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1055334 | Equatorial mount | https://en.wikipedia.org/w/index.php?title=Equatorial%20mount | Equatorial mount
design disadvantage of English or Yoke mounts by replacing the polar bearing with an open "horseshoe" structure to allow the telescope to access Polaris and stars near it. The Hale telescope is the most prominent example of a Horseshoe mount in use.
## Cross-axis mount.
The Cross-axis or English cross axis mount is like a big "plus" sign (+). The "right ascension" axis is supported at both ends, and the "declination" axis is attached to it at approximately midpoint with the telescope on one end of the declination axis and a counter weight on the other.
## Equatorial platform.
An equatorial platform is a specially designed platform that allows any device sitting on it to track on an equatorial | 25,800 |
1055334 | Equatorial mount | https://en.wikipedia.org/w/index.php?title=Equatorial%20mount | Equatorial mount
uatorial axis. It achieves this by having a surface that pivots about a "virtual polar axis". This gives equatorial tracking to anything sitting on the platform, from small cameras up to entire observatory buildings. These platforms are often used with altazimuth mounted amateur astronomical telescopes, such as the common Dobsonian telescope type, to overcome that type of mount's inability to track the night sky.
# See also.
- Altazimuth mount
- Barn door tracker
- Equatorial room
- Hexapod-Telescope
- List of telescope parts and construction
- List of telescope types
- Parallactic angle
- Polar alignment
- Polar mount - a similar mount used with satellite dishes
- Poncet Platform | 25,801 |
1055319 | Bullet with Butterfly Wings | https://en.wikipedia.org/w/index.php?title=Bullet%20with%20Butterfly%20Wings | Bullet with Butterfly Wings
Bullet with Butterfly Wings
"Bullet with Butterfly Wings" is a song by the American alternative rock band The Smashing Pumpkins and the lead single from their 1995 double album "Mellon Collie and the Infinite Sadness". The song won the Grammy Award for Best Hard Rock Performance. This song was the band's first Top 40 U.S. hit, peaking at number 22 on the "Billboard" Hot 100. It also spent six weeks at number two on the Modern Rock Tracks chart, and peaked at number four on the Mainstream Rock chart. In Canada, the song peaked at number 18 on the "RPM" Top Singles chart and spent four weeks at number one on the Alternative 30 chart, becoming Canada's most successful rock song of the year.
The | 25,802 |
1055319 | Bullet with Butterfly Wings | https://en.wikipedia.org/w/index.php?title=Bullet%20with%20Butterfly%20Wings | Bullet with Butterfly Wings
song was named the 91st best hard rock song of all time by VH1 in 2009 and ranked number 70 on the 2008 list of "The 100 Greatest Guitar Songs of All Time" of "Rolling Stone". The song came second in the Triple J Hottest 100, 1995, was later voted number 51 in the Triple J Hottest 100 of All Time, 2009 and placed at number 25 in the Triple J Hottest 100 of the Past 20 Years, 2013.
# Background.
The song had its origins during the recording of 1993's "Siamese Dream". According to frontman Billy Corgan, "somewhere, I have a tape of us from 1993 endlessly playing the 'world is a vampire' part over and over". It was not until 1995 that Corgan finished the song with the noted chorus "rat in a cage", | 25,803 |
1055319 | Bullet with Butterfly Wings | https://en.wikipedia.org/w/index.php?title=Bullet%20with%20Butterfly%20Wings | Bullet with Butterfly Wings
on an acoustic guitar during the same session that "Landslide" was recorded. The lyrics "Can you fake it, for just one more show?" may refer to the band's experience headlining the 1994 Lollapalooza festival, with Corgan calling it the "old job". Along with other parts of the album, Corgan appears to compare himself to Jesus Christ, with the line "Jesus was an only son / Tell me I'm the chosen one".
# Music video.
Filming for the music video took place in Los Angeles, California on September 30, 1995, with Samuel Bayer as director. The visual look of the video was inspired by the work of Brazilian photographer Sebastião Salgado on gold mining, while, in contrast, the band used the video to | 25,804 |
1055319 | Bullet with Butterfly Wings | https://en.wikipedia.org/w/index.php?title=Bullet%20with%20Butterfly%20Wings | Bullet with Butterfly Wings
debut their new glam rock wardrobes - notably, Billy Corgan's black shirt with the word "Zero" written in silver, and silver pants. The video also marks the last filmed appearance of Billy Corgan prior to his decision to shave his head.
When asked why the band chose Bullet for the first video, Corgan responded "the record company did a survey of K-Mart shoppers between 30 and 40 and this is the song they came up with". "This is the blue light special", said Chamberlin, though it's likely in the context of the interview that these statements were in jest.
# Track listing.
Original US/UK CD single
"...Said Sadly" features Nina Gordon of Veruca Salt on vocals.
1996 Re-issue
US 7" double A-side | 25,805 |
1055319 | Bullet with Butterfly Wings | https://en.wikipedia.org/w/index.php?title=Bullet%20with%20Butterfly%20Wings | Bullet with Butterfly Wings
single
# Cover versions.
- Scranton punk rock band The Menzingers closed many of the shows on their 2013 tour with a cover of the song.
- Melodic hardcore band Four Year Strong covered this song on their 2009 album "Explains It All" which is a cover album tributing songs that were made famous by groups in the 1990s.
- Sigue Sigue Sputnik made a cover of the song for the 2001 compilation album "A Gothic–Industrial Tribute to The Smashing Pumpkins".
- Groove metal band Skinlab covered this song on their 2004 compilation album "Nerve Damage".
- Latin metal band Ill Niño covered this song on their 2010 album "Dead New World".
- The Ghost and the Grace covered this song and released it as | 25,806 |
1055319 | Bullet with Butterfly Wings | https://en.wikipedia.org/w/index.php?title=Bullet%20with%20Butterfly%20Wings | Bullet with Butterfly Wings
a one-off single in 2009.
- Hawthorne Heights made a cover of this song, released as part of a 2007 Smashing Pumpkins tribute album from MySpace Records.
- Taking Back Sunday made a cover as apart of charity compilation called "Songs That Saved My Life."
- Karen O made a cover of this song for Amazon Video's "Hanna" TV series
# In other media.
The song is used, slightly edited, as the title song for the Animal Planet reality television series "Whale Wars", which follows the Sea Shepherd Conservation Society as they chase Japanese whalers in the Southern Ocean Whale Sanctuary. The song is also used in the "South Park" episode "Whale Whores", which parodies "Whale Wars".
"Weird Al" Yankovic | 25,807 |
1055319 | Bullet with Butterfly Wings | https://en.wikipedia.org/w/index.php?title=Bullet%20with%20Butterfly%20Wings | Bullet with Butterfly Wings
tuary. The song is also used in the "South Park" episode "Whale Whores", which parodies "Whale Wars".
"Weird Al" Yankovic performed the chorus in "The Alternative Polka" from his "Bad Hair Day" album.
The song was featured as a playable track in the video game "Guitar Hero 5".
It was also used in the launch trailer for "Dead Space 2" and TV spot for "Battlefield 1".
The song was the TNA Lockdown wrestling pay-per-view theme song for 2009.
UFC also used it for the Anderson Silva vs Nick Diaz fight in UFC 183's short trailer.
A remixed version of the song can be heard in the teaser trailer for "Rampage", and it is sampled in the film's end credits song, "The Rage", performed by Kid Cudi. | 25,808 |
1055365 | Sangaku | https://en.wikipedia.org/w/index.php?title=Sangaku | Sangaku
Sangaku
Sangaku or San Gaku (算額; lit. translation: calculation tablet) are Japanese geometrical problems or theorems on wooden tablets which were placed as offerings at Shinto shrines or Buddhist temples during the Edo period by members of all social classes.
# History.
The Sangaku were painted in color on wooden tablets (ema) and hung in the precincts of Buddhist temples and Shinto shrines as offerings to the kami and buddhas, as challenges to the congregants, or as displays of the solutions to questions. Many of these tablets were lost during the period of modernization that followed the Edo period, but around nine hundred are known to remain.
Fujita Kagen (1765–1821), a Japanese mathematician | 25,809 |
1055365 | Sangaku | https://en.wikipedia.org/w/index.php?title=Sangaku | Sangaku
of prominence, published the first collection of "sangaku" problems, his "Shimpeki Sampo" (Mathematical problems Suspended from the Temple) in 1790, and in 1806 a sequel, the "Zoku Shimpeki Sampo".
During this period Japan applied strict regulations to commerce and foreign relations for western countries so the tablets were created using Japanese mathematics, developed in parallel to western mathematics. For example, the connection between an integral and its derivative (the fundamental theorem of calculus) was unknown, so Sangaku problems on areas and volumes were solved by expansions in infinite series and term-by-term calculation.
# Select examples.
A typical problem, which is presented | 25,810 |
1055365 | Sangaku | https://en.wikipedia.org/w/index.php?title=Sangaku | Sangaku
on an 1824 tablet in the Gunma Prefecture, covers the relationship of three touching circles with a common tangent. Given the size of the two outer large circles, what is the size of the small circle between them? "The answer is:"
## In the west.
Soddy's hexlet, thought previously to have been discovered in the west in 1937, has been discovered on a Sangaku dating from 1822.
# See also.
- Recreational mathematics
- Seki Takakazu
- Japanese theorem for concyclic polygons
- Japanese theorem for concyclic quadrilaterals
- Equal incircles theorem
# References.
- Fukagawa, Hidetoshi, and Dan Pedoe. (1989). "Japanese temple geometry problems = Sangaku". Winnipeg: Charles Babbage. ; OCLC | 25,811 |
1055365 | Sangaku | https://en.wikipedia.org/w/index.php?title=Sangaku | Sangaku
). "Japanese temple geometry problems = Sangaku". Winnipeg: Charles Babbage. ; OCLC 474564475
- __________ and Dan Pedoe. (1991) Tōkyō : Mori Kitashuppan. ; OCLC 47500620
- __________ and Tony Rothman. (2008). "Sacred Mathematics: Japanese Temple Geometry." Princeton: Princeton University Press. ; OCLC 181142099
- Huvent, Géry. (2008). "Sangaku. Le mystère des énigmes géométriques japonaises." Paris: Dunod. ; OCLC 470626755
- Rehmeyer, Julie, "Sacred Geometry", "Science News," March 21, 2008.
# External links.
- Sangaku (Japanese votive tablets featuring mathematical puzzles)
- Japanese Temple Geometry Problem
- Sangaku: Reflections on the Phenomenon
- Sangaku Journal of Mathematics | 25,812 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
Travel class
A travel class is a quality of accommodation on public transport. The accommodation could be a seat or a cabin for example. Higher travel classes are designed to be more comfortable and are typically more expensive.
# Airliners.
Traditionally, an airliner is divided to, from the top, first, business, and economy cabins. In recent years, premium economy classes have been added by some airlines as an intermediate class between economy and business class.
Each cabin class is further divided into invisible booking classes, which although booked into the same cabin differ in conditions and benefits outside of the cabin class travelled such as frequent-flyer points, baggage limit, | 25,813 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
change or refund policy, etc.
# Buses.
In Mexico, bus services often have designated levels of service, the top of which is "de lujo" or "clase lujo", followed by "plus clase", "primera clase", and "segunda clase".
# Ocean liners.
Before cruise ships dominated the passenger ship trade, ocean liners had classes of service, often categorized as First Class, Second Class, and Steerage. Companies such as Cunard Line continue this tradition, offering Queen's Grill, Princess Grill and Britannia cabins, each of which have their own allocated lounges and restaurants on board.
# Trains.
Trains often have first class (the higher class) and second class (known as standard class in the UK). For trains | 25,814 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
with sleeping accommodations, there may be more levels of luxury.
## China.
Traditional trains commonly offer the following classes: soft sleeper, hard sleeper, soft seat and hard seat, depending on the route.
CRH EMUs offer the following classes: soft sleeper (available only on few overnight routes), business seat, 1st class seat and 2nd class seat.
## Taiwan.
Prior to 1949, most railway bureaus (under the direction of the Transport Ministry) had a three-class structure. As with most contemporary cases, few people could afford first class or even second class, so at times there would be no first class or second class service available in some trains. Some went as far as offering a fourth | 25,815 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
class "service" with goods wagons.
In 1949, the first "Limited Express with Reserved Seating" (特快對號車) appeared with the Railway Bureau of Taiwan, and it offered a three-class service, inherited locally from Japanese colonial rule. This structure was the norm for all trains, normal or express, until 1953.
In 1953, the "Equality Express" was introduced with second class carriages only. Eventually, all expresses save for the sole Limited Express offered only second class service, and all other, slower trains, offered only third class. This resulted in the quality of service being associated with the speed of the train. The Diesel Limited Express was introduced in 1956 with one class only.
In | 25,816 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
1960, with the reforming of Limited Expresses (the Limited Express with Reserved Seating and Diesel Limited Express merged into one fare), all passenger trains officially offered only one class. Therefore, all expresses had only second class carriages and other trains only third class. As time passes, more types of carriages were introduced, but these were thought as types instead of classes.
## Europe.
At the very beginning of the railway age in Europe, almost every railway operator offered three classes for passenger services: "First class" was the most luxurious and least demanded class, equipped with rich upholstered seats, while "second class" was also upholstered, but on a lower level | 25,817 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
and with fewer seating space. In contrast, "third class" only provided wooden benches. While most passenger trains carried just one or two "first class" and "second class" carriages, every other carriage was "third class" only.
Today there are generally two classes, known as "first class" and "second class", or the equivalent in the local language. The three-tier class structure was abolished on most European railways by the end of the 1950s in favor of a two-tier structure conceived by the UIC. In fact, the old "first class" from the pre-World War II-era was deleted without substitution because of low ridership in postwar times, therefor the old "second class" became the new "first class" | 25,818 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
and the "third class", with hardly any wooden seatings left, was declared the new "second class".
Trains in Great Britain provide a two-tier class structure, with the higher tier called "first class". The lower tier was re-branded from "third class" to "second class" by British Rail from 3 June 1956, and then to "standard class" from 11 May 1987.
A convention used by most European railway companies is that the first-class section of a train is marked in yellow, usually with a yellow band above the doors and/or windows. First-class areas may be complete carriages or at one end of a carriage, the other end being second class. Second-class compartments usually have "2+2" seating (2 seats each | 25,819 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
side of the aisle); first-class compartments are typically "2+1". In Britain and France, some short-distance Suburban trains use "2+3" for the lower class and "2+2" for first class.
Metro, suburban and local trains are sometimes second-class-only. First-class-only trains were common up to the 1980s (see Trans Europe Express) but are now rare. High-speed trains often charge more than slower-speed trains on the same route, but still have first- and second-class seats.
Trains in Ireland are primarily operated as standard-class only, with only some of the longest distance services having a higher class, called Premier on IE 22000 Class stock, CityGold on Mark 4 loco-hauled carriages and First | 25,820 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
Plus on the cross-border Enterprise service. No commuter services have premium classes. Premium benefits can be as limited as a reading light and waiter service; but reach to 2+1 recliner seating and enhanced catering options.
In Germany, there existed a "fourth class" ("4. Klasse") on almost every local train from the second half of the 19th century to 1928. It provided just a very low travel comfort, the passengers had to sit on even wooden planks with rudimentary backrests. Much of the space in the compartments was left empty to allow country folks to carry their goods and livestock inside the carriage.
## India.
The Indian Railways offers six classes of train accommodation in general.
- | 25,821 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
First Class A/C (1A) is the highest rail travel class and is not available on all trains. It offers air-conditioned cubicles in two-bed and four-bed formats with closing doors. There usually is only one 1A bogie (carriage) on a train.
- Two Tier A/C (2A) offers air conditioned cubicles in four-bed + two-bed format, but the privacy is provided by curtains instead of the doors found in 1A. There are typically one or two 2A bogies on long-distance trains.
- Three Tier A/C (3A) offers air conditioned cubicles in six-bed + two-bed format(six beds on one side and two beds on other side of the hallway). Most trains have two to five 3A bogies.
- A/C Chair Car (CC) is a feature of short-distance trains | 25,822 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
that cover the journey within a day. The seating is usually in 3x3 format.
- Sleeper Class (SL) is configured similarly to 3A but is not air conditioned. There are typically ten to fifteen SL bogies in a train.
- Second Class (Reserved) (2S) similar as CC, without the air-conditioning. These may be reserved in advance or may be unreserved.
- Second Class (II) for long-distance trains is similar to the SL cars but has wooden middle berths instead of upper berths. However, local and suburban trains may offer a different variety of second class, which has an open cabin with rows of wooden seats facing each other in pairs.
Some trains also have one of these classes:
- Third AC Economy (3E). | 25,823 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
Similar to Three Tier A/C, however this class have an additional middle berth in the side section of the air conditioned cubicle, making it a six-bed and three-bed format. This type of accommodation is created for less well off people, who desire a comfortable travel at lesser fare.
- First Class (FC), which is similar in configuration to the 1A class but lacks air conditioning. The class is currently being phased out in favor of the slightly expensive 2A and cheaper 3A classes. In 2011, it could be found only on Mumbai local train and a few trains across all of India.
- Executive AC Chair Car (EC), has a 2x2 seat configuration and includes food catering service. It is available only on the | 25,824 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
"Shatabdi Express" and "Tejas Express" trains, which link major cities located within a day-trip distance.
## Indonesia.
Indonesian trains, operated by the state-owned PT Kereta Api Indonesia (the Indonesian Railways Co.), have now four classes for long-distance travel. All types of carriages are seating-only (no sleeper cars).
- Executive/first class ("eksekutif")–the top and most expensive class, offers the most comfortable means of travel - 2–2 reclining seat configuration, on-board TV. Also, trains having Eksekutif cars are certainly the fastest ones – see the note below.
- Argo class – this is the top class that all of train names use Argo brand.
- Fauna class – below the Argos.
- | 25,825 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
Business/second class ("bisnis")–medium class, the fare is around 60% of executive classes, 2–2 seating, fixed 60 degrees seat.
- Premium economy class–the intermediate level between the business and economy classes, the fare is nearly same as business, 2-2 reclining seat configuration.
- Economy/third class ("ekonomi")–the lowest and cheapest class, below the premium class tickets are 4-5 times cheaper than business classes.
- Commercial economy class, 2-2 seat configuration
- PSO economy class, 3-2 seat configuration, split-type air conditioned (like as home air conditioners). Remember, the seat configuration is ABC-DE, "not" AB-CDE.
All classes are non-smoking and air conditioned. All | 25,826 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
passengers require a seat reservation, "except" for commuter trains. All seats can be reserved from 30–90 days before travel date until minutes before departure time when seats are still available.
Medium and long distance trains have onboard cafeteria, flushing toilets (older passenger coaches have squatting toilets), onboard customer service representative (Train Manager), onboard security, and onboard cleaning services.
Executive class trains are the fastest and stop only on a few major stations (first priority). Business trains are somewhat slower, but generally do not stop too often as well there may be economy cars in these trains (second priority). Economy trains take significantly | 25,827 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
more time to reach the destination, as they stop on many smaller stations and have to pass all executive and business class traffic going in the same direction (third priority). Many less important routes lack either business or executive service, or both. Some services have more two or three classes mixed together (executive-business, executive-economy, executive-premium economy, or executive-business-economy).
For local or commuter trains, single class service is the most common type of service. But in some areas there may be other classes as well which have different seating arrangement and travel time in which the lower classes has more stops than the upper one. For example, Jogjakarta–Solo | 25,828 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
route there are "Sriwedari" train services which is air conditioned and has transverse seating and also "Prambanan Express" train which is non air conditioned, has longitudinal seating and more stops. Meanwhile, in Jakarta metropolitan area, there's only one class of service available since mid-2013 which is air conditioned and has longitudinal seating. Commuter trains in Jakarta are operated by Kereta Commuter Indonesia, a subsidiary of the Indonesian Railways Co.
## Japan.
From 1872, Japan had a three-class structure for both seating carriages and sleeping carriages. By 1960, as conditions improved on second and third class trains, there were few passengers travelling on first class; therefore, | 25,829 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
the few remaining first class carriages were rebranded "special" carriages available for hire, and consequently moved Japan's railway system to a two-class system, of which the original second class became the first, and the original third became second.
In 1969, the class structure was abolished altogether. The first class was renamed "Green" carriages and the second "Standard" carriages.
All members of the Japan Railways Group (JR) offer separated classes of travel, with varying levels of availability on any given train.
The Kyushu Railway Company (JR Kyūshū), Hokkaido Railway Company (JR Hokkaido), and East Japan Railway Company (JR East) all offer an enhanced service known as the Green | 25,830 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
Car on nearly all of their intercity trains. Additionally, the Central Japan Railway Company (JR Central) and Shikoku Railway Company (JR Shikoku) offer a Green Car on some trains, and a few West Japan Railway Company (JR West) trains also have a Green Car. The alternative to Green Car is the Ordinary Car. Although Ordinary Car tickets may be purchased with or without reserved seating, all Green Car tickets are reserved seating. A ticket must be purchased in advance, and a special version of the Japan Rail Pass allowing travel in Green Cars is available.
Most JR Group Green Cars seats have increased width and pitch. In some stations, Green Cars are located nearer to the staircases and escalators | 25,831 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
leading to/from the train platform. Green Cars also frequently offer slippers and reading materials in Japanese.
Additionally, JR East offers a third category of service, the GranClass, available on its Hayabusa route. Features of GranClass cars include leather seats that recline to a 45 degree angle, raised footrests, adjustable dining tables and cocktail trays, and personal reading lights. Full-service meals, both Japanese and Western, are provided by specialized GranClass attendants, who also serve soft drinks and alcoholic beverages. Because the Hayabusa is a long-distance service to the Tōhoku region, overnight amenities such as slippers, blankets, and eye masks are provided.
## Great | 25,832 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
Britain.
During the Victorian era, most trains in the United Kingdom had three classes of accommodation: first class, second class and third class. From 1875, when the Midland Railway redesignated its second class accommodation as "third class", second class (equivalent to either premium economy or business class) was gradually abolished, while first class and third class were retained. This was because the Railway Regulation Act 1844 required a third-class service to be offered. In addition to this, British third class was initially of a comparable standard to continental European third class and British first class with European first class (the continent having retained three classes). This | 25,833 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
meant that boat trains in Britain still often operated with three classes of accommodation after the abolition of second class in the rest of the country. From 3 June 1956 British Railways redesignated third class as "second class", finally (as British Rail) renaming it "standard class" from 11 May 1987, in view of the pejorative overtones of "second class".
A coach with accommodation for more than one class is called a "composite coach".
## North America.
In the United States and Canada, train classes emulate the airlines, although airlines probably took the class levels from trains of the time when they were coming of age (e.g. first, business, coach). Amtrak Acela Express trains have two | 25,834 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
classes: First Class and Business Class. Amtrak Northeast Regional trains have Business Class and Coach class. Canada's Via Rail has the same classes as Amtrak. Trains with sleeper cars have additional levels. Most commuter trains in USA and Canada generally have a business class and economy class or standard fare. Although business class is offered it typically is just more spacious seats in a more modern sleek cabin. WiFi is available on commuter trains in the southern Ontario corridor, as well as southern Quebec (Via Rail). Full services, such as food and beverage, may not always be a given.
# See also.
- First class (aviation)
- First class travel
- Business class
- Premium economy
- | 25,835 |
1055318 | Travel class | https://en.wikipedia.org/w/index.php?title=Travel%20class | Travel class
gional trains have Business Class and Coach class. Canada's Via Rail has the same classes as Amtrak. Trains with sleeper cars have additional levels. Most commuter trains in USA and Canada generally have a business class and economy class or standard fare. Although business class is offered it typically is just more spacious seats in a more modern sleek cabin. WiFi is available on commuter trains in the southern Ontario corridor, as well as southern Quebec (Via Rail). Full services, such as food and beverage, may not always be a given.
# See also.
- First class (aviation)
- First class travel
- Business class
- Premium economy
- Economy class
- Passenger car (rail)
- IATA class codes | 25,836 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
Goal setting
Goal setting involves the development of an action plan designed to motivate and guide a person or group toward a goal. Goal setting can be guided by goal-setting criteria (or rules) such as SMART criteria. Goal setting is a major component of personal-development and management literature.
Studies by Edwin A. Locke and his colleagues have shown that more specific and ambitious goals lead to more performance improvement than easy or general goals. The goals should be specific, difficult, and have time constraints. As long as the person accepts the goal, has the ability to attain it, and does not have conflicting goals, there is a positive linear relationship between goal difficulty | 25,837 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
and task performance.
The theory states that the simplest most direct motivational explanation of why some people perform better than others is because they have different performance goals. The essence of the theory is fourfold. First, difficult specific goals lead to significantly higher performance than easy goals, no goals, or even the setting of an abstract goal such as urging people to do their best. Second, holding ability constant, as this is a theory of motivation, and given that there is goal commitment, the higher the goal the higher the performance. Third, variables such as praise, feedback, or the involvement of people in decision-making only influences behavior to the extent that | 25,838 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
it leads to the setting of and commitment to a specific difficult goal. Fourth, goal-setting, in addition to affecting the three mechanisms of motivation, namely, choice, effort, and persistence, can also have a cognitive benefit. It can influence choice, effort, and persistence to discover ways to attain the goal.
# History.
Cecil Alec Mace carried out the first empirical studies in 1935.
Edwin A. Locke began to examine goal setting in the mid-1960s and continued researching goal setting for more than 30 years. Locke derived the idea for goal-setting from Aristotle's form of final causality. Aristotle speculated that purpose can cause action; thus, Locke began researching the impact goals | 25,839 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
have on human activity. Locke developed and refined his goal-setting theory in the 1960s, publishing his first article on the subject, "Toward a Theory of Task Motivation and Incentives", in 1968. This article established the positive relationship between clearly identified goals and performance.
# Concept.
Goals that are difficult to achieve and specific tend to increase performance more than goals that are not. A goal can be made more specific by:
Setting goals can affect outcomes in four ways:
# Goal commitment.
People perform better when they are committed to achieving certain goals. Through an understanding of the effect of goal setting on individual performance, organizations are | 25,840 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
able to use goal setting to benefit organizational performance. Locke and Latham (2002) have indicated three moderators that indicate goal setting success:
Expanding the three from above, the level of commitment is influenced by external factors. Such as the person assigning the goal, setting the standard for the person to achieve/perform. This influences the level of commitment by how compliant the individual is with the one assigning the goal. An external factor can also be the role models of the individual. Say if they strive to be like their favorite athlete, the individual is more likely to put forth more effort to their own work and goals.
Internal factors can derive from their participation | 25,841 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
level in the work to achieve the goal. What they expect from themselves can either flourish their success, or destroy it. Also, the individual may want to appear superior to their peers or competitors. They want to achieve the goal the best and be known for it. The self-reward of accomplishing a goal, is usually one of the main keys that keep individuals committed.
## Goal–performance relationship.
Locke and colleagues (1981) examined the behavioral effects of goal-setting, concluding that 90% of laboratory and field studies involving specific and challenging goals led to higher performance than did easy or no goals.
Locke and Latham (2006) argue that it is not sufficient to urge employees | 25,842 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
to "do their best". "Doing one's best" has no external referent, which makes it useless in eliciting specific behavior. To elicit some specific form of behavior from another person, it is important that this person has a clear view of what is expected from him/her. A goal is thereby of vital importance because it helps an individual to focus his or her efforts in a specified direction. In other words, goals canalize behavior. (However, when faced with complex tasks and directions that are difficult to specify, telling someone to "do their best", with a focus on learning, can sometimes lead to the discovery of better strategies whereby specific goals can then be set.)
## Feedback.
Without proper | 25,843 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
feedback channels it is impossible for employees to adapt or adjust to the required behavior. Managers should keep track of performance to allow employees to see how effective they have been in attaining their goals. Providing feedback on short-term objectives helps to sustain motivation and commitment to the goal and without it, goal setting is unlikely to be successful. Feedback should be provided on the strategies followed to achieve the goals and the final outcomes achieved, as well. Feedback on strategies used to obtain goals is very important, especially for complex work, because challenging goals put focus on outcomes rather than on performance strategies, so they impair performance. | 25,844 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
Properly delivered feedback is also very essential, and the following hints may help for providing a good feedback:
Advances in technology can facilitate providing feedback. Systems analysts have designed computer programs that track goals for numerous members of an organization. Such computer systems may maintain every employee's goals, as well as their deadlines. Separate methods may check the employee's progress on a regular basis, and other systems may require perceived slackers to explain how they intend to improve.
More difficult goals require more cognitive strategies and well-developed skills. The more difficult the tasks, the smaller the group of people who possess the necessary skills | 25,845 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
and strategies. From an organizational perspective, it is thereby more difficult to successfully attain more difficult goals, since resources become more scarce.
## Honing goal setting using temporal motivation theory.
Locke and Latham (2004) note that goal setting theory lacks "the issue of time perspective". Taking this into consideration, Steel and Konig (2006) utilize their temporal motivation theory (TMT) to account for goal setting's effects, and suggest new hypotheses regarding a pair of its moderators: goal difficulty and proximity. The effectiveness of goal setting can be explained by two aspects of TMT: the principle of diminishing returns and temporal discounting. Similar to the | 25,846 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
expression "the sum of the parts can be greater than the whole", a division of a project into several, immediate, subgoals appears to take advantage of these two elements.
## Employee motivation.
The more employees are motivated, the more they are stimulated and interested in accepting goals. These success factors are interdependent. For example, the expected outcomes of goals are positively influenced when employees are involved in the goal setting process. Not only does participation increase commitment in attaining the goals that are set, participation influences self-efficacy as well. Additionally, feedback is necessary to monitor one's progress. When feedback is not present, an employee | 25,847 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
might think (s)he is not making enough progress. This can reduce self-efficacy and thereby harm the performance outcomes in the long run.
# In business.
In business, goal setting encourages participants to put in substantial effort. Also, because every member has defined expectations for their role, little room is left for inadequate, marginal effort to go unnoticed.
Managers cannot constantly drive motivation, or keep track of an employee's work on a continuous basis. Goals are therefore an important tool for managers, since goals have the ability to function as a self-regulatory mechanism that helps employees prioritize tasks.
Four mechanisms through which goal setting can affect individual | 25,848 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
performance are:
- 1. Goals focus attention toward goal-relevant activities and away from goal-irrelevant activities.
- 2. Goals serve as an energizer: Higher goals induce greater effort, while low goals induce lesser effort.
- 3. Goals affect persistence; constraints with regard to resources affect work pace.
- 4. Goals activate cognitive knowledge and strategies that help employees cope with the situation at hand.
# In training.
Goal setting is used to improve training outcomes. For example, Tomokazu Kishiki and colleagues performed a randomized controlled trial on surgical trainees to determine whether or not their participation in a goal-setting program would improve performance and | 25,849 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
testing scores; the addition of achievable goals appeared to be beneficial to the trainees./ref When goal setting is applied optimally during training processes, both employee motivation and organizational commitment can increase.
Furthermore, training in goal setting has been linked to higher levels of performance among adults and children with mild to severe intellectual disability.
# In personal life.
Common personal goals include losing weight, achieving good grades, and saving money. The strategy for goal setting begins with the big picture; taking a look at the big picture before breaking it into smaller components allows one to focus on the primary goal. Once the main goal is set, | 25,850 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
breaking it up into smaller, more achievable components helps in the planning portion of setting the goal. These smaller, more obtainable objectives promote self-esteem and provide instant feedback to keep the individual on task.
Time management is the practice of systematically finishing tasks assigned by superiors or one's self in an efficient and timely manner. Time management steps require identifying the objective and laying out a plan that maximizes efficiency and execution of the objective. There are many useful mobile apps that help with personal goal setting; some of the categories include budgeting, wellness, calendar and productivity apps.
# Limitations.
Goal-setting has limitations. | 25,851 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
In an organization, a goal of a manager may not align with the goals of the organization as a whole. In such cases, the goals of an individual may come into direct conflict with the employing organization. Without clearly aligning goals between the organization and the individual, overall performance may suffer. Additionally, there is evidence that suggests that goal-setting can foster unethical behavior when people do not achieve their desired goals. Goal setting also may impair performance in certain situations. Such situations include when an individual becomes overly focused on accomplishing a previously-set goal that they end up under performing on current tasks.
Goal setting may have | 25,852 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
the drawback of inhibiting implicit learning: goal setting may encourage simple focus on an outcome without openness to exploration, understanding, or growth. A solution to this limitation is to set "learning" goals as well as "performance" goals, so that learning is expected as part of the process of reaching goals.
# Developments in theory.
## Goal choice.
Self-efficacy, past performance, and various other social factors influence goal setting. Failure to meet previous goals often leads to setting lower (and more likely achievable) goals.
## Learning goals.
There are times when having specific goals is not a best option; this is the case when the goal requires new skills or knowledge. | 25,853 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
Tunnel vision is a consequence of specific goals; if a person is too focused on attaining a specific goal, he or she may ignore the need to learn new skills or acquire new information. This concept is illustrated well by the "basketball game task" study in which observers watched a video of a group of people wearing white shirts and black shirts who are passing a basketball back and forth, and the observers were instructed to count the number of times a basketball is passed between only the players wearing white shirts. During the video, a woman carrying an open umbrella walks across the screen. Of 28 observers who were focused on counting the number of passes between only the players wearing | 25,854 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
white shirts, only 6 reported noticing the woman carrying the umbrella. When observers watched the video without focusing on a specific task, all of the observers noticed the umbrella woman. In situations where the risk of tunnel vision is high, the best option is to set a "learning goal". A learning goal is a generalized goal to achieve knowledge in a certain topic or field, but it can ultimately lead to better performance in specific goals related to the learning goals.
Locke and Latham (2006) attribute this response to metacognition. They believe that "a learning goal facilitates or enhances metacognition—namely, planning, monitoring, and evaluating progress toward goal attainment". This | 25,855 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
is necessary in environments with little or no guidance and structure. Although jobs typically have set goals, individual goals and achievement can benefit from metacognition.
## Framing.
Framing, or how goals are viewed, influences performance. When one feels threatened and or intimidated by a high goal they perform poorer than those who view the goal as a challenge. The framing of a goal as a gain or a loss influences one's eventual performance.
## Affect.
Realization of goals has an effect on affect—that is, feelings of success and satisfaction. Achieving goals has a positive effect, and failing to meet goals has negative consequences. However, the effect of goals is not exclusive to | 25,856 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
one realm. Success in one's job can compensate for feelings of failure in one's personal life.
## Group goals.
The relationship between group goals and individual goals influences group performance; when goals are compatible there is a positive effect, but when goals are incompatible the effects can be detrimental to the group's performance. There is another factor at work in groups, and that is the sharing factor; a positive correlation exists between sharing information within the group and group performance. In the case of group goals, feedback needs to be related to the group, not individuals, in order for it to improve the group's performance.
## Goals and traits.
On a basic level, | 25,857 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
the two types of goals are "learning goals" and "performance goals"; each possesses different traits associated with the selected goal.
"Learning goals" involve tasks where skills and knowledge can be acquired, whereas "performance goals" involve easy-to-accomplish tasks that will make one appear successful (thus tasks where error and judgment may be possible are avoided).
A more complex trait-mediation study is the one conducted by Lee, Sheldon, and Turban (2003), which yielded the following results:
- "Amotivated orientation" (low confidence in one's capabilities) is associated with goal-avoidance motivation, and more generally, associated with lower goals levels and lower performance.
- | 25,858 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
"Control orientation" (extrinsic motivation) is associated with both avoidance and approach goals. Approach goals are associated with higher goal levels and higher performance.
- "Autonomy goals" (intrinsic motivation) leads to mastery goals, enhanced focus, and therefore enhanced performance.
## Macro-level goals.
"Macro-level goals" refer to goal setting that is applied to the company as a whole. Cooperative goals reduce the negative feelings that occur as a result of alliances and the formation of groups. The most common parties involved are the company and its suppliers. The three motivators for macro-level goals are: self-efficacy, growth goals, and organizational vision.
## Goals and | 25,859 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
subconscious priming.
The effects of subconscious priming and conscious goals are independent, although a conscious goal has a larger effect. The interaction effect is that priming can enhance the effects of difficult goals, but it has no effect on easy goals. There is also the situation in which priming and conscious goals conflict with one another, and in this situation the conscious goals have a greater effect on performance.
## General action and inaction goals.
Action goals are believed to promote the sense of action, whereas inaction goals are considered to reduce people's tendency to take actions. Common action goals can be to do something, perform a certain act, or to go someplace, | 25,860 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
whereas typical inaction goals can take the form of having a rest or to stop doing something.
Goal-regulated overall activity and inactivity tendency result from both biological conditions and social-cultural environment. Recent research revealed that most nations hold more favorable attitude towards action rather than inaction, even though some countries value action and inaction slightly differently than others.
Recent research suggested that people tend to choose inaction goals when they are making decisions among choices where uncertainty could result in negative outcomes, but they prefer action over inaction in their daily behaviors when no deliberation is needed. Timothy D. Wilson and | 25,861 |
1055344 | Goal setting | https://en.wikipedia.org/w/index.php?title=Goal%20setting | Goal setting
e making decisions among choices where uncertainty could result in negative outcomes, but they prefer action over inaction in their daily behaviors when no deliberation is needed. Timothy D. Wilson and colleagues found that many people "preferred to administer electric shocks to themselves instead of being left alone with their thoughts".
# See also.
- Big Hairy Audacious Goal
- Goal orientation
- GROW model
- Health coaching
- I-Change Model
- Immunity to change
- Motivational interviewing
- OGSM objectives, goals, strategies and measures
- OKR objectives and key results
- Performance measurement
- Positive deviance
- Remuneration
- Strategic planning
- Transtheoretical model | 25,862 |
1055369 | Japanese mathematics | https://en.wikipedia.org/w/index.php?title=Japanese%20mathematics | Japanese mathematics
Japanese mathematics
In the history of mathematics, the development of "wasan" falls outside the Western realms of people, propositions and alternate solutions. At the beginning of the Meiji period (1868–1912), Japan and its people opened themselves to the West. Japanese scholars adopted Western mathematical technique, and this led to a decline of interest in the ideas used in "wasan".
# History.
This mathematical schema evolved during a period when Japan's people were isolated from European influences. Kambei Mori is the first Japanese mathematician noted in history. Kambei is known as a teacher of Japanese mathematics; and among his most prominent students were Yoshida Shichibei Kōyū, Imamura | 25,863 |
1055369 | Japanese mathematics | https://en.wikipedia.org/w/index.php?title=Japanese%20mathematics | Japanese mathematics
Chishō, and Takahara Kisshu. These students came to be known to their contemporaries as "the Three Arithmeticians".
Yoshida was the author of the oldest extant Japanese mathematical text. The 1627 work was named "Jinkōki". The work dealt with the subject of soroban arithmetic, including square and cube root operations. Yoshida's book significantly inspired a new generation of mathematicians, and redefined the Japanese perception of educational enlightenment, which was defined in the Seventeen Article Constitution as "the product of earnest meditation".
Seki Takakazu founded "enri" (円理: circle principles), a mathematical system with the same purpose as calculus at a similar time to calculus's | 25,864 |
1055369 | Japanese mathematics | https://en.wikipedia.org/w/index.php?title=Japanese%20mathematics | Japanese mathematics
development in Europe; but Seki's investigations did not proceed from conventionally shared foundations.
# Select mathematicians.
The following list encompasses mathematicians whose work was derived from "wasan."
- Kambei Mori (early 17th century)
- Yoshida Mitsuyoshi (1598–1672)
- Seki Takakazu (1642–1708)
- Takebe Kenkō (1664–1739)
- Matsunaga Ryohitsu (fl. 1718-1749)
- Kurushima Kinai (d. 1757)
- Arima Raido (1714–1783)
- Fujita Sadasuke (1734-1807)
- Ajima Naonobu (1739–1783)
- Aida Yasuaki (1747–1817)
- Sakabe Kōhan (1759–1824)
- Fujita Kagen (1765–1821)
- Hasegawa Ken (c. 1783-1838)
- Wada Nei (1787–1840)
- Shiraishi Chochu (1796–1862)
- Koide Shuke (1797–1865)
- Omura | 25,865 |
1055369 | Japanese mathematics | https://en.wikipedia.org/w/index.php?title=Japanese%20mathematics | Japanese mathematics
Isshu (1824–1871)
# See also.
- Japanese theorem for cyclic polygons
- Japanese theorem for cyclic quadrilaterals
- Sangaku, the custom of presenting mathematical problems, carved in wood tablets, to the public in Shinto shrines
- Soroban, a Japanese abacus
# References.
- Campbell, Douglas M. and John C. Iggins. (1984). "Mathematics: People, Problems, Results." Belmont, California: Warsworth International. ; ; ; OCLC 300429874
- Endō Toshisada (1896). . Tōkyō: _____. OCLC 122770600
- Fukagawa, Hidetoshi, and Dan Pedoe. (1989). "Japanese temple geometry problems = Sangaku". Winnipeg: Charles Babbage. ; OCLC 474564475
- __________ and Dan Pedoe. (1991) Tōkyō : Mori Kitashuppan. ; OCLC | 25,866 |
1055369 | Japanese mathematics | https://en.wikipedia.org/w/index.php?title=Japanese%20mathematics | Japanese mathematics
47500620
- __________ and Tony Rothman. (2008). "Sacred Mathematics: Japanese Temple Geometry." Princeton: Princeton University Press. ; OCLC 181142099
- Horiuchi, Annick. (1994). "Les Mathematiques Japonaises a L'Epoque d'Edo (1600–1868): Une Etude des Travaux de Seki Takakazu (?-1708) et de Takebe Katahiro (1664–1739)." Paris: Librairie Philosophique J. Vrin. ; OCLC 318334322
- __________. (1998). "Les mathématiques peuvent-elles n'être que pur divertissement? Une analyse des tablettes votives de mathématiques à l'époque d'Edo." "Extrême-Orient, Extrême-Occident", volume 20, pp. 135–156.
- Kobayashi, Tatsuhiko. (2002) "What kind of mathematics and terminology was transmitted into 18th-century | 25,867 |
1055369 | Japanese mathematics | https://en.wikipedia.org/w/index.php?title=Japanese%20mathematics | Japanese mathematics
Japan from China?", "Historia Scientiarum", Vol.12, No.1.
- Kobayashi, Tatsuhiko. Trigonometry and Its Acceptance in the 18th-19th Centuries Japan.
- Morimoto, Mitsuo. "Infinite series in Japanese Mathematics of the 18th Century".
- Morimoto, Mitsuo. "A Chinese Root of Japanese Traditional Mathematics – Wasan"
- Ogawa, Tsukane. "A Review of the History of Japanese Mathematics". "Revue d'histoire des mathématiques" 7, fascicule 1 (2001), 137-155.
- Restivo, Sal P. (1992). "Mathematics in Society and History: Sociological Inquiries." Dordrecht: Kluwer Academic Publishers. ; OCLC 25709270
- Selin, Helaine. (1997). "Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western | 25,868 |
1055369 | Japanese mathematics | https://en.wikipedia.org/w/index.php?title=Japanese%20mathematics | Japanese mathematics
; OCLC 25709270
- Selin, Helaine. (1997). "Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures." Dordrecht: Kluwer/Springer. ; OCLC 186451909
- David Eugene Smith and Yoshio Mikami. (1914). "A History of Japanese Mathematics." Chicago: Open Court Publishing. OCLC 1515528; "see" online, multi-formatted, full-text book at archive.org
# External links.
- Japan Academy, Collection of native Japanese mathematics
- JapanMath, Math program focused on Math Fact Fluency and Japanese originated logic games
- Sangaku
- Sansu Math, translated Tokyo Shoseki Japanese math curriculum
- Kümmerle, Harald. "Bibliography on traditional mathematics in Japan (wasan)" | 25,869 |
1055390 | Sniper and Other Love Songs | https://en.wikipedia.org/w/index.php?title=Sniper%20and%20Other%20Love%20Songs | Sniper and Other Love Songs
Sniper and Other Love Songs
Sniper and Other Love Songs is the second studio album by the American singer/songwriter Harry Chapin, released in 1972. The album's title song is a vaguely fictionalised account of Charles Whitman's shootings from the clocktower of the Main Building of the University of Texas at Austin in August 1966. In 2004 it was released as a double CD package with "Heads & Tales" featuring several previously unreleased out-takes.
The song "Circle" was a major hit for The New Seekers (released as "Circles") and became known as the Chapin Anthem. "Sunday Morning Sunshine" cracked the Billboard Hot 100. A live version of "Better Place To Be" charted in 1976.
# Personnel.
- Harry | 25,870 |
1055390 | Sniper and Other Love Songs | https://en.wikipedia.org/w/index.php?title=Sniper%20and%20Other%20Love%20Songs | Sniper and Other Love Songs
arles Whitman's shootings from the clocktower of the Main Building of the University of Texas at Austin in August 1966. In 2004 it was released as a double CD package with "Heads & Tales" featuring several previously unreleased out-takes.
The song "Circle" was a major hit for The New Seekers (released as "Circles") and became known as the Chapin Anthem. "Sunday Morning Sunshine" cracked the Billboard Hot 100. A live version of "Better Place To Be" charted in 1976.
# Personnel.
- Harry Chapin - guitar, vocals
- John Wallace - bass, vocals
- Tim Scott - cello
- Ron Palmer - lead guitar, vocals
- Steve Chapin - keyboards
- Russ Kunkel - drums and percussion
# See also.
- 1972 in music | 25,871 |
1055391 | Copiague Harbor, New York | https://en.wikipedia.org/w/index.php?title=Copiague%20Harbor,%20New%20York | Copiague Harbor, New York
Copiague Harbor, New York
Copiague Harbor ( ) is an incorporated community in the hamlet of Copiague. It is located south of Merrick Road (or Montauk Highway), off of South Great Neck Road in Suffolk County, New York, USA, on the South Shore of Long Island. It is sometimes referred to as Great Neck Landing;
Copiague Harbor is a small, community located on a southern peninsula of Copiague, primarily composed of larger size homes deeded belonging to a homeowner's association; Great South Bay Estates Homeowner's Association (GSBEHA). This affluent private community offers amenities including a mini-beach and mini-marina on a private lagoon.
It was created in the late 1960s intended as a private | 25,872 |
1055391 | Copiague Harbor, New York | https://en.wikipedia.org/w/index.php?title=Copiague%20Harbor,%20New%20York | Copiague Harbor, New York
Shore of Long Island. It is sometimes referred to as Great Neck Landing;
Copiague Harbor is a small, community located on a southern peninsula of Copiague, primarily composed of larger size homes deeded belonging to a homeowner's association; Great South Bay Estates Homeowner's Association (GSBEHA). This affluent private community offers amenities including a mini-beach and mini-marina on a private lagoon.
It was created in the late 1960s intended as a private community, gated and guarded. From time to time residents have considered adding a gate and guard as originally intended.
Copiague Harbor is assigned to Copiague Public School District.
# Geography.
Copiague Harbor is located at . | 25,873 |
1055393 | List of wars involving Georgia (country) | https://en.wikipedia.org/w/index.php?title=List%20of%20wars%20involving%20Georgia%20(country) | List of wars involving Georgia (country)
List of wars involving Georgia (country)
The following is an incomplete list of wars involving Georgia, by Georgian people or regular armies during periods when independent Georgian states existed, from antiquity to the present day. It also includes wars fought outside of Georgia by Georgian military.
The list gives the name, the date, combatants, and the result of these conflicts following this legend:
# See also.
- List of Georgian battles | 25,874 |
1055372 | Villers-sur-Mer | https://en.wikipedia.org/w/index.php?title=Villers-sur-Mer | Villers-sur-Mer
Villers-sur-Mer
Villers-sur-Mer is a commune in the Calvados department in Normandy, northwestern France, with a population of 2,765 as of 2016.
# Geography.
The commune is located on the French coast of the English Channel, on the Côte Fleurie, between Deauville and Houlgate, approximately 200km from Paris.
It is the northernmost French commune through which falls the Prime meridian. The latter is represented on the seafront promenade with a blue mark on the ground and on the parapet. This mark is positioned 32 meters west of the actual meridian.
# History.
It seems that Villers-sur-Mer (then known as "Villers") was more akin to a group of hamlets during the early 19th century. According | 25,875 |
1055372 | Villers-sur-Mer | https://en.wikipedia.org/w/index.php?title=Villers-sur-Mer | Villers-sur-Mer
to the Cassini map (drawn in the 18th century), Villers at that time is made up of a church, two farms ("La Motte" and "Fontaine"), and a castle.
# Population.
The town had a population of 2,574 in 2006, posting a growth of just over 150 residents between then and 2016.
# Sights.
Villers-sur-Mer is known for the large topiary dinosaurs facing the sea from the garden of the office of tourism. In certain years, a baby dinosaur is added to the garden. It is the starting point of the Vaches Noires cliffsa site where many fossils have been discovered. There is a small museum in the enclosure of the office of tourism, which has an outline of the resources and discoveries. It is a place widely | 25,876 |
1055372 | Villers-sur-Mer | https://en.wikipedia.org/w/index.php?title=Villers-sur-Mer | Villers-sur-Mer
the starting point of the Vaches Noires cliffsa site where many fossils have been discovered. There is a small museum in the enclosure of the office of tourism, which has an outline of the resources and discoveries. It is a place widely known by specialists in the ammonites and other fossils.
# Transportation.
Villers-sur-Mer station is on the line from Deauville to Dives-sur-Mer. The station building is no longer open but train services operate year-round on weekends, and also on weekdays during the summer.
# See also.
- Communes of the Calvados department
- Adélaïde-Louise d'Eckmühl de Blocqueville (1815–1892), salon holder, died in Villers-sur-Mer.
# External links.
- Official site | 25,877 |
1055395 | 5th arrondissement | https://en.wikipedia.org/w/index.php?title=5th%20arrondissement | 5th arrondissement
5th arrondissement
5th arrondissement may refer to:
- France:
- 5th arrondissement of Lyon
- 5th arrondissement of Marseille
- 5th arrondissement of Paris
- Benin:
- 5th arrondissement of Porto-Novo
- 5th arrondissement of the Littoral Department | 25,878 |
1055398 | Little Indian River (Michigan) | https://en.wikipedia.org/w/index.php?title=Little%20Indian%20River%20(Michigan) | Little Indian River (Michigan)
Little Indian River (Michigan)
The Little Indian River is a river on the Upper Peninsula of the U.S. state of Michigan. It rises in a small lake on Hiawatha National Forest land in Alger County, Michigan at , flows through a lake district, then on through Schoolcraft County, and into the Indian River at .
Most of its course roughly parallels that of the Indian River a few miles to the south and west. The only major tributary is Grassy Creek, aside from the outflows of several small lakes. | 25,879 |
1055370 | Lucas pseudoprime | https://en.wikipedia.org/w/index.php?title=Lucas%20pseudoprime | Lucas pseudoprime
Lucas pseudoprime
Lucas pseudoprimes and Fibonacci pseudoprimes are composite integers that pass certain tests which all primes and very few composite numbers pass: in this case, criteria relative to some Lucas sequence.
# Baillie-Wagstaff-Lucas pseudoprimes.
Baillie and Wagstaff define Lucas pseudoprimes differently. Given integers "P" and "Q", where "P" 0 and formula_1,
let "U"("P", "Q") and "V"("P", "Q") be the corresponding Lucas sequences.
Let "n" be a positive integer and let formula_2 be the Jacobi symbol. We define
If "n" is a prime such that the greatest common divisor of "n" and "Q" (that is, GCD("n, Q")) is 1, then the following congruence condition holds:
If this equation | 25,880 |
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does "not" hold, then "n" is "not" prime.
If "n" is "composite", then this equation "usually" does not hold. These are the key facts that make Lucas sequences useful in primality testing.
Some good references are chapter 8 of the book by Bressoud and Wagon (with Mathematica code), pages 142–152 of the book by Crandall and Pomerance, and pages 53–74 of the book by Ribenboim.
# Lucas probable primes and pseudoprimes.
A Lucas probable prime for a given ("P, Q") pair is "any" positive integer "n" for which equation () above is true (see, page 1398).
A Lucas pseudoprime for a given ("P, Q") pair is a positive "composite" integer "n" for which equation () is true (see, page 1391).
A Lucas probable | 25,881 |
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prime test is most useful if "D" is chosen such that the Jacobi symbol formula_2 is −1
(see pages 1401–1409 of, page 1024 of
, or pages 266–269 of
). This is especially important when combining a Lucas test with a strong pseudoprime test, such as the Baillie-PSW primality test. Typically implementations will use a parameter selection method that ensures this condition (e.g. the Selfridge method recommended in and described below).
If formula_5 then equation () becomes
If congruence () is false, this constitutes a proof that "n" is composite.
If congruence () is true, then "n" is a Lucas probable prime.
In this case, either "n" is prime or it is a Lucas pseudoprime.
If congruence () is | 25,882 |
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true, then "n" is "likely" to be prime (this justifies the term probable prime), but this does not "prove" that "n" is prime.
As is the case with any other probabilistic primality test, if we perform additional Lucas tests with different "D", "P" and "Q", then unless one of the tests proves that "n" is composite, we gain more confidence that "n" is prime.
Examples: If "P" = 3, "Q" = −1, and "D" = 13, the sequence of "U"'s is : "U" = 0, "U" = 1, "U" = 3, "U" = 10, etc.
First, let "n" = 19. The Jacobi symbol formula_6 is −1, so δ("n") = 20, "U" = 6616217487 = 19·348221973 and we have
Therefore, 19 is a Lucas probable prime for this ("P, Q") pair. In this case 19 is prime, so it is "not" a | 25,883 |
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Lucas pseudoprime.
For the next example, let "n" = 119. We have formula_8 = −1, and we can compute
However, 119 = 7·17 is not prime, so 119 is a Lucas "pseudoprime" for this ("P, Q") pair.
In fact, 119 is the smallest pseudoprime for "P" = 3, "Q" = −1.
We will see below that, in order to check equation () for a given "n", we do "not" need to compute all of the first "n" + 1 terms in the "U" sequence.
Let "Q" = −1, the smallest Lucas pseudoprime to "P" = 1, 2, 3, ... are
# Strong Lucas pseudoprimes.
Now, factor formula_10 into the form formula_11 where formula_12 is odd.
A strong Lucas pseudoprime for a given ("P, Q") pair is an odd composite number "n" with GCD("n, D") = 1, satisfying | 25,884 |
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one of the conditions
or
for some 0 ≤ "r" "s"; see page 1396 of. A strong Lucas pseudoprime is also a Lucas pseudoprime (for the same ("P, Q") pair), but the converse is not necessarily true.
Therefore, the strong test is a more stringent primality test than equation ().
We can set "Q" = −1, then formula_15 and formula_16 are "P"-Fibonacci sequence and "P"-Lucas sequence, the pseudoprimes can be called strong Lucas pseudoprime in base "P", for example, the least strong Lucas pseudoprime with "P" = 1, 2, 3, ... are 323, 169, 119, ...
An extra strong Lucas pseudoprime
is a strong Lucas pseudoprime for a set of parameters ("P", "Q") where "Q" = 1, satisfying one of the conditions
or
for | 25,885 |
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some formula_19 pair.
# Implementing a Lucas probable prime test.
Before embarking on a probable prime test, one usually verifies that "n", the number to be tested for primality, is odd, is not a perfect square, and is not divisible by any small prime less than some convenient limit. Perfect squares are easy to detect using Newton's method for square roots.
We choose a Lucas sequence where the Jacobi symbol formula_20, so that δ("n") = "n" + 1.
Given "n", one technique for choosing "D" is to use trial and error to find the first "D" in the sequence 5, −7, 9, −11, ... such that formula_20. Note that formula_22.
(If "D" and "n" have a prime factor in common, then formula_23).
With this sequence | 25,886 |
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of "D" values, the average number of "D" values that must be tried before we encounter one whose Jacobi symbol is −1 is about 1.79; see, p. 1416.
Once we have "D", we set formula_24 and formula_25.
It is a good idea to check that "n" has no prime factors in common with "P" or "Q".
This method of choosing "D", "P", and "Q" was suggested by John Selfridge.
Given "D", "P", and "Q", there are recurrence relations that enable us to quickly compute formula_26 and formula_27 in formula_28 steps; see . To start off,
First, we can double the subscript from formula_31 to formula_32 in one step using the recurrence relations
Next, we can increase the subscript by 1 using the recurrences
If formula_37 | 25,887 |
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is odd, replace it with formula_38; this is even so it can now be divided by 2. The numerator of formula_39 is handled in the same way. (Adding "n" does not change the result modulo "n".)
Observe that, for each term that we compute in the "U" sequence, we compute the corresponding term in the "V" sequence. As we proceed, we also compute the same, corresponding powers of "Q".
At each stage, we reduce formula_40, formula_41, and the power of formula_42, mod "n".
We use the bits of the binary expansion of "n" to determine "which" terms in the "U" sequence to compute. For example, if "n"+1 = 44 (= 101100 in binary), then, taking the bits one at a time from left to right, we obtain the sequence | 25,888 |
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of indices to compute: 1 = 1, 10 = 2, 100 = 4, 101 = 5, 1010 = 10, 1011 = 11, 10110 = 22, 101100 = 44. Therefore, we compute "U", "U", "U", "U", "U", "U", "U", and "U". We also compute the same-numbered terms in the "V" sequence, along with "Q", "Q", "Q", "Q", "Q", "Q", "Q", and "Q".
By the end of the calculation, we will have computed "U", "V", and "Q", (mod "n").
We then check congruence () using our known value of "U".
When "D", "P", and "Q" are chosen as described above, the first 10 Lucas pseudoprimes are (see page 1401 of ):
323, 377, 1159, 1829, 3827, 5459, 5777, 9071, 9179, and 10877
The strong versions of the Lucas test can be implemented in a similar way.
When "D", "P", and "Q" | 25,889 |
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are chosen as described above, the first 10 "strong" Lucas pseudoprimes are: 5459, 5777, 10877, 16109, 18971, 22499, 24569, 25199, 40309, and 58519
To calculate a list of "extra strong" Lucas pseudoprimes, set formula_43.
Then try "P" = 3, 4, 5, 6, ..., until a value of formula_1 is found so that the Jacobi symbol formula_20.
With this method for selecting "D", "P", and "Q", the first 10 "extra strong" Lucas pseudoprimes are
989, 3239, 5777, 10877, 27971, 29681, 30739, 31631, 39059, and 72389
## Checking additional congruence conditions.
If we have checked that congruence () is true, there are additional congruence conditions we can check that have almost no additional computational cost.
If | 25,890 |
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"n" happens to be composite, these additional conditions may help discover that fact.
If "n" is an odd prime and formula_20, then we have the following (see equation 2 on page 1392 of ):
Although this congruence condition is not, by definition, part of the Lucas probable prime test, it is almost free to check this condition because, as noted above, the value of "V" was computed in the process of computing "U".
If either congruence () or () is false, this constitutes a proof that "n" is not prime.
If "both" of these congruences are true, then it is even more likely that "n" is prime than if we had checked only congruence ().
If Selfridge's method (above) for choosing "D", "P", and "Q" happened | 25,891 |
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to set "Q" = −1, then we can adjust "P" and "Q" so that "D" and formula_2 remain unchanged and "P" = "Q" = 5 (see Lucas sequence-Algebraic relations).
If we use this enhanced method for choosing "P" and "Q", then 913 = 11·83 is the "only" composite less than 10 for which congruence () is true (see page 1409 and Table 6 of;).
Here is another congruence condition that is true for primes and that is trivial to check.
Recall that formula_48 is computed during the calculation of formula_26.
It would be easy to save the previously-computed power of formula_42, namely, formula_51.
Next, if "n" is prime, then, by Euler's criterion,
(Here, formula_53 is the Legendre symbol; if "n" is prime, this | 25,892 |
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is the same as the Jacobi symbol).
Therefore, if "n" is prime, we must have
The Jacobi symbol on the right side is easy to compute, so this congruence is easy to check.
If this congruence does not hold, then "n" cannot be prime.
Additional congruence conditions that must be satisfied if "n" is prime are described in Section 6 of. If "any" of these conditions fails to hold, then we have proved that "n" is not prime.
# Comparison with the Miller–Rabin primality test.
"k" applications of the Miller–Rabin primality test declare a composite "n" to be probably prime with a probability at most (1/4).
There is a similar probability estimate for the strong Lucas probable prime test.
Aside from | 25,893 |
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two trivial exceptions (see below), the fraction of ("P","Q") pairs (modulo "n") that declare a composite "n" to be probably prime is at most (4/15).
Therefore, "k" applications of the strong Lucas test would declare a composite "n" to be probably prime with a probability at most (4/15).
There are two trivial exceptions. One is "n" = 9. The other is when "n" = "p"("p"+2) is the product of two twin primes. Such an "n" is easy to factor, because in this case, "n"+1 = ("p"+1) is a perfect square. One can quickly detect perfect squares using Newton's method for square roots.
By combining a Lucas pseudoprime test with a Fermat primality test, say, to base 2, one can obtain very powerful probabilistic | 25,894 |
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tests for primality, such as the Baillie–PSW primality test.
# Fibonacci pseudoprimes.
As noted above, when "P" = 1 and "Q" = −1, the numbers in the "U" sequence are the Fibonacci numbers.
A Fibonacci pseudoprime is often
(page 264 of, page 142 of, or
page 127 of )
defined as a composite number "n" for which equation () above is true with "P" = 1 and "Q" = −1 (but "n" is not divisible by 5). By this definition, the first ten Fibonacci pseudoprimes are 323, 377, 1891, 3827, 4181, 5777, 6601, 6721, 8149, and 10877 . The references of Anderson and Jacobsen below use this definition.
If "n" is congruent to 2 or 3 (mod 5), then Bressoud (, pages 272–273) and Crandall and Pomerance (, page | 25,895 |
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143 and exercise 3.41 on page 168) point out that it is rare for a Fibonacci pseudoprime to also be a Fermat pseudoprime base 2. However, when "n" is congruent to 1 or 4 (mod 5), the opposite is true, with over 12% of Fibonacci pseudoprimes under 10 also being base-2 Fermat pseudoprimes.
If "n" is prime and GCD("n", "Q") = 1, then (see equation 4 on page 1392 of ) we also have
This leads to an alternate definition of Fibonacci pseudoprime. By this definition, a Fibonacci pseudoprime is a composite number "n" for which equation (5) is true with "P" = 1 and "Q" = −1.
Using this definition, the first ten Fibonacci pseudoprimes are 705, 2465, 2737, 3745, 4181, 5777, 6721, 10877, 13201, and 15251 | 25,896 |
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( page 129) ; the latter refers to these as "Bruckman-Lucas" pseudoprimes.
Hoggatt and Bicknell studied properties of these pseudoprimes in 1974. Singmaster computed these pseudoprimes up to 100000. Jacobsen lists all 111443 of these pseudoprimes less than 10.
It has been shown that there are no even Fibonacci pseudoprimes as defined by equation (5). Using the more common first definition with equation (), they do exist .
A strong Fibonacci pseudoprime may be defined as a composite number for which equation (5) holds for all "P". It follows ( page 460) that an odd composite integer is a strong Fibonacci pseudoprime if and only if:
- 1. "n" is also a Carmichael number
- 2. 2("p" + 1) | ("n" | 25,897 |
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− 1) or 2("p" + 1) | ("n" − "p") for every prime "p" dividing "n".
The smallest example of a strong Fibonacci pseudoprime is 443372888629441 = 17·31·41·43·89·97·167·331.
# Pell pseudoprimes.
A Pell pseudoprime may be defined as a composite number "n" for which equation () above is true with "P" = 2 and "Q" = −1; the sequence "U" then being the Pell sequence. The first pseudoprimes are then 35, 169, 385, 779, 899, 961, 1121, 1189, 2419, ...
This differs from the definition in which may be written as:
with ("P", "Q") = (2, −1) again defining "U" as the Pell sequence. The first pseudoprimes are then 169, 385, 741, 961, 1121, 2001, 3827, 4879, 5719, 6215 ...
A third definition uses equation | 25,898 |
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en as:
with ("P", "Q") = (2, −1) again defining "U" as the Pell sequence. The first pseudoprimes are then 169, 385, 741, 961, 1121, 2001, 3827, 4879, 5719, 6215 ...
A third definition uses equation (5) with ("P", "Q") = (2, −1), leading to the pseudoprimes 169, 385, 961, 1105, 1121, 3827, 4901, 6265, 6441, 6601, 7107, 7801, 8119, ...
# External links.
- Anderson, Peter G. Fibonacci Pseudoprimes, their factors, and their entry points.
- Anderson, Peter G. Fibonacci Pseudoprimes under 2,217,967,487 and their factors.
- Jacobsen, Dana Pseudoprime Statistics, Tables, and Data (data for Lucas, Strong Lucas, AES Lucas, ES Lucas pseudoprimes below 10; Fibonacci and Pell pseudoprimes below 10) | 25,899 |
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