text:
Talk:Languages of East Timor

POV?
"Even many people who were supportive of East Timor take this view [Portuguese being a colonial language and shouldn't be official], again mistakenly drawing parallels with Dutch in Indonesia." [emphasis added] -- isn't stating that this view is "a mistake" POV? --Menchi 20:58, 13 Aug 2004 (UTC)

This whole paragraph does not clarify why Portuguese should be the official language of East Timor. Critising opponents of the decision by comparing them to those who doubted East Timor's ability to self-govern does not address that issue.

 * That was not the intention of the paragraph, although East Timor's circumstances are very different from Indonesia's. Nor was it the intention to compare all opponents of the decision to those who supported the Indonesian occupation. See revised text. -- Quiensabe 02:35, 30 Dec 2004 (UTC)

Wikipedia in Tetum
We are looking for speakers of Tetum (ideally, native speakers) that may cooperate in the launching of a Tetum version of the Wikipedia. Visit the test page of the Tetum Wikipedia and support this project (click in Tetum). Regards --82.102.25.163 01:23, 23 January 2006 (UTC) Manuel de Sousa
 * The above links are now deprecated, as the Tetum Wikipedia is available. A-giau 20:28, 26 May 2006 (UTC)

Language map
There's a really nice language map on this page. The author says that works can be used if cited (on the table of contents page) but I don't understand Wikipedia's copyright policy well enough to know if it can be placed here. The page also has good information that would be useful on this page (also relating to the Portuguese debate above).Rigadoun 20:44, 3 March 2006 (UTC)

Little Dutch Influence on Indonesian Language and Culture - What?
Please stop making statements just because it might suit your political belief. I say it must be political (even though I can't see how) because there's no other reason for making such an unfounded statement.

"However, whereas the Dutch culture and language had little influence on those of Indonesia, the East Timorese and Portuguese cultures became intertwined, particularly through intermarriage, as did the languages."

Bahasa Indonesia has over 10,000 Dutch loan words, and all Indonesian languages excluding those used by the Chinese minorities have adopted the Latin script.
 * But whereas the Indonesians are mainly Muslim, the East Timorese are now majority Christians (though the growth must be attributed to the local, nativized Church rather than direct Portuguese influence). A-giau 20:33, 26 May 2006 (UTC)
 * East Timor was not majority Catholic when the Portugese pulled out. It became majority Christian under the iron-fist of Indonesia's Pancasila policy. This cannot be credited as a Portugese influence, and as you have noted the church is native influenced. The point is that the article has false information especially regarding the influence of the Dutch on Indonesia which was widespread and long-lasting. —Preceding unsigned comment added by 70.134.210.107 (talk • contribs)

Languages illustrated by first photo
Does anyone know which languages are illustrated in the first photo's speech bubbles? Obviously there's Portuguese and apparently Tetum, as well. Bobonaro, on the other hand, does not appear to be a language, unless it refers to a local dialect. A-giau 20:39, 26 May 2006 (UTC)

About the "Unreferenced" Tag
I think this is unjustified. For sources, see the External Links. FilipeS 09:55, 7 October 2006 (UTC)
 * Sorry, it's not unjustified. The article makes many claims that are not backed up. POV tags could be easily justified too but that is another issue. Wikipedia needs to be made credible. People shouldn't have to look through all the external links hoping to find something to back it up. What you are essentially saying is, "trust me" it is all there. I am not saying it needs to be done now, but on the other hand, putting one main tag in there is better than putting a dozen or  tags through the article. Unfortunately, good articles need a lot of work. --Merbabu 13:36, 7 October 2006 (UTC)

If there are indeed "many" claims that are not backed up in the article, then I'm sure you'll be able to name a few... FilipeS 15:46, 7 October 2006 (UTC)
 * As i said above, i put the main tag at the top to avoid putting or  tags all through it. If you object to 1 main tag at the top, would not a number of other tags throughout the article be worse? Actually, it is not a question of "many", rather not 1 tag has a source. Sorry if I am showing something you are already familiar with this, but have a look here: . Thanks. --Merbabu 16:17, 7 October 2006 (UTC)

It seems you have nothing concrete to object to. FilipeS 16:26, 7 October 2006 (UTC)
 * Oh - it's the same person from East Timor who like to blunt revert 10 changes at once. Perhaps that explains you curt answers. Since you are not actually answer or even refer to my specific comments, would you object to a few tags? --Merbabu 17:13, 7 October 2006 (UTC)

Your "specific comments"? You've made none here. But go right ahead and replace the page tag with individual ones, since it seems to be the only way to learn what it is you're objecting to, specifically. FilipeS 18:08, 7 October 2006 (UTC)

 * Please read again WP:CITE. External links are not source of references. Editors should list references in the References section with the style conform with what is described in WP:CITE. Cheers. — Indon ( reply ) — 16:31, 8 October 2006 (UTC)

You're quite right. The article already had that format before I started to edit it, but I've changed that now. FilipeS 17:41, 8 October 2006 (UTC)
 * Good job putting some refs in, Filipe. It's not a fun job! OK, i haven't actually checked them closely yet, but when i get a chance, i hope to help out with formatting and maybe add a few more. thanks --Merbabu 22:34, 8 October 2006 (UTC)

Thanks for adding the footnotes. :-) FilipeS 19:22, 18 October 2006 (UTC)
 * I attempted translations of the (Portuguese?) institution names into English. Please confirm they are correct. Thanks.--Merbabu 23:03, 18 October 2006 (UTC)

Which expressions did you translate? FilipeS 11:39, 19 October 2006 (UTC)

POV - 2015
Most of the article reads like an anti-Portuguese rant. It's poorly connected and the only common theme seems to be cherry-picking anti-Portuguese aspects. Badly needs more balanced writing.Jeppiz (talk) 18:01, 3 February 2015 (UTC)
 * It's been 6 years and we still need this tag? Kanatonian (talk) 17:02, 17 July 2021 (UTC)

External links modified
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"East Timorese English" listed at Redirects for discussion
An editor has identified a potential problem with the redirect East Timorese English and has thus listed it for discussion. This discussion will occur at Redirects for discussion/Log/2022 April 19 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. Ten Pound Hammer • (What did I screw up now?) 05:28, 19 April 2022 (UTC)

Timor Leste
en-TL: English language (Timor Leste) pt-TL: Portuguese language (Timor Leste) tet: Tetun language Yogapamungkas866 (talk) 16:08, 17 May 2024 (UTC)

 * for example:
 * pt-PT: dívida
 * pt-BR: dívida
 * pt-TL: kutang Yogapamungkas866 (talk) 01:38, 18 May 2024 (UTC)

title: Talk:Languages of East Timor


text:
Vedavalli

Vidushi R. Vedavalli (born 9 November 1935) is a Carnatic vocalist. Musicologist M B Vedavalli (1935-2022) was a different person.

Early life
R. Vedavalli was born in Mannargudi, Tamil Nadu, India to Ramaswami Iyengar and Padmasani Ammal.

Career
R. Vedavalli's talent for music was identified early on by Maurai Srirangam Iyengar, who brought the five-year-old a harmonium, and got her started on vocal lessons. The family moved to Madras in a few years time, and Vedavalli came under the tutelage of Mudicondan Venkatarama Iyer.

She received a Central Government scholarship to specialize in Padams and Javalis with T.Muktha, and in Pallavis with Venkataramana Iyer. Though she has performed since childhood, it was Ariyakudi Ramanuja Iyengar who advised her to turn into a professional musician, when he heard her sing as an 18-year-old. She has travelled throughout India and abroad in North America, South-East Asia, the Far East and the Persian Gulf region, giving concerts and lecture demonstrations.

Vedavalli served in the Teacher's College of Music of the Madras Music Academy for several years before becoming Professor of Vocal Music in the Government College of Music Adyar. She has thus shared her deep knowledge and extensive repertoire with numerous students at these institutions apart from training some privately.

She is also trained in playing the veena, and has a good command over Tamil, Sanskrit, Kannada, Telugu, which helps her sing with greater understanding or artha bhava (meaning and emotion). She lived in Chennai with her husband D. R. Santhanam and mother Padmasani Ammal, at the turn of the century. Later she and her husband moved to Pune to be with their daughter, and D R Santhanam died in Pune in July 2021.

Awards and recognitions
From a very young age, Vedavalli won several awards in prestigious competitions including All India Radio's first prize for Classical Music and Light Classical Music, awarded by the President of India. In 2000, she received the Sangeetha Kalanidhi, which is considered the highest award in Carnatic music. She is one of the few women to have received this honor. She also received the Sangeetha Kalasikhamani award given by the Fine Arts Society, Chennai in 1995.

Disciples
Among her disciples today are accomplished performers, researchers, teachers and writers. Sumitra Vasudev and her daughter Sushruti Santhanam are her disciples. Sushruti is based in Pune and teaches music there.

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

title: Vedavalli


text:
Cetorhinidae

Cetorhinidae is a family of filter feeding mackerel sharks, whose members are commonly known as basking sharks. It includes the extant basking shark, Cetorhinus, as well as two extinct genera, Caucasochasma and Keasius.

title: Cetorhinidae


text:
Dimensions (animation)

Dimensions is a French project that makes educational movies about mathematics, focusing on spatial geometry. It uses POV-Ray to render some of the animations, and the films are released under a Creative Commons licence.

The film is separated in nine chapters, which follow this plot:

 * Chapter 1: Dimension two explains Earth's coordinate system, and introduces the stereographic projection.
 * Chapter 2: Dimension three discusses how two-dimensional beings would imagine three-dimensional objects.
 * Chapters 3 and 4: The fourth dimension talks about four-dimensional polytopes (polychora), projecting the regular ones stereographically on the three-dimensional space.
 * Chapters 5 and 6: Complex numbers are about the square root of negative numbers, transformations, and fractals.
 * Chapters 7 and 8: Fibration show what a fibration is. Complex numbers are used again, and there are circles and tori rotating and being transformed.
 * Chapter 9: Proof emphasizes the importance of proofs in mathematics, and proves the circle-conservationess of the stereographic projection as an example.

They are available for download in several languages.

title: Dimensions (animation)


text:
Barbara Cox Anthony

Barbara Blair Cox Anthony (December 8, 1922 – May 28, 2007) was the youngest daughter of James M. Cox, a Democratic governor of Ohio, newspaper publisher and broadcaster. With her sister Anne Cox Chambers and her brother James M. Cox, Jr., she inherited, via a trust, ownership and control of her father's company, now called Cox Enterprises. Upon her brother's death in 1974, the sisters received his share of the company equally.

Her net worth was estimated at $12 billion, based principally on her equity interest in Cox Enterprises, which made her one of the richest women in the United States and the richest resident of Hawaii.

She served as a Director of Cox Enterprises, one of the largest diversified media companies in the United States. It owns one of the nation's largest cable television businesses, which provides internet and telephone, publishes newspapers including the Atlanta Journal-Constitution and The Palm Beach Post, owns and operates broadcast television and radio stations and owns Manheim, an automobile auction firm. It also owns stakes in a variety of internet businesses, including AutoTrader.com, the largest retail automotive shopping site in the world. Her son James C. Kennedy is chairman of Cox Enterprises.

Well known in Hawaii for her support of philanthropic causes, Anthony helped found La Pietra: Hawaii School for Girls and served as its chair from 1978 until her death in Honolulu in 2007, aged 85, following an extended illness. She also made contributions to the Veterinary School of Colorado State University, endowing two chairs in equine health.

Personal life
Anthony was married four times. She did not have children with her first husband, Bradford Ripley, a naval aviator who died in World War II. She had two children with her second husband, airline executive Stanley C. Kennedy, Jr.: James C. Kennedy, chairman of Cox Enterprises, and Blair Parry-Okeden, Australia's richest woman. They later divorced. Her third husband was James W. Glover, a successful contractor; he died a few years after their marriage. Her fourth husband was Garner Anthony, Jr., who preceded his stepson James Kennedy as chairman of Cox Enterprises, serving in that position from 1974 to 1987. As Mrs. Bradford Williams Ripley II, she was the ship's sponsor for the aircraft carrier USS Midway (CVB 41) and christened the ship at its launch at Newport News Shipbuilding, Virginia, on March 20, 1945.

title: Barbara Cox Anthony


text:
Permalloy

Permalloy is a nickel–iron magnetic alloy, with about 80% nickel and 20% iron content. Invented in 1914 by physicist Gustav Elmen at Bell Telephone Laboratories, it is notable for its very high magnetic permeability, which makes it useful as a magnetic core material in electrical and electronic equipment, and also in magnetic shielding to block magnetic fields. Commercial permalloy alloys typically have relative permeability of around 100,000, compared to several thousand for ordinary steel.

In addition to high permeability, its other magnetic properties are low coercivity, near zero magnetostriction, and significant anisotropic magnetoresistance. The low magnetostriction is critical for industrial applications, allowing it to be used in thin films where variable stresses would otherwise cause a ruinously large variation in magnetic properties. Permalloy's electrical resistivity can vary as much as 5% depending on the strength and the direction of an applied magnetic field. Permalloys typically have the face-centered cubic crystal structure with a lattice constant of approximately 0.355 nm in the vicinity of a nickel concentration of 80%. A disadvantage of permalloy is that it is not very ductile or workable, so applications requiring elaborate shapes, such as magnetic shields, are made of other high permeability alloys such as mu metal. Permalloy is used in transformer laminations and magnetic recording heads.

Development
Permalloy was initially developed in the early 20th century for inductive compensation of telegraph cables. When the first transatlantic submarine telegraph cables were laid in the 1860s, it was found that the long conductors caused distortion which reduced the maximum signalling speed to only 10–12 words per minute. The right conditions for transmitting signals through cables without distortion were first worked out mathematically in 1885 by Oliver Heaviside. It was proposed by Carl Emil Krarup in 1902 in Denmark that the cable could be compensated by wrapping it with iron wire, increasing the inductance and making it a loaded line to reduce distortion. However, iron did not have high enough permeability to compensate a transatlantic-length cable. After a prolonged search, permalloy was discovered in 1914 by Gustav Elmen of Bell Laboratories, who found it had higher permeability than silicon steel. Later, in 1923, he found its permeability could be greatly enhanced by heat treatment. A wrapping of permalloy tape could reportedly increase the signalling speed of a telegraph cable fourfold.

This method of cable compensation declined in the 1930s, but by World War II many other uses for Permalloy were found in the electronics industry.

Other compositions
Other compositions of permalloy are available, designated by a numerical prefix denoting the weight percentage of nickel in the alloy, for example "45 permalloy" means an alloy containing 45% nickel, and 55% iron by weight. "Molybdenum permalloy" is an alloy of 81% nickel, 17% iron and 2% molybdenum. The latter was invented at Bell Labs in 1940. At the time, when used in long distance copper telegraph lines, it allowed a tenfold increase in maximum line working speed. Supermalloy, at 79% Ni, 16% Fe, and 5% Mo, is also well known for its high performance as a "soft" magnetic material, characterized by high permeability and low coercivity.

Applications
Due to its high magnetic permeability and low coercivity, Permalloy is often used in applications that require efficient magnetic field generation and sensing. This nickel-iron magnetic alloy, typically composed of about 80% nickel and 20% iron, exhibits low energy loss, which is beneficial for improving the performance of magnetic sensors, transformers, and inductors. Permalloy is also used in the production of magnetic shielding materials, which help protect electronic equipment from external magnetic interference.

title: Permalloy


text:
Flodoard

Flodoard of Reims (Flodoardus; 893/4 – 28 March 966) was a Frankish chronicler and priest of the cathedral church of Reims in the West Frankish kingdom during the decades following the dissolution of the Carolingian Empire. His historical writings are major sources for the history of Western Europe, especially France, in the early and mid-tenth century.

Biography
The sources for Flodoard's life are almost exclusively his own writings. Local tradition holds that he was born at Épernay. He was educated at the cathedral school of Reims which had been established by Archbishop Fulk.

As a young canon of Reims, he gained prominent roles in the administrations of the archbishops Heriveus (900–22) and Seulf (922–25), particularly in the cathedral scriptorium. Following Seulf's death in 925, the magnate Herbert II, Count of Vermandois installed his four-year-old son, Hugh, as the new archbishop. Flodoard refused to participate in the boy's election, and was stripped of his position and benefices. In 931, Reims was captured from Count Herbert by King Raoul and Duke Hugh the Great, who ejected Hugh and oversaw the election of a new archbishop, Artold.

Flodoard appears to have regained his charges under Artold's leadership. In 936/7, he visited Rome, perhaps on pilgrimage, where he met Pope Leo VII. Herbert recaptured Reims in 940, deposing Artold and reimposing his son Hugh on the see. Flodoard objected to the invasion of the bishopric on canonical grounds; consequently, he was detained by Herbert and once again stripped of his prebends. Between 943 and 946, Flodoard may have been away from Reims with Artold at the court of King Louis IV. In 946, Louis gained control of Reims with the assistance of the East Frankish ruler Otto I. Hugh was again deposed, and Artold was re-ordained. His claim to the see was eventually ratified at the 948 Synod of Ingelheim, which Flodoard attended.

In 951, Flodoard was sent to Otto's court at Aachen, where he represented the church of Reims in a property dispute, and he seems to have been involved in the administration of his church's property. He retired from his canonical office in 963, aged 70, and died on 28 March 966.

Works
Flodoard wrote three substantial historical works and at least two other minor works. In 922, he began writing a chronicle known today as the Annals, which he maintained for most of his career. Flodoard primarily reported major political and military events, focusing on those in West Francia but extending his coverage to the Ottonian empire and Italy. He also regularly recorded miracles and other supernatural phenomena. Flodoard seems generally to have written his annals in a year-by-year fashion, and there is no evidence that he revised his text. The Annals constitute one of the tenth century's relatively few contemporary chronicles, and the work is the only major West Frankish chronicle to have survived from this time, so Flodoard's work has been much valued by modern historians.

Flodoard's History of the Church of Reims (Historia Remensis ecclesiae) is one of the most remarkable productions of the tenth century. This work recounts the history of Reims back to its supposed origins in the time of Romulus and Remus, though it focuses principally on the Christian era up to 948. The work, a celebrated example of the genre of gesta episcoporum ("the deeds of bishops"), takes the form of serialized biographies of the church's bishops. Flodoard had access to an episcopal archive stretching back to the sixth century, and based much of his history on original documents which he summarized or reproduced extracts from. His summaries of some 450 letters of Archbishop Hincmar have been considered especially valuable.

Flodoard's poetical works are of hardly less historical interest. In the 930s he composed an epic poem known as The Triumphs of Christ (De triumphis Christi), a history of Christianity in nearly 20,000 verses. The poem narrates the victories of Christ, martyrs, saints and popes, drawing on a vast range of earlier historical and hagiographical literature. Flodoard evidently gathered material for the work when he visited Rome in 936/7, and the text is a rare witness to the history of the city and the popes in the early tenth century.

The historian wrote at least two other minor works. One, known today as the "Visions of Flothilde", records the otherworldly visions of a local girl in the early 940s, a time of great political conflict in Reims. Another work, now lost, is also referred to in the History of the Church of Reims: when discussing miracles that had taken place in and around Reims cathedral and were attributed to the Virgin Mary, Flodoard mentioned that he had previously collected these and put them into verse.

Flodoard's works were published in full by JP Migne (Patrologia Latina, vol. 135); the best modern edition of the Annales is that edited by Philippe Lauer in 1905. The History of the Church of Reims was recently re-edited for the Monumenta Germaniae Historica by Martina Stratmann (1998). There is, however, no modern edition of The Triumphs of Christ, which remains best consulted in Migne's Patrologia Latina edition.

Editions and translations

 * Annals
 * Philippe Lauer (ed.), Les annales de Flodoard. Collection des textes pour servir à l'étude et à l'enseignement de l'histoire 39. Paris: Picard, 1905. Available from Internet Archive (in Latin with a French introduction and notes)
 * Pertz, Georg Heinrich (ed.). Annales, chronica et historiae aevi Saxonici. MGH Scriptores 3. Hanover, 1839. 363-408. Available online from Digital MGH
 * Steven Fanning and Bernard S. Bachrach, The Annals of Flodoard of Reims, 919-966. Readings in Medieval Civilizations and Cultures 9. Broadview Press, 2004. ISBN 1-55111-650-2.
 * Guizot, M (tr.). Le Siège de Paris par les Normands, poème d'Abbon [etc.]. Collection des Mémoires relatifs a l'Histoire de France. Paris, 1824. 69-162. Available from Gallica (French translation)
 * History of the Church of Reims
 * Martina Stratmann (ed.). Flodoard von Reims. Die Geschichte der Reimser Kirche. MGH Scriptores 36. Hanover, 1998. Available from the Digital MGH
 * Lejeune, M. Flodoardi Historia remensis ecclesiæ. Histoire de l'église de Reims. Reims, 1854-5. Available from Google Books (French translation)
 * Guizot, M. Histoire de l'Église de Rheims. Collection des Mémoires relatifs a l'Histoire de France. Paris, 1824. Available from Gallica (French translation)
 * The Triumphs of Christ
 * Migne, J. P., Patrologia Latina 135. Paris, 1853. Available online from Documenta Catholica Omnia

title: Flodoard


text:
Quotient space (linear algebra)

In linear algebra, the quotient of a vector space $$V$$ by a subspace $$N$$ is a vector space obtained by "collapsing" $$N$$ to zero. The space obtained is called a quotient space and is denoted $$V/N$$ (read "$$V$$ mod $$N$$" or "$$V$$ by $$N$$").

Definition
Formally, the construction is as follows. Let $$V$$ be a vector space over a field $$\mathbb{K}$$, and let $$N$$ be a subspace of $$V$$. We define an equivalence relation $$\sim$$ on $$V$$ by stating that $$x \sim y$$ if $x - y \in N$. That is, $$x$$ is related to $$y$$ if one can be obtained from the other by adding an element of $$N$$. From this definition, one can deduce that any element of $$N$$ is related to the zero vector; more precisely, all the vectors in $$N$$ get mapped into the equivalence class of the zero vector.

The equivalence class – or, in this case, the coset – of $$x$$ is often denoted
 * $$[x] = x + N$$

since it is given by
 * $$[x] = \{ x + n: n \in N \}$$

The quotient space $$V/N$$ is then defined as $$V/_\sim$$, the set of all equivalence classes induced by $$\sim$$ on $$V$$. Scalar multiplication and addition are defined on the equivalence classes by It is not hard to check that these operations are well-defined (i.e. do not depend on the choice of representatives). These operations turn the quotient space $$V/N$$ into a vector space over $$\mathbb{K}$$ with $$N$$ being the zero class, $$[0]$$.
 * $$\alpha [x] = [\alpha x]$$ for all $$\alpha \in \mathbb{K}$$, and
 * $$[x] + [y] = [x+y]$$.

The mapping that associates to $v \in V$ the equivalence class $$[v]$$ is known as the quotient map.

Alternatively phrased, the quotient space $$V/N$$ is the set of all affine subsets of $$V$$ which are parallel to $N$.

Lines in Cartesian Plane
Let X = R2 be the standard Cartesian plane, and let Y be a line through the origin in X. Then the quotient space X/Y can be identified with the space of all lines in X which are parallel to Y. That is to say that, the elements of the set X/Y are lines in X parallel to Y. Note that the points along any one such line will satisfy the equivalence relation because their difference vectors belong to Y. This gives a way to visualize quotient spaces geometrically. (By re-parameterising these lines, the quotient space can more conventionally be represented as the space of all points along a line through the origin that is not parallel to Y. Similarly, the quotient space for R3 by a line through the origin can again be represented as the set of all co-parallel lines, or alternatively be represented as the vector space consisting of a plane which only intersects the line at the origin.)

Subspaces of Cartesian Space
Another example is the quotient of Rn by the subspace spanned by the first m standard basis vectors. The space Rn consists of all n-tuples of real numbers (x1, ..., xn). The subspace, identified with Rm, consists of all n-tuples such that the last n − m entries are zero: (x1, ..., xm, 0, 0, ..., 0). Two vectors of Rn are in the same equivalence class modulo the subspace if and only if they are identical in the last n − m coordinates. The quotient space Rn/Rm is isomorphic to  Rn−m in an obvious manner.

Polynomial Vector Space
Let $$\mathcal{P}_3(\mathbb{R})$$ be the vector space of all cubic polynomials over the real numbers. Then $$\mathcal{P}_3(\mathbb{R}) / \langle x^2 \rangle $$ is a quotient space, where each element is the set corresponding to polynomials that differ by a quadratic term only. For example, one element of the quotient space is $$\{x^3 + a x^2 - 2x + 3 : a \in \mathbb{R}\}$$, while another element of the quotient space is $$\{a x^2 + 2.7 x : a \in \mathbb{R}\}$$.

General Subspaces
More generally, if V is an (internal) direct sum of subspaces U and W,
 * $$V=U\oplus W$$

then the quotient space V/U is naturally isomorphic to W.

Lebesgue Integrals
An important example of a functional quotient space is an Lp space.

Properties
There is a natural epimorphism from V to the quotient space V/U given by sending x to its equivalence class [x]. The kernel (or nullspace) of this epimorphism is the subspace U. This relationship is neatly summarized by the short exact sequence
 * $$0\to U\to V\to V/U\to 0.\,$$

If U is a subspace of V, the dimension of V/U is called the codimension of U in V. Since a basis of V may be constructed from a basis A of U and a basis B of V/U by adding a representative of each element of B to A, the dimension of V is the sum of the dimensions of U and V/U. If V is finite-dimensional, it follows that the codimension of U in V is the difference between the dimensions of V and U:
 * $$\mathrm{codim}(U) = \dim(V/U) = \dim(V) - \dim(U).$$

Let T : V → W be a linear operator. The kernel of T, denoted ker(T), is the set of all x in V such that Tx = 0. The kernel is a subspace of V. The first isomorphism theorem for vector spaces says that the quotient space V/ker(T) is isomorphic to the image of V in W. An immediate corollary, for finite-dimensional spaces, is the rank–nullity theorem: the dimension of V is equal to the dimension of the kernel (the nullity of T) plus the dimension of the image (the rank of T).

The cokernel of a linear operator T : V → W is defined to be the quotient space W/im(T).

Quotient of a Banach space by a subspace
If X is a Banach space and M is a closed subspace of X, then the quotient X/M is again a Banach space. The quotient space is already endowed with a vector space structure by the construction of the previous section. We define a norm on X/M by
 * $$ \| [x] \|_{X/M} = \inf_{m \in M} \|x-m\|_X = \inf_{m \in M} \|x+m\|_X = \inf_{y\in [x]}\|y\|_X. $$

Examples
Let C[0,1] denote the Banach space of continuous real-valued functions on the interval [0,1] with the sup norm. Denote the subspace of all functions f ∈ C[0,1] with f(0) = 0 by M. Then the equivalence class of some function g is determined by its value at 0, and the quotient space C[0,1]/M is isomorphic to R.

If X is a Hilbert space, then the quotient space X/M is isomorphic to the orthogonal complement of M.

Generalization to locally convex spaces
The quotient of a locally convex space by a closed subspace is again locally convex. Indeed, suppose that X is locally convex so that the topology on X is generated by a family of seminorms {pα | α ∈ A} where A is an index set. Let M be a closed subspace, and define seminorms qα on X/M by

 * $$q_\alpha([x]) = \inf_{v\in [x]} p_\alpha(v).$$

Then X/M is a locally convex space, and the topology on it is the quotient topology.

If, furthermore, X is metrizable, then so is X/M. If X is a Fréchet space, then so is X/M.

title: Quotient space (linear algebra)


text:
Talk:Sentō

Can someone remove the reference to civic land nissei?
the sento is now closed. — Preceding unsigned comment added by 126.236.99.172 (talk) 05:26, 23 March 2016 (UTC)

Voyourism section
I think voyourism section mentioning about gay and children is bit stupid. It say more about how non Japanese feel self concious when they enter sento first time. Moved information regarding kids allowed to enter both sie to other place. FWBOarticle 21:10, 13 Aug 2004 (UTC)
 * Boys staring at adult female customers of the other sex is a problem many females have encountered in Japan. While I am unclear about the exact definition of voyerism, this staring definitely makes other people very uncomfortable. I have added the section again. -- Chris 73 | Talk 07:06, 15 Aug 2004 (UTC)
 * The reference to bandai is too esoteric, this word should be given a definition or replaced with a layman's term. Malnova 05:53, 30 December 2005 (UTC)
 * I like Bandai best, but I am open to alternatives. How would you call it? -- Chris 73 | Talk

Sento = a type of public bath house
I added distinction between "sento" and "Japanese bath house." The sento is only one type of public bath house (公衆浴場 kōshū yokujō) that meets certain criterias, and are subject to price restrictions by law. --69.214.226.246 01:30, 2 Jun 2005 (UTC)

Featured article?
With a thorough hammering of grammar and general structure, there is all the material here for a future featured article. Anyone want to go over it with me? Soo 11:44, 1 September 2005 (UTC)

Merge
This article should be merged with Sento, and also needs a major cleanup. Exploding Boy 05:48, 3 April 2006 (UTC)
 * ...um.... this is the article Sento. Should this be merged with another article? Which one? -- Chris 73 | Talk 06:49, 3 April 2006 (UTC)

Sorry, I came to it via a link in another article, which opened the page up to the Tension between social groups in sento bathhouses section. So, no merge, but yes cleanup. Exploding Boy 20:03, 3 April 2006 (UTC)

Disambiguation Page?
While there are Sentō that are bathhouses, there is also an American customer service company called SENTO. How would we best accommodate both articles? A disambiguation page? A tag like "Sento (company)"? Bo-Lingua 15:36, 25 April 2006 (UTC)
 * Sento (company) would be best. --日本穣 Nihonjoe 18:27, 25 April 2006 (UTC)
 * Would we just want to put a tag on this page saying "For the American Company see: x"? or would it be better to have a disambiguation page? Is Wikipedia not sensitive for diacritics? Bo-Lingua
 * SENTO would also work, with For the American Company see: x. On a side note, if you are an member of this company, you should restrain from creating an article, since this would be self promotion. The company should be notable enough to warrant an encyclopedia article. -- Chris 73 | Talk 19:21, 25 April 2006 (UTC)
 * Manual of Style (trademarks) discourages ALL CAPS for article titles, even if the company uses them. --日本穣 Nihonjoe 19:32, 25 April 2006 (UTC)
 * Duly noted, Chris, and good point. Thanks for the clarification of the on the Wiki Style Guide.  Bo-Lingua 19:56, 25 April 2006 (UTC)

Sentos that are anti-Yakuza
I changed a portion that said "many sentō and onsen have a no tattoo rule to keep yakuza out of their baths, often under the pretense of hygienic reasons". However, from my experiences at these places, the sentos do not hide the fact that they want to refuse services to yakuzas in particular, and they make no phoney claims about hygienic reasons either. On the streets of these neighbourhoods there are often signs that say something along the lines of "Yakuzas get out!", etc.—Tokek 14:49, 31 July 2006 (UTC)

I feel this commentator has the sento mixed up with supersento and ryokan. Sento which are members of the bathhouse association in each prefecture have no discriminatory rules as far as I have seen. Supersento which are private businesses and ryokan which are not members of the bathhouse association still reserve the right to refuse service to customers with tattoos and have signs about it. --219.106.152.19 (talk) 03:53, 18 April 2014 (UTC)

actual tempretures
what are the actual tempretures of the baths? i have heard that japanese like very hot baths, for instance ≈60 degrees C. which is very hot, it's scalding. is this correct?

I have read that in america water heaters for private baths (spas, jacuzzis) are not allowed over 104°F (40°C, not very hot) by law.

i think the article should mention actual temperatures. -unsigned

 * Typically they are in the range of 12 - 45 °C. The baths in the mid to upper 40's are considered "very hot", while the baths in the teens °C are usually taken to cool down, after a sauna, for example. Rumors of ≈60°C were greatly exaggerated. —MangoCurry 10:41, 28 October 2006 (UTC)
 * There is one onsen (not sento), where the water used to come out at 60, and they stirred it like mad for a few minutes to bring the temp down, so they could spend 1:30 min in there. But I think the water flows changed and it s no longer so hot. Nowadays supposedly they do it only for tourists. Otheriwse the temp in sentos can be adjusted by the customers, and even the attendants often do not know the actual temp. -- Chris 73 | Talk 07:58, 29 October 2006 (UTC)

Discrimintion
I removed the following sentence "However, except for a single case in a small town in Hokkaido, racial discrimination at public baths virtually does not exist." on the grounds that this is not verifiable either way.

I also alter this sentence " such racist situations are very rare" to "rarely reported".

There is not intention to imply that racism is rampant at sentos, the statements were just one person's opinions. —unsigned

There is lack of facts or reason to speculate that racism is anything but rare to nonexistant at a sentō. To give an impression otherwise would be misleading the reader. The "such racist situations are very rare" snippet may have been another person's addition to the article, if so, that'd mean it wasn't "just one person's opinion." IMHO, an encyclopedia shouldn't exceed reasonable speculation.

Before I added the snippet you mention, I did search Google for other instances, but I couldn't find any. My searches did not suggest racism was a widely reported issue save for one instance. If someone has better reseach skills, that's fine with me. However as a general rule X shall be innocent of Y until proven otherwise. —Tokek 11:03, 1 November 2006 (UTC)

Sento history - Mixed-sex vs. single-sex
I'm under the impression that traditionally, i.e. before the opening of Japan to the West, most sento were mixed-sex, meaning men and women bathed together. If my impression is correct, it would seem there's been a significant cultural change in the sento during the past hundred years. Shouldn't such a major alteration get a fairly prominent mention in the article? T.129.93.16.77 01:42, 28 March 2007 (UTC)
 * My understanding is that mixed bathing was forbidden during various times in historiy with various levels of enforcement, and the current separation originates from commodore Perry. - Chris 73 | Talk 06:14, 28 March 2007 (UTC)

 * I noticed that you seem to have edited the onsen article to agree with your supposition. I did note that the earlier edit claimed it was a rural tradition - that edit was unsourced as well, however - being "under the impression" is not a valid source for a claim in a wikipedia article.  I have added citation needed, but am going to look around and see if there is a source that would resolve this.72.205.55.200 21:30, 2 September 2007 (UTC)

This is all very well, but it doesn't address my inquiry. T.129.93.17.106 (talk) 16:13, 25 February 2009 (UTC)

Etiquete section removal.
The entire section was practically "PUBLIC BATHES: The Walkthrough". While it might be educational, it's highly inappropriate for wikipedia. Maybe wikiversity or even a wikibook on japanese culture/visiting japan (actually, that seems like a good idea) would be better, and then post a link to another wiki. Or explain the etiquette without using "you", or post a link to a site that explains 'the rules' (there has to be tons out there), but just not on wikipedia -- Phoeba WrightOBJECTION! 12:26, 21 May 2007 (UTC)
 * I disagree. I removed a couple of sentences that give advice, but otherwise i think the basic procedure is a description that is useful for the article. -- Chris 73 | Talk 03:52, 22 May 2007 (UTC)

I don't know what the etiquette section was line before the changes above, but the article is now virtually content-free in information about how someone actually uses a public bath. The article says that foreigners have occasionally polluted the baths by getting in unwashed (so presumably one washes first), and another part of the article says that some customers bring their own buckets (so presumably a bucket is involved somehow), but other than that the article tells the reader nothing. Could this the intention of the changes? —Preceding unsigned comment added by 208.46.159.158 (talk) 04:16, 29 April 2008 (UTC)

Public baths used to be very popular in Russia as well, and aforementioned proper etiquette is an accepted norm of behaviour for most of the Post-Soviet nationals/residents. This is very characteristic for Japanese, for very closed culture, to generalize other nations and discriminate against. A person having read "drunken Russian sailors debauch in baths" would think that all Russian sailors are drunk savages. Why not re-place it with "Some foreign nationals did not adhere to local etiquette, and that is why baths are now open only to Japanese"? — Preceding unsigned comment added by 99.235.65.208 (talk) 18:04, 22 December 2012 (UTC)

Requested move

 * The following discussion is an archived discussion of the . Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

Sentō → Public bathing in Japan — Some factors to explain my position: —MangoCurry 23:06, 14 August 2007 (UTC)
 * 1) This article has grown to become pretty much the default "public bathing in Japan" article
 * 2) The fact that sento are not the only kind of public baths in Japan makes this article title inappropriate for a generic "Public bathing in Japan" article, even though they are one of the most common types of public baths in the country
 * 3) The distinction between a sento and a non-sento public baths are trivial and not important enough to have a new "Public bathing in Japan" article that is separate from the "Sento" article

Survey

 * Feel free to state your position on the renaming proposal by beginning a new line in this section with  or  , then sign your comment with  . Since polling is not a substitute for discussion, please explain your reasons, taking into account Wikipedia's naming conventions.

 * Oppose The current article still primarily seems to be about Sentō, even if it has expanded to include other things. There's a separate article at onsen, so I think we can keep this about Sentō. John Smith's 22:51, 15 August 2007 (UTC)
 * Sentō combined with onsen does not cover everything, so the mere existence of an onsen article doesn't quite provide a perfect solution. (They also overlap anyway - some sento can have onsen as well.) --MangoCurry 04:19, 17 August 2007 (UTC)
 * Oppose, though I think creating a redirect from Public bathing in Japan to Sentō would be a good idea. ··· 日本穣 ? · Talk to Nihonjoe 01:11, 16 August 2007 (UTC)
 * Do you think the redirect should be a temporary one until a separate "Public bathing in Japan" article is created? Or do you think the redirect should be a permanent solution and that the Sentō article should be expanded beyond just sentō and that the scope of the Sentō article should basically be "Public bathing in Japan" in general? --MangoCurry 04:19, 17 August 2007 (UTC)
 * Absolutely. If enough sourced material can be gathered for a separate article, I'm all for having a separate Public bathing in Japan article. ··· 日本穣 ? · Talk to Nihonjoe 04:57, 19 August 2007 (UTC)
 * Oppose. I agree with 日本穣. BTW, it's not tatami mat in the changing room but goza/茣蓙/蓙/ござ on the (mostly wooden) floor. Oda Mari 06:00, 16 August 2007 (UTC)
 * That's for sure. Tatami would rot and fall apart within a few weeks in such a wet environment. ··· 日本穣 ? · Talk to Nihonjoe 06:02, 16 August 2007 (UTC)

Discussion

 * Any additional comments:

 * Information for all. It's the definition of Sento from jp.wiki.

法律上は、公衆浴場として、次の定義がされている.

この法律で「公衆浴場」とは、温湯、潮湯又は温泉その他を使用して、公衆を入浴させる施設をいう. この法律で「公衆浴場」とは、公衆浴場法（昭和二十三年法律第百三十九号）第一条第一項に規定する公衆浴場であつて、物価統制令（昭和二十一年勅令第百十八号）第四条の規定に基づき入浴料金が定められるものをいう.
 * 「公衆浴場法」第1条の規定
 * 「公衆浴場の確保のための特別措置に関する法律」第2条の規定

さらに、各都道府県の条例で、「普通公衆浴場」（おおよそ「日常生活における保健衛生上必要な入浴のために設けられた公衆浴場」と定義される）と「その他の公衆浴場」（自治体によっては「特殊公衆浴場」とも呼ぶ）に分けられており、「普通公衆浴場」を一般に「銭湯」と呼ぶ.

なお、入浴料金は物価統制令（現憲法発布前に出された勅令. 法律としての効力を持つ）の規定により、各都道府県知事の決定で上限が定められている. そのため都道府県ごとで料金が違う. Oda Mari 05:19, 19 August 2007 (UTC)

 * It may be useful to post a translation for anyone who doesn't read Japanese. ··· 日本穣 ? · Talk to Nihonjoe 05:29, 19 August 2007 (UTC)

 * I'm not good at J to E translation. To translate the long definition short, 普通公衆浴場/standard public bath/Sento is a public bath house to keep one's body in good hygiene in daily life basis. Not for recreation or luxuary. Correct my English, please. Thank you. Oda Mari 06:07, 19 August 2007 (UTC)

 * The above discussion is preserved as an archive of the . Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

It was requested that this article be renamed but there was no consensus for it to be moved. --Stemonitis 11:46, 20 August 2007 (UTC)

I have removed Discrimination and Lawsuit
As the introductions to both the Sento and Onsen articles report, the two are different and should be distinguished. The place that debito went to was an onsen, not a sento. It's dishonest to report all bathhouses (onsen and sento) as practising discrimination, and it's particulary egregious for debito to be advertising his lawsuit against Yunohana Onsen on the sento page, when said reported discrimination didn't occur at a sento.

His publicity still appears on the onsen page, along with all the requisite links to his own page, so I don't see any need for it to be duplicated here. Recall that there are no other published examples of discrimination at a sento. Simon-in-sagamihara (talk) 08:08, 15 November 2009 (UTC)

Difference between "sento" and "onsen" -- local usage in Kansai
I have changed previous text stated, "They are not exclusive: A sentō can be called an onsen if it derives its bath water from naturally heated hot springs. A legal definition exists that can classify a public bathing facility as sentō."

In Kanto that is for more or less true, but in Kansai the nomenclature "onsen" merely means bathhouse and has no connection to if there is a hot spring fed baths. While there are numourous sento (members of the prefecture bathhouse association) that do have true natural hot spring water filling at least one of their tubs, there are even more bathing facilities in the region that only use tap or well water for their baths. The Japanese page for the absolutly wonderful, but normal water, Gengahara Onsen in Osaka contains the following caveat: なお、｢○○温泉｣は上方に於ける伝統的な風呂屋の屋号であり、天然温泉を意味するものではない. "In the Kyoto area the word onsen is a traditional name for a bathouse, it does not mean that there is a natural hot spring." --219.106.152.19 (talk) 04:13, 18 April 2014 (UTC)

Wiki Education assignment: Writing 1 MW
— Assignment last updated by LN080205 (talk) 06:47, 13 December 2023 (UTC)

title: Talk:Sentō


text:
Inchtuthil

Inchtuthil is the site of a Roman legionary fortress situated on a natural platform overlooking the north bank of the River Tay southwest of Blairgowrie, Perth and Kinross, Scotland (Roman Caledonia).

It was built in AD 82 or 83 as the advance headquarters for the forces of governor Gnaeus Julius Agricola in his campaign against the Caledonian tribes. Positioned at the head of one of the main routes in and out of the Scottish Highlands, it was occupied by Legion XX Valeria Victrix and covered a total area of 21.5 ha.

Construction of the large fortress would have taken two or three seasons and a temporary camp was built nearby to house and protect the soldiers over the winter. Additional, smaller forts were built further north and south at the mouth of each nearby glen forming what are now referred to as the Glenblocker forts.

The fort at Inchtuthil is thought to be part of the Glenblocker forts, as well as others in Strathmore, such as Cardean and Stracathro, formed a uniform system composed of several elements, the forts and watchtowers on the Roman road of the Gask Ridge, the Glenblockers and the Strathmore forts. Inchtuthil as the largest military base would have functioned as the lynch-pin and the only site large enough to launch an invasion into the Highlands and beyond.

Layout and garrison
Unlike other legionary fortresses in Britain, Inchtuthil was not later built over and its layout was still largely preserved when Sir Ian Richmond excavated it between 1952 and 1965. It is therefore notable as the site which provides the only complete plan of a legionary fortress anywhere in the Roman empire. Its defences consisted of a turf rampart faced with stone, with an outside ditch and gatehouses on each side, following the standard Roman plan. The legion it accommodated would have numbered 5,400 at full strength, though there would have been additional specialist troops accompanying them.

Facilities included a hospital (valetudinarium) that covered 5,000 square metres, a workshop covering 3,500 square metres and 64 barrack buildings. The timber walls of these buildings have been calculated to have had a total perimeter of seven miles (10 km). A headquarters building containing an aedes where the legion's colours and images of the emperor would have been kept has also been identified in the insula in the centre of the fortress. However, it was much smaller than would be expected for a legionary fortress, and must have been of a temporary nature. The large empty insula to its east should have been the site for the Praetorium, the commander's house. However, no signs of building foundations for such a large structure were found though the site had been levelled and prepared.

Inchtuthil was only briefly occupied and was evacuated around summer AD 86 and certainly no later than early in AD 87. The reason for this was probably that Legio II Adiutrix had been called to Moesia from its base in Deva Victrix (Chester) to deal with a Dacian invasion in 86 and XX Valeria Victrix was obliged to move back south to take its place. However recent archaeology has cast some doubt on this, indicating that the fortress may have been in use for considerably longer than previously thought.

Nail hoard
During the excavations started by Richmond in the 1950s, a large pit was found in the summer of 1960 containing 875,400 complete iron nails (Square shaft) ranging from 2 - 16 in plus another 28 (round shaft nails) weighing 7 tons, together with other iron objects, including cartwheel rims weighing a combined total weight of ten tonnes. The nails and ironwork were found in a pit which was elaborately concealed. They were almost certainly buried by the Roman troops when they dismantled the fortress before departure to deny them to the local tribes.

Many of the nails were sent to museums while some of the hoard was sold to the public and other interested organisations with an offer of 5 shillings for a 7 - 10 in nail and 25 shillings for a boxed set of five nails. David Colville & Sons (Iron and Steel refiners) was given the task of sorting and storing the nails; the process of sorting, gifting and selling all complete nails was done by 1963, three years after their discovery.

The almost 2000-year-old iron nails from Inchtuthil have been used by atomic scientists to estimate the corrosion effects on barrels of nuclear waste.

title: Inchtuthil


text:
Euler's equations (rigid body dynamics)

In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. Their general vector form is

\mathbf{I} \dot{\boldsymbol\omega} + \boldsymbol\omega \times \left( \mathbf{I} \boldsymbol\omega \right) = \mathbf{M}. $$

where M is the applied torques and I is the inertia matrix. The vector $$\dot{\boldsymbol\omega}$$ is the angular acceleration. Again, note that all quantities are defined in the rotating reference frame.

In orthogonal principal axes of inertia coordinates the equations become

\begin{align} I_1\,\dot{\omega}_{1} + (I_3-I_2)\,\omega_2\,\omega_3 &= M_{1}\\ I_2\,\dot{\omega}_{2} + (I_1-I_3)\,\omega_3\,\omega_1 &= M_{2}\\ I_3\,\dot{\omega}_{3} + (I_2-I_1)\,\omega_1\,\omega_2 &= M_{3} \end{align} $$

where Mk are the components of the applied torques, Ik are the principal moments of inertia and ωk are the components of the angular velocity.

In the absence of applied torques, one obtains the Euler top. When the torques are due to gravity, there are special cases when the motion of the top is integrable.

Derivation
In an inertial frame of reference (subscripted "in"), Euler's second law states that the time derivative of the angular momentum L equals the applied torque:

\frac{d\mathbf{L}_{\text{in}}}{dt} = \mathbf{M}_{\text{in}} $$ For point particles such that the internal forces are central forces, this may be derived using Newton's second law. For a rigid body, one has the relation between angular momentum and the moment of inertia Iin given as
 * $$\mathbf{L}_{\text{in}} = \mathbf{I}_{\text{in}} \boldsymbol\omega$$

In the inertial frame, the differential equation is not always helpful in solving for the motion of a general rotating rigid body, as both Iin and ω can change during the motion. One may instead change to a coordinate frame fixed in the rotating body, in which the moment of inertia tensor is constant. Using a reference frame such as that at the center of mass, the frame's position drops out of the equations. In any rotating reference frame, the time derivative must be replaced so that the equation becomes

\left(\frac{d\mathbf{L}}{dt}\right)_\mathrm{rot} + \boldsymbol\omega\times\mathbf{L} = \mathbf{M} $$ and so the cross product arises, see time derivative in rotating reference frame. The vector components of the torque in the inertial and the rotating frames are related by $$ \mathbf{M}_{\text{in}} = \mathbf{Q}\mathbf{M}, $$ where $$\mathbf{Q}$$ is the rotation tensor (not rotation matrix), an orthogonal tensor related to the angular velocity vector by $$\boldsymbol\omega \times \boldsymbol{u} = \dot{\mathbf{Q}} \mathbf{Q}^{-1}\boldsymbol{u}$$ for any vector u. Now $$\mathbf{L} = \mathbf{I} \boldsymbol\omega$$ is substituted and the time derivatives are taken in the rotating frame, while realizing that the particle positions and the inertia tensor does not depend on time. This leads to the general vector form of Euler's equations which are valid in such a frame

\mathbf{I} \dot{\boldsymbol\omega} + \boldsymbol\omega \times \left( \mathbf{I} \boldsymbol\omega \right) = \mathbf{M}. $$ The equations are also derived from Newton's laws in the discussion of the resultant torque.

More generally, by the tensor transform rules, any rank-2 tensor $$\mathbf{T}$$ has a time-derivative $$\mathbf{\dot T} $$ such that for any vector $$ \mathbf{u}$$, one has $$\mathbf{\dot T} \mathbf{u} = \boldsymbol{\omega}\times (\mathbf{T} \mathbf{u}) - \mathbf{T}(\boldsymbol{\omega}\times \mathbf{u})$$. This yields the Euler's equations by plugging in $$\frac{d}{dt} \left( \mathbf{I} \boldsymbol\omega \right) = \mathbf{M}.$$

Principal axes form
When choosing a frame so that its axes are aligned with the principal axes of the inertia tensor, its component matrix is diagonal, which further simplifies calculations. As described in the moment of inertia article, the angular momentum L can then be written

\mathbf{L} = L_{1}\mathbf{e}_{1} + L_{2}\mathbf{e}_{2} + L_{3}\mathbf{e}_{3} = \sum_{i=1}^3 I_{i}\omega_{i}\mathbf{e}_{i} $$ Also in some frames not tied to the body can it be possible to obtain such simple (diagonal tensor) equations for the rate of change of the angular momentum. Then ω must be the angular velocity for rotation of that frames axes instead of the rotation of the body. It is however still required that the chosen axes are still principal axes of inertia. The resulting form of the Euler rotation equations is useful for rotation-symmetric objects that allow some of the principal axes of rotation to be chosen freely.

Torque-free precessions
Torque-free precessions are non-trivial solution for the situation where the torque on the right hand side is zero. When I is not constant in the external reference frame (i.e. the body is moving and its inertia tensor is not constantly diagonal) then I cannot be pulled through the derivative operator acting on L. In this case I(t) and ω(t) do change together in such a way that the derivative of their product is still zero. This motion can be visualized by Poinsot's construction.

Generalized Euler equations
The Euler equations can be generalized to any simple Lie algebra. The original Euler equations come from fixing the Lie algebra to be $$\mathfrak{so}(3)$$, with generators $${t_1, t_2, t_3}$$ satisfying the relation $$[t_a, t_b] = \epsilon_{abc}t_c$$. Then if $$\boldsymbol\omega(t) = \sum_a \omega_a(t)t_a$$ (where $$t$$ is a time coordinate, not to be confused with basis vectors $$t_a$$) is an $$\mathfrak{so}(3)$$-valued function of time, and $$\mathbf{I} = \mathrm{diag}(I_1, I_2, I_3)$$ (with respect to the Lie algebra basis), then the (untorqued) original Euler equations can be written

To define $$\mathbf{I}$$ in a basis-independent way, it must be a self-adjoint map on the Lie algebra $$\mathfrak{g}$$ with respect to the invariant bilinear form on $$\mathfrak{g}$$. This expression generalizes readily to an arbitrary simple Lie algebra, say in the standard classification of simple Lie algebras.

This can also be viewed as a Lax pair formulation of the generalized Euler equations, suggesting their integrability.

title: Euler's equations (rigid body dynamics)


text:
Fridlevus II

Fridleif (Ynglinga saga) was a son of Fróði of the Skjöldung (Scylding) lineage. In that work he was the brother of Halfdan and the father of Áli the Strong.

title: Fridlevus II


text:
List of people in the Warsaw Uprising

This is a list of notable individuals who were involved in the Warsaw Uprising, a Polish insurgence during the Second World War that begun on August 1, 1944.

Polish Home Army (Armia Krajowa)

 * Krzysztof Kamil Baczyński, poet and Home Army soldier, KIA on August 4
 * Gustaw Billewicz, codename Sosna, commander of Battalion 'Chrobry I'
 * Tadeusz Bór-Komorowski, codename Generał Bór, highest commander of the Home Army in Poland. During Warsaw Uprising fought in Wola, Stare Miasto and Southern Śródmieście.
 * Antoni Chruściel, codename Monter, commander of Home Army Warsaw district (later renamed to Warsaw Home Army Corps - Warszawski Korpus Armii Krajowej); direct commander of Polish forces in Warsaw Uprising.
 * Jan Mazurkiewicz, codename Radosław, commander of Group 'Radosław'
 * Mieczysław Niedzielski, codename Żywiciel, commander of II Sector: Żoliborz, after September 20 commander of the reconstructed 8th Romuald Traugutt Infantry Division
 * Jan Nowak-Jeziorański, the Courier from Warsaw
 * Eugeniusz Lokajski - a photographer
 * Leopold Okulicki, codename Niedźwiadek, a cichociemni, chief of operations, later also Chief of Staff
 * Witold Pilecki, codename Druh, commander of second company of 'Chrobry II' battalion, fought in Northern Śródmieście, commander of the fortified area "Great Bastion of Warsaw"
 * Tadeusz Pełczyński, codename Grzegorz, Chief of Staff of Home Army Warsaw district, second in command to Generał Bór. Fought in Starówka and Śródmieście, commanded the second assault on Dworzec Gdański. Wounded on September 9.

Civilians

 * Jan Franciszek Czartoryski - chaplain

Soviet military

 * Zygmunt Berling, commander of the 1st Polish Army (Wojsko Polskie) in the Soviet armies which was the only "Soviet" group to aid the uprising.
 * Konstantin Rokossovsky, commander of the Russian Central Front, including the forces which failed to support the uprising.

German military

 * Erich von dem Bach, SS-Obergruppenführer, commander of all troops fighting against the Warsaw Uprising (Korpsgruppe Bach)
 * Oskar Dirlewanger, commander of Battle Group Dirlewanger
 * Heinz Reinefarth, SS-Gruppenfuhrer, commander of Battle Group Reinefarth
 * Günter Rohr, Major General, commander of Battle Group Rohr
 * Willy Schmidt, commander of Battle Group Schmidt
 * Rainer Stahel, Lieutenant General, commander of Warsaw Garrison
 * Bronislav Kaminski, commander of the infamous RONA brigade

title: List of people in the Warsaw Uprising