teaching up until the 1960s. It was a core part of CPE until 1975 and an optional part until 1989.

However, CPE was also influenced by Henry Sweet and his book published in 1900: A Practical Study of Languages: A Guide for Teachers and Learners, which argued that "the most natural method of teaching languages was through conversation." Due to this influence, speaking was part of Cambridge English exams from the very beginning.

Exam questions in 1913
Candidates were required to translate from English into French/German and translate from French/German into English. Here is a short segment from one of the passages candidates were asked to translate from English into German: "The sentiments which animated Schiller's poetry were converted into principles of conduct; his actions were as blameless as his writings were pure. With his simple and high predilections, with his strong devotedness to a noble cause, he contrived to steer through life, unsullied by its meanness, unsubdued by any of its difficulties or allurements ..."In the English Essay paper, candidates were asked to write an essay for two hours, on one of the following subjects: the effect of political movements upon nineteenth-century literature in England; English Pre-Raphaelitism; Elizabethan travel and discovery; the Indian Mutiny; the development of local self-government; or Matthew Arnold. The exam board provided little or no formal structure. Concepts such as audience and purpose, and the length of the essay, were left for the candidate to decide.

The questions in the English Literature section were borrowed from the university's Language and Literature matriculation exams for native speakers and included questions on Shakespeare's Coriolanus and Milton's Paradise Lost. Here is an example question: explain fully and comment on the following passages, stating the connexions in which they occur and any difficulties of reading, phraseology or allusion: "Wert thou the Hector, That was the whip of your bragg'd progency, Thou should'st not 'scrape me here." It was not until 1930 that a Literature paper was designed specifically for CPE candidates.

The grammar section contained questions about grammar and lexis, e.g. give the past tense and past participle of each of the following verbs, dividing them into strong and weak ..., and questions about grammar and lexis usage, e.g. embody each of the following words into a sentence in such a way as to show that you clearly apprehend its meaning: commence, comment, commend ... At the time, this mirrored the approach to learning grammar in Latin and Greek (as well as modern languages).

Finally, a Phonetics paper was included as it was thought to be useful in the teaching of pronunciation. The paper required candidates to make phonetic transcriptions of long pieces of continuous text; describe the articulation of particular sounds; explain phonetic terms, and suggest ways of teaching certain sounds. Here are two example questions: explain the terms: "glide", "narrow vowel", "semi-vowel" and give two examples of each in both phonetic and ordinary spelling and how would you teach a pupil the correct pronunciation of the vowel sounds in: fare, fate, fat, fall, far?

Revisions to the 1913 exam
The 1913 CPE exam was taken by just three candidates. The candidates "were able to converse fluently, expressing themselves on the whole, with remarkable ease and accuracy." However, all three candidates failed the exam and none of them was awarded a CPE certificate.

In its second year (1914), CPE gained in popularity, with 18 candidates and four passing. However, for the next 15 years candidature remained static. Italian and Spanish were added as languages for the translation paper in 1926.

In 1928, CPE had only 14 candidates and by 1929 it was in danger of being discontinued. Jack Roach, Assistant Secretary to the Syndicate from 1925 to 1945, decided to "save it from the scrapheap" and introduced a number of changes. The Phonetics paper was dropped and the essay questions became more a test of writing proficiency rather than a test of knowledge about British culture. Questions such as "The best month of the year" were preferred to the more culture-bound topics set in 1913, such as "Elizabethan travel and discovery." The target candidature was broadened beyond teachers, to "all foreign students who desire to obtain evidence of their practical knowledge of the languages, both written and spoken, as of their ability to read with comprehension standard works of English literature."

In 1932 it was decided to establish overseas exam centres. The first overseas centres were set up in Hamburg, Paris and San Remo (1933), followed by further centres in Italy (Rome and Naples), the Netherlands, Sweden and Switzerland. Latin America also became an exam area in the 1930s, with centres in Argentina and Uruguay.

In 1935 CPE started providing alternatives to the Literature paper, with an Economic and Commercial Knowledge paper – an early forerunner of English for Specific Purposes.

Then, in 1937–38, the University of Cambridge and University of Oxford decided to accept CPE as representing the standard in English required of all students, British or foreign, before the entrance to their university. To this day, CPE still serves as a qualification for entry to higher education. Following these changes CPE candidate numbers instantly began to rise, reaching 752 by the outbreak of World War II.

World War II
From 1939 onwards, thousands of refugees from the Spanish Civil War and occupied Europe started arriving in the UK and began taking UCLES exams while stationed in the UK.

UCLES launched the Lower Certificate in English (LCE) to meet the demand for certification at a lower level than CPE. A Preliminary exam, at a lower level than LCE, was also offered in 1944 as a special test to meet the contingencies of war. These were the first steps toward developing language assessments at different levels.

Polish servicemen and women made up a large proportion of the candidature. In 1943, over a third of all LCE Certificates were awarded to candidates from the Polish army and air force. This pattern continued throughout the war and into the post-war period. On one single day in 1948, no fewer than 2,500 Polish men and women of the Polish Resettlement Corps took the LCE.

UCLES tests were made available for prisoners of war in Britain and in Germany. In Britain, 1,500 prisoners of war took the exams, almost 900 of them Italians. In Germany, the War Organisation of the British Red Cross and Order of St John of Jerusalem made arrangements for UCLES examinations to be offered at prisoner-of-war camps with many Indian prisoners of war, in particular, taking LCE or School Certificate exams.

Examiners were asked to report on "disturbance, loss of sleep, etc., caused by air raids, and on any exceptional difficulties ... during the examination period." One report noted that the candidates had been spending "most of each day in the air-raid shelter"; that candidate 5224, a probationer nurse, had been showing strain caused by helping with "rescue work"; and that the house of candidate 5222 had been bombed, whilst she was at school, with fatalities. Such were the circumstances of wartime exam takers and administrators.

Exams were also maintained clandestinely in continental European exam centres, which frequently meant unusual measures, including acts of determination and courage. However, UCLES was unable to fund and support the growing international network of English language examination centres around the world. Meanwhile, the British Council had a brief to disseminate British culture and educational links. In March 1941 a formal 'Joint Agreement' was signed between the two organisations to collaborate on the distribution of UCLES exams around the world. This started a long-lasting relationship, which continues to this day.

Post-war
By 1947, there were over 6,000 UCLES candidates, with LCE double the size of CPE. Exam centres had been set up in Europe (17), Latin America (9), the Middle East (8), Africa (4) and the USA (1). Candidate numbers continued to grow, reaching over 20,000 by 1955, 44,000 by 1965, and over 66,000 by 1975.

However, by the 1970s demand was growing for exams at more clearly defined levels of proficiency. This set the scene for the Council of Europe and the development of the Common European Framework of Reference for Languages (CEFR), which was initiated in 1971.

Qualification at different levels
UCLES had a few attempts at developing language assessments at different levels. During the Second World War, there was a three-level system: the Preliminary English Test, LCE and CPE. After the war, a new three-level system was introduced: LCE, CPE and DES (The Diploma of English Studies). However, as an extremely advanced exam, DES candidature never rose beyond a few hundred and was later discontinued.

In the 1980s and 1990s, the levels stabilised and the suite of exams we recognise today became established. A five-level system was developed, which characterises Cambridge English's general English exams to the present day and laid the foundations for the levels in the CEFR.

 * Level 1: the Key English Test (KET) was launched in 1994. It is now known as A2 Key.
 * Level 2: the Preliminary English Test (PET) was originally used during the Second World War years. It reappeared in 1980 under close monitoring and was fully launched in the 1990s. It is now known as B1 Preliminary.
 * Level 3: LCE, operational since the Second World War, continued under a new name: the First Certificate in English. It is now known as B2 First.
 * Level 4: the Certificate in Advanced English (CAE) was launched in 1991. It is now known as C1 Advanced.
 * Level 5: CPE, operational since 1913, became Cambridge English's highest level qualification. It is now known as C2 Proficiency.

During this period there were also substantial revisions to the existing exams: B2 First and C2 Proficiency. These revisions included improving the authenticity of texts and tasks; increasing the weight on Listening and Speaking; improving the balance between grammar and vocabulary items in the Reading paper; and adding a broader range of texts in the Composition and Use of English papers, (e.g. letter-writing, dialogues, speeches, note-taking, and discursive and descriptive compositions).

With increased weight on Listening and Speaking, UCLES joined forces with the BBC. However, in the BBC recording booths, there was tension between the BBC's approach, which focused on dramatic potential, and UCLES' need for clarity of speech. For example, a man abseiling down a mountain was highly entertaining but unacceptable for test purposes. It was finally agreed that at least 35% of listening tests would comprise an original BBC recording, largely made up of programmes from World Service and Woman's Hour broadcasts.

IELTS
With learners increasingly requiring English language certification for their studies, UCLES, along with the British Council and the Australian International Development Programme (IDP), developed a test in the 1980s which focused specifically on English for academic purposes.

An English Language Testing Service (ELTS) test was first launched in 1980 with tasks based on language use in academic and occupational contexts in the "real world". However, the ELTS test was very complex to administer and only two full versions were ever produced.

In 1989, a simplified and shortened test became operational under a new name: the International English Language Testing System (IELTS).

It was clear that different forms of the test would need to be equated. All IELTS materials were therefore pretested and calibrated to a common scale on the basis of the Rasch model. This was the first time that UCLES had used the Rasch model, which now forms the cornerstone of the level testing system.

RSA and teaching qualifications
In 1988, the EFL exams developed by The Royal Society of Arts (RSA) Examination Board were merged with those of UCLES. The RSA Examination Board had been established in 1754, long before UCLES, and by taking over the RSA TEFL schemes UCLES became responsible for "the running of the world's most respected and widely recognised schemes for validating training courses for teachers of English as a Foreign Language."

The two sets of qualifications were integrated and syllabuses for the revised qualifications were developed in consultation with the ESL sector, in order to re-integrate the ESL and EFL teacher communities. In 1999 the RSA Certificate in Teaching English as a Foreign Language to Adults (CTEFLA) and the RSA Diploma in Teaching English as a Foreign Language to Adults officially became known as the CELTA and Delta qualifications. These qualifications were joined in 2004 by ICELT (a revised version of its predecessor, COTE) – which is a purely in-service professional qualification.

At the start of the 21st century, there was growing demand from government ministries and schools for a professional qualification without any in-service (teaching practice) component. This led to the introduction of the Teaching Knowledge Test (TKT), which focuses solely on core professional knowledge. Following consultations with worldwide teacher training institutions and trials with 1,500 English language teachers in Europe, Latin America and Asia, TKT went live in 2005. In the first six months thousands of candidates sat the test in 36 different countries. It was also incorporated into government plans, e.g. plans in Chile to retrain all in-service teachers, and was incorporated into state university teacher training programmes.

China and business English
The early 1990s saw China developing its market economy very rapidly. Recognising the importance of English as a language of international business and trade, the Chinese government asked Cambridge Assessment English to develop a suite of Business English Certificates (BEC).

BEC Preliminary (now known as B1 Business Preliminary) examinations were first taken in 1993 by 5,000 candidates from seven cities across China. BEC Vantage (now known as B2 Business Vantage) was launched in 1994 and BEC Higher (now known as C1 Business Higher) in 1996. This was followed in 1997 by the launch of the Business Language Testing Service (BULATS) for companies.

Young learners
In the 1990s, there was growing demand from Cambridge English centres in the Far East, Latin America and Europe for assessments designed specifically for younger learners. At the time, relatively little research had been carried out into the assessment of second language learning in children.

UCLES worked with Homerton College (a teacher training college within the University of Cambridge) to trial test questions with over 3,000 children in Europe, South America and South East Asia. The feedback was used to construct the first Young Learners English (YLE) tests, targeted at learners aged 6–12, which went live in 1997.

The YLE tests introduced a new level. The addition of the 'breakthrough' level created a six-level system that was mirrored by the CEFR, published in 2001.

Candidates
In 1988, with just two established exams (B2 First and C2 Proficiency), exam candidature was around 180,000. By 2002, with a more comprehensive range of exams, the exam candidature was over 1 million; by 2007, it was over 2 million, by 2013, it was over 4 million; and by 2017, it was over 5.5 million.

The Cambridge English Scale
In January 2015, a new way of reporting results was introduced – the Cambridge English Scale. The scale aims to provide exam users with more information about their exam performance.

Candidates get more detailed results – receiving an overall score and a score for each skill/paper. In addition, the Cambridge English Scale makes it easier to see the progression and compare performance across different Cambridge English exams.

B2 First, C1 Advanced and C2 Proficiency have reported results on the Cambridge English Scale since January 2015. A2 Key and Key for Schools, B1 Preliminary and Preliminary for Schools and Business Certificates have reported results on the scale since February 2016.

Timeline 1209–2021

 * 1209: University of Cambridge founded.
 * 1534: Cambridge University Press founded.
 * 1858: University of Cambridge Local Examinations Syndicate (UCLES) founded.
 * 1913: Certificate of Proficiency in English (CPE) introduced. Now known as C2 Proficiency.
 * 1939: Lower Certificate in English (LCE) introduced. Renamed First Certificate in English (FCE) in 1975 and now known as B2 First.
 * 1941: Joint agreement with the British Council – British Council centres established.
 * 1943–1947: Preliminary English Test (PET) introduced. It was reintroduced in 1980 and is now known as B1 Preliminary.
 * 1971: Common European Framework of Reference for Languages (CEFR) initiated.
 * 1988: The Royal Society of Arts (RSA) Examination Board becomes part of UCLES.
 * 1989: Specialist EFL research and evaluation unit established.
 * 1989: IELTS launched. A simplified and shortened version named ELTS was launched in 1980.
 * 1990: Association of Language Testers in Europe (ALTE) founded.
 * 1991: Certificate in Advanced English (CAE) introduced. Now known as C1 Advanced.
 * 1993: Business English Certificates (BEC) launched.
 * 1994: Key English Test (KET) introduced. Now known as A2 Key.
 * 1995: University of Oxford Delegacy of Local Examinations (UODLE) becomes part of UCLES.
 * 1997: Young Learners English Tests (YLE) introduced. Now known as Pre-A1 Starters, A1 Movers, and A2 Flyers.
 * 1997: BULATS launched.
 * 2001: CEFR published.
 * 2002: UCLES EFL renamed University of Cambridge ESOL Examinations (Cambridge ESOL).
 * 2002: One million Cambridge ESOL exam candidates.
 * 2010: CaMLA established (Cambridge Michigan Language Assessments).
 * 2011: Cambridge Exams Publishing joint venture with Cambridge University Press established.
 * 2013: Cambridge ESOL renamed Cambridge English Language Assessment.
 * 2015: Cambridge English Scale introduced.
 * 2016: Linguaskill reading and listening introduced.
 * 2016: Linguaskill writing introduced.
 * 2017: Cambridge English Language Assessment renamed Cambridge Assessment English.
 * 2020: The University of Cambridge announces its plans to merge two of its non-teaching departments, Cambridge Assessment and Cambridge University Press.
 * 2021: Cambridge Assessment and Cambridge University Press merge to become Cambridge University Press & Assessment

title: Cambridge Assessment English


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User talk:Buoren

NPOV on Taiwan Article
Thanks for the feedback, point duly noted! Loren 06:31, 1 Dec 2004 (UTC)

Hand evaluation
You seem to have an interest in bridge so I would apprecioate your comments on this new article I am writing. I am new but keen. Abtract 00:12, 14 May 2006 (UTC)

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

title: User talk:Buoren


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Mercedes-Benz Citaro

The Mercedes-Benz Citaro is a single-decker, rigid or articulated bus manufactured by Mercedes-Benz/EvoBus. Introduced in 1997, the Citaro is available in a range of configurations, and is in widespread use throughout Europe and parts of Asia, with more than 55,000 produced by December 2019.

History
The first generation Citaro was launched in 1997, as a successor to the Mercedes-Benz O405.

In 2005, an updated version of the Citaro to coincide with the introduction of Euro IV- (and later Euro V- and EEV-) compliant engines. Apart from minor technical alterations, mainly to accommodate the new generation of engines, the external design received a facelift to give the buses a less angular look, with internal panelling altered accordingly. Production of the old model ceased by autumn 2006.

In 2006 the Citaro received a much more substantial facelift, which can be seen from the outside by a revised front and rear design (analogous to the recently introduced low-entry buses). The hitherto characteristic feature of the first series, the "washboard trim" on the front of the vehicle, which was also available as a front advertising area and smooth surface without Mercedes star, accounted for a somewhat rounded front baffle. The lateral sweep of the front turn signals was reversed.

In May 2011, the second generation Citaro, referred to internally as the C2, was launched. From 2012, the C2 could also be equipped with Euro 6 engines. The C2 versions of the Citaro LE models were the last to be presented, at Busworld Kortrijk in October 2013.

Models
There are three basic versions of the Citaro available in 2019: The standard 12m Citaro, the shorter 10m Citaro K and the articulated 18m Citaro G. Hybrid versions of all three lengths and one full electric version with standard and articulated versions are also available.

Urban model (Current)
The standard urban model is available in a number of versions:
 * O530 diesel: solo bus, length 12m, 2 axles, horizontal or vertical engine, 2 or 3 doors, even with front door only (in countries with left-hand traffic)
 * O530 eCitaro/battery-electric: solo bus with full electric drive (battery), length 12m, 2 axles, 2 or 3 doors
 * O530 diesel-electric Hybrid: solo bus with diesel-electric drive, length 12m, 2 axles, 2 or 3 doors
 * O530 NGT: solo bus with natural gas drive, length 12m, 2 axles, 2 or 3 doors
 * O530 NGT Hybrid: solo bus with natural gas-electric drive, length 12m, 2 axles, 2 or 3 doors
 * O530 G diesel: articulated bus, length 18m, 3 axles, horizontal or vertical engine, 3 or 4 doors, also with 2 doors only (in countries with left-hand traffic)
 * O530 G diesel-electric Hybrid: articulated bus with diesel-electric drive, length 18m, 3 axles, 3 or 4 doors
 * O530 G NGT: articulated bus with natural gas drive, length 18m, 3 axles, 3 or 4 doors
 * O530 GL: articulated bus (long) (CapaCity), length 19.5m, 4 axles, 3 or 4 doors
 * O530 GL II: articulated bus (long) (CapaCity L), length 21.0m, 4 axles, 4 or 5 doors (metro package)
 * O530 K diesel: midibus, length 10.5m, 2 axles, horizontal or vertical engine, 2 or 3 doors
 * O530 K diesel-electric Hybrid: midibus with diesel-electric drive, length 10.5m, 2 axles, 2 or 3 doors
 * O530 LE diesel: low entry solo bus, length 12m, 2 axles, horizontal engine, 2 or 3 doors (the 3rd door is only available as single door)
 * O530 LE Hybrid: low entry solo bus with diesel-electric drive, length 12m, 2 axles, 2 or 3 doors (the 3rd door is only available as single door)

Suburban / interurban model (Current)
A series of suburban/interurban versions is also produced, with single front doors and all seats fitted on platforms:
 * O530 GÜ: articulated bus, length 18m, 3 axles, 3 doors
 * O530 LE Ü: low-entry solo bus, length 12m, 2 axles, 2 doors
 * O530 LE MÜ: low-entry (medium length), length 13m, 2 axles, 2 or 3 doors (the 3rd door is only available as single door)
 * O530 Ü diesel: solo bus, length 12m, 2 axles, 2 doors
 * O530 Hybrid Ü: solo bus with diesel-electric drive, length 12m, 2 axles, 2 doors

Urban

 * O530 CNG: natural gas drive, length 12m, 2 axles, 2 or 3 doors (renamed as O530 NGT)
 * O530 G CNG: articulated bus with natural gas drive, length 18m, 3 axles, 3 or 4 doors (renamed as O530 G NGT)
 * O530 FuelCell Hybrid: hydrogen-fuel cell hybrid drive, length 12m, 2 axles, 3 doors
 * O530 G BlueTec Hybrid: articulated bus with diesel-electric hybrid drive, length 18m, 3 axles, 3 or 4 doors
 * O530 L: solo bus (long), length 15m, 3 axles, 2 or 3 doors

Suburban / interurban

 * O530 MÜ: solo bus (medium length), length 13m, 2 axles, 2 doors
 * O530 LÜ: solo bus (long), length 15m, 3 axles, 2 or 3 doors

Specifications
Operators are able to choose between two different front stylings: the standard design features an angled destination display, like a roof dome, and is primarily marketed for urban buses, while a version with a one-piece windscreen covering the destination display also is available and is primarily intended for interurban use. However, all models are available with either version.

With the introduction of 2nd generation Citaro, the front destination display was slightly enlarged, which juts a bit out of the vehicle roof. As a result, Mercedes-Benz designed a small fairing at both sides of destination display. This fairing is available on all models by default. Later, after the introduction of Euro VI version, which results a complete structural change in engine compartment, also the rear destination display was enlarged and added with a fairing. However, afterwards, customers are also able to order a front display without fairing, whether urban or interurban versions.

Other customizations include the number and type of doors as well as the interior layout. Two types of seats are offered as part of the standard range, again with a basic model for urban use and an enhanced version for longer-distance routes, although both also are available on all models.

Aside from the usual diesel engines, the Citaro is also available with a powerful Euro VI natural gas engine M936G rated by 222 kW. It can be optionally combined with the new hybrid system of Mercedes-Benz, which helps to save more fuel and lower emissions.

Non-standard bodies
As a one-off, German operators üstra of Hanover and LVB of Leipzig took delivery of a batch of Citaros bodied to a special design by James Irvine for Expo 2000. Leipzig's vehicles were lent to Hanover for the duration of the exhibition, but subsequently returned to normal service in their home city. All other Citaros bodied by Mercedes-Benz were to standard designs, however a number of chassis were bodied by independent manufacturers, most notably Hess of Switzerland. However, the Citaro has more recently only been sold as a complete product.

In 2007 the workshops of the Szeged (Hungary) bus operator SZKT converted a regular Citaro to a trolleybus. As of April 2010, five such buses are already serving as a trolley and more examples are in preparation in the near future.

In 2009, the Centre of Ambulance Services in Dubai took delivery of three Citaros, which had been modified to become the world's largest ambulances.

In 2010, the French city Rennes ordered a longer version of the Citaro, the Citaro M, which is 13 meters long with an urban arrangement. 15 vehicles were built over the chassis of the Setra S416NF.

Hydrogen fuel cell version

Even though the usual Citaro models are powered by diesel or natural gas, there is also a hydrogen fuel cell-powered version, designated Citaro BZ or O530BZ (BZ stands for "Brennstoffzelle" in German, or "fuel cell" in English). During the combustion process, only water steam are produced, so the vehicle is very environmentally friendly. The hydrogen tanks are located in the roof, which results an increased vehicle height at 3.68 m. These buses have 3 doors, low floor configurations, and are capable for a top speed of 70 km/h. About 35 of these buses have been in service in a variety of different world cities in order to test the feasibility of hydrogen fuel cells in numerous countries or continents (including UK, Australia and China), different operating circumstances and different conditions, especially weather conditions.

Hybrid electric version
The Mercedes-Benz Citaro G BlueTec Hybrid is a series-hybrid articulated bus with a compact 450 kg, 4-cylinder, 4.8-litre, 160 kW, Euro 4 OM-924LA diesel engine providing power for a roof-mounted 19.4 kWh lithium-ion battery pack, and four 80 kW electric wheel hub motors located on the centre and rear axles. (Contrast a conventional bus diesel engine: 6-cylinder, 12-litre, 1,000 kg.) The battery pack is also charged by regenerative braking (recuperation). The manufacturer anticipates fuel consumption 20% lower than conventional diesel Citaros. In 2010, selected bendy buses were delivered in hybrid version to Wuppertal, Stuttgart, Krefeld, Hamburg and Mülheim. Other buses were also delivered to Essen, Duisburg, Munich, Mainz, Hamburg and Rostock are also in the rigid versions. The Dresden and Leipzig also delivered their Citaro hybrid buses in 2011.

Eventually, Daimler decided to not to upgrade BlueTec Hybrid variants to second generation of Citaro. Instead, in 2017, they launched Citaro Hybrid variants of Citaro (diesel) and NGT, which uses mild hybrid drive, much cheaper to manufacture than BlueTec Hybrid drive. It uses 14 kW, disc-shaped electric motor mounted between combustion engine and transmission for energy recuperation and can provide a torque of up to 220 Nm.

Battery version / eCitaro
Since 2015, Aachen Transport runs a battery-powered Citaro articulated bus as a test in scheduled operation. The vehicle was converted in 2014 from a hybrid bus to a battery bus. They removed all diesel components and installed 1300 traction batteries with a total capacity of approximately 180 kWh. The axle loads remained unchanged. The vehicle has four wheel hub motors with 60 kW continuous power on the second and third axle and has a range of more than 50 km. The conversion was carried out as part of the EU project Civitas (Cleaner and better transport in cities) and was funded by the Aachen Transport Association to 75 percent. The costs for the hardware (e.g. batteries) amounted to approximately 700,000 euros.

Mercedes-Benz tested prototypes of the Citaro with full electric drive. The bus features a modular battery pack design and use the same electric wheel hub motors as the Citaro G BlueTec Hybrid. It was launched at the IAA Commercial Vehicles show in Hanover in September 2018 as eCitaro. It uses modified bodywork of standard Citaro with front adopted from Daimler's concept Future Bus. It was first launched as 12 m solo bus. Later, an articulated 18 m version of eCitaro (also known as eCitaro G) was added to offer.

On 15 November 2018, the first series of eCitaro was delivered to its first customer: Hochbahn AG, a public transport company in Hamburg, with a total of 20 at last. In year 2019, more customers started operating eCitaros, including Rhein-Neckar-Verkehr GmbH (RNV), Berliner Verkehrsbetriebe (BVG), Zugerland Verkehrsbetriebe (ZVB), and Bus Ostschweiz (BOS). This was also followed with orders from Verkehrsbetriebe Hamburg-Holstein (VHH) with 16 buses, ESWE Verkehrsgesellschaft mbH from Wiesbaden with 56, and ÜSTRA from Hannover with 48. Mercedes-Benz also received orders from foreign countries, which contains Luxembourg, Norway, and Sweden. In addition, the eCitaro has been crowned to City Bus of the Year 2019 in Spain on 11 February 2019. In 2021, the national bus operator of Hungary, Volánbusz ordered 40 eCitaros, and in 2023, Transdev Blazefield in the United Kingdom ordered 35 eCitaros for their Harrogate Bus Company and Keighley Bus Company subsidiaries.

In 2023, a version with a Toyota hydrogen fuel cell range extender will be offered, allowing a range of up to 400 km, compared to 280 km for the battery electric model.

Overhead wire version
Because EvoBus itself does not offer trolleybuses, the transport companies of the Hungarian city of Szeged independently built six second-hand Citaro solo vehicles into trolleybuses between 2006 and 2010. This is expected to save on spare parts inventory - this can be done together with the same diesel buses of the dispenser series - as well as lower acquisition costs compared to standard production trolleybuses. The modified type designation is O-530 Tr12, the six wagons bear the operating numbers T-860 to T-865.

In 2012, two Citaro trolleybuses also went into operation in Polish Gdynia. The cars with the numbers 3053 and 3054 originated from used acquired diesel buses from Berlin, which had been delivered in 2002.

CapaCity
Mercedes-Benz CapaCity (also known as O530 GL) is a large-capacity articulated bus based on Citaro G, which was introduced in year 2007. The 1st generation CapaCity is 19.54m long and can carry up to 186 passengers. It features exactly the same turning circle as that of its shorter related Citaro G (17.94m length) thanks actively steered electro hydraulic fourth axle. The safety is guaranteed by Electronic Braking System (EBS), anti-lock brakes (ABS), acceleration skid control (ASR), and the passenger comfort is improved by independent front suspensions. It is both available with 3 and 4 doors. There are also CapaCitys with BRT-Design, which can be recognized by their changed exterior. These buses are currently in service in Istanbul, Turkey, and Bratislava, Slovakia.

The 2nd generation CapaCity was first presented in year 2014. However, it is the long version "CapaCity L" (21m) which became available at the beginning. The shorter version "CapaCity" with a length of 19.7m was added later. They are all based on the modular system of Mercedes-Benz Citaro. The new feature "Articulation Turntable Controller" (ATC) prevents additionally from jackknifing. CapaCity L can carry 191 passengers with standard equipment, CapaCity 182 passengers. They are offered with four doors by default, but with "Metro Package", CapaCity L is also available with five doors, which is better constructed for BRT services. According to Daimler, CapaCity L is the diesel powered urban bus which uses the least fuel per passenger space.

Conecto
In year 2007, the 2nd generation Conecto was presented and is both available as standard 12m and articulated 18m version. They are however only available with 3 doors (solo version) and 4 doors (articulated version). Unlike its predecessor as an independent model series (a step-entrance bus derived from O405, model designation O345), it is a technically simplified version of Citaro or Citaro G, with low floor configuration and vertical engines. It is recognizable with the changed exterior design and small differences in interior's design in opposition to Citaro and is mainly sold in eastern Europe, the Middle East and west Asia. The 3rd generation is, since 2018, also sold in Italy (when low-floor Conecto was never officially sold before).

Like previous step-entrance Conecto models, the low-floor Conecto is also produced at Mercedes-Benz Türk factory in Istanbul, Turkey.

In September 2016, the 3rd generation Conecto was presented in Warsaw, Poland. Several improvements were done for the new Conecto, as well as driving safety, passenger comfort, handling and Euro 6 engines, while the operation costs still stay low. Examples for high standard of safety are Electronic Stability Program (ESP) on solo versions and Articulation Turntable Controller (ATC) on articulated versions. Conecto and Conecto G NGT powered by natural gas are also available for the first time. Like the 2nd generation, the 3rd generation Conecto is solely available with 3 doors (solo version) and 4 doors (articulated version). In 3rd generation Conecto, only Euro VI-compliant engines are available (OM936 in 12 m, OM470 in 18 m and M936G in gas versions); the 2nd generation Conecto, with Euro V-compliant engines (OM926LA in 12 m and OM457LA in 18 m models), continues to be marketed in certain non-EU developing markets in eastern Europe, the Middle East and west Asia, alongside the 3rd generation Conecto.

Production
The Citaro is currently built in factories in Mannheim, Germany, and Ligny-en-Barrois, France. It was also built in Sámano in Spain.

The low-cost-variant Conecto is produced by Mercedes-Benz Türk A.Ş. in Hoşdere, Başakşehir, Istanbul, Turkey.

Germany
In May 2018, the Berliner Verkehrsbetriebe (BVG) placed an order for a total of 950 new Citaros: 350 Citaros and 600 Citaro Gs, the first of which was delivered on 20 November 2018. Their engines all meet the Euro VI standard, have low fuel consumption and lower emissions. The BVG also placed a second order for 15 eCitaro, which were delivered in the first quarter of 2019.

The Mercedes-Benz Citaro is also widely used in the rest of Germany. The Hamburger Hochbahn has operated the Citaro since 1997 and has over time, ordered over 1000 in total. DB Stadtverkehr GmbH, a subsidiary of Deutsche Bahn, operates a large number of Citaro or rather Citaro G. They are used in scheduled urban and interurban services in numerous federal states and cities, e.g. Aachen, Düsseldorf, München, Münster, and Stuttgart.

Austria
The Citaro lineup is also very popular in Austria and is used in many cities. There are extensive Citaro fleets in Vienna (134 Citaro NL, 227 Citaro NG, 62 CapaCity NG XL; augmented by additional Citaro variants operated by private operators), Graz (174 vehicles of various variants), Linz (55 vehicles), among others.

Slovakia
In 2008 to 2013 Bratislava ordered 41 large buses of type Mercedes-Benz CapaCity to replace buses of types Ikarus 435 and Diesel buses Karosa B741. The first bus entered into service in December 2008 on route 96 with evidence number 1999. In 2010 ordered in total 25 buses and in 2012 ordered 15 buses. Bratislava also ordered 1 Citaro CNG with number 2020. Citaro CNG entered to service in November 2009 To February 2018 and today bus Citaro CNG is sold to private owner.

In 2002 Nitra ordered 1 Citaro only for route 28. Original transparents are being replaced in summer 2013 with R&G Mielec.

Public transport in Poprad operates 16 buses of versions C2 K (delivered in 1/22 – 12/22) 8pcs, O 530 2pcs, C2 6pcs delivered in (2020)

In 2022 Blaguss Slovakia purchased 5 buses from Wiener Linien for public transport in Ružomberok.

Hungary
In Hungary, VT-Arriva purchased 159 to operate services in Budapest for Budapesti Közlekedési Központ (BKK) in 2013, followed by two more units the year after. But these were replaced in 2023 by MAN NLC.

The Netherlands

Connexxion had ordered a total of 255 buses throughout 1998 and 2014. That 255 contains the order of the 75 buses in 2019. Besides that they placed another order of 33 Capacity L buses.

The RET, from Rotterdam, has made 2 orders in 2006 and 2008 for a total of 166 Citaro buses. In 2010 they made another small order of 2 hybrid Citaro articulated buses.

Syntus, in the eastern side of the Netherlands, placed two orders for 33 buses. 11 Citaro CNG single buses under the moniker "Gelderland" and 22 articulated CNG buses under the moniker "Veluwelijn".

In 2009, Qbuzz ordered 390 while Connexxion ordered 75. As of 2018 Connexxion under the R-Net moniker took delivery of several CapaCity L models. In 2014 Qbuzz ordered another 138 buses for Utrecht under the moniker "U-OV."

Romania
Between 2005 and 2009 Regia Autonomă de Transport București (now called STB) purchased 1,000 Citaros, 500 euro 3 first model and 500 euro 4 from the Mercedes-Benz Citaro facelift.

In September 2019, STB ordered 130 Citaro Hybrid buses with deliveries to begin in the spring of 2020.

Citaro C2 Hybrid buses can also be seen in Brașov operated by RATBV.

Spain
In 2016, Empresa Municipal de Transportes de Madrid (EMT Madrid) ordered 82 natural gas versions of the Citaro, known as the Citaro NGT. The following year, it placed an order for a further 314 buses, and in 2018 it placed another order for a further 276 buses, for a total of 672 buses, all of which are due to enter service by 2020.

Portugal
In 2000, Companhia de Carris de Ferro de Lisboa (CCFL) acquired 39 diesel variants of the Citaro, with 3 doors, ZF 5HP502 and OM457hla chassis and, later that year, Sociedade de Transportes Colectivos do Porto (STCP) bought 75 bodywork-based Citaros, with Salvador Caetano CityGold bodywork, OM906hla chassis and Voith D851.3 gearbox, the only series in the world with a 3-speed gearbox. Afterwards, Transportes Colectivos do Barreiro (TCB) and Serviços Municipalizados dos Transportes Urbanos de Coimbra (SMTUC) purchased (since 2001) this model, the case of the first one between the Euro 2, Euro 3, Euro 4 and the Facelift versions, and the second company just the Euro 2 and Euro 3 variants. Both companies also acquired used Citaros, with TCB purchasing four ex-De Lijn vehicles with Euro 3 and SMTUC with a 1997 ex-Hochbahn Citaro (previously owned by Linhares, and also the first used Citaro to Portugal), four ex-Nobina with 3-door and anti-fire system (one already out due to fire) and one with vertical engine, originally a temporary bus, but since 2021 as theirs. In 2022, three Citaro Facelift, originated from TCB after staying out of service for a few years, along with five Volvo B7RLE with Marcopolo Viale Midi buses, both vehicle types from 2009, were purchased for additional service in Coimbra. These vehilcles were bought with money originally used to buy a private vehicle for the city council, and they came in a very good condition, although their Voith gearbox have their reatrders always set off, since TCB did disable those on their buses with Voith. Besides the ex-Hochbahn Citaro in Linhares, Rodoviária de Lisboa purchased the Uberland variant of the Citaro, being the second vehicle as second hand purchase. In 2004, STCP tested three Citaro Fuel Cell models for two years, part of the CUTE project for the hydrogen tests through some European countries. Along with those, three Euro 3 Citaros were offered to the company to complement the Fuel Cell tests. One of the hydrogen buses is saved as part of a possible museum (this one has its engine removed) and two of the Citaros are still in circulation (one of them was burned down caused by the engine in December 2016). Since 2008, CCFL purchased the articulated variant of the Citaro Facelift (Citaro G) in two gearbox segments: Voith Diwa 5 and ZF EcoLife. These ones allowed to replace the older Volvo B10M articulated buses from 1991 through 1993 (20 at 2008 and 30 at 2010). In 2010, Empresa de Transportes Gondomarense bought five Citaro K (midi variant) for bus lines with small numbers of passengers. Since then, various Citaro models were second hand buses from Spain and Germany, mostly. In 2018, part of the PO-SEUR project from the Portuguese Government, CCFL acquired 40 Citaro C2G NGT (natural gas) buses to replace the 1995 and 1997 Volvo B10M articulated buses, along with 125 CaetanoBus bodied MAN 18.310 CNG. Besides these ones, Scotturb also acquired 1+20 Citaro C2K, 10 of them are hybrid, for the Circuito da Pena line. This is also from the time when second hand Citaro C2 are put in circulation, like in Rodoviária de Lisboa having 2013 C2 ex-Dr. Richard, from Vienna. In 2022, Área Metropolitana de Lisboa (AML) offered 633 Conectos, 157 Intouros and 50 Citaros (all with Euro 6 engines and Voith Diwa 6 gearbox). Maia transportes, an operator based in Portuguese city, Maia, in Porto, also bought some citaros second handed from Germany. Maia transportes also has 2 ex-Rodoviaria de Lisboa Citaro's Ü.

Italy

In 2001, ATAC of Rome ordered 183 Citaro MU interurban model with a blue livery and two doors. This was followed by 301 Citaros urban and suburban model in the normal ATAC grey livery with 2 and 3 doors, in 2004. They operate on many routes, including 63, 88, 98, 443, 559, 775 and 881 and many lines around Ostia. ATAC have also introduced 100 new Citaro C2 Hybrid 12m buses entering service in June 2021.

Outside of the capital, ATM of Milan took a delivery of 112 Citaro G bendy buses (in late 2008). These are fleet numbered 2901-2984 (4 door model) and 1300-1327 (3 door model) and are mainly seen on routes 70, 73, 94 (2900-2984), 727 and 729 (1300-1327). This was followed by a batch of 2 Citaro G Hybrid in 2011 (2590 and 2591), only allocated to route 94, as well as 3 Citaro Hydrogen 12m in 2012 (2000 to 2002), allocated to route 84. More Citaros (C2 Hybrid 12m) are currently being delivered to Milan.

In 2008, ANM of Naples took delivery of 44 gas powered Citaro Facelift CNG 12m TPLITALIA.IT. These currently run on routes R2 and 151, but can often be seen on other routes operated from the Via delle Puglie depot (such as 601 and R5). Previously, some of these were branded for the ALIBUS route (Airport to City Centre) route until late 2018, when they got displaced by a new fleet of MenariniBus Citymood 10m buses. The buses were supplied by a regional order by Campania which included a total of 58 buses being ordered. The other 14 went to BusItalia of Salerno (at the time CSTP), fleet numbered CITA01-CITA14 TPLITALIA.IT. Once again by a regional order, a further 20 Citaro K C2 Euro 6 were delivered to Naples, fleet numbered N201 to N220.

Citaros are also operated in Venice (ACTV), Trieste (Trieste Trasporti), Cagliari (CTM and ARST) and Bologna (TPER), among other cities. Some of these companies also run Citaro U interurban buses.

Greece
In 2007, Thessaloniki local bus operator OASTH introduced 28 Citaro G buses, with 14 more coming in 2012. In 2009, a 12 meter Citaro was ordered for the cultural route of Thessaloniki. It is equipped with screens that displays information about landmarks and comes with a microphone for the tour guide to speak. The citaro is also widely used in other cities of Greece. From 2020 to 2023 both Athens and Thessaloniki have rented used Citaro buses from PAPADAKIS BROS S.A. that were previously owned by several european bus operators including Connexxion, Qbuzz, BVG and more.

London
Right-hand drive versions of the articulated Citaro G were introduced in London on 2 June 2002, on routes 507 and 521. They were eventually used on 12 routes across London, and were operated by various Transport for London operators including East London, First London, London Central, London General and Selkent.

In 2003 and 2004, four Citaro Gs caught fire, although there were no casualties involved. One was burnt on its delivery journey. Mercedes-Benz did address the problem, though the buses were withdrawn for some time which the saw the brief return of the just-retired AEC Routemasters. Unfortunately, the fires are said to have marred the reputation of articulated buses in the United Kingdom, and some people nicknaming them Chariots of Fire. The final Citaro G in London was withdrawn in December 2011. Eighty-one of Arriva London's examples were exported for use with Arriva Malta.

The first Citaros in London were 12 rigids introduced by First London on 27 April 2002 on route RV1. Others purchasers of rigids were London General for routes 507 and 521 in 2008, and Quality Line for routes X26 in 2011 and 413 in 2016.

Rest of the UK
Many of the former London Citaro Gs saw further service with various Arriva, FirstGroup, Go-Ahead Group, National Express and Stagecoach Group fleets outside of London.

In 2008, First York purchased 15 Citaro Gs for its York Park & Ride operation. In 2015 Blackpool Transport received 10 Citaros for use on Palladium branded routes. In 2015 Cardiff Bus received 20 Citaros.

France
The RATP Bus Network of Paris operates 426 Citaros of which 349 are standard, 12m length and the other 77 are 18m length bendy buses.

China
In year 2006, 3 hydrogen-fuelcell-powered Citaro buses began their test launch in Beijing, China. They ran on an 18.2 km long ring-line, which contains 11 stations and uses Summer Palace North Gate as departure/terminal station. The operating hours ranged from 9am to 3pm, the bus came approx. every 40 minutes. Each ride costs 2 CNY. During the launch, these 3 Citaro left a very positive impression to the passengers.

Japan
In 2010, Keisei Bus ordered 15 articulated Citaro G buses, primarily for service in east Tokyo.

Nishitetsu also operates several Citaro G buses on the Fukuoka BRT.

Singapore

SMRT Buses trialed a Euro V demonstrator unit in 2010, which proved to be successful and an additional 10 buses were purchased with a follow-up order of another 40.

In 2010, SBS Transit had made an initial purchase of 300 buses to replace all the remaining Volvo B10M Mark III, as well as a few Volvo B10M Mark IV (Duple Metsec and Walter Alexander Strider), Additional orders were being made to replace all Volvo B10Ms, with another order of 450 (increased to 474) in 2012 and a further 250 (increased to 330) in 2014.

By 2017, a grand total of 1,155 Citaro buses have been registered.

In 2022, SBS Transit had redeployed several MAN NL323F buses and Mercedes-Benz O530 Citaro buses to replace Scania K230UBs on cross-border bus routes, which are the last diesel single-deck buses to use in Singapore. Those allocated under the Bus Contracting Model were redeployed to SBS Transit.

In March 2020, SBS Transit introduced a Mercedes-Benz Citaro hybrid with C2 bodywork, registered as SG4004B as part of a 1-year trial and transition to sustainable transport. It was deployed on service 93 and 272, and had returned to Mercedes-Benz in 2021, which is due to the subsequent transition to the electric Citaro fleet in the future. SG4004B was eventually exported to the UK in late 2023.

Australia
In Australia, between September 2004 and September 2007, Transperth trialled three hydrogen powered O530BZs. One was preserved by the Bus Preservation Society of Western Australia with the other two scrapped at the end of the trial. In 2016, Brisbane Transport trialled a Citaro demonstrator.

Saudi Arabia
The Saudi Public Transport Company (SAPTCO), in a joint venture with RATP Group, placed an order for 200 Citaros and 400 Citaro Gs on 16 May 2017. These Citaros are specially adapted for use in the hot desert conditions of Saudi Arabia, with an uprated air conditioning system, circulating air blowers in the doors and double-glazed, darkened side windows. The first vehicles were due for delivery in 2018.

United Arab Emirates
By 2009, 180 Citaros had been delivered to the city of Al Ain.

United States
In 2008, the MTA of New York City trialled a Citaro G Facelift bendy bus.

Latin America
In Latin America, Citaros are not present in large quantities in public transport systems.

Chile
Currently in Santiago, Chile, operates a single bus on line 104 of Red Metropolitana de Movilidad since 2020.

Mexico
Mexico City has 14 Spanish-built Citaros for the BRT Internal System of UNAM.

title: Mercedes-Benz Citaro


text:
User talk:194.203.201.92

Proposed deletion of Zirconium propanoate

The article Zirconium propanoate has been proposed for deletion because of the following concern: "this compound nor anything like it exists."

While all constructive contributions to Wikipedia are appreciated, pages may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the page to address the issues raised. Removing will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Smokefoot (talk) 22:35, 20 November 2021 (UTC)

title: User talk:194.203.201.92


text:
Supercritical

Supercritical may refer to:

Condensed matter physics

 * Critical temperature, TC, a temperature above which distinct liquid and gas phases do not exist for a given material
 * Supercritical drying, a process used to remove liquid in a precisely controlled way, similar to freeze drying
 * Supercritical fluid, a substance at a temperature and pressure above its thermodynamic critical point:
 * Supercritical carbon dioxide:
 * Supercritical fluid chromatography, a form of liquid chromatography using supercritical carbon dioxide as the mobile phase
 * Supercritical water:
 * Supercritical steam generator, a steam generator operating above the critical point of water, hence having no water–steam separation
 * Supercritical water oxidation or SCWO, a process that occurs in water at temperatures and pressures above a mixture's thermodynamic critical point
 * Supercritical water reactor (SCWR), a Generation IV nuclear reactor concept that uses supercritical water as the working fluid

Flows

 * Supercritical flow, where flow velocity is larger than wave velocity
 * Supercritical airfoil, an airfoil designed to delay the onset of wave drag in the transonic speed regime

Nuclear physics

 * Supercritical mass, an amount of fissile material that will undergo a sustained nuclear chain reaction at an increasing rate

Mathematics

 * Hopf bifurcation, in mathematics, a local bifurcation; when the first Lyapunov coefficient is negative, the bifurcation is called supercritical
 * Pitchfork bifurcation, in mathematics, similar to Hopf bifurcation

Other uses

 * Super Critical, an album by British pop/rock group The Ting Tings

title: Supercritical


text:
Namli Mera Union Council

Namli Mera is a residential town and a mountainous rural area located in Abbottabad District, Khyber Pakhtunkhwa province, Pakistan.

It is one of the 51 union councils of Abbottabad District, and takes its name from the two largest hamlets in the Union Council, Namli and Mera. Its capital is New kalwan city. These settlements are nestled on mountain ridges about 20 kilometres from the city of Abbottabad, in the foothills of Miranjani, the highest peak in the district. A metalled road connects Namli Mera to the main Abbottabad—Nathia Gali road and is an alternate route to reach Nathia Gali from Abbottabad. Namli Mera is around 3 kilometres away Bagnotar on the main road.

Climate and crops
Being at a high altitude, this region hosts extreme winters (starting October) and a temperate and slightly humid summer (April onwards) which temperatures reaching 30C. July and August also see the monsoon which cause a pleasant drop in temperature.

Farming is the main occupation of the population. The farming is done by oxen in remote areas but in villages with better accessibility the land is ploughed by machinery. The two crops grown there are rabi and Kharif crop. The major rabi crops grown in the area are potato and maize, and the kharif crop is only wheat, in a very small area of village. The wheat is used for cattle and for grain only. Some vegetables are also found here, including turnip, radish, peas, pumpkin, beans and mustard.

Fruits like pear, apple, black grapes, grapes, fig, peach, damson plum, mulberry, wild fig, lemon, apricot, charry are found in abundance in Namli Mera. As the hill people lack awareness of the markets, they are unable to get a proper return. These fruits are therefore used for subsistence.

Most of the area around these mountain villages is covered with trees. Peaks are covered with evergreen trees including pine, walnut, oak and maple trees. Herbs, shrubs, wild flowers and thorny bushes can be seen in abundance. Goats and other pet animals graze the pastures.

Livelihood and economy
The main occupation of the people is subsistence farming and cattle breeding. Farmers cultivate one crop per season as climatic conditions do not permit double cropping. The other occupation is cattle breeding. Cows, sheep and goats are kept to supply milk for daily use of the household. Bullocks are used to work the plough. Poverty has forced many people to seek economic opportunities in the plains. Besides earning livelihood doing jobs in nearby towns, many have joined the army and civil service. Hotels in the nearby hill towns of Nathia Gali, Ayubia and Murree provide another source of employment to the locals. After turmoil in Swat, Namli Mera is gradually becoming popular with tourists from down country.

Wood is the primary source of fuel and home construction, as there is no gas in Namli Mera. People go to forests and cut trees so that they can light fires for cooking and other activities. Those who can afford them use LPG gas cylinders.

People
The population of Namli Mera is Muslim, belonging to the Sunni sect. About 90% belong to the Karlal (Sardar) tribe. Other tribes in this area include Turks, Awan, Abbasi and a handful of Mughals.

The mother language of the people of Namli Mera is Pahari پہاڑی, which is slightly different from Pothwari. Locals also speak and understand Hindko, Urdu, Pashto and English. The elderly people of the area can also speak and understand Persian and Arabic.

Education
Namli Mera village has one of the highest literacy rates for the district. The literacy rate of Namli Mera is about 92%. But some says its 99.99%. Government and private schools cater to the elementary educational needs of the residents. There are Primary schools for boys and girls, Government Boys High School and Girls High School. A number of private schools are also available. Habib Public School, Abaseen Public School, Model Public School are the oldest and famous school of the village. Al-falah Public School in Chanati and Iqra Public School in Upper Mera Kalan are the other private schools.

Tourism
Since the earthquake of 2005 tourists prefer Nathi Gali and surrounding areas like Namli Mera, Kala Bagh, Thandiani and Mushkpuri. The approach to Namli Mera is the same from Murree and Abbottabad (32 km from either side). Miranjani (also known as "Choki") is one of the most popular sites of Namli Mera. Mirajani stands approximately 9,000 feet above sea level. There is an old track adjacent to Mirajani which connects Nathia Gali to Thandiani. Along the track lies a British-era forest rest house, called Dagri Bangla by the locals. The location of the building, in the middle of thick forest, colonial style of construction and remoteness give it an aura of mystery.

2005 earthquake
On 8 October 2005, an earthquake of magnitude 7.6 struck the northern areas and Kashmir, causing significant damage to housing and a large number of deaths. Aftershocks were felt through December.

title: Namli Mera Union Council


text: User talk:202.75.80.6

title: User talk:202.75.80.6


text:
Category:Californios

 * Californios — colonial people living in Spanish Las Californias Province (1769-1822) and Mexican Alta California (1822-1848).
 * Californios remained residents after the region became a U.S. territory (1848) and the U.S. state of California' (1850).

title: Category:Californios


text:
MKULTRA (disambiguation)

Project MKUltra is the code name for a CIA mind-control research program that began in the 1950s.

MKULTRA or MK-ULTRA may also refer to:

 * MK Ultra (film), 2022 psychological thriller film written and directed by Joseph Sorrentino
 * mk Ultra (California band), a defunct alternative band
 * The MK Ultra, a music project by British rock musician James Ray
 * "MKultra", a song by American band Unwound on the album A Single History: 1991–1997
 * "MK Ultra", a song by British rock band Muse on the 2009 album The Resistance
 * "MK Ultra Ragman", a song by the Canadian electro band platEAU from the 2007 album Kushbush
 * "MK Ultra", a song by the American prog metal band Periphery from the 2015 album Juggernaut: Alpha

title: MKULTRA (disambiguation)


text:
Wikipedia:Articles for deletion/Herbal preparations

Herbal preparations was proposed for deletion. This page is an archive of the discussion about the proposed deletion. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was delete

Herbal preparations
Useless, biased, potentially harmful medical advice.--119 09:10, 29 Nov 2004 (UTC)
 * Delete. Any proven effects (not affects) can be incorporated in existing articles on vitamins and other additives. [[User:MacGyverMagic|Mgm|(talk)]] 09:47, Nov 29, 2004 (UTC)
 * Delete. See above.  --Randy 12:21, 29 Nov 2004 (UTC)
 * Delete: DCEdwards1966 17:44, Nov 29, 2004 (UTC)
 * Delete: See above. -Willmcw 22:51, 1 Dec 2004 (UTC)

This page is now preserved as an archive of the debate and, like other '/delete' pages is no longer 'live'. Subsequent comments on the issue, the deletion or on the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.


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User:Cde Laski

Hello, I'm Cde. Laski, CPUSA (ML).

title: User:Cde Laski


text:
Talk:Wainuiomata

Untitled
Wow i cant belive Wainuiomata is on here - yes it is and now all we need is people to expand this topic —Preceding unsigned comment added by Ajgio (talk • contribs) 07:54, 3 September 2007 (UTC) )

I am reasonably sure parts of Without a paddle http://www.imdb.com/title/tt0364751/ were filmed in Wainuiomata (up Moores valley road). Also worth mentioning is the mountain bike park, including the motor cycle park also the bmx track.

the partial tunnel that was build around 1912? is probably worth mentioning too. — Preceding unsigned comment added by 14.1.85.229 (talk) 09:16, 14 October 2014 (UTC)

 * Presumably your mention of a tunnel is a reference to the planned road tunnel that was started in 1932? As there is already an article for this, a brief mention in this (Wainuiomata) article would suffice.  — Matthew25187 (talk) 11:45, 15 October 2014 (UTC)

Wai Mata
A correct translation for wai is 'fresh water', not 'water'. Paradoxaly, because tears are somewhat salted, wai CAN be used for tears cf. marquesan : vaimata but the common word is roimata (also in tahitian, cook island maori). In one of the explanation, it is implied that 'mata' means face, which is true, but more frequently 'eye(s)'. Conclusion, if it were about the tears, it would be roimata, or waimata. Wainuiomata is more probably about the river OF someone called Mata or about eyes in the river, gasp. stefjourdan — Preceding unsigned comment added by 163.47.106.146 (talk) 01:30, 16 January 2017 (UTC)
 * Interesting take, but tears is given in the dictionary as a translation of ‘wai’ and also the word doesn’t necessarily mean fresh water, but any liquid or even juice. See [Māori Dictionary] Piwaiwaka (talk) 23:48, 13 March 2019 (UTC)

title: Talk:Wainuiomata


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Walter Hamilton (VC)

Walter Richard Pollock Hamilton VC (18 August 1856 – 3 September 1879) was born in Inistioge, County Kilkenny and was an Irish recipient of the Victoria Cross, the highest and most prestigious award for gallantry in the face of the enemy that can be awarded to British and Commonwealth forces. He is featured in M. M. Kaye's epic novel The Far Pavilions.

Details
Hamilton was a great nephew of General Sir George Pollock who led the Army of Retribution in the First Afghan War. He was educated at Felsted. Hamilton was 22 years old, and a lieutenant in the Staff Corps and Corps of Guides, Indian Army during the Second Afghan War when the following deed took place on 2 April 1879 at Futtehabad, Afghanistan, for which he was awarded the VC: "For conspicuous gallantry during the action at Futtehabad on the 2nd April, 1879, in leading on the Guide Cavalry in a charge against very superior numbers of the enemy, and particularly at a critical moment when his Commanding Officer (Major Wigram Battye) fell, Lieutenant Hamilton, then the only Officer left with the Regiment, assumed command and cheered on his men to avenge Major Battye's death. In this charge Lieutenant Hamilton, seeing Sowar Dowlut Ram down, and attacked by three of the enemy, whilst entangled with his horse (which had been killed) rushed to the rescue, and followed by a few of his men cut down all three and saved the life of Sowar Dowlut Ram."

The scene of Hamilton's death was the Bala Hissar, an enclosure within the city of Kabul. He commanded a small force of 20 Cavalry and 50 Infantry, all from the Corps of Guides, which formed an escort for Sir Louis Cavagnari the Envoy who was to set up the Residency in Kabul following the Treaty of Gandamak. After a riot by mutinous Afghan troops, who were demanding arrears of pay, the Residency was attacked on 3 September 1879. Fierce fighting took place between the Guides and the attackers, during which Cavagnari and all the Guides were killed.

On 15 May 1879, six weeks after the action at Futtehabad, the Government in India forwarded a Victoria Cross recommendation for Hamilton to London which on 6 August determined that his act was not covered by the Victoria Cross regulations. There was a change of heart when the Secretary of State for India, Lord Cranbrook, noted that Hamilton's actions were similar to those of Captain John Cook and Lieutenant Reginald Hart who had both been awarded the Victoria Cross two months earlier. By this stage Hamilton had been killed at Kabul on 3 September and in order to avoid the precedent of seeming to approve a posthumous award the submission to the Queen on 28 September was backdated to 1 September 1879. The award was gazetted on 7 October 1879, the 12th Victoria Cross recommendation approved after the death of the recipient.

Memorials
A slightly over-life-size statue of Hamilton striding over an Afghan threatening him with a knife was produced in bronze-painted plaster by Charles Bell Birch in Dublin in around 1880. It is now on display in the National Army Museum, Chelsea, as is a plaque to him (set up in the Punjab Frontier Force Chapel, then in the sanctum crypt of St. Lukes Chapel, Chelsea).

In the media
Walter Hamilton is a character in the novel "The Far Pavilions", in the HBO-miniseries adaption he was portrayed by Benedict Taylor.

title: Walter Hamilton (VC)


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Sturm's theorem

In mathematics, the Sturm sequence of a univariate polynomial $p$ is a sequence of polynomials associated with $p$ and its derivative by a variant of Euclid's algorithm for polynomials. Sturm's theorem expresses the number of distinct real roots of $p$ located in an interval in terms of the number of changes of signs of the values of the Sturm sequence at the bounds of the interval. Applied to the interval of all the real numbers, it gives the total number of real roots of $p$.

Whereas the fundamental theorem of algebra readily yields the overall number of complex roots, counted with multiplicity, it does not provide a procedure for calculating them. Sturm's theorem counts the number of distinct real roots and locates them in intervals. By subdividing the intervals containing some roots, it can isolate the roots into arbitrarily small intervals, each containing exactly one root. This yields the oldest real-root isolation algorithm, and arbitrary-precision root-finding algorithm for univariate polynomials.

For computing over the reals, Sturm's theorem is less efficient than other methods based on Descartes' rule of signs. However, it works on every real closed field, and, therefore, remains fundamental for the theoretical study of the computational complexity of decidability and quantifier elimination in the first order theory of real numbers.

The Sturm sequence and Sturm's theorem are named after Jacques Charles François Sturm, who discovered the theorem in 1829.

The theorem
The Sturm chain or Sturm sequence of a univariate polynomial $P(x)$ with real coefficients is the sequence of polynomials $$P_0, P_1, \ldots,$$ such that
 * $$\begin{align}

P_0&=P,\\ P_1&=P',\\ P_{i+1}&=-\operatorname{rem}(P_{i-1},P_i), \end{align}$$ for $i ≥ 1$, where $P'$ is the derivative of $P$, and $$\operatorname{rem}(P_{i-1},P_i)$$ is the remainder of the Euclidean division of $$P_{i-1}$$ by $$P_{i}.$$ The length of the Sturm sequence is at most the degree of $P$.

The number of sign variations at $ξ$ of the Sturm sequence of $P$ is the number of sign changes (ignoring zeros) in the sequence of real numbers
 * $$P_0(\xi), P_1(\xi),P_2(\xi),\ldots.$$

This number of sign variations is denoted here $V(ξ)$.

Sturm's theorem states that, if $P$ is a square-free polynomial, the number of distinct real roots of $P$ in the half-open interval $(a, b]$ is $V(a) − V(b)$ (here, $a$ and $b$ are real numbers such that $a < b$).

The theorem extends to unbounded intervals by defining the sign at $+∞$ of a polynomial as the sign of its leading coefficient (that is, the coefficient of the term of highest degree). At $–∞$ the sign of a polynomial is the sign of its leading coefficient for a polynomial of even degree, and the opposite sign for a polynomial of odd degree.

In the case of a non-square-free polynomial, if neither $a$ nor $b$ is a multiple root of $p$, then $V(a) − V(b)$ is the number of distinct real roots of $P$.

The proof of the theorem is as follows: when the value of $x$ increases from $a$ to $b$, it may pass through a zero of some $$P_i$$ ($i > 0$); when this occurs, the number of sign variations of $$(P_{i-1}, P_i, P_{i+1})$$ does not change. When $x$ passes through a root of $$P_0=P,$$ the number of sign variations of $$(P_0, P_1)$$ decreases from 1 to 0. These are the only values of $x$ where some sign may change.

Example
Suppose we wish to find the number of roots in some range for the polynomial $$p(x)=x^4+x^3-x-1$$. So

 * $$\begin{align} p_0(x) &=p(x)=x^4+x^3-x-1 \\

p_1(x)&=p'(x)=4x^3+3x^2-1 \end{align}$$

The remainder of the Euclidean division of $p_{0}$ by $p_{1}$ is $$-\tfrac{3}{16}x^2-\tfrac{3}{4}x-\tfrac{15}{16};$$ multiplying it by $−1$ we obtain
 * $$p_2(x)=\tfrac{3}{16}x^2+\tfrac{3}{4}x+\tfrac{15}{16}$$.

Next dividing $p_{1}$ by $p_{2}$ and multiplying the remainder by $−1$, we obtain
 * $$p_3(x)=-32x-64$$.

Now dividing $p_{2}$ by $p_{3}$ and multiplying the remainder by $−1$, we obtain
 * $$p_4(x)=-\tfrac{3}{16}$$.

As this is a constant, this finishes the computation of the Sturm sequence.

To find the number of real roots of $$p_0$$ one has to evaluate the sequences of the signs of these polynomials at $−∞$ and $∞$, which are respectively $(+, −, +, +, −)$ and $(+, +, +, −, −)$. Thus
 * $$V(-\infty)-V(+\infty) = 3-1=2,$$

where $V$ denotes the number of sign changes in the sequence, which shows that $p$ has two real roots.

This can be verified by noting that $p(x)$ can be factored as $(x^{2} − 1)(x^{2} + x + 1)$, where the first factor has the roots $−1$ and $1$, and second factor has no real roots. This last assertion results from the quadratic formula, and also from Sturm's theorem, which gives the sign sequences $(+, –, –)$ at $−∞$ and $(+, +, –)$ at $+∞$.

Generalization
Sturm sequences have been generalized in two directions. To define each polynomial in the sequence, Sturm used the negative of the remainder of the Euclidean division of the two preceding ones. The theorem remains true if one replaces the negative of the remainder by its product or quotient by a positive constant or the square of a polynomial. It is also useful (see below) to consider sequences where the second polynomial is not the derivative of the first one.

A generalized Sturm sequence is a finite sequence of polynomials with real coefficients
 * $$P_0, P_1, \dots, P_m$$

such that
 * the degrees are decreasing after the first one: $$\deg P_{i} <\deg P_{i-1}$$ for $i = 2, ..., m$;
 * $$P_m$$ does not have any real root or has no sign changes near its real roots.
 * if $P_{i}(ξ) = 0$ for $0 < i < m$ and $ξ$ a real number, then $P_{i −1 }(ξ) P_{i + 1}(ξ) < 0$.

The last condition implies that two consecutive polynomials do not have any common real root. In particular the original Sturm sequence is a generalized Sturm sequence, if (and only if) the polynomial has no multiple real root (otherwise the first two polynomials of its Sturm sequence have a common root).

When computing the original Sturm sequence by Euclidean division, it may happen that one encounters a polynomial that has a factor that is never negative, such a $$x^2$$ or $$x^2+1$$. In this case, if one continues the computation with the polynomial replaced by its quotient by the nonnegative factor, one gets a generalized Sturm sequence, which may also be used for computing the number of real roots, since the proof of Sturm's theorem still applies (because of the third condition). This may sometimes simplify the computation, although it is generally difficult to find such nonnegative factors, except for even powers of $x$.

Use of pseudo-remainder sequences
In computer algebra, the polynomials that are considered have integer coefficients or may be transformed to have integer coefficients. The Sturm sequence of a polynomial with integer coefficients generally contains polynomials whose coefficients are not integers (see above example).

To avoid computation with rational numbers, a common method is to replace Euclidean division by pseudo-division for computing polynomial greatest common divisors. This amounts to replacing the remainder sequence of the Euclidean algorithm by a pseudo-remainder sequence, a pseudo remainder sequence being a sequence $$p_0, \ldots, p_k$$ of polynomials such that there are constants $$a_i$$ and $$b_i$$ such that $$b_ip_{i+1}$$ is the remainder of the Euclidean division of $$a_ip_{i-1}$$ by $$p_i.$$ (The different kinds of pseudo-remainder sequences are defined by the choice of $$a_i$$ and $$b_i;$$ typically, $$a_i$$ is chosen for not introducing denominators during Euclidean division, and $$b_i$$ is a common divisor of the coefficients of the resulting remainder; see Pseudo-remainder sequence for details.) For example, the remainder sequence of the Euclidean algorithm is a pseudo-remainder sequence with $$a_i=b_i=1$$ for every $i$, and the Sturm sequence of a polynomial is a pseudo-remainder sequence with $$a_i=1$$ and $$b_i=-1$$ for every $i$.

Various pseudo-remainder sequences have been designed for computing greatest common divisors of polynomials with integer coefficients without introducing denominators (see Pseudo-remainder sequence). They can all be made generalized Sturm sequences by choosing the sign of the $$b_i$$ to be the opposite of the sign of the $$a_i.$$ This allows the use of Sturm's theorem with pseudo-remainder sequences.

Root isolation
For a polynomial with real coefficients, root isolation consists of finding, for each real root, an interval that contains this root, and no other roots.

This is useful for root finding, allowing the selection of the root to be found and providing a good starting point for fast numerical algorithms such as Newton's method; it is also useful for certifying the result, as if Newton's method converge outside the interval one may immediately deduce that it converges to the wrong root.

Root isolation is also useful for computing with algebraic numbers. For computing with algebraic numbers, a common method is to represent them as a pair of a polynomial to which the algebraic number is a root, and an isolation interval. For example $$\sqrt 2$$ may be unambiguously represented by $$(x^2-2, [0,2]).$$

Sturm's theorem provides a way for isolating real roots that is less efficient (for polynomials with integer coefficients) than other methods involving Descartes' rule of signs. However, it remains useful in some circumstances, mainly for theoretical purposes, for example for algorithms of real algebraic geometry that involve infinitesimals.

For isolating the real roots, one starts from an interval $$(a,b]$$ containing all the real roots, or the roots of interest (often, typically in physical problems, only positive roots are interesting), and one computes $$V(a)$$ and $$V(b).$$ For defining this starting interval, one may use bounds on the size of the roots (see ). Then, one divides this interval in two, by choosing $c$ in the middle of $$(a,b].$$ The computation of $$V(c)$$ provides the number of real roots in $$(a,c]$$ and $$(c,b],$$ and one may repeat the same operation on each subinterval. When one encounters, during this process an interval that does not contain any root, it may be suppressed from the list of intervals to consider. When one encounters an interval containing exactly one root, one may stop dividing it, as it is an isolation interval. The process stops eventually, when only isolating intervals remain.

This isolating process may be used with any method for computing the number of real roots in an interval. Theoretical complexity analysis and practical experiences show that methods based on Descartes' rule of signs are more efficient. It follows that, nowadays, Sturm sequences are rarely used for root isolation.

Application
Generalized Sturm sequences allow counting the roots of a polynomial where another polynomial is positive (or negative), without computing these root explicitly. If one knows an isolating interval for a root of the first polynomial, this allows also finding the sign of the second polynomial at this particular root of the first polynomial, without computing a better approximation of the root.

Let $P(x)$ and $Q(x)$ be two polynomials with real coefficients such that $P$ and $Q$ have no common root and $P$ has no multiple roots. In other words, $P$ and $P'Q$ are coprime polynomials. This restriction does not really affect the generality of what follows as GCD computations allows reducing the general case to this case, and the cost of the computation of a Sturm sequence is the same as that of a GCD.

Let $W(a)$ denote the number of sign variations at $a$ of a generalized Sturm sequence starting from $P$ and $P'Q$. If $a < b$ are two real numbers, then $W(a) – W(b)$ is the number of roots of $P$ in the interval $$(a,b]$$ such that $Q(a) > 0$ minus the number of roots in the same interval such that $Q(a) < 0$. Combined with the total number of roots of $P$ in the same interval given by Sturm's theorem, this gives the number of roots of $P$ such that $Q(a) > 0$ and the number of roots of $P$ such that $Q(a) < 0$.

title: Sturm's theorem


text:
Talk:Warhellride

-Mike Zawadzki

Huh? Brianjd 09:17, 2004 Nov 29 (UTC)

This should most definitely be merged with Wesley Willis and the full term is "demon war hellride." BabuBhatt 05:33, 7 February 2006 (UTC)

Merging this with the Wesley Willis article makes a lot of sense. There's not enough material here to warrant a separate article. - dharmabum 08:25, 7 February 2006 (UTC)

Definitely merge. I vote YES. --Doctorcherokee 22:19, 8 February 2006 (UTC)

I wholeheartedly agree with the reasons above. This needs to be merged. Eric 03:51, 14 February 2006 (UTC)

Yes it should merge, it gives greater depth. I also think there should be more information about Wesley's ART included on the main site Caniman 08:04, 7 March 2006 (UTC)

Merge it and redirect this page there. Cat Parade 22:03, 15 March 2006 (UTC)

Yes, merge. A term used by one person should be part of their page. BlackTerror 04:40, 16 March 2006 (UTC)

merge --Quiddity 22:44, 22 March 2006 (UTC)

title: Talk:Warhellride


text:
File:VCDonaldEdwardGarland.jpg

Photo of Victoria Cross recipient Donald Edward Garland, migrated from the Victoria Cross Reference site with permission. Photo submitted by Neil Hutton. Note: Further information appears for this recipient and is highly likely to need some extra formatting.

title: File:VCDonaldEdwardGarland.jpg


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Donald Garland

Flying Officer Donald Edward Garland, VC (28 June 1918 – 12 May 1940) was a bomber pilot in the Royal Air Force and a recipient of the Victoria Cross, the highest award for gallantry in the face of the enemy that can be awarded to British and Commonwealth forces.

Early life
Born in Ballinacor, County Wicklow, Garland was the son of Dr. Patrick Joseph Garland, CMG. He was a pupil at Cardinal Vaughan Memorial School, Holland Park, London from 1929 to 1935, and left with a good all-round School Certificate.

After spending some time at an insurance office, he joined the Royal Air Force (RAF) on a short-term commission. Mgr. Canon J. Vance, who became headmaster of Cardinal Vaughan School in 1928: "In those days I questioned young men closely before recommending their applications for short-term commissions because of a lurking fear that they might be forced to start life again at an awkward age, for Donald I had no misgivings whatever. He could start his life again at any time and was bound to succeed because of his independence and of his resourcefulness. I salute Garland's great heroism"

Victoria Cross
Garland was 21 years old, and a flying officer in No. 12 Squadron during the Second World War, when the following deed took place for which he was awarded the VC.

On 12 May 1940, over the Albert Canal, Belgium, two bridges, Veldwezelt and Vroenhoven, were being used by the invading army, with protection from fighter aircraft, anti-aircraft and machine-guns. The RAF was ordered to demolish one of these vital bridges, and five Fairey Battle bombers were despatched, with Flying Officer Garland leading the attack. They encountered heavy anti-aircraft fire, and the bridge was hit but not put out of commission. Garland and his navigator, Sergeant Thomas Gray, attacked the bridge at Veldwezelt. They died either crashing in the village of Lanaken or in the hospital in Maastricht, Netherlands. Only one bomber managed to return to base. Sergeant Gray was also awarded the VC for this action in a joint citation with Garland.

Garland is buried at the Heverlee War Cemetery in Leuven, Belgium.

Both Garland and Gray were awarded the Victoria Cross posthumously. Leading Aircraftman Reynolds, the third member of the crew, did not receive a medal because he was not in a "decision making" position. Garland's Victoria Cross is displayed at the Royal Air Force Museum London, England.

He had three brothers, all of whom served with the RAF and also died on service:
 * Pilot Officer Desmond William Garland – killed in Belgium on 5 June 1942 aged 27
 * Flight Lieutenant John Cuthbert Garland – died on 28 February 1943 aged 32
 * Flight Lieutenant Patrick James Garland – killed in Holland on 1 January 1945 aged 36

Victoria Cross citation
The announcement and accompanying citation for the decoration was published in supplement to the London Gazette on 11 June 1940, reading

"Air Office, 11th June, 1940

The KING has been graciously pleased to confer the VICTORIA CROSS on the undermentioned officer and non-commissioned officer in recognition of most conspicuous bravery :-

Flying Officer Donald Edward Garland (40105)

563627 Sergeant Thomas Gray

Flying Officer Garland was the pilot and Sergeant Gray was the observer of the leading aircraft of a formation of five aircraft that attacked a bridge over the Albert Canal which had not been destroyed and was allowing the enemy to advance into Belgium. All the aircrews of the squadron concerned volunteered for the operation, and, after five crews had been selected by drawing lots, the attack was delivered at low altitude against this vital target. Orders were issued that this bridge was to be destroyed at all costs. As had been expected, exceptionally intense machine-gun and anti-aircraft fire were encountered. Moreover, the bridge area was heavily protected by enemy fighters. In spite of this, the formation successfully delivered a dive-bombing attack from the lowest practicable altitude. British fighters in the vicinity reported that the target was obscured by the bombs bursting on it and near it. Only one of the five aircraft concerned returned from this mission. The pilot of this aircraft reports that besides being subjected to extremely heavy anti-aircraft fire, through which they dived to attack the objective, our aircraft were also attacked by a large number of enemy fighters after they had released their bombs on the target. Much of the success of this vital operation must be attributed to the formation leader, Flying Officer Garland, and to the coolness and resource of Sergeant Gray, who in most difficult conditions navigated Flying Officer Garland's aircraft in such a manner that the whole formation was able successfully to attack the target in spite of subsequent heavy losses. Flying Officer Garland and Sergeant Gray did not return."

Memorials
A Vickers VC-10 Serial 'XR807' of 101 Squadron was named 'Donald Garland VC & Thomas Gray VC'.

During 2005, to mark its 90th anniversary, No.12 Squadron RAF flew a Tornado GR4 with Flying Officer Garland's and Sgt Gray's name painted under the cockpit as a mark of respect.

There is a monument on the bridge to the operation.

title: Donald Garland


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Minden Hills

Minden Hills is a township in and the county seat of Haliburton County, Ontario, Canada. It is an amalgam of the townships of Snowdon, Lutterworth, Anson, Hindon and Minden. It is usually referred to as Minden, after its largest community.

The township was formed on January 1, 2001, by combining the townships of Lutterworth, Snowdon, Anson, Hindon and Minden.

Communities
The primary residential and commercial centre of the township is Minden, located just off Highway 35 ( 44.92611°N, -78.72583°W ).

The township also includes the smaller communities of Blairhampton, Brady Lake, Buller, Carnarvon, Deep Bay, Dutch Line, Gelert, Hindon Hill (abandoned community), Howland, Ingoldsby, Irondale, Kilcoo Harbour, Lochlin, Lutterworth, Miners Bay, and Moore Falls.

Minden
Minden, named after a town in the North Rhine–Westphalia federal state in Germany, was first surveyed in 1858. Before that, the settlement was called Gull River. Settlers were first drawn to the region (via the Bobcaygeon Road, an original colonization road), because of its timber resources. The town lies on the banks of the Gull River and during the 19th and 20th centuries, loggers used the river to move timber to sawmills downstream.

Since the 1940s the town has become an increasingly popular summer destination given its close proximity to larger cities in southern Ontario. The population grows dramatically during the summer months as a result of tourism. The Minden Times and The Highlander are the local newspapers, and the local post office on Water St. serves residents with lock boxes and three rural routes.

The Minden Hills Cultural Centre is home to the Agnes Jamieson Gallery, named after Dr. Agnes Jamieson, the first female coroner in Ontario. The Gallery houses the largest known collection of André Lapine's work. Both Lapine and Jamieson lived in Minden during part of their lives. The Cultural Centre is also home to the Minden Hills Museum, which includes seven heritage buildings, including a school, a blacksmith shop and a church. R.D. Lawrence Place, an interactive learning centre celebrating Canadian author Ron Lawrence, is also located here.

2013 flood
The Gull River flooded in April 2013, leading to a state of emergency declaration on April 20. By May 3, officials were predicting another two weeks of abnormally high water levels in the Trent-Severn Waterway system. The excess water that was held back in the reservoir lakes north of Minden was being slowly released and moved through the village so as not to cause increased damage. The use of the reservoir lakes north of Minden to collect water was necessary to avert a threat to the essential utilities of water, hydro and sewage treatment. However, it extended the flood damage area north throughout the entire Gull River Watershed. Many of the properties on those lakes were damaged.

Residents of the area were evacuated from their homes on short notice and remained out until mid-May. Claims by residents to the Ontario Disaster Relief Assistance Program totaled 1.8 million dollars by November 2013, in addition to an estimated 2.2 million dollars in insured claims. The township spent $370,000 on flood related costs.

2017 flood
Residents of Minden Hills were again affected by flooding only four years since the massive flood of 2013. Watershed flooding was at its maximum capacity in the reservoir lakes of the Trent Severn Waterway only to be hit with 129 millimeters of rain in late April, increasing flood levels. A state of emergency was put into place on May 6, 2017, for the town of Minden Hills. The Gull River through Minden recorded 5 centimeters lower than the record 2013 flood. A new automated sandbag machine was purchased earlier in March, helping with handling sandbags at a much faster rate for flood relief. Close to 40,000 sandbags being filled by the end of the weekend. Provincial aid was provided after Reeve Brent Devolin had been in contact with Premier Kathleen Wynne. The Ontario Disaster Relief Assistance Program offered reimbursement for homeowners affected.

2015 Pan Am Games
Minden Wild Water Preserve was a venue of the 2015 Pan Am Games, hosting canoe events.

Demographics
In the 2021 Census of Population conducted by Statistics Canada, Minden Hills had a population of $6,971$ living in $3,229$ of its $6,019$ total private dwellings, a change of NaN% from its 2016 population of $6,088$. With a land area of 847.37 km2, it had a population density of in 2021.

Local government

The town's council includes a mayor, deputy mayor, councillor at large and four councillors elected on the basis of two for Ward 1 and one each for Wards 2 & 3, who are elected to join the mayor at meetings of Minden Hills Council. The members of council elected in 2022 are:
 * Mayor: Bob Carter
 * Deputy Mayor: Lisa Schell
 * Councillors:
 * At Large: Tammy McKelvey
 * Ward 1: Ivan Ingram
 * Ward 1: Shirley Johanessen
 * Ward 2: Pam Sayne
 * Ward 3: Bob Sisson

Transportation
Ontario Highway 35 is the major throughfare passing to the east and connects Minden to neighbouring areas and beyond.

A Heliport servicing Minden Hospital is the only airport in Minden, the closest airport is south in Peterborough, Ontario.

Services
Minden Hospital provides local health needs with more advance care to the south in Peterborough or Bracebridge, Ontario to the northwest.

Ontario Provincial Police Haliburton Detachment is located in Minden.

Fire services is provided by Minden Hills Fire Department and ambulance by Haliburton County EMS both located near along highway 35.

title: Minden Hills