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Octopus card

The Octopus card (, Cantonese) is a reusable contactless stored value smart card for making electronic payments in online or offline systems in Hong Kong. Launched in September 1997 to collect fares for the territory's mass transit system, it has grown into a widely used system for transport and other retail transactions in Hong Kong. It is also used for purposes such as recording school attendance and permitting building access. The cards are used by 98 percent of the population of Hong Kong aged 15 to 64 and the system handles more than 15 million transactions, worth over HK$220 million, every day.

The Octopus card system was the world's second contactless smart card system, after the Korean Upass. It won the Chairman's Award at the World Information Technology and Services Alliance's 2006 Global IT Excellence Awards for, among other things, being the world's leading complex automatic fare collection and contactless smart card payment system. Its success led to the development of similar systems elsewhere, including Navigo card in Paris, Oyster card in London, Opal card in New South Wales, and NETS FlashPay and EZ-Link in Singapore.

History
When Hong Kong's Mass Transit Railway (MTR) began operations in 1979, it used recirculating magnetic stripe cards as fare tickets. The Kowloon-Canton Railway (KCR) adopted the same magnetic cards in 1984. The Common Stored Value Ticket was a version that held a balance for use over multiple trips. In 1989, the Common Stored Value Ticket system was extended to Kowloon Motor Bus (KMB) buses providing a feeder service to MTR and KCR stations, and to Citybus. It was also extended to a limited number of non-transport applications, such as transactions and payments at photo booths and for fast food vouchers.

In 1993, MTR Corporation announced it would move to use contactless smart cards. In 1994 it partnered with four other major transit companies in Hong Kong, Kowloon-Canton Railway Corporation, Kowloon Motor Bus, Citybus, and Hongkong and Yaumati Ferry, to create a joint-venture business, then known as Creative Star Limited.

After three years of trials, the Octopus card was launched on 1 September 1997. Three million cards were issued in the first three months. The system's quick success was because MTR and KCR required all holders of Common Stored Value Tickets to replace them with Octopus cards within three months or have their tickets expire. Another reason was a coin shortage in Hong Kong in 1997. With the transfer of Hong Kong away from British rule, there was a belief that older Hong Kong coins embossed with Queen Elizabeth II's head would rise in value, so many people held on to them waiting for their value to increase.

The Octopus system was quickly adopted by other Creative Star partners. KMB reported that by 2000 most bus journeys were completed using an Octopus card. Boarding a bus in Hong Kong without using the Octopus card requires giving exact change, making it cumbersome compared to using the Octopus card. By November 1998, 4.6 million cards had been issued, and rising to 9 million by January 2002.

In 2000, the Hong Kong Monetary Authority granted a deposit-taking company licence to the operator. This increased the proportion of permitted non-transport–related Octopus card transactions from 15% of turnover to 50%. About HK$416 million was deposited in the Octopus system at any given time as of 2000.

On 6 November 2005, Octopus Cards Limited launched Octopus Rewards, a program that allows cardholders to earn rewards with participating merchants. Founding partners for the Octopus Rewards program included HSBC, UA Cinemas and Wellcome. The rewards are in the form of points, or reward dollars, stored on the card. The rate at which reward points are earned per dollar spent differs between merchants. Reward points can be redeemed as payment for purchases at partner merchants for at least HK$1 per reward dollar.

New cards with greater levels of security were launched in 2015. Holders of first generation cards could voluntarily replace their cards at an Octopus Service Point without charge. From January 2018, first generation cards started to become unusable.

From 26 March 2024 onwards, Octopus card launched a new China T-Union version, which could be used in 336 mainland China cities.

Etymologies and logo
The Cantonese name for the Octopus card, Baat Daaht Tùng, translates literally as "eight-arrived pass", where Baat Daaht may translate as "reaching everywhere". Less literally, the meaning is taken as the "go-everywhere pass". It was selected by the head of the MTR Corporation, the parent company of Octopus Cards Limited, in a naming competition in 1996. The number eight refers to the cardinal and ordinal directions, and the four-character idiom, a common expression loosely translated as "reachable in all directions". Eight is also considered a lucky number in Chinese culture, and the phrase can possibly be associated with the similar-sounding, which means "getting wealthy"  in Cantonese.

The English name Octopus card was also selected in the naming competition. It also references the number eight, since an octopus has eight tentacles. The logo used on the card features an infinity symbol.

Card usage

The Octopus card was originally introduced for fare payment on the MTR; but usage quickly expanded to other retail businesses in Hong Kong. The card is now commonly used in most public transport, fast food restaurants, supermarkets, vending machines, convenience stores, photo booths, parking meters, car parks, and many other retails business where small payments are frequently made. Over 33 million Octopus cards are in circulation as of 2018, with the card being used by 99 per cent of Hong Kong residents.

Notable businesses that started accepting Octopus cards at an early stage included PARKnSHOP, Wellcome, Watsons, 7-Eleven, Starbucks, McDonald's, and Circle K. Between June 2003 and November 2004, the Hong Kong Government replaced its 17,000 parking meters with an Octopus card–operated system. Octopus card was then the only accepted form of payment until 2021 when new meters were introduced that accepted contactless payment, Faster Payment System and QR code payment.

Octopus cards also double as access control cards in buildings and for school administrative functions. At certain office buildings, residential buildings, and schools, use of an Octopus card is required for entry.

Payments

Payments are made by holding the card against or within a few centimetres of an Octopus card reader. The reader acknowledges payment by emitting a beep, and displaying the amount deducted and the remaining balance of the card. The standard transaction time for readers used for public transport is 0.3 seconds, and for retailers' card readers is 1 second.

Public transport
When using the MTR heavy rail system, each passenger's entry point is recorded and the appropriate fare based on distance travelled is deducted when they validate their cards again at the exit point.

The MTR usually charges less for journeys made using an Octopus card instead of conventional single-journey tickets. For example, the adult fare of a single journey from Chai Wan to Tung Chung is HK$25.7 with an Octopus card, and HK$28.5 with a single journey ticket. Other public transport operators also offer intermittent discounts for using Octopus cards on higher fares and round-trip transits on select routes.

Taxis
The first trial of using Octopus card readers in Hong Kong taxis started in June 2006 with the Yellow Taxi Group in the New Territories. It was reported on 30 October that eight of the twenty taxis participating in the trial had dropped out. Part of the reason was technical – drivers needed to return to the office every day for accounting. Most taxi drivers in Hong Kong are self-employed and prefer to account their profit and rent on a daily basis, while Octopus transferred money through a bank after one working day, so drivers could be left over a weekend or longer waiting for their account to be reconciled. Installation and service fees are also a concern.

Wong Yu-ting, the managing director of the Yellow Taxi Group, wanted retailers to offer discounts to Octopus taxi passengers, but the Transport Department objected as taxi fare discount is illegal in Hong Kong.

In March 2018, Octopus Cards Limited announced plans to re-enter the taxi payment market with a new mobile app for taxi drivers. The mobile app is able to receive funds by tapping the passenger's Octopus card to the device's Near-field communication (NFC) reader, or by allowing passengers to scan a QR code.

In October 2020, Octopus Cards Limited launched Octopus Mobile POS, a more compact version of the Octopus reader to help taxi drivers and small- and medium-sized retailers accept cashless payments. The new Octopus Mobile POS, that works with the mobile app was opportune during the COVID-19 pandemic, as it helped provide merchants customers with peace of mind regarding potential virus transmission. By July 2021, over 15,000 taxi drivers had installed Octopus Mobile POS.

Outside Hong Kong
In collaboration with China UnionPay, Octopus Cards Limited introduced Octopus card usage to two Fairwood restaurants in Shenzhen in August 2006. In 2008, five Café de Coral locations in Shenzhen also started accepting Octopus. Value cannot be reloaded to Octopus cards in Shenzhen, but the Automatic Add Value Service is available to automatically deduct money value from a customer's credit card to reload an Octopus card. The two Fairwood restaurants in Shenzhen that were enabled for Octopus card payments are located at Luohu Commercial City and Shenzhen railway station. Shenzhen became the first city outside Hong Kong in which Octopus cards may be accepted as payment.

In Macau, the Octopus card was introduced in December 2006 when two Kentucky Fried Chicken restaurants in the territory adopted its usage as payment. Similar to its usage in Shenzhen, an Octopus card may not be reloaded in Macau, and the currency exchange rate between the Macanese pataca and the Hong Kong dollar when using an Octopus card is MOP1:HKD1. The two Kentucky Fried Chicken restaurants in Macau that adopted the Octopus card for payment are located at the Rua do Campo and the Sands Casino.

Shenzhen Tong cards are now widely used in Shenzhen instead, and a combined Shenzhen Tong – Hong Kong Octopus card is available, called the Hu Tong Xing, with RMB & HKD in different purses. The Macau Pass is now widely used in Macau.

Balance enquiry

Enquiry machines are available in all MTR stations, and Octopus Service Points are in some MTR stations. Placing any Octopus product on these machines will display the current balance and a history of the last ten transactions. Card users may also check the balance and last 3 months' transactions on mobile with Octopus app. For some Octopus products, like the 20th Anniversary Special Edition, up to 40 transactions can be checked on the app. After each payment, the remaining value and cash deducted are also shown on the card reader as well as on the receipt.

Top-up
Money can be credited to the card through a number of ways. All cards can top-up in multiples of HK$50, and Elder cards, Personalised Octopus Cards with "Student" or "Person with Disabilities" identity can also be topped-up in multiples of HK$10 at MTR Customer Service Centres.

"Add Value Machines" are installed at all MTR stations and they accept cash only. Alternatively, cards may be topped up with cash at authorised service providers such as PARKnSHOP, Wellcome, Watsons, 7-Eleven, Circle K, and Café de Coral, and at customer service centres and ticketing offices at transport stations. In selected stores, change can also be put on to an Octopus card after a cash payment. Spare coins can also be added on to Octopus cards at "Coin Carts", a vehicle operated by Hong Kong Monetary Authority.

The Octopus "Automatic Add Value Service" (AAVS) is an automatic top-up method. It allows money to be automatically deducted from a credit card and credited to an Octopus card when the value of the Octopus card is less than zero. The credit card used must be one offered by one of 22 financial institutions that participate in AAVS. Participating banks include HSBC, Bank of China, and Hang Seng Bank. Depend on users' settings, HK$150/250/500 is added to the card each time value is automatically added.

The "O! ePay" mobile wallets, which is also run by Octopus company, allows users to transfer money between itself and Octopus cards. The transfer amount can be in values as small as 10 cents.

An Octopus card may store a maximum value of HK$3000, with an On-Loan card having an initial deposit value of HK$50 and a Sold card having no initial deposit value. Negative value is incurred on a card if it is used with insufficient funds – both types of cards may carry a maximum negative value of HK$35 or HK$50 (dependent on card issue date) before value needs to be added to be able to use them again.

Card refund
An Octopus card may be returned to any MTR Customer Service Centre for a refund of the remaining credit stored on it. A handling fee may be charged for the refund – HK$11 for an anonymous On-Loan card that had been in use for fewer than 90 days, and HK$10 for a Personalised On-Loan card that was issued on or after 1 November 2004. A refund is immediately provided at the time an anonymous On Loan card is returned, unless it has more than HK$500 stored on it. A Personalised On-Loan card or an anonymous On-Loan card with more than HK$500 stored on it needs to be sent back to Octopus Cards Limited for refund processing, in which case, the refund for a Personalised On-Loan card would be available in eight days, and that of an anonymous On-Loan card would be available in five days. If a damaged On-Loan card is returned for refund, a HK$30 levy would be charged to the cardholder.

Octopus Administrative Fee
Since 1 October 2020, Octopus has charged a HK$15 Inactive Octopus Administrative Fee each year for customers aged 18 – 59 without a concession. Once the whole balance is deducted, the card is decommissioned and cannot be reactivated. On-Loan Adult Octopus cards issued since 1 October 2017 that have not had any add value or payment transaction for three years become an Inactive Octopus.

Types of cards
There are two main types of Octopus card (On-Loan and Sold), and two less common types (Airport Express Tourist and MTR Airport Staff).

On-Loan cards
On-Loan cards are issued for use in day-to-day functions, primarily for fare payment in transport systems. They are further classified into Child, Adult, Elder, and Personalised categories, with the first three based on age and different amounts of fare concession. With the exception of the Personalised cards, On-Loan cards are anonymous; no personal information, bank account, or credit card details are stored on the card, and no identification is required for the purchase of these cards. If an owner loses a card, only the stored value and the deposit of the card are lost. On-Loan Octopus cards may be purchased at all MTR stations, the KMB Customer Service Centre, New World First Ferry (NWFF) Octopus Service Centres, and the New World First Bus (NWFB) Customer Service Centre. A student on-loan Octopus Card was initially issued, but was discontinued in 2005.

Personalised cards
The Personalised card is available on registration. The name and, if requested, a photo of the holder are imprinted on the cards. They can function automatically as a Child, Adult, or Elder card by recognising the cardholder's age stored on the card, hence incurring concessionary fares. As of 2003, there were 380,000 holders of Personalised Octopus cards. In addition to the functions of an ordinary card, this card can be used as a key card for access to residential and office buildings. If a Personalised card is lost, the holder may report the loss by phone or on the web to prevent unauthorised use of the card. A refund or a new personalised card, depending on the holder's choice, will then be mailed to the holder. The refund contains the deposit and the value that remained on the card three hours after the loss was reported, minus a HK$30 card cost and a HK$20 handling fee.

A Personalised card with "student status" is available for students in Hong Kong. To be eligible for this card, the applicant must be a full-time Hong Kong student aged between 12 and 25. This type of Personalised card is automatically issued to a student who applies for student concessionary privileges. Additionally, they can be used for school administrative tasks such as the recording of student attendance and the management of library loans.

Sold cards
In contrast to On-Loan cards, Sold cards are sponsored and branded cards. Souvenir cards are frequently released by Octopus Cards Limited with designs based on fictional characters in popular culture or inspired by Chinese cultural events such as Chinese New Year. These cards are sold at a premium, have limited or no initial stored value, and cannot be refunded, but they can otherwise be used as ordinary cards. An example of the Sold card is the McMug and McDull collection. Launched at the end of January 2007 to coincide with the beginning of the Year of the Pig, it features two differently designed versions of the card and is sold for HK$138 per set. Each set comes with an Adult Octopus card, with a pouch for the card, a matching strap and a Mcmug or Mcdull ornament. Octopus Cards Limited has launched new collections of these cards for such occasions as the Mid-Autumn Festival, the passing of the year 2004, and the release of the movie DragonBlade. Sold Octopus cards may be purchased at selected MTR stations, and all 7-Eleven stores.

Alternative designs (Sold cards)
Other than the Octopus card itself, operator Octopus Cards Limited also sells watches and mobile phone covers that function as anonymous Octopus cards. The types of watches available include wrist watches, pocket watches, and watch key chains. The mobile phone covers were specifically designed for Nokia models 3310 and 3330, and iPhone 4 and 4S. As with regular cards, these products are used by waving them over a card reader. They may be reloaded with money by the methods as regular Octopus cards except that they cannot be reloaded at Add Value Machines due to their shapes. An Octopus watch or mobile phone cover may be stored with a maximum of HK$3,000, but does not have any initial stored value at the time of its purchase. It may have a maximum negative value of HK$35 as with an Octopus card. These products are not refundable for their costs, but the remaining value stored on them may be refunded if they are damaged, with the damaged product itself also returned to the customer.

In June 2007, a new set of limited edition products was announced, featuring Mini Octopus cards and Child Octopus Wristbands. The Mini Octopus cards, available in Adult and Elder editions, measure 4.7 cm by 3 cm (1.85 in by 1.18 in) and work as regular anonymous Octopus cards. The Child Octopus Wristbands are plastic wristbands with a watch-like round face and work as regular Child Octopus cards. The same value-adding abilities and limitations as the watches and mobile phone covers apply.

Special-purpose cards
The special-purpose card, Airport Express Tourist Octopus, was introduced by Octopus Cards Limited to target tourists in Hong Kong. Two versions of this card are offered: a HK$250 card with a free single ride on the Airport Express (the MTR line that runs between the Hong Kong International Airport and the urban areas of Hong Kong), and a HK$350 card with two free single rides included. The airport journeys are valid for 180 days from the date of purchase. Both versions allow three days of unlimited rides on the MTR and include a HK$50 refundable deposit. Usable value on these cards may be added if necessary. These tourist Octopus cards may be used only by tourists staying in Hong Kong for 14 or fewer days; users may be required to produce a passport showing their arrival date in Hong Kong. Airport Express Tourist Octopus is available for purchase at all MTR stations.

The other special-purpose card, the MTR Airport Staff Octopus, is available for staff of Hong Kong International Airport and AsiaWorld-Expo, a convention centre close to the airport, for commuting at a reduced fare between the airport and MTR stations via the Airport Express. Staff who apply for the card may use it for a discount of up to 64 percent for Airport Express single journey fares. The MTR Airport Staff Octopus is available upon application via the customer's employer.

Some local banks in Hong Kong have integrated the Octopus Card into their ATM cards and credit cards.

Samsung Pay
Since 14 December 2017, the cardless Octopus, named "Smart Octopus", is available with Samsung Pay, a mobile payment platform provided by Samsung. By using the phone's NFC function and magnetic secure transmission (MST) technology, users can tap their selected Samsung devices on Octopus readers, paying in a similar way as a normal physical Octopus cards.

Users can choose to transfer their card data from an existing anonymous On-Loan Adult or Elder Octopus to the Smart Octopus. All card value and reward points are transferred and held in the Samsung Pay app. The physical card is then deactivated and can no longer be used. Users can also choose to purchase a new Adult or Elder Smart Octopus in the app.

Smart Octopus provides features like instant transaction notification and in-app top-up function. In-app top-ups initially incurred a 2.5% handling fee  but this fee was removed in June 2020 when support for Apple Pay was launched.

Apple Pay
Since 2 June 2020, Octopus cards can be added to Apple Pay. As Octopus cards use FeliCa technology, only Apple Watch 3, iPhone 8, and subsequent model are supported. Octopus for Tourists was launched in August 2020.

Users can choose to create a virtual Octopus card inside Apple Pay by topping up with their loaded credit cards, or to transfer data from an existing physical Octopus card. It supports Apple Pay's Express Transit function, which allows payments to be made from the iPhone or Apple Watch without needing to switch on the phone or authenticating the payment with Face ID, Touch ID, or password.

Huawei Pay
Since 9 December 2020, Octopus card can be added to Huawei Pay. But it can only be used on Huawei phones sold in Hong Kong, Macau and China

Users can download the Octopus app from Huawei AppGallery to purchase new Octopus cards or transfer physical Octopus cards. If users have a UnionPay credit card, they can also purchase new Octopus cards in Huawei Wallet.

Technology

The Australia-based company ERG Group (now Vix Technology) was selected in 1994 to lead development of the Octopus project. It designed, built and installed the Octopus system. Operations, maintenance and development were undertaken by Octopus Cards Limited, and in 2005, it replaced the central transaction clearing house with its own system.

The Octopus card is the first major public transport system to use the Sony 13.56 MHz FeliCa radio frequency identification (RFID) chip. It is a contactless system, so users need only hold the card in close proximity to the reader. Data is transmitted at up to 212 kbit/s (the maximum speed for Sony FeliCa chips), compared to 9.6 kbit/s for other smart card systems like Mondex and Visa Cash. The card has a storage capacity of 1 to 64 kB, compared to 125 bytes provided by magnetic stripe cards.

Octopus pre-dates the ISO/IEC 14443 standards so uses a nonstandard RFID system. The operating range of the reader/writer is between 30 and 100 mm (1.2 and 3.9 in) depending on the model used.

Octopus is designed so that transactions are relayed for clearing on a store and forward basis, without any requirement for reader units to have realtime round-trip communications with a central database or computer. The stored data may be transmitted after hours, or in the case of offline mobile readers, may be retrieved by a hand held device, for example a Pocket PC.

In practice, different data collection mechanisms are used by different transport operators, depending on the nature of their business. The MTR equips its stations with local area networks that connect the components that deal with Octopus cards – turnstiles, Add Value Machines, value-checking machines and customer service terminals. Transactions from these stations are relayed to the MTR's Kowloon Bay headquarters through a Frame Relay wide area network, and then on to the central clearing house system (CCHS). Similar arrangements are in place for retailers such as 7-Eleven. Handheld devices are used to scan offline mobile readers, including those installed on minibuses. Buses either use handheld devices or a wireless system, depending on operator.

Security
The Octopus card uses encryption for all airborne communication and performs mutual authentication between the card and reader based on the ISO 9798-2 three-pass mutual authentication protocol. In other words, data communications are only established when the card and reader have mutually authenticated based on a shared secret access key. This means that the security of the Octopus card system would be jeopardized should the access key be exposed. A stolen Octopus card reader could be used with stolen Octopus software, for example, to add value (up to HK$3,000) to any Octopus card without authorization. Nevertheless, as of 2003, the Octopus card and system had never been hacked.

Octopus card readers include a fail-safe that prevents them from initiating a transaction when more than one card is detected at a time. On 11 February 2009, Sing Tao Daily reported that the fail-safe has been abused for fare evasion through the railway station turnstile. Passengers were stacking four or more cards on the reader before breaking through the turnstile, deliberately triggering the fail-safe to avoid deduction of credit from their cards. If challenged they could blame a malfunction and present an Octopus card with a record of an unsuccessful transaction.

Operator
The Octopus card system is owned and operated by Octopus Cards Limited, a wholly owned subsidiary of Octopus Holdings Limited. Founded as Creative Star Limited in 1994, it was renamed Octopus Cards Limited in 2002.

In January 2001, the shares of Hongkong and Yaumati Ferry were transferred to New World First Bus and New World First Ferry. In the same year, together with MTR Corporation, the company changed from non-profit making status to a profit making enterprise.

Due to the expansion of the company's businesses, Octopus Holdings Limited was established in 2005 with Octopus Cards Limited restructured as a subsidiary. Being a payment business, Octopus Cards Limited is regulated by the Hong Kong Monetary Authority. Octopus' non-payment businesses are not subjected to such regulation and are operated by other subsidiaries of Octopus Holdings Limited.

As of 2007, Octopus Holdings Limited was a joint-venture business owned by five transport companies in Hong Kong; 57.4% by the MTR Corporation, 22.1% by the Kowloon-Canton Railway Corporation, 12.4% by Kowloon Motor Bus, 5% by Citybus, and 3.1% by New World First Bus. The Government of Hong Kong owns 76.54% of the MTR Corporation (as of 31 December 2005) and wholly owns the Kowloon-Canton Railway Corporation, so is the biggest effective shareholder of Octopus Holdings Limited, and of Octopus Cards Limited.

Awards
The Octopus card is recognised internationally. It won the Chairman's Award at the World Information Technology and Services Alliance's 2006 Global IT Excellence Awards for being the world's leading complex automatic fare collection and contactless smartcard payment system, and for innovative use of technology.

EPS add-value glitch
In February 2007 it was found that when customers added value to their cards at self-service add-value points in MTR and Light rail stations, their bank accounts were debited even if the transactions had been cancelled. Octopus Cards Limited claimed that the fault was due to an upgrade of communication systems. Initially, two cases were reported. The company then announced that use Electronic Payment Services (EPS) at add-value service points would be suspended until further notice, and that it had started an investigation into the reasons for the problem.

On 27 July 2007 it was announced that faulty transactions had been traced back to 2000, and that a total of 3.7 million Hong Kong dollars had been wrongly deducted in 15,270 cases. The company reported that there might be cases prior to 2000, but that only the past seven years’ transactions were stored. The company stated it would co-operate with banks and EPS Company Limited, operator of Electronic Payment Services, to contact customers involved and arrange a refund within ten weeks.

On 21 December 2007 the company announced it would permanently cease all transactions using EPS because it could not guarantee such problems would not occur again.

Privacy abuse
On 15 July 2010, a former employee of the CIGNA insurance company claimed CIGNA purchased records for 2.4 million Octopus users. On 20 July, Octopus acknowledged selling customers' personal details to CIGNA and Card Protection Plan Limited, and started an internal review of their data practices. Octopus Holdings made 44 million Hong Kong dollars ($5.7M USD) over 4.5 years. Roderick Woo Bun, Hong Kong's Privacy Commissioner for Personal Data, gave radio interviews and called for transparent investigation, but his term expired at the end of July 2010. Allan Chiang Yam-wang was announced as the incoming Privacy Commissioner. This news was met with protests and international outrage, due to his prior history of privacy invasions involving cameras used to spy on employees at the Post Office, and disclosing hundreds of job applicants' personal data to corporations. Outgoing Privacy Commissioner Woo pledged to finish a preliminary report on the Octopus privacy abuse before his term ended, and called for a new law making it a criminal offence for companies to sell personal data.

Technology
As NFC and cardless payment are more popular in mainland China, some question the slow technology development of Octopus company. Among these commentaries, some suggest market monopoly and government attitude to Octopus are the contributing factor, as the social transportation subsidies are solely through the Octopus system. Octopus CEO Sunny Cheung stated that new technology would be launched in short period of time, such as QR code payment, integration of Octopus card with Samsung Pay and peer-to-peer lending.

title: Octopus card


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Nonprobability sampling

Nonprobability sampling is a form of sampling that does not utilise random sampling techniques where the probability of getting any particular sample may be calculated.

Nonprobability samples are not intended to be used to infer from the sample to the general population in statistical terms. In cases where external validity is not of critical importance to the study's goals or purpose, researchers might prefer to use nonprobability sampling. Researchers may seek to use iterative nonprobability sampling for theoretical purposes, where analytical generalization is considered over statistical generalization.

Advantages and disadvantages
While probabilistic methods are suitable for large-scale studies concerned with representativeness, nonprobability approaches may be more suitable for in-depth qualitative research in which the focus is often to understand complex social phenomena. The in-depth analysis of a small purposive sample or case study enables the discovery and identification of patterns and causal mechanisms that do not draw time and context-free assumptions. Another advantage of nonprobability sampling is its lower cost compared to probability sampling.

Nonprobability sampling is often not appropriate in statistical quantitative research.

Examples
Nonprobability sampling is widely used in qualitative research. Examples of nonprobability sampling include:
 * Convenience sampling, where members of the population are chosen based on their relative ease of access. Such samples are biased because researchers may unconsciously approach some kinds of respondents and avoid others, and respondents who volunteer for a study may differ in important ways from others.
 * Consecutive sampling, also known as total enumerative sampling, is a sampling technique in which every subject meeting the criteria of inclusion is selected until the required sample size is achieved.
 * Snowball sampling, involving the first respondent referring an acquaintance, and so on. Such samples are biased because they give people with more social connections an unknown but higher chance of selection, but lead to higher response rates.
 * Judgment sampling or purposive sampling, where the researcher chooses the sample based on who they think would be appropriate for the study. This is used primarily when there is a limited number of people that have expertise in the area being researched, or when the interest of the research is on a specific field or a small group. Types of purposive sampling include:
 * Deviant case: The researcher obtains cases that substantially differ from the dominant pattern. The case is selected in order to obtain information on unusual cases that can be specially problematic or specially good.
 * Case study: The research is limited to one group, often with a similar characteristic or of small size.

 * Quota sampling. This is similar to stratified random sampling, in which the researcher identifies subsets of the population of interest and then sets a target number for each category in the sample. Next, the researcher samples from the population of interest nonrandomly until the quotas are filled.

Studies intended to use probability sampling sometimes unintentionally end up using nonprobability samples because of characteristics of the sampling method. The statistical model used can also render the data a nonprobability sample.

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

title: Nonprobability sampling


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Jean Goldkette

John Jean Goldkette (March 18, 1893 – March 24, 1962) was a jazz pianist and bandleader.

Life
Goldkette was reportedly born on March 18, 1893, in Valenciennes, France, but there is evidence that he was born in Patras, Greece. His mother, Angela Goldkette, was a circus performer from Denmark. His father is unknown.

He spent his childhood in Greece and Russia, where he studied piano at the Moscow Conservatory as a child prodigy. The family emigrated to the United States in 1911. He performed in a classical ensemble in Chicago at the age of 18, later joining one of Edgar Benson's dance orchestras.

He leased a ballroom in Detroit and formed a band which grew to success, and was the foundation for a business empire acting as an agency for twenty orchestras and owning many dance halls. In 1936, he filed for bankruptcy; however, over the next three decades, he built up business again as a musician, conductor, and promoter. He married Lee McQuillen, a newspaperwoman, on March 4, 1939.

Music career
He led many jazz and dance bands, of which the most popular was his Victor Recording Orchestra of 1924–1929. The band defeated Fletcher Henderson in a battle of the bands contest. The head arranger was Bill Challis and the musicians included Bix Beiderbecke, Steve Brown, Hoagy Carmichael, Jimmy Dorsey, Tommy Dorsey, Eddie Lang, Chauncey Morehouse, Don Murray, Bill Rank, and Spiegle Willcox. Rex Stewart, a member of Henderson's band, wrote that "It was, without any question, the greatest in the world...the original predecessor to any large white dance orchestra that followed, up to Benny Goodman." Brian Rust also called it "the greatest band of them all."

Goldkette was music director for the Detroit Athletic Club for over 20 years and co-owned the Graystone Ballroom in Detroit with Charles Horvath, who performed with the Goldkette Victor Band in its early years. He owned his own entertainment company, Jean Goldkette's Orchestras and Attractions, working out of the Book-Cadillac Hotel in Detroit. He co-wrote the song "It's the Blues (No. 14 Blues)" which was recorded in Detroit and released by Victor. He also wrote the words to the 1926 song "New Steps".

In 1927, Paul Whiteman hired most of Goldkette's better players due to Goldkette's inability to meet payroll for his top-notch musicians. Goldkette helped organize McKinney's Cotton Pickers and Glen Gray's Orange Blossoms, which became popular as the Casa Loma Orchestra. In the 1930s, he left jazz to work as a booking agent and classical pianist. In 1939, he organized the American Symphony Orchestra which debuted at Carnegie Hall. Frankie Laine worked as Goldkette's librarian.

Death
He moved to California in 1961 and the following year died in Santa Barbara, California, of a heart attack at the age of 69. He took a taxi to the hospital by himself and died that same day. He is buried in the Angelus-Rosedale Cemetery in Los Angeles, California.

title: Jean Goldkette


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Edmund Mortimer, 5th Earl of March

Edmund Mortimer, 5th Earl of March, 7th Earl of Ulster (6 November 1391 – 18 January 1425), was an English nobleman and a potential claimant to the throne of England. A great-great-grandson of King Edward III of England, he was heir presumptive to King Richard II of England (both his paternal first cousin twice removed and maternal half grand-uncle) when he was deposed in favour of Henry IV. Edmund Mortimer's claim to the throne was the basis of rebellions and plots against Henry IV and his son Henry V, and was later taken up by the House of York in the Wars of the Roses, though Mortimer himself was an important and loyal vassal of Henry V and Henry VI. Edmund was the last Earl of March of the Mortimer family.

Early life
Edmund Mortimer, 5th Earl of March, was born at New Forest, Westmeath, one of his family's Irish estates, on 6 November 1391, the son of Roger Mortimer, 4th Earl of March, and Eleanor Holland. He had a younger brother, Roger (1393 – c. 1413), and two sisters: Anne, who married Richard, Earl of Cambridge, younger son of the Duke of York (executed 1415), and Eleanor, who married Sir Edward de Courtenay (d. 1418), and had no issue.

Edmund Mortimer's mother was the daughter of Thomas Holland, 2nd Earl of Kent, and Alice FitzAlan. Thomas Holland's mother, Joan of Kent, a granddaughter of Edward I, was the mother of Richard II by her second marriage; Alice Fitzalan was the daughter of Richard FitzAlan, 3rd Earl of Arundel, and his second wife, Eleanor, daughter of Henry, 3rd Earl of Lancaster, grandson of King Henry III.

Edmund Mortimer was thus a descendant of Henry III and Edward I and a half-grandnephew of Richard II through his mother, and more importantly a descendant of King Edward III through his paternal grandmother Philippa of Clarence, only child of King Edward III's second surviving son, Lionel of Antwerp, Duke of Clarence. Because King Richard II had no issue, Edmund's father, Roger Mortimer, 4th Earl of March, was heir presumptive during his lifetime, and at his death in Ireland on 20 July 1398 his place in the succession fell to his eldest son, Edmund. Thus in terms of male primogeniture Edmund was heir-presumptive to the throne over and above the house of Lancaster, the children of Edward III's third son John of Gaunt, Duke of Lancaster.

However, on 30 September 1399, when Edmund Mortimer was not yet eight years of age, his fortunes changed entirely. Richard II was deposed by Henry Bolingbroke, the new Duke of Lancaster, who became King Henry IV and had his own son, the future King Henry V, recognized as heir apparent at his first Parliament. The King put the young Edmund and his brother Roger in the custody of Sir Hugh Waterton at Windsor and Berkhamsted castles, but they were treated honourably, and for part of the time brought up with the King's own children, John and Philippa.

Rebellion against Henry IV
On 22 June 1402, Edmund's uncle, Sir Edmund Mortimer, son of the 3rd Earl, was captured by the Welsh rebel leader, Owain Glyndŵr, at the Battle of Bryn Glas. Henry IV accused Sir Edmund of deserting to Glyndŵr, refused to ransom him, and confiscated his property. Sir Edmund then married Glyndŵr's daughter, and on 13 December 1402 proclaimed in writing that his nephew Edmund was the rightful heir to King Richard II.

Sir Edmund's sister, Edmund's aunt, was married to Henry "Hotspur" Percy, son of the Earl of Northumberland. In 1403, the Percys rose in rebellion in collusion with Glyndŵr and Sir Edmund. Hotspur was defeated and slain at Shrewsbury.

The alliance of Glyndŵr, Sir Edmund, and the Percys survived this setback. In February 1405, they agreed to a three-way division of the kingdom. This agreement was apparently connected to a plot to free Edmund and his brother Roger from King Henry's custody and carry them into Wales. On 13 February 1405, the boys were abducted from Windsor Castle, but they were quickly recaptured near Cheltenham. Constance of York was held responsible and arrested. She implicated her brother, the Duke of York, who was imprisoned at Pevensey Castle for seventeen weeks. As a result of the failed abduction, on 1 February 1406, Edmund and Roger were put under stricter supervision at Pevensey Castle under Sir John Pelham (d.1429), where they remained until 1409. On 1 February 1409 Edmund and Roger were given in charge to the King's son, the Prince of Wales, who was only five years older than Edmund. They remained in custody for the remainder of Henry IV's reign.

Edmund Mortimer's sisters, Anne and Eleanor, who were in the care of their mother until her death in 1405, were not well treated by Henry IV, and were described as 'destitute' after her death.

Reign of Henry V
On his accession in 1413 Henry V set Edmund Mortimer at liberty, and on 8 April 1413, the day before the new King's coronation, Edmund Mortimer and his brother Roger were made Knights of the Bath.

On 9 June 1413, the King granted Edmund Mortimer livery of his estates. Henry IV's Queen, Joan of Navarre, had been granted authority over Edmund's marriage on 24 February 1408, but she later ceded this to Henry while Prince of Wales. On 17 January 1415 Edmund obtained a papal dispensation to marry 'a fit woman' related to him in the third degree of kindred or affinity. This allowed him to marry his second cousin once removed, Anne Stafford, the daughter of Anne of Gloucester and Edmund Stafford, 5th Earl of Stafford. Like Mortimer, she was a descendant of Edward III. The King was displeased, and imposed an enormous fine of 10,000 marks.

Despite this momentary discord, Edmund Mortimer was entirely loyal to Henry V. He never made any claim to the throne, despite being senior in descent. He was one of Henry's most trusted counsellors.

On 16 April 1415 Mortimer was present at the council which determined on war with France, and on 24 July 1415, he was a witness to the King's will.

While preparations for the invasion were underway, some discontented nobles launched the Southampton Plot, to take Mortimer to Wales and proclaim him king. The chief plotter was his sister Anne's husband, the Earl of Cambridge. When Mortimer was made privy to this plan, he revealed the conspiracy to the King at Portchester on 31 July. Afterwards, he sat on the commission which condemned Cambridge and the other conspirators to death; they were beheaded on 2 and 5 August. On 7 August, the King formally pardoned Mortimer for any nominal involvement in the plot.

Mortimer was deeply in debt when he accompanied Henry V's forces to France. He took part in several campaigns in Normandy, including the Siege of Harfleur, where he contracted dysentery, and was forced to return to England. On 15 August 1416 he was appointed a captain of the expedition sent to relieve Harfleur under John, Duke of Bedford, and Sir Walter Hungerford, and was with the army which conquered Normandy in 1417 and 1418. In July 1420 he was at the siege of Melun.

In February 1421 Mortimer accompanied the King back to England with his bride, Catherine of Valois, and bore the sceptre at Catherine's coronation on 21 February. He returned to France with Henry V in June 1421, and was at the Siege of Meaux, where the King fell mortally ill, dying on 31 August 1422.

Final years
Henry V was succeeded by his nine-month-old son, King Henry VI, and on 9 December 1422 Mortimer was appointed to the Regency Council of the regency government, 1422–1437.

On 9 May 1423 he was appointed the King's lieutenant in Ireland for nine years, but at first exercised his authority through a deputy, Edward Dantsey, Bishop of Meath, and remained in England. However, after a violent quarrel with the King's uncle Humphrey, Duke of Gloucester, and the execution of his kinsman, Sir John Mortimer, Mortimer was "sent out of the way to Ireland". He arrived there in the autumn of 1424, and on 18 or 19 January 1425 died of plague at Trim Castle. He was buried at Stoke-by-Clare, Suffolk, where he had founded a college of secular canons in 1414. Mortimer had no issue, and at his death the Mortimer line of the Earls of March became extinct. The heir to his estates and titles was the son of his sister Anne and the Earl of Cambridge, Richard of York, 3rd Duke of York (1411–1460). Richard also inherited Mortimer's claim to the throne, which he eventually raised, causing the Wars of the Roses.

His widow, Anne, married, before 6 March 1427, John Holland, 2nd Duke of Exeter. She died on 20 or 24 September 1432, and was buried in the church of St Katharine's by the Tower.

The Wigmore chronicle describes Edmund Mortimer as "severe in his morals, composed in his acts, circumspect in his talk, and wise and cautious during the days of his adversity".

Shakespeare and the Mortimers
Events in the life of Sir Edmund Mortimer, uncle of Edmund Mortimer, 5th Earl of March, were dramatized by Shakespeare in Henry IV, Part 1. In the play, Shakespeare accurately identifies the former as Hotspur's brother-in-law, but simultaneously conflates him with his nephew by referring to him as "Earl of March".

The Southampton Plot is dramatized in Shakespeare's play Henry V. However, its intent is misstated, and Mortimer's role in exposing it and condemning the plotters is completely omitted.

Edmund Mortimer also appears in Henry VI, Part 1. He is incorrectly depicted as an old man who has been imprisoned in the Tower of London since the rise of Henry IV. Furthermore, in an entirely fictional scene, Mortimer explains to his nephew Richard their family's claim to the throne, praises the efforts of Richard's father to make Mortimer king, and urges Richard to pursue his own claim to the throne. In reality, Richard was thirteen years old when his uncle died, and at the time was being raised in the north of England as a ward of the crown by Ralph Neville, 1st Earl of Westmorland.

title: Edmund Mortimer, 5th Earl of March


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Lists of airports in North America

This page contains the lists of airports in North America by country, grouped by region. The lists include both military air bases and civilian airports.

Northern America

 * List of airports in Bermuda
 * List of airports in Canada
 * List of airports in Greenland
 * List of airports in Saint Pierre and Miquelon
 * List of airports in the United States

Central America

 * List of airports in Belize
 * List of airports in Costa Rica
 * List of airports in El Salvador
 * List of airports in Guatemala
 * List of airports in Honduras
 * List of airports in Mexico
 * List of airports in Nicaragua
 * List of airports in Panama

Caribbean

 * List of airports in Anguilla
 * List of airports in Antigua and Barbuda
 * List of airports in Aruba
 * List of airports in the Bahamas
 * List of airports in Barbados
 * List of airports in British Virgin Islands
 * List of airports in the Cayman Islands
 * List of airports in Cuba
 * List of airports in Curaçao
 * List of airports in Dominica
 * List of airports in Dominican Republic
 * List of airports in Grenada
 * List of airports in Guadeloupe
 * List of airports in Haiti
 * List of airports in Jamaica
 * List of airports in Martinique
 * List of airports in Montserrat
 * List of airports in Puerto Rico
 * List of airports in Saint Barthélemy
 * List of airports in Saint Kitts and Nevis
 * List of airports in Saint Lucia
 * List of airports in Saint Vincent and the Grenadines
 * List of airports in Sint Maarten
 * List of airports in Trinidad and Tobago
 * List of airports in the Turks and Caicos Islands
 * List of airports in United States Virgin Islands

title: Lists of airports in North America


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Buena Vista Social Club (film)

Buena Vista Social Club is a 1999 documentary film directed by Wim Wenders about the music of Cuba. It is named for a danzón that became the title piece of the album Buena Vista Social Club. The film is an international co-production of Germany, the United States, the United Kingdom, France, and Cuba.

In 2020, the film was selected for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically or aesthetically significant.

Content
The film documents how Ry Cooder, a long-time friend of Wenders, brought together the ensemble of legendary Cuban musicians to record an album (also called Buena Vista Social Club) and to perform twice with a full line-up: in April 1998 in Amsterdam (two nights) and the 1st of July 1998 in the United States (at the Carnegie Hall, New York City). Although they are geographically close, travel between Cuba and the United States is restricted due to the political tension between the two countries, so many of the artists were travelling there for the first time. The film shows their reactions to this experience, as well as including footage of the resultant sell-out concert. It also includes interviews with each of the main performers.

Musicians

 * Francisco Repilado, aka Compay Segundo (vocals and tres)
 * Eliades Ochoa (vocals and guitar)
 * Ry Cooder (slide guitar)
 * Joachim Cooder, Ry's son (percussion)
 * Ibrahim Ferrer (vocals, congas, claves, bongos)
 * Omara Portuondo (vocals)
 * Rubén González (piano)
 * Orlando "Cachaito" López (Double bass)
 * Amadito Valdés
 * Manuel "Guajiro" Mirabal (trumpet)
 * Barbarito Torres (laúd)
 * Pío Leyva
 * Manuel "Puntillita" Licea (vocals)
 * Juan de Marcos González (güiro)

Songs

 * 1) "Chan Chan" (Francisco Repilado)
 * 2) "Silencio" (Rafael Hernandez)
 * 3) "Chattanooga Choo Choo" (Harry Warren and Mack Gordon)
 * 4) "Dos Gardenias" (Isolina Carillo)
 * 5) "Veinte Años" (María Teresa Vera)
 * 6) "Y Tu Que Has Hecho?" (Eusebio Delfin)
 * 7) "Black Bottom" (Ray Henderson, Lew Brown and B. G. De Sylva)
 * 8) "Canto Siboney" (Ernesto Lecuona Casado)
 * 9) "El Carretero" (Jose "Guillermo Portabales" Quesada del Castillo)
 * 10) "Cienfuegos (tiene su guaguanco)" (Victor Lay)
 * 11) "Begin the Beguine" (Cole Porter)
 * 12) "Buena Vista Social Club" (Orestes Lopez, inventor of the mambo in 1937)
 * 13) "Mandinga" (also known as "Bilongo", Guillermo Rodriguez Fiffe)
 * 14) "Candela" (Faustino Oramas),
 * 15) "Chanchullo" (Israel "Cachao" Lopez, the father of Cachaito)
 * 16) "El Cuarto de Tula" (son/descarga, Sergio Siaba)
 * 17) "Guateque Campesino" (Celia Romero "Guateque")
 * 18) "Nuestra Ultima Cita" (Forero Esther)
 * 19) "Quizás, Quizás, Quizás" (bolero by Oswaldo Farres)

Critical reception
Buena Vista Social Club received critical acclaim. On Rotten Tomatoes, the film has a 92% score based on 48 reviews, with an average rating of 7.52/10. Metacritic reports an 81 out of 100 rating based on 19 critics.

Accolades
The film was nominated for an Academy Award for best documentary feature in 2000. It won as best documentary in the European Film Awards as well as many others. The album Buena Vista Social Club features studio versions of the music heard in the film.

Influence
The film helped the musicians, some of them already in their nineties, become known to a worldwide audience, with some going on to release popular solo albums. These included Ibrahim Ferrer, Compay Segundo, Rubén González and Elíades Ochoa. The latter went on to support younger musicians making the same style of music beyond 2010 under the name "Buena Vista Social Club".

title: Buena Vista Social Club (film)


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McKinney's Cotton Pickers

McKinney's Cotton Pickers were an American jazz band, founded in Detroit, Michigan, United States in 1926, and led by William McKinney, who expanded his Synco Septet to ten players. Cuba Austin took over for McKinney on drums, with the latter becoming the band's manager. Between 1927 and 1931, they were one of the most popular African American bands. Many of their records for Victor were bestsellers.

In 1927, Fletcher Henderson's arranger and saxophone player Don Redman was invited to become the Cotton Pickers' musical director and he assembled a band. John Nesbitt helped Redman with arrangements and rehearsals. The band in 1928 included Cuba Austin (drums and vocals), Langston Curl (trumpet), Ralph Escudero (tuba), Claude Jones, Redman (clarinet, alto saxophone, baritone saxophone, vocals), Todd Rhodes (piano, celeste), Prince Robinson (clarinet, tenor saxophone), Milton Senior (trombone), George Thomas (clarinet, alto saxophone, tenor saxophone, vocals) and Dave Wilborn (banjo, vocals).

Other band members included George Bias (vocals), Benny Carter (clarinet, alto saxophone), Doc Cheatham (trumpet), Bill Coti (vocals), Ed Cuffee (trombone), Lois Deppe (vocals), Jimmy Dudley (clarinet, tenor saxophone), Robert Inge (clarinet, (alto saxophone), Quentin Jackson (trombone), Moxey-Hilton Jefferson (clarinet, alto saxophone), James P. Johnson (piano), Buddy Lee (trumpet), Donald King (vocals), Frank Marvin (vocals), Theodore McCord (clarinet, tenor saxophone), Jim Napier (vocals), Rex Stewart (cornet), and Billy Taylor (tuba). Towards the end of 1929, multiple soloists who were not regular members of the band sat in for a series of recordings. These included Leonard Davis (trumpet), Sidney de Paris (trumpet), Coleman Hawkins (clarinet, tenor saxophone), Fats Waller (piano, celeste), Joe "Fox" Smith  (trumpet, cornet), and Kaiser Marshall (drums).

In 1931, Redman left to form a band and was replaced by Benny Carter. The Cotton Pickers disbanded in 1934, unable to make money during the Great Depression. Manager of the band was Jean Goldkette who arranged for the group to record "Birmingham Bertha" for him in July 1929.

A New McKinney's Cotton Pickers was organized in the early 1970s by David Hutson, using the arrangements by Don Redman. The band recorded several albums and featured banjoist Dave Wilborn, who was the only surviving original member. The new group recorded music with Detroit trombonist Al Winters, as well as other leading members of Detroit's jazz scene during the era of the 1970s though the 1990s.

Discography

 * 1928–29 The Chronological McK C P 1928–1929 (Classics, 1991)
 * 1929–30The Chronological McK C P 1929–1930 (Classics, 1991)
 * 1930–31 McKinney's Cotton Pickers, 1930–1931/Don Redman & His Orchestra, 1939–1940 (Classics, 1992)

title: McKinney's Cotton Pickers


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Sinc filter

In signal processing, a sinc filter can refer to either a sinc-in-time filter whose impulse response is a sinc function and whose frequency response is rectangular, or to a sinc-in-frequency filter whose impulse response is rectangular and whose frequency response is a sinc function. Calling them according to which domain the filter resembles a sinc avoids confusion. If the domain is unspecified, sinc-in-time is often assumed, or context hopefully can infer the correct domain.

Sinc-in-time
Sinc-in-time is an ideal filter that removes all frequency components above a given cutoff frequency, without attenuating lower frequencies, and has linear phase response. It may thus be considered a brick-wall filter or rectangular filter.

Its impulse response is a sinc function in the time domain:

$$\frac{\sin(\pi t)}{\pi t}$$

while its frequency response is a rectangular function:

 * $$H(f) = \operatorname{rect} \left( \frac{f}{2B} \right)

= \begin{cases} 0,          & \text{if } |f| > B, \\ \frac{1}{2}, & \text{if } |f| = B, \\ 1,          & \text{if } |f| < B, \end{cases} $$

where $$B$$ (representing its bandwidth) is an arbitrary cutoff frequency.

Its impulse response is given by the inverse Fourier transform of its frequency response:

\begin{align} h(t) = \mathcal{F}^{-1} \{ H (f)\} &= \int_{-B}^B \exp(2\pi i f t) \, df \\ &= 2B \operatorname{sinc}(2 B t) \end{align} $$

where sinc is the normalized sinc function.

Brick-wall filters
An idealized electronic filter with full transmission in the pass band, complete attenuation in the stop band, and abrupt transitions is known colloquially as a "brick-wall filter" (in reference to the shape of the transfer function). The sinc-in-time filter is a brick-wall low-pass filter, from which brick-wall band-pass filters and high-pass filters are easily constructed.

The lowpass filter with brick-wall cutoff at frequency BL has impulse response and transfer function given by:

 * $$ h_{LPF}(t) = 2B_L \operatorname{sinc}\left(2B_L t\right)$$

 * $$ H_{LPF}(f) = \operatorname{rect}\left( \frac{f}{2B_L} \right).$$

The band-pass filter with lower band edge BL and upper band edge BH is just the difference of two such sinc-in-time filters (since the filters are zero phase, their magnitude responses subtract directly):

 * $$ h_{BPF}(t) = 2B_H \operatorname{sinc}\left(2B_H t\right) - 2B_L \operatorname{sinc}\left(2B_L t\right)$$

 * $$ H_{BPF}(f) = \operatorname{rect}\left( \frac{f}{2B_H} \right) - \operatorname{rect}\left( \frac{f}{2B_L} \right).$$

The high-pass filter with lower band edge BH is just a transparent filter minus a sinc-in-time filter, which makes it clear that the Dirac delta function is the limit of a narrow-in-time sinc-in-time filter:

 * $$ h_{HPF}(t) = \delta(t) - 2B_H \operatorname{sinc}\left(2B_H t\right)$$

 * $$ H_{HPF}(f) = 1 - \operatorname{rect}\left( \frac{f}{2B_H} \right).$$

Unrealizable
As the sinc-in-time filter has infinite impulse response in both positive and negative time directions, it is non-causal and has an infinite delay (i.e., its compact support in the frequency domain forces its time response not to have compact support meaning that it is ever-lasting) and infinite order (i.e., the response cannot be expressed as a linear differential equation with a finite sum). However, it is used in conceptual demonstrations or proofs, such as the sampling theorem and the Whittaker–Shannon interpolation formula.

Sinc-in-time filters must be approximated for real-world (non-abstract) applications, typically by windowing and truncating an ideal sinc-in-time filter kernel, but doing so reduces its ideal properties. This applies to other brick-wall filters built using sinc-in-time filters.

Stability
The sinc filter is not bounded-input–bounded-output (BIBO) stable. That is, a bounded input can produce an unbounded output, because the integral of the absolute value of the sinc function is infinite. A bounded input that produces an unbounded output is sgn(sinc(t)). Another is sin(2$\pi$Bt)u(t), a sine wave starting at time 0, at the cutoff frequency.

Frequency-domain sinc
The simplest implementation of a sinc-in-frequency filter uses a boxcar impulse response to produce a simple moving average (specifically if divide by the number of samples), also known as accumulate-and-dump filter (specifically if simply sum without a division). It can be modeled as a FIR filter with all $$N$$ coefficients equal. It is sometimes cascaded to produce higher-order moving averages (see and cascaded integrator–comb filter).

This filter can be used for crude but fast and easy downsampling (a.k.a. decimation) by a factor of $$N.$$ The simplicity of the filter (accumulate $$N$$ data samples, output the accumulator result, zero the accumulator, and repeat) is foiled by its mediocre low-pass capabilities. Its poorest attenuation in the stop-band is -13.3 dB and most high frequency components are only slightly more attenuated than that. An $$N$$-sample filter sampled at $$f_S$$ will alias all non-fully attenuated signal components lying above $\frac{f_S}{2N}$ to the baseband ranging from DC to $\frac{f_S}{2N}.$ A group averaging filter processing $$N$$ samples has $$\tfrac{N}{2}$$ transmission zeroes evenly-spaced by $$\tfrac{f_S}{N},$$ with the lowest zero at $$\tfrac{f_S}{N}$$ and the highest zero at $$\tfrac{f_S}{2}$$ (the Nyquist frequency). Above the Nyquist frequency, the frequency response is mirrored and then is repeated periodically above $$f_S$$ forever.

The magnitude of the frequency response (plotted in these graphs) is useful when one wants to know how much frequencies are attenuated. Though the sinc function really oscillates between negative and positive values, negative values of the frequency response simply correspond to a 180-degree phase shift.

An inverse sinc filter may be used for equalization in the digital domain (e.g. a FIR filter) or analog domain (e.g. opamp filter) to counteract undesired attenuation in the frequency band of interest to provide a flat frequency response.

See for application of the sinc kernel as the simplest windowing function.

title: Sinc filter


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Lists of military installations

This list of military installations consists of a collection of military related lists worldwide:

Africa

 * List of South African military bases
 * List of bases of the South African Air Force

Americas

 * List of Brazilian military bases
 * List of Canadian Forces Bases
 * List of Honduran military bases
 * List of Mexican military installations

United States

 * List of United States Air Force installations
 * List of United States Space Force installations
 * List of former United States Army installations
 * List of United States Navy installations
 * List of United States Marine Corps installations
 * List of United States Coast Guard stations
 * List of United States Army installations in Afghanistan
 * Bulgarian–American Joint Military Facilities
 * List of United States Army installations in Germany
 * List of United States Army installations in Italy
 * List of United States Military installations in Iraq
 * List of United States Army installations in Kosovo
 * List of United States Army installations in Kuwait
 * List of United States Army installations in South Korea

Asia

 * List of Burmese military installations
 * List of Chinese Air Force Bases
 * List of Indian Air Force stations
 * List of Israel Defense Forces bases
 * List of Pakistan Air Force Bases
 * Military installations of Turkey
 * List of military installations in Iraq
 * List of military installations in Saudi Arabia
 * List of Singapore Armed Forces bases
 * List of Sri Lankan air force bases

Europe

 * List of Bulgarian military bases
 * List of Danish Military Installations
 * List of Greek military bases
 * List of Irish military installations

Multinational installations

 * Papa Air Base, Hungary - Strategic Airlift Capability

United Kingdom

 * List of British Army installations
 * List of Royal Air Force stations
 * List of Battle of Britain airfields
 * List of V Bomber dispersal bases
 * List of air stations of the Royal Navy
 * List of Royal Navy shore establishments
 * List of airfields of the Army Air Corps (United Kingdom)
 * List of UK Thor missile bases
 * British Forces Germany

Oceania

 * List of Australian military bases
 * List of Royal Australian Air Force installations
 * List of Royal Australian Navy bases
 * List of New Zealand military bases

Others

 * List of countries with overseas military bases
 * List of Soviet Air Force bases

NATO installations
See Category:Military installations of NATO

Headquarters
 * SHAPE (Supreme Headquarters Allied Powers Europe) in Casteau, north of Mons (Belgium), since 1966 (before in Paris). SHAPE is since 2003 the headquarters of Allied Command Operations (ACO) controlling all allied operations worldwide.
 * NATO Communications and Information Agency (NCI Agency) in The Hague, Mons (Belgium) and Brussels
 * Headquarters Allied Command Transformation (based in Norfolk, Virginia. Other ACT organisations include the Joint Warfare Centre (JWC) located in Stavanger, Norway (in the same site as the former Norwegian NJHQ); the Joint Force Training Centre (JFTC) in Bydgoszcz, Poland; the Joint Analysis and Lessons Learned Centre (JALLC) in Monsanto, Portugal; and the NATO Undersea Research Centre (NURC), La Spezia, Italy.
 * Parts of Allied Command Transformation (based in Norfolk, Virginia) in SHAPE's headquarters.
 * the three Joint Force Commands - Allied Joint Force Command Brunssum in Brunnsum, Netherlands; Naples, and Norfolk;

Bases
 * NATO Air Base Geilenkirchen, Germany - hosts NATO Airborne Early Warning Force (NAEWF) Boeing E-3 Sentry aircraft.
 * Chièvres Air Base, Belgium - operated by U.S. Army and U.S. Air Force but "considered an installation of SHAPE."

title: Lists of military installations


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William McKinney

William "Bill" McKinney (September 17, 1895 – October 14, 1969) was an American jazz drummer who led a series of musical groups, most notably McKinney's Cotton Pickers.

Early life
McKinney was born in Cynthiana, Kentucky. He worked as a drummer in a circus band, then after serving in the United States Army in World War I settled in Springfield, Ohio where he took over leadership of the Synco Jazz Band.

Career
After hiring drummer Cuba Austin, McKinney worked as leader and business manager. After touring the U.S. Midwest, they got a residency at the Arcadia Ballroom in Detroit, Michigan in 1926. In Detroit they were heard by bandleader and music promoter Jean Goldkette, who arranged a more lucrative home base for the band in Detroit's Graystone Ballroom. The band was renamed McKinney's Cotton Pickers.

After the band broke up in 1934 during the Great Depression, McKinney for a time led and played with a dance band in Boston, From 1937 on McKinney managed a Detroit Cafe with a dance floor and live bands who McKinney booked; he also booked bands for other locations on the side.

Bill McKinney retired in the 1950s and spent his last years in his childhood hometown of Cynthiana.

title: William McKinney


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British Army of the Rhine

British Army of the Rhine (BAOR) was the name given to two British Army formations of the same name. Both were originally occupation forces in Germany, the first after the First World War and the other, active after the Second World War and during the Cold War, eventually becoming part of NATO's contribution to allied forces there. Both formations had areas of responsibility located around the German section of the River Rhine.

During the Cold War, the second formation was attached to NATO's Northern Army Group (NORTHAG) and tasked with defending the North German Plain, in the northern part of West Germany, from the armies of the Warsaw Pact. The BAOR by then constituted the bulk of British forces in West Germany, and was a part of British Forces Germany (BFG). The BFG was made up of elements of the three services based in West Germany, and the BAOR controlled the elements of the Army stationed there.

1919–1929
The first British Army of the Rhine was set up in March 1919 to implement the occupation of the Rhineland. It was originally composed of five corps, composed of two divisions each, plus a cavalry division:

II Corps: Commanded by Sir Claud Jacob
 * Light Division (formed from 2nd Division): Commanded by Major-General George Jeffreys
 * Southern Division (formed from 29th Division): Commanded by Major-General William Heneker

IV Corps: Commanded by Sir Alexander Godley
 * Lowland Division (formed from 9th (Scottish) Division)
 * Highland Division (formed from 62nd (2nd West Riding) Division)

VI Corps: Commanded by Sir Aylmer Haldane
 * Northern Division (formed from 3rd Division)
 * London Division (formed from 41st Division)

IX Corps: Commanded by Sir Walter Braithwaite and later by Ivor Maxse
 * Western Division (formed from 1st Division)
 * Midland Division (formed from 6th Division)

X Corps: Commanded by Sir Thomas Morland
 * Lancashire Division (formed from 32nd Division)
 * Eastern Division (formed from 34th Division)

Cavalry Division (formed from 1st Cavalry Division)

Most of these units were progressively dissolved, so that by February 1920 there were only regular battalions:

 * 1st Battalion Royal Irish Regiment
 * 4th Battalion Worcestershire Regiment
 * 2nd Battalion Black Watch (Royal Highlanders)
 * 1st Battalion Middlesex Regiment
 * 3rd Battalion Middlesex Regiment
 * 1st Battalion Durham Light Infantry

In August 1920 Winston Churchill, as Secretary of State for War, told Parliament that the BAOR was made up of approximately 13,360 troops, consisting of staff, cavalry, Royal Artillery, Royal Engineers, infantry, machine gun corps, tanks and the usual ancillary services. The troops were located principally in the vicinity of Cologne at an approximate cost per month of £300,000. The Cologne Post was a newspaper published for members of the BAOR during this period.

From 1922 the BAOR was organised into two brigades:

1st Rhine Brigade
 * 1st Battalion Northumberland Fusiliers 1922–1926
 * 1st Battalion West Yorkshire Regiment 1922–1926
 * 2nd Battalion Queen's Own Cameron Highlanders 1922–1926
 * 1st Battalion York and Lancaster Regiment 1922–1924
 * 2nd Battalion Royal Berkshire Regiment 1926–1928
 * 2nd Battalion Royal Welch Fusiliers Nov 1926 – Oct 1929
 * 2nd Battalion Worcestershire Regiment 1926–1928

2nd Rhine Brigade
 * 2nd Battalion Duke of Cornwall's Light Infantry 1922–1924
 * 1st Battalion King's Own Yorkshire Light Infantry 1922–1924
 * 2nd Battalion King's Royal Rifle Corps 1922–1925
 * 1st Battalion Royal Ulster Rifles 1922–1926
 * 1st Battalion Manchester Regiment 1923–1924
 * 2nd Battalion King's Shropshire Light Infantry 1924–1927
 * 1st Battalion Oxford and Bucks Light Infantry 1925–1927
 * 2nd Battalion Royal Fusiliers 1926–1929
 * 2nd Battalion Leicestershire Regiment 1927–1929
 * 2nd Battalion Dorsetshire Regiment 1928–1929

Commanders-in-chief
The commanders were:
 * Field Marshal Lord Plumer 1918–1919
 * General Sir William Robertson 1919–1920
 * General Sir Thomas Morland 1920–1922
 * General Sir Alexander Godley 1922–1924
 * General Sir John Du Cane 1924–1927
 * General Sir William Thwaites 1927–1929

Cold War (1945–1991)
The second British Army of the Rhine was formed on 25 August 1945 from the British Liberation Army. Its original function was to control the corps districts which were running the military government of the British zone of Allied-occupied Germany. After the assumption of government by civilians, it became the command formation for the troops in West Germany only, rather than being responsible for administration as well.

As the potential threat of Soviet invasion across the North German Plain into West Germany increased, BAOR became more responsible for the defence of West Germany than its occupation. It became the primary formation controlling the British contribution to NATO, after the formation of the alliance in 1949. Its primary combat formation was British I Corps. From 1952, the commander-in-chief of the BAOR was also the commander of NATO's Northern Army Group (NORTHAG) in the event of a general war with the Soviet Union and its Warsaw Pact allies. The BAOR's 50 Missile Regiment Royal Artillery was formerly armed with tactical nuclear weapons, including the MGM-52 Lance surface-to-surface tactical nuclear missile. In 1967, the force was reduced in strength to 53,000 soldiers, compared with 80,000, ten years earlier.

Post 1994
With the end of the Cold War, the 1993 Options for Change defence cuts resulted in BAOR being reduced in size, and in 1994 it became British Forces Germany. This force, roughly 25,000 strong, was divided between Headquarters Allied Command Europe Rapid Reaction Corps, 1st Armoured Division, other combat support and combat service support forces, and administrative elements headed by United Kingdom Support Command (Germany). Garrisons which closed at this time included Soest (home of the 6th Armoured Brigade), Soltau (home of the 7th Armoured Brigade) and Minden (home of the 11th Armoured Brigade).

Following the 2010 Strategic Defence and Security Review, the permanent deployment of British Army units in Germany was reduced. The last military base was handed to the German Bundeswehr in February 2020.

Commanders-in-chief
The commanders were:
 * Field Marshal Viscount Montgomery 1945–1946
 * Lieutenant General Sir Richard McCreery 1946–1948
 * Lieutenant General Sir Brian Horrocks 1948
 * Lieutenant General Sir Charles Keightley 1948–1951
 * General Sir John Harding 1951–1952
 * General Sir Richard Gale 1952–1957
 * General Sir Dudley Ward 1957–1960
 * General Sir James Cassels 1960–1963
 * General Sir William Stirling 1963–1966
 * General Sir John Hackett 1966–1968
 * General Sir Desmond Fitzpatrick 1968–1970
 * General Sir Peter Hunt 1970–1973
 * General Sir Harry Tuzo 1973–1976
 * General Sir Frank King 1976–1978
 * General Sir William Scotter 1978–1980
 * General Sir Michael Gow 1980–1983
 * General Sir Nigel Bagnall 1983–1985
 * General Sir Martin Farndale 1985–1987
 * General Sir Brian Kenny 1987–1989
 * General Sir Peter Inge 1989–1992
 * General Sir Charles Guthrie 1992 – May 1994 (command disbanded)

Garrisons

 * Bergen-Hohne Garrison
 * Osnabrück Garrison
 * Westfalen Garrison

title: British Army of the Rhine