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Nell Arthur

Ellen Lewis Arthur (née Herndon; August 30, 1837 – January 12, 1880), known as Nell Arthur, was the wife of the 21st president of the United States, Chester A. Arthur. She died of pneumonia in January 1880; her husband was elected vice-president that November. He succeeded to the presidency in September 1881 when President James A. Garfield was assassinated.

Early life
Ellen Lewis Herndon, called "Nell," was born in the town of Culpeper Court House, Virginia on August 30, 1837, the daughter of William Lewis Herndon and Frances Elizabeth Hansbrough. (October 10, 1817 – April 5, 1878). Her father was a naval officer who gained national renown in 1857 when he went down with his ship, the mail steamer SS Central America, along with more than 400 passengers and crew. It was the largest ever loss of life in a commercial shipping disaster at the time. Herndon had safely evacuated 152 women and children to another vessel during the severe hurricane off Cape Hatteras, but his ship could not be saved. Nell was 20 when her father died. One of her father's cousins was Matthew Fontaine Maury, another notable naval officer and explorer.

Herndon was raised and educated in Washington, D.C. until 1856, when her father relocated the family to New York City. At age 16, she accompanied Matthew Maury, his two daughters and a cousin on an extended tour of Europe. A talented contralto, when she lived in Washington, Herndon's singing ability resulted in an invitation to join the choir at St. John's Episcopal Church, which she accepted.

Marriage and family
Nell and the future U.S. President Chester A. Arthur were introduced in 1856 by her cousin Dabney Herndon Maury, a friend of Arthur, in New York City. Arthur proposed to her on the porch of the U.S. Hotel in Saratoga Springs, New York after a brief courtship.

Arthur, aged 30, married Herndon, aged 22, on October 25, 1859, at Calvary Episcopal Church in New York City. The day was her father's birthday. Arthur, who was from rural Vermont, is said to have learned refined dressing while at Union College in upstate New York, where he was in the debating society, and the ways of high society from her socially prominent family. The couple were known for their parties in their Lexington Avenue townhouse in Manhattan.

After relocating to New York City, Nell Arthur continued to sing as a member of the Mendelssohn Glee Club and performed at benefits around New York. The Arthurs appeared to have a strong marriage, but it was strained by both Chester's political activities, which took much of his time, and their divided loyalties on the Civil War. While Arthur was serving in the New York militia during the conflict, his wife privately sympathized with the Confederacy, for which many of her Virginia kinfolk were fighting.

The Arthurs had two sons, one of whom died young, and a daughter:
 * William Lewis Arthur (1860–1863), died of convulsions at age two and a half, devastating his parents
 * Chester Alan Arthur II (1864–1937) – He graduated from Princeton University in 1885 and went on to Columbia Law School. He became a gentleman of leisure. President Arthur on his deathbed warned his son not to go into politics.  Alan Arthur traveled extensively, maintained a fine stable of horses, and relied on polo for exercise. A celebrated playboy, at age 36 he married Myra Townsend Fithian, a California heiress.  The couple separated after 16 years of marriage and divorced in 1927. Eventually, he settled in Colorado Springs. In 1934 he married Rowena Graves, a real estate and insurance businesswoman. From his first marriage, he was the father of two children: a daughter, Myra, who did not survive, and Chester Alan "Gavin" Arthur III (1901-1972), who married but had no children.
 * Ellen Hansbrough Herndon Arthur (1871–1915) – Still a child while her father was president, she was shielded from the press. She married Charles Pinkerton and lived in New York City.

Social prominence
Nell's social network among the élite families of New York widened Chester's political contacts. The pair became a prominent pairing noted for their ambition to gain the recognition and prestige that would accompany Chester's rise in politics. Among Nell’s friends were Vanderbilts, Astors, and Roosevelts. Her mother's wealth allowed them luxuries such as the three-story Lexington Avenue brownstone townhouse with expensive furnishings from Tiffany’s, which Arthur could not have afforded by himself. Freed from the need to earn enough income to support the lifestyle the couple enjoyed, Arthur was able to devote himself to the New York Republican party, eventually rising through political patronage to Quartermaster General of the New York Militia, with the rank of brigadier general during the Civil War, and Collector of the Port of New York after the war. Her singing as a soloist at the Mendelssohn Glee Club earned her renown of her own.

Premature death
On January 10, 1880, Nell Arthur came down with a cold. She quickly developed pneumonia and died two days later on January 12, 1880, at age 42 in New York City, New York. She was buried in the Arthur family plot in Albany, New York.

The president's sister Mary Arthur McElroy served as hostess and unofficial First Lady for Arthur's social activities as president. She also cared for the Arthur children, who were then 16 and 9 years of age.

Arthur deeply mourned the death of his wife. After taking office as president, Arthur, who could see St. John's Episcopal Church from his office, commissioned a stained glass window dedicated to his wife at the church. He had it installed where he could view it at night, as the lights were kept on within the church. Additionally, he ordered fresh flowers placed daily before her portrait in the White House.

title: Nell Arthur


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Meelick

Meelick may refer to the following places in the West of Ireland:

 * Meelick, County Clare
 * Meelick, County Mayo
 * Meelick, County Galway

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

title: Meelick


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Blue danio

The blue danio, Kerr's danio or turquoise danio (Danio kerri), is a tropical fish belonging to the genus Danio in family Cyprinidae.

Distribution and habitat
The blue danio is found on the islands of Langkawi and Ko Yao Yai in Malaysia.

Description
It is a blue-colored, deep-bodied danio with several pinkish/gold lines from tail to gills which may or may not be continuous, over a powder blue side.

In the aquarium
The blue danio is a peaceful, active schooling fish, so is usually kept in groups. They prefer a well-planted environment, but still need plenty of space to school. Blue danios are often kept in water with a 6.5 – 7.0 pH, a water hardness of 8 – 12 dGH, and a temperature range of 73 – 77 °F (23–25 °C).

Mating
Blue danios are egg-scatterers that spawn over coarse gravel beds. They will typically spawn at the first light of day. The eggs will hatch in about 36 hours.

Etymology
The taxonomic name honors A.F.G. Kerr, who collected the first specimen on Ko Yao Yai in 1929.

title: Blue danio


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Source-available software

Source-available software is software released through a source code distribution model that includes arrangements where the source can be viewed, and in some cases modified, but without necessarily meeting the criteria to be called open-source. The licenses associated with the offerings range from allowing code to be viewed for reference to allowing code to be modified and redistributed for both commercial and non-commercial purposes.

Distinction from free and open-source software
Any software is source-available in the broad sense as long its source code is distributed along with it, even if the user has no legal rights to use, share, modify or even compile it. It is possible for a software to be both source-available software and proprietary software (e.g. id Software's Doom).

In contrast, the definitions of free software and open-source software are much narrower. Free software and/or open-source software is also always source-available software, but not all source-available software is also free software and/or open-source software. This is because the official definitions of those terms require considerable additional rights as to what the user can do with the available source (including, typically, the right to use said software, with attribution, in derived commercial products).

In the broad sense, any FOSS license is a source-available license. In the narrow sense, the term source-available specifically excludes FOSS software.

Non-free licenses
The following source-available software licenses are considered non-free licenses because they have limitations that prevent them from being open-source according to the Open Source Initiative and free to the Free Software Foundation.

Commons Clause
The Commons Clause, created by Fossa, Inc., is an addendum to an open-source software license that restricts users from selling the software. Under the combined license, the software is source-available, but not open-source.

On August 22, 2018, Redis Labs shifted some Redis Modules from the GNU Affero General Public License to a combination of the Apache License 2.0 and the Commons Clause.

In September 2018, Matthew Garrett criticized Commons Clause calling it an "older way of doing things" and said it "doesn't help the commons".

Business Source License
Business Source License has been introduced by MariaDB Corporation in 2016 and rapidly became one of the most adopted "delayed open source" licenses. It prohibits use of the code in production environments, where a commercial license is required.

Functional Source License
Functional Source License has been introduced in November 2023 by Sentry, as a simpler alternative to Business Source License. It prohibits any "competing" use of the code, to preserve the rights of the author to economically exploit it, but applies for a limited time, after which the code itself is considered to be available under Apache License or MIT License.

GitLab Enterprise Edition License (EE License)
The GitLab Enterprise Edition License is used exclusively by GitLab's commercial offering. GitLab also releases a Community Edition under the MIT License.

GitLab Inc. openly discloses that the EE License makes their Enterprise Edition product "proprietary, closed source code." However, the company makes the source code of the Community Edition public, as well as the repository's issue tracker, and allows users to modify the source code. The dual release of the closed-source Enterprise Edition and the open-source Community Edition makes GitLab an open core company.

Mega Limited Code Review Licence
In 2016, Mega Ltd. released the source code of their Mega clients under the Mega Limited Code Review Licence, which only permits usage of the code "for the purposes of review and commentary". The source code was released after former director Kim Dotcom stated that he would "create a Mega competitor that is completely open source and non-profit" following his departure from Mega Ltd.

Microsoft Shared Source Initiative
Microsoft's Shared Source Initiative, launched in May 2001, comprises 5 licenses, 2 of which are open-source and 3 of which are restricted. The restricted licenses under this scheme are the Microsoft Limited Public License (Ms-LPL), the Microsoft Limited Reciprocal License (Ms-LRL), and the Microsoft Reference Source License (Ms-RSL).

Old Scilab License
Prior to version 5, Scilab described itself as "the open source platform for numerical computation" but had a license that forbade commercial redistribution of modified versions. Versions 5 and later are distributed under the GPL-compatible CeCILL license.

Server Side Public License
The Server Side Public License is a modification of the GNU Affero General Public License created by the MongoDB project. It modifies a clause relating to usage of the licensed work over a network, stating that if SSPL-licensed software is incorporated into a "service" offered to other users, the source code for the entirety of the service (including without limitation all software and APIs that would be required for a user to run an instance of the service themselves) must be released under the SSPL. The license is considered non-free by the Open Source Initiative, Debian and Red Hat, as it contains conditions that are unduly discriminatory towards commercial use of the software.

SugarCRM Public License
In 2007 Michael Tiemann, president of OSI, had criticized companies such as SugarCRM for promoting their software as "open source" when in fact it did not have an OSI-approved license. In SugarCRM's case, it was because the software is so-called "badgeware" since it specified a "badge" that must be displayed in the user interface. SugarCRM's open source version was re-licensed under the GPL version 3 in 2007, and later the GNU Affero GPL version 3 in 2010.

TrueCrypt License
The TrueCrypt License was used by the TrueCrypt disk encryption utility. When TrueCrypt was discontinued, the VeraCrypt fork switched to the Apache License, but retained the TrueCrypt License for code inherited from TrueCrypt.

The Open Source Initiative rejects the TrueCrypt License, as "it has elements incompatible with the OSD." The Free Software Foundation criticizes the license for restricting who can execute the program, and for enforcing a trademark condition.

BeeGFS End User License Agreement
BeeGFS EULA is the license of the distributed parallel file system BeeGFS, except the client for Linux, which is licensed under GPLv2.

BeeGFS source code is publicly available from their website, and because of this they claiming BeeGFS as "Open-Source" software; it is in fact not because this license prohibits distributing modified versions of the software, or using certain features of the software without authorization.

title: Source-available software


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Dnepr (motorcycle)

Dnepr (Дніпро Russian: Днепр) is a motorcycle brand produced in Kyiv, Ukraine. It has been in use since 1967.

Motorcycles have been produced in Kyiv since 1946 at the Kyiv Motorcycle Plant (Kyivskyi Mototsykletnyi Zavod (KMZ), Київський Мотоциклетний Завод, (КМЗ)). Initial production was of a 98 cc two-stroke model that was confiscated from the German firm Wanderer as reparations. The original design for KMZ heavy motorcycles, and their cousin the IMZ, is taken from the pre-World War II German BMW motorcycle R71, which the Soviet Union licensed in 1940. The plant and equipment needed to make the M-72 (the Soviet derivative of the BMW R71) was transferred from the Gorky Motorcycle Plant (Gorkovskyi Mototsykletnyi Zavod, GMZ located in the city of Gorkiy (Nizhny Novgorod) in 1949. The first batch of M-72 motorcycles was produced in 1952 with the supply of 500 engines from IMZ. In 1958 KMZ replaced the plunger framed M72-N with the swingarm framed K-750.  In 1964, KMZ introduced a military model, the MV-750 with a differential two-wheel drive to the sidecar wheel.

In 1967, to celebrate the 50th Anniversary of the Great October Socialist Revolution, KMZ released their first OHV engine in the "Dnepr" K-650. Unlike the earlier sidevalve engines with their roller bearing crankshafts, this engine featured a sleeve bearing crankshaft as found in the World War II Zündapp KS750. The K-650 was superseded by model MT-9 650 cc, which was available in both solo and sidecar models (often referred to as the best "Cossack") as it was reliable and featured a new transmission with reverse gear and an automatic declutching mechanism incorporated into the riders foot pedal. The MT-10 was the first Soviet motorcycle to feature 12 volt electrics.

The Dnepr is famous for its off-road capability. Armed services models equipped with sidecars had two-wheel drive and as much as 15 cm of ground clearance. The present engine is a 650 cc OHV boxer twin. Current models are fitted with engines ranging from the factory standard 650 to 750 and 1,000 cc.

Between 1973 and 1979 Dnepr was one of the makes marketed by Satra in the United Kingdom as Cossack motorcycles.

Since the demise of the Soviet Union, the factory fell on hard times. Production decreased to only remnants of former glory. All shops were closed, and machine tools were taken out of the city limits.

title: Dnepr (motorcycle)


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User:Mu Gamma

I'm in my early 20's and working on many projects. I'm an avid gamer and writer.

I may reveal more about myself at a later point, but am new to Wikipedia and wish to be conservative (for now).

I've been editing, anonymously, for about 3 months.

title: User:Mu Gamma


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Portoferraio

Portoferraio is a town and comune in the province of Livorno, on the edge of the eponymous harbour of the island of Elba. It is the island's largest city. Because of its terrain, many of its buildings are situated on the slopes of a tiny hill bordered on three sides by the sea.

History

It was founded by Cosimo I de' Medici, Grand Duke of Tuscany, in 1548, with the name of Cosmopoli ("Cosimo's City"), to balance the presence of the Spanish citadel in Porto Azzurro. It had three forts (Forte Stella, Forte Falcone, and Forte Inglese) and a massive line of walls, all still visible today.

The name evolved from Ferraia with etruscan, Fabricia with Romans and Ferraio with Grand Duchy of Tuscany.

The city remained attached to the Grand Duchy of Tuscany until the late 18th century, when, due to its strategic position, it came into contention with France, Great Britain, and Austria. A British garrison withstood the Siege of Porto Ferrajo in 1801, but the 1802 Treaty of Amiens transferred the town to France. In 1814 it was handed over to Napoleon Bonaparte, as the seat of his first exile. In the 19th century, the city grew quickly, due to the construction of infrastructures and the exploitation of new iron mills in Rio Marina. Portoferraio then became the main shipping port of the ore to the mainland, whence the current name, meaning "Iron Port" in Italian. After the end of the Napoleonic Era, Portoferraio returned to Tuscany and became part of the Kingdom of Italy in 1860. Here brigand Carmine Crocco was imprisoned until his death for his revolution against the reign of Victor Emmanuel II and the anarchist Giovanni Passannante who attempted to kill King Umberto I.

During World War II, Portoferraio became the scene of battle when Elba was occupied by German forces. In late June 1944, an Allied force composed mainly of Free French troops liberated the island in a fight that lasted two days. Portoferraio was taken by French troops on 18 June but was damaged by the fighting and the bombing raids which preceded the invasion.

Portoferraio's economy suffered from the end of mining activities starting from the 1970s, but in the following decades, it gained status as an internationally renowned seaside destination.

The Jewish community
The first Jews arrived in Portoferraio at the beginning of the 17th century following the publication of the edict of 1556 in which Cosimo I de' Medici granted special privileges to all those who settled in Cosmopoli. In 1593, Ferdinando I de' Medici issued letters patent, called La Livornina, by which more privileges were granted to foreign merchants, Jews in particular, who were willing to settle in the new free ports on Elba and in Leghorn.

The first synagogue was built in 1631–1632 when there were barely over ten Jewish families living on the island. At the beginning of the 18th century, the Jewish community numbered more than 50 people.

In 1702, by order of the Grand Duke, the Jews of Portoferraio were required to live on a designated street, Via degli Ebrei or Street of the Hebrews (now called via Elbano Gasperi) which constituted a small ghetto which they were not allowed to leave after 1 o’clock in the morning. At about this time, Abraham Pardo, son of Isaac, was forbidden to build a new synagogue near the church. He was forced to build it in a garden behind his home, below Fort Stella. All Jewish rituals were celebrated in the synagogue and were attended by Jews from Piombino, Maremme and the rest of the island of Elba. The ecclesiastical authorities sought to isolate the Jewish community by preventing Christians from having any contact with the Jewish community. There were restrictions on all workers and in particular on wet nurses who had to apply for special dispensations from the Vicar Forane. In 1765, authorization was granted to build a wall around a field designated for use as a Jewish cemetery. The field was situated over the Ponticello ditch, behind Ghiaie beach on the site of the present-day Hotel Villa Ombrosa. The wall with its central door is still visible. Until 1954, there was an inscription on the door which read: Cimitero Israelitico. In 1964, the remaining tombs, about 40 of them, with their inscriptions in Hebrew and Spanish and dating from 1646 to the end of the 19th century, were transferred to the new Jewish cemetery in Livorno. The ground was deconsecrated and sold by the Jewish community to a neighbor. It is now the garden of the villa behind it.

In 1826, the Governor, at the request of the heads of 10 Jewish families, drew up a set of rules for the Jewish community. The rules were approved by the Grand Duke, Leopold II who nominated two massari ("bailiffs") to represent the community. In the second half of the 18th century, the Jewish community declined in number due to the worsening of economic conditions on the island. Peace had been signed with the Ottoman Empire resulting in a reduction of military garrisons and the suppression of the “compagnia urbana” made up of 180 men. At the beginning of the 20th century, the construction of a steel mill attracted new Jewish families to the island. However, due to the anti-Jewish laws and persecutions, these families left the island. Alfonso Preziosi, in his book, cited above, wrote “generally, the Jews found the island of Elba to be an oasis of peace thanks to the privileges granted by the Medici and the Lorraine which allowed them to develop their trade with Eastern ports.”

Main sights
The town center is crowded around the small marina lying in a natural cove.

Main points of interest include:

 * Forte Stella
 * Forte Falcone
 * Forte Inglese
 * Archeological museum
 * Napoleon's house

Portoferraio lighthouse
The lighthouse stands on the northern rampart of Forte Stella built in 1548 by Cosimo I de' Medici. It was built by Leopold II Grand Duke of Tuscany in 1788; the stone tower is 25 metres high and has a double balcony and lantern. The lighthouse is fully automated, operated by Marina Militare and identified by the code number 2072 E.F.; the lantern is 63 metres above sea level and emits a group of three white lightning strikes in a 14-second period visible up to 16 nautical miles (roughly 30 km). On the same tower is an additional light identified by the number 2072.2.E.F. that emits a red fixed light at 60 metres above sea level.

title: Portoferraio


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Thomas Bateman (antiquary)

Thomas Bateman (8 November 1821 (baptised) – 28 August 1861) was an English antiquary and barrow-digger.

Biography
Thomas Bateman was born in Rowsley, Derbyshire, England, the son of the amateur archaeologist William Bateman. After the death of his father in 1835, Bateman was raised by his grandfather, and from the age of 16 he helped run the family estate at Middleton Hall in Middleton-by-Youlgreave, during which time he became interested in archaeology: Sir Richard Colt Hoare's Ancient History of North and South Wiltshire influenced him greatly. He built Lomberdale Hall in 1844 as his private residence. Bateman had a long affair with Mary Ann Mason, but she was already married. He married Sarah Parker on 2 August 1847 and they had four daughters and a son. Bateman's first archaeological experience was observing the demolition of a medieval church in Bakewell. He joined the British Archaeological Association in 1843 and in 1844, whilst at an archaeological congress in Canterbury, participated in the excavation of barrows in the surrounding countryside. The following year he excavated 38 barrows in Derbyshire and Staffordshire, earning himself the nickname "The Barrow Knight". In 1847, he published Vestiges of the Antiquities of Derbyshire which united his work with that of earlier excavators in the area. With the help of Samuel Carrington of Wetton he continued to excavate barrows, 50 in the period 1848–1849 and a further 22 between 1851 and 1861, when he died. His second book was Ten Years' Diggings in Celtic and Saxon Grave Hills in the Counties of Derby, Stafford and York, published in the year of his death and it had the details of his work including Heath Wood barrow cemetery. He was buried, following his instructions, in unconsecrated ground on a hillside in Middleton-by-Youlgreave His tomb is a Grade II listed building.

After his death, his son sold most of Bateman's collections, parts of which were acquired by the Sheffield City Museum (now called the Weston Park Museum) in 1893, including the celebrated Benty Grange helmet found in Benty Grange, Derbyshire. A daughter, Clara Theodora Bateman, married Harcourt Clare.

In 2006, a bequest allowed Derbyshire Libraries to purchase a collection that had been amassed by Bateman by inserting documents into the four Derbyshire volumes of Lysons' Magna Britannia. Among the prints was an image of his museum at his home which is dated from around his death. A long description of his museum is found in Eliza Meteyard's novel Dora and her Papa.

Publications

 * Vestiges of the Antiquities of Derbyshire, and the Sepulchral Usages of Its Inhabitants (1848), with Stephen Glover

title: Thomas Bateman (antiquary)


text:
Talk:Propagation of uncertainty/Archive 1

The Resistance example is wrong, I think.
The errors should add in quadrature. So square each element and take the square root. Take the example Y=A+B. Then the error is \sqrt(dA^2+dB^2), not dA+dB. That is what you get when you use the equation right above the example problem. —Preceding unsigned comment added by 132.163.47.52 (talk) 23:21, 4 July 2010 (UTC)

I fixed the error. And I corrected the Absolute Error Box. I am fairly certain they were incorrect. —Preceding unsigned comment added by 132.163.47.52 (talk) 23:59, 4 July 2010 (UTC)

This article is extremely important, and needs improving
I genuinely think that this article is important for the whole of science. Too many scientists (including myself) graduate without becoming confident with error calculations, and I suspect that many scientists never do so. I see here an opportunity to improve the quality of a whole body of scientific work.

Currently, the approach is too mathematical (and not even rigorous), and does not deal with the subtleties of error calculations, like the difference between using errors and standard deviations, and which situations it is ok to use approximations.

When the equations are approximations, why not use the "is approximately equal to" instead of the equals sign? The fact that it is an approximation should be clearly marked, in any case.

I suggest the article should clearly delineate the different possible approaches - perhaps this could even become the basis for standardisation of error calculations in future publications. Thanks, MichaelR 83.72.194.27 11:12, 7 October 2007 (UTC)

Contradiction between formula and example?
It seems there is a conflict between the general formula and the very first example - perhaps I'm missing something here, but it strikes me as confusing that the error is given as $$\Delta X=\Delta A+\Delta B$$ when the equation suggests it should be $$\Delta X=(\Delta A^{2}+\Delta B^{2})^{\frac{1}{2}}$$.

Thanks gabe_rosser 00:20, 23 May 2007 (BST)

 * Yes, Gabe's formula above is much closer to what I use. I'm no statististian, but the sources that showed me how to do it that way are. I think maybe some of the formulas presented in the article are approximations to make things simpler for hand calculation. If that's what they are, it should be clearly stated, because it is obviously causing confusion. ike9898 18:23, 8 August 2007 (UTC)

 * I agree with Gabe, the formula given for ΔR does not follow from the described method of finding ΔR. I am a 4th year Mechanical Engineering student, and I am certain that Gabe is correct; thus, I will be correcting the error.

i or j
Is it necessary to use both i and j as indices for the summation of the general formulae? it appears to me that i only appears in the maths whilst j only appears in the english. True? If not, it could be more clearly explained as to the reasons for the change / use of both.

Thanks Roggg 09:35, 20 June 2006 (UTC)

Geometric mean
Example application: the geometric mean? Charles Matthews 16:33, 12 May 2004 (UTC)

 * From the article (since May 2004!): "the relative error ... is simply the geometric mean of the two relative errors of the measured variables" -- It's not the geometric mean. If it were, it would be the product of the two relative errors in the radical, not the sum of the squares.  I'll fix this section. --Spiffy sperry 21:47, 5 January 2006 (UTC)

Delta?
In my experience, the lower-case delta is used for error, while the upper-case delta (the one currently used in the article) is used for the change in a variable. Is there a reason the upper-case delta is used in the article? --LostLeviathan 02:01, 20 Oct 2004 (UTC)

Missing Definition of Δxj
A link exists under the word "error" before the first expression of Δxj in the article, but this link doesn't take one to a definition of this expression. The article can be improved if this expression is properly defined. —Preceding unsigned comment added by 65.93.221.131 (talk • contribs) 4 October 2005

Formulas
I think that the formula given in this article should be credited to Kline-Mcklintock. —lindejos

First, I'd like to comment that this article looks like Klingonese to the average user, and it should be translated into English.

Anyway, I was looking at the formulas, and I saw this allegation: X = A ± B (ΔX)² = (ΔA)² + (ΔB)², which I believe is false.

As I see it, if A has error ΔA then it means A's value could be anywhere between A-ΔA and A+ΔA. It follows that A±B's value could be anywhere between A±B-ΔA-ΔB and A±B+ΔA+ΔB; in other words, ΔX=ΔA+ΔB.

If I am wrong, please explain why. Am I referring to a different kind of error, by any chance?

aditsu 21:41, 22 February 2006 (UTC)

 * As the document I added to External links explain it, we are looking at ΔX as a vector with the variables as axes, so the error is the length of the vector (the distance from the point where there is no error).
 * It still seems odd to me, because this gives the distance in the "variable plane" and not in the "function plane". But the equation is correct. —Yoshigev 22:14, 23 March 2006 (UTC)

 * Now I found another explanation: We assume that the variables has Gaussian distribution. The addition of two Gaussians gives a new Gaussians with a width equals the quadrature of the width of the originals. (see ) —Yoshigev 22:27, 23 March 2006 (UTC)

Article title
The current title "Propagation of errors resulting from algebraic manipulations" seems to me not so accurate. First, the errors don't result from the algebraic manipulations, they "propagate" by them. Second, I think that the article describe the propagation of uncertainties. And, third, the title is too long.

So I suggest moving this article to "Propagation of uncertainty". Please make comments... —Yoshigev 23:39, 23 March 2006 (UTC)

 * Seems okay. A problem with the article is that the notation x + Δx is never explained. From your remarks, it seems to mean that the true value is normally distributed with mean x and variance Δx. This is one popular error model, leading to the formula (Δ(x+y))² = (Δx)² + (Δy)².
 * Another one is that x + Δx means that the true value of x is in the interval $$[x-\Delta x, x+\Delta x]$$. This interpretation leads to the formula $$\Delta(x+y) = \Delta x + \Delta y$$, which aditsu mentions above.
 * I think the article should make clear which model is used. Could you please confirm that you have the first one in mind? -- Jitse Niesen (talk) 00:58, 24 March 2006 (UTC)

 * Not exactly. I have in mind that for the measured value x, the true value might be in $$[x-\Delta x, x+\Delta x]$$, like your second interpretation. But for that true value, it is more probable that it will be near x. So we get a normal distribution of the probable true value around the measured value x. Then, 2Δx is the width of that distribution (I'm not sure, but I think the width is defined by the standard deviation), and when we add two of them we use (Δx)² + (Δy)², as explained in Sum of normally distributed random variables.
 * I will try to make it clearer in the article. —Yoshigev 17:45, 26 March 2006 (UTC)

As you can see, I rewrote the header and renamed the article. —Yoshigev 17:44, 27 March 2006 (UTC)

This artical was a disgrace to humanity
First the article defined $$\Delta A$$ as the absolute error of $$A$$ but then the example formulas section went ahead and defined error propagation with respect to $$\Delta A$$ as the standard deviation of $$A$$. Even then the examples had constants that weren't even considered in the error propagation. Then to add insult to injury I found a journal article which shows that at least two of the given definitions were only approximations so I had to redo the products formula and added notes to the remaining formulas explaining that they were only approximations with an example of how they are only approximations. (doesn't it seem just a little bit crazy to only find approximations to the errors when you can have an exact analysis of the error propagation, to me it just seems like approximating an approximation.) So now there are TWO columns: ONE for ABSOLUTE ERRORS and ANOTHER for STANDARD DEVIATIONS! sheash! it's not that hard to comprehend that absolute errors and standard deviations are NOT EQUIVILANT! $$\sigma_A$$ is the standard deviation of $$A$$, and $$\Delta A$$ is the absolute error NOT the standard deviation of $$A$$. --ANONYMOUS COWARD0xC0DE 04:02, 21 April 2007 (UTC)

 * The problem is now the formula given in the table don't match the stated general formula for absolute error in terms of partial derivatives. I think this makes the article rather confusing, particularly for those readers who don't have access to the journal article you've linked.  One is left without a clear idea (1) where the general formula comes from, (2) why it is inexact for the case of a product of two or more quantities, and (3) where the exact forms come from.

 * The answer is relatively simple. The general form given is basically a Taylor series, truncated after the first order term.  It is valid only if the errors are small enough that we can neglect all higher order terms.  Of course, if we have a product of n quantities we would need an n-th order Taylor series to produce the exact result.  The article needs to be edited to make this clear.

 * This is the person who wrote the absolute error box, that is actually incorrect. —Preceding unsigned comment added by 132.163.47.52 (talk) 15:33, 5 July 2010 (UTC)

 * Specifically, the general form should look something like this:

\Delta f(x_1,\cdots,x_k) = \sum_{n_1=0}^{\infin} \cdots \sum_{n_k=0}^{\infin} \left | \frac{\partial^{n_1} \cdots \partial^{n_k} f}{{\partial x_1^{n_1}} \cdots \partial x_k^{n_k}} \right | \frac{(\Delta x_1)^{n_1}\cdots (\Delta x_1)^{n_k}}{n_1!\cdots n_k!} $$
 * However the term with $$n_1 \cdots n_k$$ all equal to zero is excluded. Note that this expression simplifies to the approximate form if we include only the lowest order terms (i.e., terms with $$n_1 + \cdots + n_k = 1$$)
 * --Tim314 05:15, 30 May 2007 (UTC)

Caveats?
Can we get some caveats placed in here? i.e. a statement that these formula are only valid for small sigma/mean and that the formula for the quotient particularly is problematic given Hodgson's paradox and the discussion in ratio distribution. The Goodman (1960) article has some exact formula that modify the approximate forms here as well.169.154.204.2 01:17, 23 August 2007 (UTC)

Re-wrote example table
I searched for this page to remind myself of one of the formulae, which I use on a regular basis. (When I'm at work, I flip to a tabbed page in my copy of [Bevington].) I could see that the table contained many errors, mostly due to confusions between $$\Delta A\!\,$$ and $$\left(\Delta A\right)^2 \!\,$$, and some of the table entries included extra terms, presumably for correlations between $$A\text{, }B\text{, }C\!\,$$, though they are stated in the caption to be uncorrelated. I didn't notice it right away, but the table had a third column with $$\Delta A\!\,$$ replaced with an undefined (but commonly used) $$\sigma_A\!\,$$.

In its current form, the table is (exactly, not approximately) correct for uncorrelated, normally-distributed real variables. Hopefully, it also gives an indication of how these rules can be combined. (Some are special cases of others, but they all derive from the general rule in the previous section, anyway.)

So what about formulae for correlated variables? I don't know much about that because I always use the general derivative method for problems with correlations. I only use the example formulae for simple cases. Jim Pivarski 23:25, 7 October 2007 (UTC)

Pitfall of linear error propagation: eg dividing by zero
There is an important exception to the usual treatment of error propagation. That is when a power series expansion of the function F(x) to be calculated breaks down within the uncertainty of the variable x. The usual treatment assumes that the function is smooth and well-behaved over a sufficiently large domain of x near the measured value x_0. Then one expands in a power series about x_0 and takes only the first linear term. However, if F is not well-behaved (for example if F(x) goes to infinity at some point near x_0) the correct uncertainty on F(x) may be completely different from the usual formula Delta F = F'(x_0) Delta x.

The simplest example is the uncertainty in 1/x. If we measure x=100 with an uncertainty of 1%, then 1/x has an uncertainty of 1% also. If we measure x=100 with an uncertainty of 100%, then 1/x has an *infinitely* large uncertainty, because x may take the value 0!

Is this effect treated in any known texts? --Tdent 15:09, 24 October 2007 (UTC)

caveats added, but more details needed
I put in a couple of references to problems with ratios alluded to above, but what is required is a better quantification for when these issues are important. The Geary-Hinkel transformation has limits of validity and they can be used to show when that formula (which reduces to the standard case in favorable circumstances) is useful. Hopefully someone can add to that? 74.64.100.223 (talk) 16:07, 29 November 2007 (UTC)

Incorrect Taylor Series Expansion
I think the Taylor series expansion in the section in Non-linear combinations is wrong

 * $$f_k \approx f^0_k+ \sum_i^n \frac{\partial f_k}{\partial {x_i}} x_i +\sum_i^n\sum_{j (j \ne i)}^n \frac{\partial f_k}{\partial {x_i}}\frac{\partial f_k}{\partial {x_j}}x_ix_j$$

should read

 * $$f_k \approx f^0_k+ \sum_i^n \frac{\partial f_k}{\partial {x_i}} x_i +\sum_i^n\sum_{j}^n \frac{\partial^2 f_k}{\partial {x_i}\partial {x_j}}x_ix_j$$

This is a major difference. Using only the first-order approximation,

 * $$f_k \approx f^0_k+ \sum_i^n \frac{\partial f_k}{\partial {x_i}} x_i$$

which is what I think the author of that section is after. This can be used to estimate error under a linear approximation (a hyperplane tangent to the non-linear function) using the functions in the previous section. Perhaps I'm missing something here, but if not, the section and examples are seriously flawed. Schomerus (talk) 22:38, 22 February 2008 (UTC)
 * Technically you are right. However the missing term $$+\sum_i^n \left(\frac{\partial f_k}{\partial {x_i}}\right)^2 x_i^2$$ does not contribute to the error propagation formula. In that sense the approximation is acceptable. Rest assured that the error propagation formulas are correct and can be found in numerous text-books. Petergans (talk) 09:20, 23 February 2008 (UTC)

 * My concern over the Taylor series expansion is that the correct coefficient for the second order term should be given by the second derivative of $$f$$ not the product of first derivatives. It is definitely not the case in general that

 * $$\frac{\partial f_k}{\partial {x_i}}\frac{\partial f_k}{\partial {x_j}} = \frac{\partial^2 f_k}{\partial {x_i}\partial {x_j}}$$

 * in any sense, approximate or otherwise. For example, in the linear case

 * $$f = x_1 + x_2$$

 * expanding around $$(0,0)'$$ according to the the first formula

 * $$f \approx x_1 + x_2 +x_1x_2$$

 * which makes little sense given that a first order approximation to a linear equation should be exact, not an approximation at all, and in any case shouldn't contain any second order terms. If I've misunderstood something here could you provide a reference so I can check the derivation for myself?Schomerus (talk) 17:50, 23 February 2008 (UTC)

Now I see it. I think that the mistake is that it's not a Taylor series expansion, but a total derivative sort of thing. total derivative appears to be similar to the expression I'm looking for, though not exactly. I'm sure that the expression
 * $$\sigma^2_f=\left(\frac{\partial f}{\partial a}\right)^2\sigma^2_a+\left(\frac{\partial f}{\partial b}\right)^2\sigma^2_b+2\frac{\partial f}{\partial a}\frac{\partial f}{\partial b}COV_{ab}$$

is correct, but clearly it is not derived in the way that I thought. I don't have any references to hand. Can you help me out here? Petergans (talk) 22:38, 23 February 2008 (UTC)
 * I finally figured it out - the second term is not needed at all. The function is linearized by Taylor series expansion to include first derivatives only so thay the error propagation formula for linear combinations can be applied. Thanks for spotting the error. Petergans (talk) 08:05, 24 February 2008 (UTC)

That's right. The expression is a direct consequence of applying the formula for linear combinations to the linear approximation (hyperplane tangent at $$ f(\bar{x})$$ ) obtained by first order Taylor series expansion. Thanks for making the corrections in the article. You could add that the approximation expands around $$\bar{x}$$ making $$f_0= f(\bar{x})$$, which is another potential source of inaccuracy when the linear approximation fails since for non-linear functions in general $$\overline{f(x)} \ne f(\bar{x})$$Schomerus (talk) 17:34, 24 February 2008 (UTC)

The equation that is currently in place with absolute values being taken can not generate the example equation 4 ( A/B ) -> -cov(ab) the absolute value bars would make A*B error propagation the same as A/B. —Preceding unsigned comment added by 129.97.120.140 (talk) 18:31, 28 January 2011 (UTC)

Useful Reference?
Been trying to understand this for a while (and how the formula are derived) and not that easy to understand from this page. Finally found a useful reference which then makes the rest of this page make sense so thougt I'd share. The reference is

Taylor, J. R., 1997: An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements. 2nd ed. University Science Books, 327 pp.

and section 9.2 helps make things clear.

Added a comment here as I don't have time to edit main page. —Preceding unsigned comment added by 139.166.242.47 (talk) 11:44, 29 February 2008 (UTC)

Better books that covers these issues is "Propagation of Errors" by Mike Peralta. This entry April 2013. — Preceding unsigned comment added by 144.15.255.227 (talk) 17:45, 29 April 2013 (UTC)

Undefined variable in caveats section
In the caveats section, the formula
 * $$y=mz+c: \sigma^2_y=z^2\sigma^2_m+\sigma^2_c+2z\rho \sigma_m\sigma_c$$

is written, but the variable $$\rho$$ is not defined. Please fill in its definition. Zylorian (talk) —Preceding undated comment was added at 17:04, 6 October 2008 (UTC).

Additionally, this formula is wrong. It's not the correct formula for uncertainty in a linear regression; that uncertainty can't be arrived at through error propagation. I'm not sure that the idea of error propagation could ever be correctly applied to least squares parameters. Perhaps that paragraph should be removed from the caveats section. DrPronghorn (talk) 04:04, 9 February 2012 (UTC)

OK, I went ahead and removed that section. It's not clear to me that error propagation is the correct place to discuss the errors in fitted parameters. In the case of fitted models, the errors are governed by the fitting process and original fit dataset, not by error propagation. DrPronghorn (talk) 04:19, 22 February 2012 (UTC)

Better book that covers these issues is "Propagation of Errors" by Mike Peralta. — Preceding unsigned comment added by 144.15.255.227 (talk) 17:43, 29 April 2013 (UTC)

Errors in section 1 and confusions in section "Partial derivatives"
The third equation for $$M^f_{ij}$$ is wrong or inconsistent with itself. The term $$A_{ik}$$ should have its subscripts reversed, right?

Likewise, the same error in the next equation down.

This is my first post on wikipedia, I leave this to the author to correct it if it needs to be done.

In agreement with the comments above, I found the section "Partial derivatives" a bit contradictory or at least lacking explanation. It is contradictory because in the third paragraph $$\Delta x$$ is said to be commonly given to be the standard deviation $$\sigma$$, which is the square root of the variance $$\sigma^2$$, yet in the section "Partial derivatives" the square root of the variance is not equal to the absolute error in the table. It was precisely this issue for which I had consulted wikipedia. However there is enough information here to have helped me solve my problem.

Dylan.jayatilaka (talk) 05:23, 7 January 2009 (UTC)

Created new article on this subject
...rather than try to edit this one. Take a look: Experimental uncertainty analysis. Right or wrong, I believe it to be far more "accessible" than this one is. How to reconcile my new article with this one and with Uncertainty analysis remains to be seen. Please give me a week or so to produce the table at the bottom of "my" article- it will go beyond the table in this article, and I think it will be a very useful thing for many readers. Also I have a mention and a reference related to the 1/x thing I see above here- the solution of course is to use a higher-order expansion, and the necessary eqns are in that book. Regards... Rb88guy (talk) 18:30, 12 March 2009 (UTC)


text:
Silesian Voivodeship (1920–1939)

The Silesian Voivodeship (województwo śląskie; German: Woiwodschaft Schlesien) was an autonomous province (voivodeship) of the Second Polish Republic. The bulk of its territory had formerly belonged to the German/Prussian Province of Silesia and became part of the newly reborn Poland as a result of the 1921 Upper Silesia plebiscite, the Geneva Conventions, three Upper Silesian Uprisings, and the eventual partition of Upper Silesia between Poland, Germany and Czechoslovakia. The remainder had been the easternmost portion of Austrian Silesia (see Cieszyn Silesia) which was partitioned between Poland and Czechoslovakia following the collapse of Austria-Hungary, the Polish–Czechoslovak War and the Spa Conference of 1920. The capital of the voivodeship was Katowice.

The voivodeship was dissolved on 8 October 1939 following the German invasion of Poland, and its territory was incorporated into the German Province of Silesia. After the defeat of Nazi Germany in World War II, its territory was incorporated into a new, larger Silesian Voivodeship which existed until 1950.

General description
The Silesian Voivodeship was one of the richest and best developed provinces of inter-war Poland. It owed its wealth to rich deposits of coal, which resulted in the construction of numerous coal mines and steelworks. For this reason, this Voivodeship was crucial to Polish armaments production. However, its location on the border with Germany made it vulnerable. In the mid-1930s, the Polish government decided to move some sectors of heavy industry to the nation's heartland, creating the Central Industrial Region. Due to efficient agricultural practices, the Silesian Voivodeship also was a major producer of food, in spite of its small size.

According to the 1931 Polish census, 92.3% of the population stated Polish as their mother tongue. Germans made up 7% and Jews only 1.5%. Poles lived mainly in the villages (95.6% of the population there), while Germans and Jews preferred cities (12.9% of Polish Upper Silesian cities' population was German, especially Bielsko and Katowice).

Population density was the highest in the country at 299 persons per 1 km2. On 1 January 1937, forested areas made up 27.9% of the province. Rail density was the highest in the country at 18.5 km per 100 km2. In 1931, the illiteracy rate was the lowest in the country at 1.5% of the population.

History
After the First World War a dispute arose about the future of Upper Silesia. This part of the Silesia region was the least affected by centuries of Germanisation. The population was predominantly Slavic, especially in rural areas. Many of them considered themselves Poles (majority), and some Czechs (minority). The rest did not feel any strong connections to either of those nations; according to Wojciech Korfanty's estimations, this last group represented up to a quarter of the total whole population of the region.

The Treaty of Versailles resolved that a plebiscite be conducted so that the local population could decide whether Upper Silesia should be assigned to Poland or to Germany. Before the plebiscite took place, two Silesian Uprisings supporting the Polish option had broken out. A third uprising occurred after the plebiscite.

Based on the results of the plebiscite, which was held on 20 March 1921, Upper Silesia was divided between Poland and Germany. The Polish part was incorporated as the Silesian Voivodeship. After the referendum of 1921, the German-Polish Accord on East Silesia (Geneva Convention) was concluded on 15 May 1922 and dealt with the constitutional and legal future of Upper Silesia, as part of it had become Polish territory.

The voivodeship was one of the most economically-developed parts of Poland. It had been granted autonomous status by an Act of the Polish Sejm dated 15 July 1920. That status was secure until the May Coup in 1926, which started various attempts to limit it in favour of a strong and centralised state.

After the German invasion of Poland, the voivodeship was dissolved on 8 October 1939, and its territory was incorporated into the German Province of Upper Silesia. The territory returned to Polish possession at the end of the war, and the 1920 act giving autonomous powers to the Silesian Voivodeship was formally repealed by a law of 6 May 1945. An enlarged Silesian Voivodeship (unofficially called Silesia-Dąbrowa Voivodeship, województwo śląsko-dąbrowskie) continued in existence until 1950, when it was divided into Katowice Voivodeship and Opole Voivodeship. (For details, see Administrative division of the People's Republic of Poland.)

Politics
The voivodeship possessed wide autonomy in domestic matters excluding foreign and military policy. It had its own Silesian Parliament with 48 MPs (24 since 1935) elected in democratic elections. Legislation, however, had to be consistent with the Polish constitution. The voivodeship also had its own national treasury - the Silesian Treasury (Skarb Śląski). Only around 10% of taxes were transferred to Polish national treasury. The head of the administration was headed by a voivode appointed by the president of Poland to act as a representative of the central government.

Counties (powiaty)
In mid-1939, in the wake of invasion, the population of the voivodeship was 1,533,500 (together with Trans-Olza, annexed in October 1938. Its total area was 5,122 km2. The voivodeship was divided into the following counties; with largest cities based on the 1931 population census).

Voivodes

 * Józef Rymer 16 June 1922 – 5 December 1922
 * Zygmunt Żurawski 15 December 1922 – 1 February 1923 (acting)
 * Antoni Schultis 1 February 1923 – 3 March 1924
 * Tadeusz Koncki 15 October 1923 – 2 May 1924 (acting until 3 March 1924)
 * Mieczysław Bilski 6 May 1924 – 3 September 1926
 * Michał Grażyński 6 September 1926 – 5 September 1939

title: Silesian Voivodeship (1920–1939)


text:
Talk:Wirbelwind

Number produced
I've read articles that state 87 Wirbelwinds were produced and others that state 105. To make things worse Achtung Panzer! states "Overall from May to November of 1944, only 87(105) Wirbelwinds were made", which doesn't really help. Anyone have an explanation? Oberiko 16:38, 12 May 2004 (UTC)

 * Acording to this site (German text), there was some discrepancy between Ostbau Werke's recorded production numbers and the numbers actually being accepted by the Wehrmacht - I haven't found been able to find out if production numbers were higehr or lower than numbers in Wehrmacht service records, but I suppose that's where the two different numbers on Achtung Panzer come from. Shall we follow Achtung Panzer and just put both numbers in the article?

 * And as a side note, do we really need a separate article for the Ostwind? I think it would contain pretty much the same text as the Wirbelwind article...redirect Ostwind to Wirbelwind and add a little note? Ferkelparade 18:21, 12 May 2004 (UTC)

 * I wouldn't mind giving each article it's own page (it's not like it'll save space to keep them on one) and then provide a two-way link. It'll also help with external links, as we won't have to specify which vehicle it's referring to.  I'm not adamant about that though.

 * As for the numbers, I agree we should follow their lead and put perhaps (87-105) and then a footnote to explain it. Oberiko 18:59, 12 May 2004 (UTC)

 * Alright, I've added a short disclaimer on the numbers and created a new article for the Ostwind (pretty much just a copy&paste of the WIrbelwind article, with some minor tweaks) Ferkelparade 21:07, 12 May 2004 (UTC)

It is entirely likely that 105 were produced and that the German Army accepted only 87 of them. Someone may want to put that into the article. 72.227.230.250 (talk) 17:43, 30 May 2008 (UTC)

 * Yes, that is a possible explanation, but it is only a guess. The language as it is now is fine. The fact is we don't know, and may never know. Regards, DMorpheus (talk) 20:00, 30 May 2008 (UTC)

Flakvierling
The wiki article on the 20mm flak 30 and 38 does a good job explaining the notion that the Flak 38 was a gun, mounted in various ways including the 4-gun flakvierling mount. "Vier" being German for "four", I would think it is pretty obvious. The Flakvierling is NOT a four-barrelled gun; each flak 38 had its own full mechanisms and each gun fired on its own. So it is analogous to a US quad fifty caliber MG mount, but not to, say, a true multibarrel gun such as a minigun. The current edit makes sense. Regards, DMorpheus (talk) 16:12, 19 February 2008 (UTC)
 * Exactly, it is similar to the Maxson Mount, which is also not a "single gun with four barrels." Graff977 (talk) 21:15, 20 February 2008 (UTC)

"Thereafter . . . "
"Thereafter, the 2 cm shells proved less effective against aircraft . . . " is messy, IMO, on a couple of counts. "Thereafter", grammatically, presupposes a 'there' for the 'after' to be after, but no date is given or even inferred. And "less effective" grammatically requires something else for it to be less effective then. Now I know that the writer almost certainly meant than the 37mm gun (in the Ostwind) but this isn't stated, and as the Ostwind hadn't been developed at this point the statement wouldn't make sense even if it were so stated.

So I am editing this to "However, the 2cm shells proved ineffective against aircraft . . . ".

Actually I am not too happy with this, as what I really mean is something like 'insufficiently effective". So, cancel the above, I am going to edit the start of the sentence to "However, in combat the 2cm shells were felt to be insufficiently effective against aircraft and so. . . "

I know - a very long justification of a simple edit. Gog the Mild (talk) 17:12, 25 July 2015 (UTC)

title: Talk:Wirbelwind


text: User talk:199.74.97.78

title: User talk:199.74.97.78


text:
Porter Square

Porter Square is a neighborhood in Cambridge and Somerville, Massachusetts, located around the intersection of Massachusetts Avenue and Somerville Avenue, between Harvard and Davis Squares. The Porter Square station serves both the MBTA Red Line and the Commuter Rail Fitchburg Line. A major part of the Lesley University campus is located within the Porter Square area.

In 2004–06 the principal intersection, including the area adjacent to the shopping center, underwent extensive construction both to improve access for vehicles, pedestrians, bicyclists, and mass transit users, and to improve drainage and storm water conditions. The artist Toshihiro Katayama of Harvard University, in conjunction with the landscape architect Cynthia Smith, designed a new visual look for the new circulation design, including contrasting light and dark concrete paving, stone walls and boulders.

History
Previously called Union Square, Porter Square was renamed in 1899 for the now-vanished Porter's Hotel, operated by Zachariah B. Porter, who also left his name to the hotel's specialty, the cut of steak known as porterhouse. The hotel was demolished in 1909. The square, formerly flanked by cattle yards that used the Porter rail head to transport their beef throughout the US, was an important center for commerce and light industry as early as the late 18th century. A tunnel for moving cattle to and from the railroad without interfering with street traffic, known as the Walden Street Cattle Pass, was built in 1857. The tunnel survives under the nearby Walden Street Bridge, and in 2007–08 was preserved and restored. The "most dramatic loss" of early 19th century landscape in the square was the leveling of the old Rand Estate in 1952 to make way for the Porter Square Shopping Center.

In 1984 the Red Line was extended from Harvard through Porter and Davis Square to its present terminus at Alewife, a project that also left Porter with its most visible landmark, Susumu Shingu's 46-foot painted steel and aluminum kinetic sculpture entitled Gift of the Wind. Porter Square railroad history is covered in greater detail in the Porter Square station article.

Lesley University
Lesley University continues to expand in the Porter Square neighborhood, with the relocation of its College of Art and Design to the North Prospect Church and a new building built on the church's former site at the corner of Massachusetts Avenue and Roseland Street.

In addition to University Hall at 1815 Massachusetts Avenue and the Lunder Arts Center at 1801 Massachusetts Avenue, Lesley also has administrative offices at 815 Somerville Avenue and parking areas across Massachusetts Avenue from University Hall.

Porter Square Shopping Center
The Porter Square Shopping Center consists of two buildings and a parking lot. As of July 2017, it is home to the following stores & eateries:

Porter Square Galleria
Adjacent to the Porter Square Shopping Center is a small mall called the Porter Square Galleria. In recent years it has lost several large tenants. A Target is being built in the space formerly occupied by Walgreens. As of September 2018, it is home to:

 * Anna's Taqueria
 * Sprint
 * Parelli Optical

The Shops at Porter and local "Japantown"
A prominent feature of the Porter Square skyline is the tower on the Art Deco-style building located at 1815 Massachusetts Avenue. The building, now known as University Hall, was originally a Sears, Roebuck store from 1928 to 1985. In 1991, Lesley University began leasing classroom space there, and in 1994 the university bought the building, which now houses its Graduate School of Education, bookstore, administrative offices, art and dance studios, and classrooms.

Porter Square and The Shops at Porter have a recent history of being a center for Boston's Japanese community. In May 2009, Lesley University ousted Kotobukiya, a Japanese grocery store, from The Shops at Porter, after 20 years in business there. Lesley wanted the space to expand its bookstore.

As of July 2017, The Shops at Porter is home to many Japanese eateries and businesses. Izakaya Ittoku and Shaking Crab are full-size restaurants, and the other eateries are located in a food court-like area with limited seating.

Other restaurants
Other restaurants in the area (as of July 2017) include:

title: Porter Square


text:
Talk:Pre calculus

I think this is Americo-centric. It's not a mathematical discipline I recognize. It's a pedagogic stage; and this article should be formulated in mathematical education terms, therefore.

Charles Matthews 16:42, 12 May 2004 (UTC)

title: Talk:Pre calculus


text:
Tangerinn

The Tangerinn is a bar in Tangier, Morocco, a place of nostalgia for fans of beat generation or beatnik poets. The bar is adjoined to the Hotel El Muniria where author William S. Burroughs wrote his famous novel Naked Lunch in room #9. Pictures of beat generation poets such as Allen Ginsberg and Jack Kerouac hang on the walls.

title: Tangerinn


text: User talk:65.125.82.250

title: User talk:65.125.82.250


text:
Binary clock

A binary clock is a clock that displays the time of day in a binary format. Originally, such clocks showed each decimal digit of sexagesimal time as a binary value, but presently binary clocks also exist which display hours, minutes, and seconds as binary numbers. Most binary clocks are digital, although analog varieties exist. True binary clocks also exist, which indicate the time by successively halving the day, instead of using hours, minutes, or seconds. Similar clocks, based on Gray coded binary, also exist.

Binary-coded decimal clocks

Most common binary clocks use six columns of LEDs to represent zeros and ones. Each column represents a single decimal digit, a format known as binary-coded decimal (BCD). The bottom row in each column represents 1 (or 20), with each row above representing higher powers of two, up to 23 (or 8).

To read each individual digit in the time, the user adds the values that each illuminated LED represents, then reads these from left to right. The first two columns represent the hour, the next two represent the minute and the last two represent the second. Since zero digits are not illuminated, the positions of each digit must be memorized if the clock is to be usable in the dark.

Binary-coded sexagesimal clocks

Binary clocks that display time in binary-coded sexagesimal also exist. Instead of representing each digit of traditional sexagesimal time with one binary number, each component of traditional sexagesimal time is represented with one binary number, that is, using up to 6 bits instead of only 4.

For 24-hour binary-coded sexagesimal clocks, there are 11 or 17 LED lights to show the time. There are 5 LEDs to show the hours, there are 6 LEDs to show the minutes, and there are 6 LEDs to show the seconds (which aren't used in clocks with 11 LED lights).

A format exists also where hours, minutes and seconds are shown on three lines instead of columns as binary numbers.

Binary time
Less commonly, the day could be divided in binary fractions, such as ½ day, ¼ day, etc. The clock would show the time in 16 bits, where the smallest unit would be exactly $1/65536$ day, or $675/512$ (about 1.318) seconds. An analog format also exists of this type. However, it is much easier to write and express this in hexadecimal, which would be hexadecimal time.

title: Binary clock