text:
Beaverton, Oregon

Beaverton is a city in the Tualatin Valley, located in Washington County in the U.S. state of Oregon, with a small portion bordering Portland. The city is among the main cities that make up the Portland metropolitan area. Its population was 97,494 at the 2020 census, making it the second most populous city in the county and the seventh most populous city in Oregon. Beaverton is an economic center for Washington County along with neighboring Hillsboro.

Early settlement
According to Oregon Geographic Names, Beaverton's name is derived from the settlement's proximity to a large body of water resulting from beaver dams.

The area of Tualatin Valley that became Beaverton was originally the home of a Native American tribe known as the Atfalati, which settlers mispronounced as Tualatin. The Atfalati population dwindled in the latter part of the 18th century, and the prosperous tribe was no longer dominant in the area by the 19th century when settlers arrived. The tribe named their village Chakeipi, which translates to "place of the beaver", which early settlers referred to as "Beaverdam."

Early settlers include the Hall Family from Kentucky, the Denneys who lived on their claim near present-day Scholls Ferry Road and Hall Blvd, and Orin S. Allen, from western New York. Lawrence Hall purchased 640 acre in Beaverdam in 1847 and built a grist mill with his brother near present-day Walker Road. His was the first land claim in the area. He was soon followed by Thomas Denney in 1848, who came to the area and built its first sawmill. In 1860, a toll plank road from Portland to Beaverton was completed over a trail called Canyon Road.

After the American Civil War, numerous other settlers, including Joshua Welch, George Betts, Charles Angel, W. P. Watson, and John Henry, laid out what is now known as Beaverton hoping they could bring a railroad to an area once described as, "mostly swamps & marshes connected by beaver dams to create what looked like a huge lake." In 1872, Beaverton's first post office opened in a general store operated by Betts, who also served as the first postmaster of the community. Betts Street, where the current post office now stands, is named in honor of him. In 1893, Beaverton, which by that time had a population of 400, was officially incorporated. Alonzo Cady, a local businessman, served as the first mayor. Many major roads in Beaverton are named for these early settlers.

20th century

Beaverton was an early home to automobile dealerships. A Ford Motor Company dealership was established there in 1915; it was purchased by Guy Carr in 1923 and over the years Carr expanded it into several locations throughout Beaverton. There are still several dealerships near the intersection of Walker and Canyon Roads.

In the early 1920s, Beaverton was home to Premium Picture Productions, a movie studio which produced about fifteen films. The studio site was later converted into Watt's Field and associated aircraft manufacturing facilities. A second Beaverton airport, Bernard's Airport, was later developed farther north, at the present location of the Cedar Hills Crossing mall.

The town's first library opened in 1925. Originally on the second floor of the Cady building, it has been moved repeatedly; in 2000 it was moved to its current location on Hall Boulevard and 5th Street. A branch location was opened for the first time in June 2010, when the Murray-Scholls location opened near the Murrayhill neighborhood. The Beaverton libraries and 15 other local libraries participate in the Washington County Cooperative Library Services.

21st century

In December 2004, the city and Washington County announced an "interim plan" which would lead to Beaverton becoming the second-largest city in Oregon, second only to Portland. The "interim" plan actually covered a period of more than ten years; from the county's perspective, the plan supported its strategy of having cities and special districts provide urban services. The city of Beaverton also attempted to annex certain businesses, including Nike, which responded with a legal and lobbying effort to resist the annexation. The lobbying effort succeeded quickly, with the Oregon Legislative Assembly enacting Senate Bill 887, which prohibited Beaverton from annexing Nike without the company's consent. The bill also applied to property owned by Electro Scientific Industries, Columbia Sportswear, and Tektronix, and in August 2008 the Oregon Land Use Board of Appeals ruled that the bill also barred the city from annexing property belonging to Leupold & Stevens. (See below, under Economy.) Beaverton's legal efforts to annex Nike cost the city over one million dollars.

The Oregon State Legislature has also passed legislation which redetermined Washington County's urban growth boundary to include more development. In 2018, the Metro Council voted to once again expand the urban growth boundary to include the Cooper Mountain urban reserve area.

In 2016, voters approved a $35 million bond for a new 75,000 ft2 Public Safety Center built to withstand a major earthquake. The center, which opened in fall of 2020, now houses the city's Emergency Management and Police Departments. Construction began in September 2018.

The city has tried to encourage transit-oriented development around the city's MAX Light Rail stations. The Round, a mixed-use development around Beaverton Central MAX Station on the site of a former sewer plant, was announced in 1996. In 2014, the City of Beaverton moved its city hall into The Beaverton Building, an office building in The Round. The Round currently consists of 24,000 square foot of retail space with 63 residential condominiums located above. BG's Food Cartel, Beaverton's first food cart pod, opened in 2018 and has 31 food carts, a speakeasy bar, and an event venue. Adjacent to The Round, the 550 seat Patricia Reser Center for the Arts opened in 2022, and was made possible by pledges from the Beaverton Arts Foundation and Pat Reser along with public sources. The groundbreaking was performed on November 13, 2019. In addition to the Reser Center, a new 125-room hotel opened next to The Round in February 2021. The performing arts center, apartments, city hall, hotel, MAX light rail station, plazas, food carts, and nearby businesses are collectively known as Downtown Beaverton.

Geography
Beaverton covers a total area of 19.7 sqmi, all of it land except for small creeks, ponds, and lakes. The city is located along the eastern edge of the Tualatin Valley just west of the Tualatin Mountains. It is bordered by Portland to the east, Hillsboro to the west, and Tigard to the south. Much of the remaining area surrounding Beaverton in the north and southwest constitutes unincorporated Washington County land. The elevation within city limits ranges from as high as 698.2 ft above sea level to as low as 131.7 ft above sea level. The city averages at 189 ft above sea level.

Neighborhoods
The city of Beaverton is divided into 13 neighborhoods: Central Beaverton, Denney Whitford, Raleigh West, Five Oaks, Triple Creek, Greenway, Highland, Neighbors Southwest, Sexton Mountain, South Beaverton, Vose, West Beaverton, and West Slope. Each neighborhood runs a Neighborhood Association Committee (NAC) to discuss neighborhood affairs, with the exception of Five Oaks and Triple Creek, and Denney Whitford and Raleigh West each sharing a NAC.

2020 Census
As of the census of 2020, there were 97,494 people. The racial makeup of the city was 59% Non-Hispanic White, 2.9% African American, 1.0% Native American, 12.2% Asian, 0.5% Pacific Islander, 8.7% from other races, and 12.5% from two or more races. Hispanic or Latino residents of any race were 18.1% of the population.

As of 2020 the median income for a household in the city was $38,261, and the median income for a family was $71,806. Males had a median income of $41,683 versus $31,204 for females. The per capita income for the city was $25,419. About 5.0% of families and 7.8% of the population were below the poverty line, including 8.5% of those under age 18 and 6.8% of those age 65 or over.

2010 census
As of the census of 2010, there were 89,803 people, 37,213 households, and 21,915 families residing in the city. The population density was 4794.6 PD/sqmi. There were 39,500 housing units at an average density of 2108.9 /sqmi. The racial makeup of the city was 73.0% White, 2.6% African American, 0.6% Native American, 10.5% Asian, 0.5% Pacific Islander, 8.2% from other races, and 4.5% from two or more races. Hispanic or Latino residents of any race were 16.3% of the population.

There were 37,213 households, of which 31.0% had children under the age of 18 living with them, 43.7% were married couples living together, 10.6% had a female householder with no husband present, 4.6% had a male householder with no wife present, and 41.1% were non-families. 30.9% of all households were made up of individuals, and 8.5% had someone living alone who was 65 years of age or older. The average household size was 2.39 and the average family size was 3.03.

The median age in the city was 34.7 years. 22.9% of residents were under the age of 18; 9.2% were between the ages of 18 and 24; 33% were from 25 to 44; 24.5% were from 45 to 64; and 10.4% were 65 years of age or older. The gender makeup of the city was 48.6% male and 51.4% female.

Company headquarters
Reser's Fine Foods, processor and distributor of freshly prepared foods, has headquartered in Beaverton since 1960. Leupold & Stevens, maker of rifle scopes and other specialty optics, has been located on property adjacent to the City of Beaverton since 1968. The Beaverton City Council annexed that property in May 2005, and Leupold & Stevens challenged that annexation. The company eventually won the legal fight in 2009 with the city, thus the company was de-annexed from the city.

Technology companies
As part of the Silicon Forest, Beaverton is the location of numerous technology organizations and companies, including Linux Technology Center of IBM, Tektronix, ADI formerly known as Maxim Integrated Products, VeriWave, Khronos Group and Oregon Technology Business Center (OTBC), a non-profit tech startup incubator. Phoenix Technologies operates its Northwestern Regional Office in Beaverton.

Largest employers
According to the City's 2021 Comprehensive Annual Financial Report, the largest employers in the city are:

Tourist attractions

 * Beaverton Farmer's Market
 * BG's Food Cartel
 * Cooper Mountain Nature Park
 * Cooper Mountain Vineyards
 * Hyland Forest Park
 * Patricia Reser Center for the Arts
 * Tualatin Hills Nature Park
 * Veterans Memorial Park
 * Jenkins Estate

Shopping
Cedar Hills Crossing is a shopping mall within the city of Beaverton. Facilities include a variety of restaurants, big-box retailers, a bowling alley, and more. Progress Ridge Town Square is a lifestyle center also in Beaverton which includes shops and restaurants.

Government
The current mayor of Beaverton is Lacey Beaty, who was first elected in 2020. The Beaverton City Council consists of six councilors. The Mayor and City Councilors are all elected at large to serve four-year terms in a council-manager form of government where the Beaverton City Council and Mayor hire a city manager who is the administrative head of the city.

Sports
The Howard M. Terpenning Recreation Complex, opened in 1978, features swimming, athletics, tennis, baseball, softball and basketball facilities.

Little League
In 2014, the Beaverton–Aloha Little League Intermediate baseball team won the state tournament and traveled to Nogales, Arizona to play in the regional tournament, where they accumulated a 2–2 record.

In 2006, the Murrayhill Little League baseball team qualified for the 2006 Little League World Series, the first Oregon team in 48 years to go that far. Murrayhill advanced to the semi-finals before losing; the third-place game was rained out and not rescheduled. In addition, a Junior Softball team from Beaverton went to 2006 World Series in Kirkland, Washington, ending in sixth place.

In 2002, Beaverton's Little League Softball team took second place to Waco, Texas, in the Little League Softball World Series.

Curling
In January 2013, Beaverton became the first city in Oregon to have an ice rink dedicated to the sport of curling, the Evergreen Curling Club. In January 2017, the Evergreen Curling Club hosted the United States Curling Association Senior Women's National Championship.

Education
The public schools serving most of Beaverton are part of the Beaverton School District. There are six public high schools in the district – Aloha High School, Beaverton High School, Mountainside High School, Southridge High School, Sunset High School, and Westview High School. It also has several public option schools serving grades 6-12 like the International School of Beaverton, Arts and Communication Magnet Academy, and Beaverton Academy of Science and Engineering. Merlo Station High School is another alternative learning school within the district.

Portions of Beaverton are in the Hillsboro School District and the Portland Public Schools school district.

Private schools in the area include German American School, Holy Trinity School, Jesuit High School, Saint Cecilia Grade School, Southwest Christian School, Valley Catholic School, Willamette Valley Academy, and WoodHaven School.

Colleges and universities

 * Portland Community College (PCC) — Although it is based in Portland, some facilities operate in Beaverton.

Infrastructure
Fire protection is provided through Tualatin Valley Fire and Rescue. EMS services are provided by Metro West Ambulance.

Transportation

Beaverton is served by transit bus, commuter rail, and light rail services operated by the Portland metropolitan area's regional transit agency, TriMet. MAX Light Rail serves the city with seven light rail stations; from west to east, they are: Elmonica/Southwest 170th Avenue, Merlo Road/Southwest 158th Avenue, Beaverton Creek, Millikan Way, Beaverton Central, Beaverton Transit Center, and Sunset Transit Center. The MAX Blue Line serves all seven stations while the MAX Red Line serves only Beaverton Transit Center and Sunset Transit Center. Beaverton Transit Center, TriMet's busiest transit center, in addition to MAX, serves as a transit hub for bus routes mostly operating on the west side and as the northern terminus of WES Commuter Rail. Hall/Nimbus, the second station southbound on WES, is also located in Beaverton. Intercity bus services with stops in Beaverton include POINT and TCTD.

Oregon Electric and Red Electric interurban lines once served the city in the early 20th century. In the 1940s, Tualatin Valley Stages, a division of Portland Stages, Inc., provided limited bus transit service between the city and downtown Portland; it operated later as a separate company, Tualatin Valley Buses, Inc., through the 1960s. This was one of four privately owned bus companies that served the Portland metropolitan area and were collectively known as the "Blue Bus" lines. All four companies were replaced in 1970 by TriMet, which expanded bus service to cover more areas of Beaverton.

The city is the location of a major freeway interchange for U.S. Route 26 (US 26; Sunset Highway) and Oregon Route 217 (OR 217). The Sunset Highway connects Beaverton to Hillsboro and the Oregon Coast to the west and Portland to the east. OR 217 travels from Beaverton south through Tigard and terminates at an interchange with Interstate 5 (I-5).

Notable people

 * James Allsup – far-right political commentator
 * Shoshana Bean - singer, actress
 * Charles E. Bernard – aviator
 * Cameron Brink - Basketball Player
 * John Brotherton – actor
 * Mike Byrne – drummer for The Smashing Pumpkins
 * Janet Chvatal – actress
 * Grace Crunican – general manager for Bay Area Rapid Transit
 * Ward Cunningham – inventor of the wiki
 * Brad Fitzpatrick – programmer
 * Ted Geoghegan – screenwriter
 * Barrie Gilbert – inventor
 * Erik Hurtado – professional soccer player
 * Ian Karmel – stand-up comedian and writer
 * Gloria Calderon Kellett – writer
 * Anne Kenney – television producer
 * Morten Lauridsen – composer
 * Michael McQuilken – director
 * Moultrie Patten – jazz musician
 * Rubio Rubin – professional soccer player
 * Ari Shapiro – radio journalist
 * Royal Skousen – professor
 * Todd Snider – musician
 * Courtney Taylor-Taylor – lead singer of The Dandy Warhols
 * James B. Thayer – Army brigadier general
 * Tommy Thayer – lead guitarist for Kiss

Sister cities
Beaverton's sister cities are:
 * 🇯🇵 Gotemba, Japan (1987)
 * 🇹🇼 Hsinchu, Taiwan (1988)
 * 🇰🇷 Cheonan, South Korea (1989)
 * 🇷🇺 Birobidzhan, Russia (1990)
 * 🇩🇪 Trossingen, Germany (1993)
 * 🇫🇷 Cluses, France (1999)

title: Beaverton, Oregon


text:
Talk:Amiga demos

Untitled
Informal discussion:

I (Shd) added Fanatic and Mystic demos to the list since I've coded them, and they can't be considered famous.

Should we create entries for Amiga demo groups like this? amigademoscene:groupname

Should we add demo party names to the demo list?

 * why not? It's up to you.

Article fix-up
I've taken the liberty of copyediting and wikifying the article. I also reorganized the demo list by putting it in its own section and separating the demos into sublists under the respective groups. I also made sure every group name is linked and that every reference to a year goes to the corresponding Wikipedia article, and I added " (demo group)" to the title in the link for any groups whose names are ambiguous. I also fixed the URL link in there. Finally, removed the copyedit tag.

Now you just need more content. :-) Ddawson 18:44, 9 Apr 2005 (UTC)

Suggestions
This list would work much better if there were dates associated with the demo names, possibly even listed in chronological order to show progression over time. --Jolyonralph 00:09, 23 Apr 2005 (UTC)
 * I suggest doing away with the list altogether. How does anyone decide what goes or doesn't go on it?  If we're going to list some demos, we're going to have to pick some criteria and agree on it.  --Vossanova o< 00:45, 2 September 2006 (UTC)
 * Or else move the list to its own article and link it from this article. - Richardcavell 21:53, 11 December 2006 (UTC)

Style cleanup
I decided to do a little style cleanup on this page. In accordance with one of the style guidelines, I've changed the essentially empty Fred Fish section into a See-also section referencing the article. (I know that article is a stub, but there's at least something there, as opposed to here.) Ddawson 15:25, 20 August 2005 (UTC)

Article Cleanup Co-Ordination Point
{| style="width:100%;background:none" ! bgcolor="#abcdef" colspan="2" bgcolor="#abcdef" | Cleanup Co-ordination The article may have been flagged as needing cleanup because it has been suggested that: For a full list of possible problems see Manual of Style.
 * width=60 bgcolor="#ffdead" |[[Image:Janitor's bucket with mop.jpg|100px]]
 * bgcolor="#ffdead" | This article has recently been tagged as requiring cleanup to meet Wikipedia's quality standards.
 * bgcolor="#ffdead" | This article has recently been tagged as requiring cleanup to meet Wikipedia's quality standards.
 * the article needs formatting, proofreading, or rephrasing in comprehensible English.
 * the article has multiple overlapping problems.
 * the article is very short and might need expanding, removal or merging with a broader article

As part of the cleanup process, the automated bot PocKleanBot has generated this notice as a focus of cleanup efforts, and also contacted several contributing editors of the article to bring their attention to the problem. You should use this section to discuss possible resolution of the problem and achieve consensus for action. Only when there is a consensus that the article is now cleaned up should you then de-list it by deleting the cleanup tag from the article, this causes the article to drop off the monthly cleanup-needed list page.
 * colspan="2" bgcolor="white" |
 * colspan="2" bgcolor="white" |

Discussion

 * }

Image copyright problem with Image:Ptn-gift.jpg
The image Image:Ptn-gift.jpg is used in this article under a claim of fair use, but it does not have an adequate explanation for why it meets the requirements for such images when used here. In particular, for each page the image is used on, it must have an explanation linking to that page which explains why it needs to be used on that page. Please check

 * That there is a non-free use rationale on the image's description page for the use in this article.
 * That this article is linked to from the image description page.

This is an automated notice by FairuseBot. For assistance on the image use policy, see Media copyright questions. --00:30, 2 October 2008 (UTC)

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

title: Talk:Amiga demos


text:
Security (finance)

A security is a tradable financial asset. The term commonly refers to any form of financial instrument, but its legal definition varies by jurisdiction. In some countries and languages people commonly use the term "security" to refer to any form of financial instrument, even though the underlying legal and regulatory regime may not have such a broad definition. In some jurisdictions the term specifically excludes financial instruments other than equity and fixed income instruments. In some jurisdictions it includes some instruments that are close to equities and fixed income, e.g., equity warrants.

Securities may be represented by a certificate or, more typically, they may be "non-certificated", that is in electronic (dematerialized) or "book entry only" form. Certificates may be bearer, meaning they entitle the holder to rights under the security merely by holding the security, or registered, meaning they entitle the holder to rights only if they appear on a security register maintained by the issuer or an intermediary. They include shares of corporate capital stock or mutual funds, bonds issued by corporations or governmental agencies, stock options or other options, limited partnership units, and various other formal investment instruments that are negotiable and fungible.

United Kingdom and United States
In the United Kingdom, the Financial Conduct Authority functions as the national competent authority for the regulation of financial markets; the definition in its Handbook of the term "security" applies only to equities, debentures, alternative debentures, government and public securities, warrants, certificates representing certain securities, units, stakeholder pension schemes, personal pension schemes, rights to or interests in investments, and anything that may be admitted to the Official List.

In the United States, a "security" is a tradable financial asset of any kind. Securities can be broadly categorized into:

 * Debt securities (e.g., banknotes, bonds, and debentures)
 * Equity securities (e.g., common stocks)
 * Derivatives (e.g., forwards,  futures, options, and swaps).

The company or other entity issuing the security is called the issuer. A country's regulatory structure determines what qualifies as a security. For example, private investment pools may have some features of securities, but they may not be registered or regulated as such if they meet various restrictions.

Securities are the traditional method used by commercial enterprises to raise new capital. They may offer an attractive alternative to bank loans - depending on their pricing and market demand for particular characteristics. A disadvantage of bank loans as a source of financing is that the bank may seek a measure of protection against default by the borrower via extensive financial covenants. Through securities, capital is provided by investors who purchase the securities upon their initial issuance. In a similar way, a government may issue securities when it chooses to increase government debt.

Debt and equity
Securities are traditionally divided into debt securities and equities.

Debt
Debt securities may be called debentures, bonds, deposits, notes or commercial paper depending on their maturity, collateral and other characteristics. The holder of a debt security is typically entitled to the payment of principal and interest, together with other contractual rights under the terms of the issue, such as the right to receive certain information. Debt securities are generally issued for a fixed term and redeemable by the issuer at the end of that term. Debt securities may be protected by collateral or may be unsecured, and, if they are unsecured, may be contractually "senior" to other unsecured debt meaning their holders would have a priority in a bankruptcy of the issuer. Debt that is not senior is "subordinated".

Corporate bonds represent the debt of commercial or industrial entities. Debentures have a long maturity, typically at least ten years, whereas notes have a shorter maturity. Commercial paper is a simple form of debt security that essentially represents a post-dated cheque with a maturity of not more than 270 days.

Money market instruments are short term debt instruments that may have characteristics of deposit accounts, such as certificates of deposit, Accelerated Return Notes (ARN), and certain bills of exchange. They are highly liquid and are sometimes referred to as "near cash". Commercial paper is also often highly liquid.

Euro debt securities are securities issued internationally outside their domestic market in a denomination different from that of the issuer's domicile. They include eurobonds and euronotes. Eurobonds are characteristically underwritten, and not secured, and interest is paid gross. A euronote may take the form of euro-commercial paper (ECP) or euro-certificates of deposit.

Government bonds are medium or long term debt securities issued by sovereign governments or their agencies. Typically they carry a lower rate of interest than corporate bonds, and serve as a source of finance for governments. U.S. federal government bonds are called treasuries. Because of their liquidity and perceived low risk, treasuries are used to manage the money supply in the open market operations of non-US central banks.

Sub-sovereign government bonds, known in the U.S. as municipal bonds, represent the debt of state, provincial, territorial, municipal or other governmental units other than sovereign governments.

Supranational bonds represent the debt of international organizations such as the World Bank, the International Monetary Fund, regional multilateral development banks and others.

Equity
An equity security is a share of equity interest in an entity such as the capital stock of a company, trust or partnership. The most common form of equity interest is common stock, although preferred equity is also a form of capital stock. The holder of an equity is a shareholder, owning a share, or fractional part of the issuer. Unlike debt securities, which typically require regular payments (interest) to the holder, equity securities are not entitled to any payment. In bankruptcy, they share only in the residual interest of the issuer after all obligations have been paid out to creditors. However, equity generally entitles the holder to a pro rata portion of control of the company, meaning that a holder of a majority of the equity is usually entitled to control the issuer. Equity also enjoys the right to profits and capital gain, whereas holders of debt securities receive only interest and repayment of principal regardless of how well the issuer performs financially. Furthermore, debt securities do not have voting rights outside of bankruptcy. In other words, equity holders are entitled to the "upside" of the business and to control the business.

Hybrid
Hybrid securities combine some of the characteristics of both debt and equity securities.

Preference shares form an intermediate class of security between equities and debt. If the issuer is liquidated, preference shareholders have the right to receive interest or a return of capital prior to ordinary shareholders. However, from a legal perspective, preference shares are capital stocks and therefore may entitle the holders to some degree of control depending on whether they carry voting rights.

Convertibles are bonds or preferred stocks that can be converted, at the election of the holder of the convertibles, into the ordinary shares of the issuing company. The convertibility, however, may be forced if the convertible is a callable bond, and the issuer calls the bond. The bondholder has about one month to convert it, or the company will call the bond by giving the holder the call price, which may be less than the value of the converted stock. This is referred to as a forced conversion.

Equity warrants are options issued by the company that allow the holder of the warrant to purchase a specific number of shares at a specified price within a specified time. They are often issued together with bonds or existing equities, and are, sometimes, detachable from them and separately tradeable. When the holder of the warrant exercises it, he pays the money directly to the company, and the company issues new shares to the holder.

Warrants, like other convertible securities, increases the number of shares outstanding, and are always accounted for in financial reports as fully diluted earnings per share, which assumes that all warrants and convertibles will be exercised.

Classification
Securities may be classified according to many categories or classification systems:

 * Currency of denomination
 * Ownership rights
 * Terms to maturity
 * Degree of liquidity
 * Income payments
 * Tax treatment
 * Credit rating
 * Industrial sector or "industry". ("Sector" often refers to a higher level or broader category, such as Consumer Discretionary, whereas "industry" often refers to a lower level classification, such as Consumer Appliances. See Industry for a discussion of some classification systems.)
 * Region or country (such as country of incorporation, country of principal sales/market of its products or services, or country in which the principal securities exchange where it trades is located)
 * Market capitalization
 * State (typically for municipal or "tax-free" bonds in the US)

Type of holder
Investors in securities may be retail, i.e., members of the public investing personally, other than by way of business.

In distinction, the greatest part of investment in terms of volume, is wholesale, i.e., by financial institutions acting on their own account, or on behalf of clients. Important institutional investors include investment banks, insurance companies, pension funds and other managed funds. The "wholesaler" is typically an underwriter or a broker-dealer who trades with other broker-dealers, rather than with the retail investor.

This distinction carries over to banking; compare Retail banking and Wholesale banking.

Investment
The traditional economic function of the purchase of securities is investment, with the view to receiving income or achieving capital gain. Debt securities generally offer a higher rate of interest than bank deposits, and equities may offer the prospect of capital growth. Equity investment may also offer control of the business of the issuer. Debt holdings may also offer some measure of control to the investor if the company is a fledgling start-up or an old giant undergoing restructuring. In these cases, if interest payments are missed, the creditors may take control of the company and liquidate it to recover some of their investment.

Collateral
The last decade has seen an enormous growth in the use of securities as collateral. Purchasing securities with borrowed money secured by other securities or cash itself is called "buying on margin". Where A is owed a debt or other obligation by B, A may require B to deliver property rights in securities to A, either at inception (transfer of title) or only in default (non-transfer-of-title institutional). For institutional loans, property rights are not transferred but nevertheless enable A to satisfy its claims in case B fails to make good on its obligations to A or otherwise becomes insolvent. Collateral arrangements are divided into two broad categories, namely security interests and outright collateral transfers. Commonly, commercial banks, investment banks, government agencies and other institutional investors such as mutual funds are significant collateral takers as well as providers. In addition, private parties may utilize stocks or other securities as collateral for portfolio loans in securities lending scenarios.

On the consumer level, loans against securities have grown into three distinct groups over the last decade:
 * 1) Standard Institutional Loans, generally offering low loan-to-value with very strict call and coverage regimens, akin to standard margin loans;
 * 2) Transfer-of-Title (ToT) Loans, typically provided by private parties where borrower ownership is completely extinguished save for the rights provided in the loan contract; and
 * 3) Non-Transfer-of-Title Credit Line facilities where shares are not sold and they serve as assets in a standard lien-type line of cash credit.

Of the three, transfer-of-title loans have fallen into the very high-risk category as the number of providers has dwindled as regulators have launched an industry-wide crackdown on transfer-of-title structures where the private lender may sell or sell short the securities to fund the loan. Institutionally managed consumer securities-based loans on the other hand, draw loan funds from the financial resources of the lending institution, not from the sale of the securities.

Collateral and sources of collateral are changing, in 2012 gold became a more acceptable form of collateral. By 2015, recently Exchange-traded funds (ETFs) previously seen by many as unpromising had started to become more readily available and acceptable.

Primary and secondary market
Public securities markets are either primary or secondary markets. In the primary market, the money for the securities is received by the issuer of the securities from investors, typically in an initial public offering (IPO). In the secondary market, the securities are simply assets held by one investor selling them to another investor, with the money going from one investor to the other.

An initial public offering is when a company issues public stock newly to investors, called an "IPO" for short. A company can later issue more new shares, or issue shares that have been previously registered in a shelf registration. These later new issues are also sold in the primary market, but they are not considered to be an IPO but are often called a "secondary offering". Issuers usually retain investment banks to assist them in administering the IPO, obtaining SEC (or other regulatory body) approval of the offering filing, and selling the new issue. When the investment bank buys the entire new issue from the issuer at a discount to resell it at a markup, it is called a firm commitment underwriting. However, if the investment bank considers the risk too great for an underwriting, it may only assent to a best effort agreement, where the investment bank will simply do its best to sell the new issue.

For the primary market to thrive, there must be a secondary market, or aftermarket that provides liquidity for the investment security—where holders of securities can sell them to other investors for cash. Otherwise, few people would purchase primary issues, and, thus, companies and governments would be restricted in raising equity capital (money) for their operations. Organized exchanges constitute the main secondary markets. Many smaller issues and most debt securities trade in the decentralized, dealer-based over-the-counter markets.

In Europe, the principal trade organization for securities dealers is the International Capital Market Association. In the U.S., the principal trade organization for securities dealers is the Securities Industry and Financial Markets Association, which is the result of the merger of the Securities Industry Association and the Bond Market Association. The Financial Information Services Division of the Software and Information Industry Association (FISD/SIIA) represents a round-table of market data industry firms, referring to them as Consumers, Exchanges, and Vendors. In India the equivalent organisation is the securities exchange board of India (SEBI).

Public offer and private placement
In the primary markets, securities may be offered to the public in a public offering. Alternatively, they may be offered privately to a limited number of qualified persons in a private placement. Sometimes a combination of the two is used. The distinction between the two is important to securities regulation and company law. Privately placed securities are not publicly tradable and may only be bought and sold by sophisticated qualified investors. As a result, the secondary market is not nearly as liquid as it is for public (registered) securities.

Another category, sovereign bonds, is generally sold by auction to a specialized class of dealers.

Listing and over-the-counter dealing
Securities are often listed in a stock exchange, an organized and officially recognized market on which securities can be bought and sold. Issuers may seek listings for their securities to attract investors, by ensuring there is a liquid and regulated market that investors can buy and sell securities in.

Growth in informal electronic trading systems has challenged the traditional business of stock exchanges. Large volumes of securities are also bought and sold "over the counter" (OTC). OTC dealing involves buyers and sellers dealing with each other by telephone or electronically on the basis of prices that are displayed electronically, usually by financial data vendors such as SuperDerivatives, Reuters, Investing.com and Bloomberg.

There are also eurosecurities, which are securities that are issued outside their domestic market into more than one jurisdiction. They are generally listed on the Luxembourg Stock Exchange or admitted to listing in London. The reasons for listing eurobonds include regulatory and tax considerations, as well as the investment restrictions.

Securities services
Securities Services refers to the products and services that are offered to institutional clients that issue, trade, and hold securities. The bank engaged in securities services are usually called a custodian bank. Market players include BNY Mellon, J.P. Morgan, HSBC, Citi, BNP Paribas, Société Générale etc.

Market
London is the centre of the eurosecurities markets. There was a huge rise in the eurosecurities market in London in the early 1980s. Settlement of trades in eurosecurities is currently effected through two European computerized clearing/depositories called Euroclear (in Belgium) and Clearstream (formerly Cedelbank) in Luxembourg.

The main market for Eurobonds is the EuroMTS, owned by Borsa Italiana and Euronext. There are ramp up market in Emergent countries, but it is growing slowly.

Certificated securities
Securities that are represented in paper (physical) form are called certificated securities. They may be bearer or registered.

DRS securities
Securities may also be held in the Direct Registration System (DRS), which is a method of recording shares of stock in book-entry form. Book-entry means the company's transfer agent maintains the shares on the owner's behalf without the need for physical share certificates. Shares held in un-certificated book-entry form have the same rights and privileges as shares held in certificated form.

Bearer securities

Bearer securities are completely negotiable and entitle the holder to the rights under the security (e.g., to payment if it is a debt security, and voting if it is an equity security). They are transferred by delivering the instrument from person to person. In some cases, transfer is by endorsement, or signing the back of the instrument, and delivery.

Regulatory and fiscal authorities sometimes regard bearer securities negatively, as they may be used to facilitate the evasion of regulatory restrictions and tax. In the United Kingdom, for example, the issue of bearer securities was heavily restricted firstly by the Exchange Control Act 1947 until 1953. Bearer securities are very rare in the United States because of the negative tax implications they may have to the issuer and holder.

In Luxembourg, the law of 28 July 2014 concerning the compulsory deposit and immobilization of shares and units in bearer form adopts the compulsory deposit and immobilization of bearer shares and units with a depositary allowing identification of the holders thereof.

Registered securities

In the case of registered securities, certificates bearing the name of the holder are issued, but these merely represent the securities. A person does not automatically acquire legal ownership by having possession of the certificate. Instead, the issuer (or its appointed agent) maintains a register in which details of the holder of the securities are entered and updated as appropriate. A transfer of registered securities is effected by amending the register.

Non-certificated securities and global certificates
Modern practice has developed to eliminate both the need for certificates and maintenance of a complete security register by the issuer. There are two general ways this has been accomplished.

Non-certificated securities
In some jurisdictions, such as France, it is possible for issuers of that jurisdiction to maintain a legal record of their securities electronically.

In the United States, the current "official" version of Article 8 of the Uniform Commercial Code permits non-certificated securities. However, the "official" UCC is a mere draft that must be enacted individually by each U.S. state. Though all 50 states (as well as the District of Columbia and the U.S. Virgin Islands) have enacted some form of Article 8, many of them still appear to use older versions of Article 8, including some that did not permit non-certificated securities.

Global certificates, book entry interests, depositories
To facilitate the electronic transfer of interests in securities without dealing with inconsistent versions of Article 8, a system has developed whereby issuers deposit a single global certificate representing all the outstanding securities of a class or series with a universal depository. This depository is called The Depository Trust Company, or DTC. DTC's parent, Depository Trust & Clearing Corporation (DTCC), is a non-profit cooperative owned by approximately thirty of the largest Wall Street players that typically act as brokers or dealers in securities. These thirty banks are called the DTC participants. DTC, through a legal nominee, owns each of the global securities on behalf of all the DTC participants.

All securities traded through DTC are in fact held, in electronic form, on the books of various intermediaries between the ultimate owner, e.g., a retail investor, and the DTC participants. For example, Mr. Smith may hold 100 shares of Coca-Cola, Inc. in his brokerage account at local broker Jones & Co. brokers. In turn, Jones & Co. may hold 1000 shares of Coca-Cola on behalf of Mr. Smith and nine other customers. These 1000 shares are held by Jones & Co. in an account with Goldman Sachs, a DTC participant, or in an account at another DTC participant. Goldman Sachs in turn may hold millions of Coca-Cola shares on its books on behalf of hundreds of brokers similar to Jones & Co. Each day, the DTC participants settle their accounts with the other DTC participants and adjust the number of shares held on their books for the benefit of customers like Jones & Co. Ownership of securities in this fashion is called beneficial ownership. Each intermediary holds on behalf of someone beneath him in the chain. The ultimate owner is called the beneficial owner. This is also referred to as owning in "Street name".

Among brokerages and mutual fund companies, a large amount of mutual fund share transactions take place among intermediaries as opposed to shares being sold and redeemed directly with the transfer agent of the fund. Most of these intermediaries such as brokerage firms clear the shares electronically through the National Securities Clearing Corp. or "NSCC", a subsidiary of DTCC.

Other depositories
Besides DTC, two other large securities depositories exist, both in Europe: Euroclear and Clearstream.

Divided and undivided security
The terms "divided" and "undivided" relate to the proprietary nature of a security.

Each divided security constitutes a separate asset, which is legally distinct from each other security in the same issue. Pre-electronic bearer securities were divided. Each instrument constitutes the separate covenant of the issuer and is a separate debt.

With undivided securities, the entire issue makes up one single asset, with each of the securities being a fractional part of this undivided whole. Shares in the secondary markets are always undivided. The issuer owes only one set of obligations to shareholders under its memorandum, articles of association and company law. A share represents an undivided fractional part of the issuing company. Registered debt securities also have this undivided nature.

Fungible and non-fungible securities
In a fungible security, all holdings of the security are treated identically and are interchangeable.

Sometimes securities are not fungible with other securities, for example different series of bonds issued by the same company at different times with different conditions attaching to them.

Regulation
In the US, the public offer and sale of securities must be either registered pursuant to a registration statement that is filed with the U.S. Securities and Exchange Commission (SEC) or are offered and sold pursuant to an exemption therefrom. Dealing in securities is regulated by both federal authorities (SEC) and state securities departments. In addition, the brokerage industry is supposedly self policed by self-regulatory organizations (SROs), such as the Financial Industry Regulatory Authority (FINRA), formerly the National Association of Securities Dealers (or NASD), or the Municipal Securities Rulemaking Board (MSRB).

With respect to investment schemes that do not fall within the traditional categories of securities listed in the definition of a security (Sec. 2(a)(1) of the Securities Act of 1933 and Sec. 3(a)(10) of the 34 act) the US Courts have developed a broad definition for securities that must then be registered with the SEC. When determining if there is an "investment contract" that must be registered the courts look for an investment of money, a common enterprise and expectation of profits to come primarily from the efforts of others. See SEC v. W.J. Howey Co.

title: Security (finance)


text:
Talk:Arthur Andersen

Duplication
In the "Enron Scandal" section of this article there are these two extracts which pretty-much duplicate one another:
 * Because the U.S. Securities and Exchange Commission will not accept audits from convicted felons, the firm agreed to surrender its CPA licenses and its right to practice before the SEC on August 31, 2002—effectively putting the firm out of business. It had already started winding down its American operations after the indictment, and many of its accountants joined other firms.
 * In 2002, just nine months after the scandal broke, the firm was found guilty of crimes in the auditing of Enron. By that time, Arthur Andersen had lost most of its business and two-thirds of its 28,000 employees, and was facing multi-million dollar lawsuits. On August 31, 2002, the company surrendered its licenses to practice as certified public accountants in the United States, effectively putting the company out of business.

Is there any scope for merging them together, perhaps presenting the section chronologically? AndyJones (talk) 16:00, 18 July 2023 (UTC)

Seems like we're all about the fact that the form was legally dissolved and don't care what happened to anybody working there.
Dissolving a corporation is just legal paperwork but it seems like it's the center of this article. 2604:3D09:D78:1000:1075:CB3:E575:5AA1 (talk) 14:52, 16 April 2024 (UTC)

This article gives the impression that somebody was found guilty
But it doesn't say when that happened or who the judge was or anything. 2604:3D09:D78:1000:1075:CB3:E575:5AA1 (talk) 14:53, 16 April 2024 (UTC)

title: Talk:Arthur Andersen


text:
User:GillianAnderson

Hi ya cutie.

Links

 * http://www.gilliananderson.ws/
 * GillianAnderson
 * GillianAnderson
 *

title: User:GillianAnderson


text:
Beam

Beam may refer to:

Streams of particles or energy

 * Light beam, or beam of light, a directional projection of light energy
 * Laser beam
 * Radio beam
 * Particle beam, a stream of charged or neutral particles
 * Charged particle beam, a spatially localized group of electrically charged particles
 * Cathode ray, or electron beam or e-beam, streams of electrons observed in discharge tubes
 * X-ray beam, a penetrating form of high-energy electromagnetic radiation
 * Molecular beam, a beam of particles moving at approximately equal velocities

Arts, entertainment and media

 * Anong Beam, Canadian Ojibwe artist and curator
 * Beam (music), a connection line in musical notation
 * Beam, to transport matter using the Transporter in the Star Trek fictional universe
 * Beam (rapper), American hip hop artist
 * BEAM.TV, an online digital delivery and content management platform
 * BEAM Channel 31, a Philippines television network
 * Beam (website), later Mixer, a former video game live streaming platform
 * BeamNG.drive, an open-world vehicle simulation video game
 * The Beam (fairy tale), the Brothers Grimm tale 149
 * Carl Beam (1943-2005), indigenous Canadian artist

Businesses

 * Beam Software, later Krome Studios Melbourne, an Australian video game development studio
 * Beam Suntory, a division of Suntory that produces distilled beverages, including Jim Beam
 * Broadcast Enterprises and Affiliated Media, a telecommunications company in the Philippines
 * Beam Energy, an energy provision arrangement of British company Robin Hood Energy

Science and technology

 * BEAM (Erlang virtual machine), a virtual machine at the core of the Erlang Open Telecom Platform
 * BEAM robotics (biology, electronics, aesthetics and mechanics), a style of robotics
 * Beam search, a heuristic search algorithm
 * Bigelow Expandable Activity Module, an experimental expandable space station module
 * Apache Beam, a data processing programming model
 * Beam (structure), a structural element that resists lateral loads

Other uses

 * Beam (horse), a racehorse
 * Beam (nautical), the width of a ship at its widest point
 * Beam, Great Torrington, an estate in Devon, England
 * Balance beam, or beam, a piece of gymnastics equipment
 * The Beam (geological outcrop), in South Hero, Vermont, U.S.

title: Beam


text:
Data communication

Data communication, including data transmission and data reception, is the transfer of data, transmitted and received over a point-to-point or point-to-multipoint communication channel. Examples of such channels are copper wires, optical fibers, wireless communication using radio spectrum, storage media and computer buses. The data are represented as an electromagnetic signal, such as an electrical voltage, radiowave, microwave, or infrared signal.

Analog transmission is a method of conveying voice, data, image, signal or video information using a continuous signal which varies in amplitude, phase, or some other property in proportion to that of a variable. The messages are either represented by a sequence of pulses by means of a line code (baseband transmission), or by a limited set of continuously varying waveforms (passband transmission), using a digital modulation method. The passband modulation and corresponding demodulation is carried out by modem equipment.

Digital communications, including digital transmission and digital reception, is the transfer of either a digitized analog signal or a born-digital bitstream. According to the most common definition, both baseband and passband bit-stream components are considered part of a digital signal; an alternative definition considers only the baseband signal as digital, and passband transmission of digital data as a form of digital-to-analog conversion.

Distinction between related subjects
Courses and textbooks in the field of data transmission as well as digital transmission  and digital communications  have similar content.

Digital transmission or data transmission traditionally belongs to telecommunications and electrical engineering. Basic principles of data transmission may also be covered within the computer science or computer engineering topic of data communications, which also includes computer networking applications and communication protocols, for example routing, switching and inter-process communication. Although the Transmission Control Protocol (TCP) involves transmission, TCP and other transport layer protocols are covered in computer networking but not discussed in a textbook or course about data transmission.

In most textbooks, the term analog transmission only refers to the transmission of an analog message signal (without digitization) by means of an analog signal, either as a non-modulated baseband signal or as a passband signal using an analog modulation method such as AM or FM. It may also include analog-over-analog pulse modulated baseband signals such as pulse-width modulation. In a few books within the computer networking tradition, analog transmission also refers to passband transmission of bit-streams using digital modulation methods such as FSK, PSK and ASK. Note that these methods are covered in textbooks named digital transmission or data transmission, for example.

The theoretical aspects of data transmission are covered by information theory and coding theory.

Protocol layers and sub-topics
Courses and textbooks in the field of data transmission typically deal with the following OSI model protocol layers and topics: It is also common to deal with the cross-layer design of those three layers.
 * Layer 1, the physical layer:
 * Channel coding including
 * Digital modulation schemes
 * Line coding schemes
 * Forward error correction (FEC) codes
 * Bit synchronization
 * Multiplexing
 * Equalization
 * Channel models
 * Layer 2, the data link layer:
 * Channel access schemes, media access control (MAC)
 * Packet mode communication and Frame synchronization
 * Error detection and automatic repeat request (ARQ)
 * Flow control
 * Layer 6, the presentation layer:
 * Source coding (digitization and data compression), and information theory.
 * Cryptography (may occur at any layer)

Applications and history
Data (mainly but not exclusively informational) has been sent via non-electronic (e.g. optical, acoustic, mechanical) means since the advent of communication. Analog signal data has been sent electronically since the advent of the telephone. However, the first data electromagnetic transmission applications in modern time were electrical telegraphy (1809) and teletypewriters (1906), which are both digital signals. The fundamental theoretical work in data transmission and information theory by Harry Nyquist, Ralph Hartley, Claude Shannon and others during the early 20th century, was done with these applications in mind.

In the early 1960s, Paul Baran invented distributed adaptive message block switching for digital communication of voice messages using switches that were low-cost electronics. Donald Davies invented and implemented modern data communication during 1965-7, including packet switching, high-speed routers, communication protocols, hierarchical computer networks and the essence of the end-to-end principle. Baran's work did not include routers with software switches and communication protocols, nor the idea that users, rather than the network itself, would provide the reliability. Both were seminal contributions that influenced the development of computer networks.

Data transmission is utilized in computers in computer buses and for communication with peripheral equipment via parallel ports and serial ports such as RS-232 (1969), FireWire (1995) and USB (1996). The principles of data transmission are also utilized in storage media for error detection and correction since 1951. The first practical method to overcome the problem of receiving data accurately by the receiver using digital code was the Barker code invented by Ronald Hugh Barker in 1952 and published in 1953. Data transmission is utilized in computer networking equipment such as modems (1940), local area network (LAN) adapters (1964), repeaters, repeater hubs, microwave links, wireless network access points (1997), etc.

In telephone networks, digital communication is utilized for transferring many phone calls over the same copper cable or fiber cable by means of pulse-code modulation (PCM) in combination with time-division multiplexing (TDM) (1962). Telephone exchanges have become digital and software controlled, facilitating many value-added services. For example, the first AXE telephone exchange was presented in 1976. Digital communication to the end user using Integrated Services Digital Network (ISDN) services became available in the late 1980s. Since the end of the 1990s, broadband access techniques such as ADSL, Cable modems, fiber-to-the-building (FTTB) and fiber-to-the-home (FTTH) have become widespread to small offices and homes. The current tendency is to replace traditional telecommunication services with packet mode communication such as IP telephony and IPTV.

Transmitting analog signals digitally allows for greater signal processing capability. The ability to process a communications signal means that errors caused by random processes can be detected and corrected. Digital signals can also be sampled instead of continuously monitored. The multiplexing of multiple digital signals is much simpler compared to the multiplexing of analog signals. Because of all these advantages, because of the vast demand to transmit computer data and the ability of digital communications to do so and because recent advances in wideband communication channels and solid-state electronics have allowed engineers to realize these advantages fully, digital communications have grown quickly.

The digital revolution has also resulted in many digital telecommunication applications where the principles of data transmission are applied. Examples include second-generation (1991) and later cellular telephony, video conferencing, digital TV (1998), digital radio (1999), and telemetry.

Data transmission, digital transmission or digital communications is the transfer of data over a point-to-point or point-to-multipoint communication channel. Examples of such channels include copper wires, optical fibers, wireless communication channels, storage media and computer buses. The data are represented as an electromagnetic signal, such as an electrical voltage, radiowave, microwave, or infrared light.

While analog transmission is the transfer of a continuously varying analog signal over an analog channel, digital communication is the transfer of discrete messages over a digital or an analog channel. The messages are either represented by a sequence of pulses by means of a line code (baseband transmission), or by a limited set of continuously varying wave forms (passband transmission), using a digital modulation method. The passband modulation and corresponding demodulation (also known as detection) is carried out by modem equipment. According to the most common definition of a digital signal, both baseband and passband signals representing bit-streams are considered as digital transmission, while an alternative definition only considers the baseband signal as digital, and passband transmission of digital data as a form of digital-to-analog conversion.

Data transmitted may be digital messages originating from a data source, for example a computer or a keyboard. It may also be an analog signal such as a phone call or a video signal, digitized into a bit-stream for example using pulse-code modulation (PCM) or more advanced source coding (analog-to-digital conversion and data compression) schemes. This source coding and decoding is carried out by codec equipment.

Serial and parallel transmission
In telecommunications, serial transmission is the sequential transmission of signal elements of a group representing a character or other entity of data. Digital serial transmissions are bits sent over a single wire, frequency or optical path sequentially. Because it requires less signal processing and less chances for error than parallel transmission, the transfer rate of each individual path may be faster. This can be used over longer distances and a check digit or parity bit can be sent along with the data easily.

Parallel transmission is the simultaneous transmission of related signal elements over two or more separate paths. Multiple electrical wires are used which can transmit multiple bits simultaneously, which allows for higher data transfer rates than can be achieved with serial transmission. This method is typically used internally within the computer, for example, the internal buses, and sometimes externally for such things as printers. Timing skew can be a significant issue in these systems because the wires in parallel data transmission unavoidably have slightly different properties so some bits may arrive before others, which may corrupt the message. This issue tends to worsen with distance making parallel data transmission less reliable for long distances.

Communication channels
Some communications channel types include:
 * Data transmission circuit
 * Full-duplex
 * Half-duplex
 * Simplex
 * Multi-drop:
 * Bus network
 * Mesh network
 * Ring network
 * Star network
 * Wireless network
 * Point-to-point

Asynchronous and synchronous data transmission
Asynchronous serial communication uses start and stop bits to signify the beginning and end of transmission. This method of transmission is used when data are sent intermittently as opposed to in a solid stream.

Synchronous transmission synchronizes transmission speeds at both the receiving and sending end of the transmission using clock signals. The clock may be a separate signal or embedded in the data. A continual stream of data is then sent between the two nodes. Due to there being no start and stop bits, the data transfer rate may be more efficient.

title: Data communication


text:
Dual number

In algebra, the dual numbers are a hypercomplex number system first introduced in the 19th century. They are expressions of the form $a + bε$, where $a$ and $b$ are real numbers, and $ε$ is a symbol taken to satisfy $$\varepsilon^2 = 0$$ with $$\varepsilon\neq 0$$.

Dual numbers can be added component-wise, and multiplied by the formula
 * $$ (a+b\varepsilon)(c+d\varepsilon) = ac + (ad+bc)\varepsilon, $$

which follows from the property $ε2 = 0$ and the fact that multiplication is a bilinear operation.

The dual numbers form a commutative algebra of dimension two over the reals, and also an Artinian local ring. They are one of the simplest examples of a ring that has nonzero nilpotent elements.

History
Dual numbers were introduced in 1873 by William Clifford, and were used at the beginning of the twentieth century by the German mathematician Eduard Study, who used them to represent the dual angle which measures the relative position of two skew lines in space. Study defined a dual angle as $θ + dε$, where $θ$ is the angle between the directions of two lines in three-dimensional space and $d$ is a distance between them. The $n$-dimensional generalization, the Grassmann number, was introduced by Hermann Grassmann in the late 19th century.

Modern definition
In modern algebra, the algebra of dual numbers is often defined as the quotient of a polynomial ring over the real numbers $$(\mathbb{R})$$ by the principal ideal generated by the square of the indeterminate, that is
 * $$\mathbb{R}[X]/\left\langle X^2 \right\rangle.$$

It may also be defined as the exterior algebra of a one-dimensional vector space with $$\varepsilon$$ as its basis element.

Division
Division of dual numbers is defined when the real part of the denominator is non-zero. The division process is analogous to complex division in that the denominator is multiplied by its conjugate in order to cancel the non-real parts.

Therefore, to evaluate an expression of the form
 * $$\frac{a + b\varepsilon}{c + d\varepsilon}$$

we multiply the numerator and denominator by the conjugate of the denominator:
 * $$\begin{align}

\frac{a + b\varepsilon}{c + d\varepsilon} &= \frac{(a + b\varepsilon)(c - d\varepsilon)}{(c + d\varepsilon)(c - d\varepsilon)}\\[5pt] &= \frac{ac - ad\varepsilon + bc\varepsilon - bd\varepsilon^2}{c^2 + cd\varepsilon - cd\varepsilon - d^2\varepsilon^2}\\[5pt] &= \frac{ac - ad\varepsilon + bc\varepsilon - 0}{c^2 - 0}\\[5pt] &= \frac{ac + \varepsilon(bc - ad)}{c^2}\\[5pt] &= \frac{a}{c} + \frac{bc - ad}{c^2}\varepsilon \end{align}$$

which is defined when $c$ is non-zero.

If, on the other hand, $c$ is zero while $d$ is not, then the equation
 * $${a + b\varepsilon = (x + y\varepsilon) d\varepsilon} = {xd\varepsilon + 0}$$

This means that the non-real part of the "quotient" is arbitrary and division is therefore not defined for purely nonreal dual numbers. Indeed, they are (trivially) zero divisors and clearly form an ideal of the associative algebra (and thus ring) of the dual numbers.
 * 1) has no solution if $a$ is nonzero
 * 2) is otherwise solved by any dual number of the form $b⁄d + yε$.

Matrix representation
The dual number $$a + b \epsilon$$ can be represented by the square matrix $$\begin{pmatrix}a & b \\ 0 & a \end{pmatrix}$$. In this representation the matrix $$\begin{pmatrix}0 & 1 \\ 0 & 0 \end{pmatrix}$$ squares to the zero matrix, corresponding to the dual number $$\varepsilon$$.

There are other ways to represent dual numbers as square matrices. They consist of representing the dual number $$1$$ by the identity matrix, and $$\epsilon$$ by any matrix whose square is the zero matrix; that is, in the case of $2×2$ matrices, any nonzero matrix of the form
 * $$\begin{pmatrix}a & b \\ c & -a \end{pmatrix}$$

with $$a^2+bc=0.$$

Differentiation
One application of dual numbers is automatic differentiation. Any polynomial

 * $$P(x) = p_0 + p_1x + p_2x^2 + \cdots + p_nx^n$$

with real coefficients can be extended to a function of a dual-number-valued argument,

 * $$\begin{align}

P(a + b\varepsilon) &= p_0 + p_1(a + b\varepsilon) + \cdots + p_n(a + b\varepsilon)^n \\[2mu] &= p_0 + p_1 a + p_2 a^2 + \cdots + p_n a^n + p_1 b\varepsilon + 2 p_2 a b\varepsilon + \cdots + n p_n a^{n-1} b\varepsilon \\[5mu] &= P(a) + bP'(a)\varepsilon, \end{align}$$

where $$P'$$ is the derivative of $$P.$$

More generally, any (analytic) real function can be extended to the dual numbers via its Taylor series:

 * $$f(a + b\varepsilon) = \sum_{n=0}^\infty \frac{f^{(n)} (a)b^n \varepsilon^n}{n!} = f(a) + bf'(a)\varepsilon,$$

since all terms involving $ε^{2}$ or greater powers are trivially $0$ by the definition of $ε$.

By computing compositions of these functions over the dual numbers and examining the coefficient of $ε$ in the result we find we have automatically computed the derivative of the composition.

A similar method works for polynomials of $n$ variables, using the exterior algebra of an $n$-dimensional vector space.

Geometry
The "unit circle" of dual numbers consists of those with $a = ±1$ since these satisfy $zz* = 1$ where $z* = a − bε$. However, note that
 * $$ e^{b \varepsilon} = \sum^\infty_{n=0} \frac{\left(b\varepsilon\right)^n}{n!} = 1 + b \varepsilon,$$

so the exponential map applied to the $ε$-axis covers only half the "circle".

Let $z = a + bε$. If $a ≠ 0$ and $m = b⁄a$, then $z = a(1 + mε)$ is the polar decomposition of the dual number $z$, and the slope $m$ is its angular part. The concept of a rotation in the dual number plane is equivalent to a vertical shear mapping since $(1 + pε)(1 + qε) = 1 + (p + q)ε$.

In absolute space and time the Galilean transformation
 * $$\left(t', x'\right) = (t, x)\begin{pmatrix} 1 & v \\0 & 1 \end{pmatrix}\,,$$

that is
 * $$t' = t,\quad x' = vt + x,$$

relates the resting coordinates system to a moving frame of reference of velocity $v$. With dual numbers $t + xε$ representing events along one space dimension and time, the same transformation is effected with multiplication by $1 + vε$.

Cycles
Given two dual numbers $p$ and $q$, they determine the set of $z$ such that the difference in slopes ("Galilean angle") between the lines from $z$ to $p$ and $q$ is constant. This set is a cycle in the dual number plane; since the equation setting the difference in slopes of the lines to a constant is a quadratic equation in the real part of $z$, a cycle is a parabola. The "cyclic rotation" of the dual number plane occurs as a motion of its projective line. According to Isaak Yaglom, the cycle $Z = {z : y = αx^{2} }$ is invariant under the composition of the shear
 * $$x_1 = x ,\quad y_1 = vx + y $$

with the translation
 * $$x' = x_1 = \frac{v}{2a} ,\quad  y' = y_1 + \frac{v^2}{4a}. $$

Applications in mechanics
Dual numbers find applications in mechanics, notably for kinematic synthesis. For example, the dual numbers make it possible to transform the input/output equations of a four-bar spherical linkage, which includes only rotoid joints, into a four-bar spatial mechanism (rotoid, rotoid, rotoid, cylindrical). The dualized angles are made of a primitive part, the angles, and a dual part, which has units of length. See screw theory for more.

Algebraic geometry
In modern algebraic geometry, the dual numbers over a field $$k$$ (by which we mean the ring $$k[\varepsilon]/(\varepsilon^2)$$) may be used to define the tangent vectors to the points of a $$k$$-scheme. Since the field $$k$$ can be chosen intrinsically, it is possible to speak simply of the tangent vectors to a scheme. This allows notions from differential geometry to be imported into algebraic geometry.

In detail: The ring of dual numbers may be thought of as the ring of functions on the "first-order neighborhood of a point" – namely, the $$ k$$-scheme $$ \operatorname{Spec} (k[\varepsilon]/(\varepsilon^2))$$. Then, given a $$ k$$-scheme $$ X$$, $$ k$$-points of the scheme are in 1-1 correspondence with maps $$ \operatorname{Spec} k \to X $$, while tangent vectors are in 1-1 correspondence with maps $$ \operatorname{Spec} (k[\varepsilon]/(\varepsilon^2)) \to X $$.

The field $$k$$ above can be chosen intrinsically to be a residue field. To wit: Given a point $$x$$ on a scheme $$S$$, consider the stalk $$S_x$$. Observe that $$S_x$$ is a local ring with a unique maximal ideal, which is denoted $$\mathfrak m_x$$. Then simply let $$k = S_x / \mathfrak m_x$$.

Generalizations
This construction can be carried out more generally: for a commutative ring $R$ one can define the dual numbers over $R$ as the quotient of the polynomial ring $R[X]$ by the ideal $(X^{2})$: the image of $X$ then has square equal to zero and corresponds to the element $ε$ from above.

Arbitrary module of elements of zero square
There is a more general construction of the dual numbers. Given a commutative ring $$R$$ and a module $$M$$, there is a ring $$R[M]$$ called the ring of dual numbers which has the following structures:

It is the $$R$$-module $$R \oplus M$$ with the multiplication defined by $$(r, i) \cdot \left(r', i'\right) = \left(rr', ri' + r'i\right)$$ for $$r, r' \in R$$ and $$i, i' \in I.$$

The algebra of dual numbers is the special case where $$M = R$$ and $$\varepsilon = (0, 1).$$

Superspace
Dual numbers find applications in physics, where they constitute one of the simplest non-trivial examples of a superspace. Equivalently, they are supernumbers with just one generator; supernumbers generalize the concept to $n$ distinct generators $ε$, each anti-commuting, possibly taking $n$ to infinity. Superspace generalizes supernumbers slightly, by allowing multiple commuting dimensions.

The motivation for introducing dual numbers into physics follows from the Pauli exclusion principle for fermions. The direction along $ε$ is termed the "fermionic" direction, and the real component is termed the "bosonic" direction. The fermionic direction earns this name from the fact that fermions obey the Pauli exclusion principle: under the exchange of coordinates, the quantum mechanical wave function changes sign, and thus vanishes if two coordinates are brought together; this physical idea is captured by the algebraic relation $ε^{2} = 0$.

Projective line
The idea of a projective line over dual numbers was advanced by Grünwald and Corrado Segre.

Just as the Riemann sphere needs a north pole point at infinity to close up the complex projective line, so a line at infinity succeeds in closing up the plane of dual numbers to a cylinder.

Suppose $D$ is the ring of dual numbers $x + yε$ and $U$ is the subset with $x ≠ 0$. Then $U$ is the group of units of $D$. Let $B = {(a, b) ∈ D × D : a ∈ U or b ∈ U}$. A relation is defined on B as follows: $(a, b) ~ (c, d)$ when there is a $u$ in $U$ such that $ua = c$ and $ub = d$. This relation is in fact an equivalence relation. The points of the projective line over $D$ are equivalence classes in $B$ under this relation: $P(D) = B/~$. They are represented with projective coordinates $[a, b]$.

Consider the embedding $D → P(D)$ by $z → [z, 1]$. Then points $[1, n]$, for $n^{2} = 0$, are in $P(D)$ but are not the image of any point under the embedding. $P(D)$ is mapped onto a cylinder by projection: Take a cylinder tangent to the double number plane on the line ${yε : y ∈ R}$, $ε^{2} = 0$. Now take the opposite line on the cylinder for the axis of a pencil of planes. The planes intersecting the dual number plane and cylinder provide a correspondence of points between these surfaces. The plane parallel to the dual number plane corresponds to points $[1, n]$, $n^{2} = 0$ in the projective line over dual numbers.

title: Dual number