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Licinia Eudoxia

Licinia Eudoxia (Greek: Λικινία, 422 – c. 493) was a Roman Empress, daughter of Eastern Roman Emperor Theodosius II. Her husbands included the Western Roman Emperors Valentinian III and Petronius Maximus.

Family
Eudoxia was born in 422, the daughter of Theodosius II, Eastern Roman Emperor and his consort Aelia Eudocia, a woman of Greek origin. Her only known siblings, Arcadius and Flacilla, predeceased their parents. Their paternal grandparents were Arcadius and Aelia Eudoxia. Their maternal grandfather was Leontius, a sophist from Athens.

The identity of her maternal grandfather was first given by Socrates of Constantinople. John Malalas later gave a more detailed account of her mother Eudocia's history, which is also summarised in The History of the Decline and Fall of the Roman Empire by Edward Gibbon. The identity of Eudoxia's maternal grandmother is not recorded.

First marriage

In 424, Eudoxia was betrothed to Valentinian III, her first cousin, once removed. The year of their betrothal was recorded by Marcellinus Comes. At the time of their betrothal, Valentinian was approximately four years old, Eudoxia only two. Gibbon attributes the betrothal to "the agreement of the three females who governed the Roman world", meaning Galla Placidia, her niece Pulcheria, and Pulcheria's sister-in-law Eudocia. Galla Placidia was Valentinian III's mother and a younger, paternal half-sister of Arcadius. Valentinian III was at the time being prepared to claim the throne of the Western Roman Empire, which was held by Joannes. The latter was not a member of the Theodosian dynasty and thus regarded a usurper by the Eastern court. Within 424, Valentinian was proclaimed a Caesar in the Eastern court. The following year, Joannes was defeated and executed. Valentinian replaced him as Augustus of the West.

Eudoxia and Valentinian III married on 29 October 437, in Thessalonike, their marriage marking the reunion of the two halves of the House of Theodosius. The marriage was recorded by Socrates of Constantinople, the Chronicon Paschale and Marcellinus Comes. In 439, Eudoxia was granted the title of Augusta, with the birth of their first daughter Eudocia. They also had a second daughter, Placidia. The births and eventual fates of the two daughters were recorded by Priscus, Procopius, John Malalas and the Chronicon Paschale.

On 16 March 455, Valentinian III was killed in the Campus Martius, Rome by Optila and Thraustila. According to the fragmentary chronicle of John of Antioch, a 7th-century monk tentatively identified with John of the Sedre, Syrian Orthodox Patriarch of Antioch from 641 to 648 "Maximus, failing in both his hopes, was bitterly angry. He summoned Optila and Thraustila, brave Scythians who had campaigned with Aëtius and had been assigned to attend on Valentinian, and talked to them. He gave and received guarantees, put the blame for Aëtius' murder on the Emperor, and urged that the better course would be to take revenge on them. Those who avenged the fallen man, he said, would justly have the greatest blessings. Not many days later, Valentinian rode in the Field of Ares with a few bodyguards and the followers of Optila and Thraustila. When he had dismounted from his horse and proceeded to archery, Optila and his friends attacked him. Optila struck Valentinian on his temple and when turned around to see the striker he dealt him a second blow on the face and felled him, and Thraustila slew Heraclius. Taking the Emperor's diadem and horse, they hastened to Maximus... "(John of Antioch fr.201.4–5: Gordon trans., pp. 52–53). Heraclius is identified as "a eunuch who had the greatest influence with the emperor" and his associate in murdering Aetius.

Second marriage
Valentinian had no male descendants and had never designated an heir. Several candidates claimed the throne. Petronius Maximus, who was the highest-ranking of all Roman senators, was among them. A second candidate was Maximianus, son of Domninus. Domninus was a merchant from Egypt who had earned a considerable fortune. Maximianus had served as a domesticus, member of an elite guard unit of the late Roman Empire, under Aetius. Eudoxia promoted her own candidate, in the person of Majorian.

John of Antioch reports that Maximus secured his own succession by buying the loyalties of palace officials and the local military. Eudoxia was forced to marry him or face execution. Their marriage secured the connection of Maximus to the Theodosian dynasty. Prosper of Aquitaine reports that Maximus befriended the murderers of Valentinian III instead of punishing them. Both Prosper and Victor of Tonnena place the marriage of Eudoxia to Maximus only days following the death of her first husband, commenting with disapproval that the empress was not given a period to grieve for Valentinian.

John of Antioch mentions, but does not name, a previous wife of Maximus. She had reportedly been raped by Valentinian III, an event which the chronicle sees as the reason Maximus turned against his former master. The eventual fate of his first wife is not recorded. She may be presumed to have committed suicide, following the example of Lucretia. Regardless, Maximus arranged the marriage of his son Palladius to his new stepdaughter Eudocia, the daughter of Eudoxia from her first marriage, again to secure a dynastic relation to the Theodosian dynasty.

The historical study "Fifth-century Gaul: A Crisis of Identity?" (1992) by John Drinkwater and Hugh Elton considers it likely that the first wife of Maximus was also a sister to Avitus, his magister militum (Master of Soldiers). The writers have also suggested that Flavius Magnus was another son of Maximus from his first marriage, considering Flavius Probus to be a grandson. They also argue for placing the marriage of Placidia the Younger to Olybrius at this point, considering it to be the third marriage between a member of the Theodosian dynasty and a member of the extended Anicii family within the same year. They view Olybrius as a third son of Maximus, grandson through him of Anicius Probinus and grand-nephew of Anicius Hermogenianus Olybrius. However, considering the other possible filiation of Flavius Magnus given by Christian Settipani, as well as the lack of the name of Flavius Probus' mother, it can be assumed that he was a grandson of Petronius Maximus but from his mother.

Maximus appointed Avitus as his Magister militum praesentalis ("Master of Soldiers in Attendance") and send him to Toulouse. There Avitus was to try to secure the loyalty of Theodoric II of the Visigoths to the new emperor. However his reign was to prove short. According to the chronicler Malchus, "Around this time, the empress Eudoxia, the widow of the emperor Valentinian and the daughter of the emperor Theodosius and Eudocia, remained unhappily at Rome and, enraged at the tyrant Maximus because of the murder of her spouse, she summoned the Vandal Gaiseric, king of Africa, against Maximus, who was ruling Rome. He came suddenly to Rome with his forces and captured the city, and having destroyed Maximus and all his forces, he took everything from the palace, even the bronze statues. He even led away as captives surviving senators, accompanied by their wives; along with them he also carried off to Carthage in Africa the empress Eudoxia, who had summoned him; her daughter Placidia, the wife of the patrician Olybrius, who then was staying at Constantinople; and even the maiden Eudocia. After he had returned, Gaiseric gave the younger Eudocia, a maiden, the daughter of the empress Eudoxia, to his son Huneric in marriage, and he held them both, the mother and the daughter, in great honor" (Chron. 366).

Eudoxia was presumably following the example of her sister-in-law Justa Grata Honoria who had summoned Attila the Hun for help against an unwanted marriage. According to Prosper, Maximus was in Rome when the Vandals arrived. He gave anyone who could permission to flee the city. He attempted to flee himself but was assassinated by the imperial slaves. He had reigned for seventy-seven days. His body was thrown into the Tiber and never recovered. Victor of Tonnena agrees, adding the detail that Pope Leo I negotiated with Geiseric for the security of the city's population.

Hydatius attributes the assassination to revolting troops of the Roman army, enraged at Maximus' attempted flight. The Chronica Gallica of 511 attributes the assassination to a rioting crowd. Jordanes identifies a single assassin as "Ursus, a Roman soldier". Ursus is Latin for "bear". Sidonius Apollinaris makes a cryptic comment regarding a Burgundian whose "traitorous leadership" led the crowd to panic and to the slaughter of the Emperor. His identity is unknown, presumably a general who failed to face the Vandals for one reason or the other. Later historians have suggested two high-ranking Burgundians as possible candidates, Gondioc and his brother Chilperic. Both joined Theodoric II in invading Hispania later in 455.

Widow
The three women stayed prisoners in Carthage for seven years. In 462, Leo I, Eastern Roman Emperor, paid a large ransom for Eudoxia and Placidia. Eudoxia returned to Constantinople after an absence of twenty-five years, Placidia joining her. Eudocia stayed in Africa and took Huneric as her husband. They were parents to Hilderic, king of the Vandals from 523 to 530.

title: Licinia Eudoxia


text: Category:Lisbon

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

title: Category:Lisbon


text:
Waterloo Moraine

The Waterloo Moraine is a landform and sediment body that was created as a moraine in the Regional Municipality of Waterloo, in Ontario, Canada. It covers a large portion of the cities of Waterloo and Kitchener and the township of Wilmot, and some parts of the townships of Wellesley and North Dumfries. About 90% of the water supply of the Regional Municipality of Waterloo is derived from groundwater of the Waterloo Moraine aquifer system.

During late 1989 and early 1990, groundwater contamination in Elmira forced the Region to shut down some well fields. As a result, new land use management guidelines and water protection measures have been enacted.

The Waterloo Moraine is the largest of fourteen moraines in the Region, spanning approximately 400 square kilometres. It is an interlobate moraine, consisting primarily of sand and gravel. It contains large aquifers, which discharge into the Grand River and its tributaries and maintain a base water flow rate into that system.

Origin
The Waterloo Moraine was formed as the three ice lobes of the Laurentide Ice Sheet retreated across what is now Waterloo Region from Lake Huron in the west, Georgian Bay in the northeast, Lake Ontario in the east and Lake Erie in the southeast. As the glacier moved, it carried with it huge boulders, sand, gravel and debris. As the ice disappeared, the Waterloo Moraine remained, a huge complex of glacial sediments that is between 30 metres and more than 100 metres thick. Meltwater streams cascading from the surface of the ice lobes carried enormous deposits of sand and gravel and blocks of bedrock.

The glacial sediments constituting the moraine rest upon the Guelph and Salina carbonate bedrock formations.

Significance
The Waterloo Moraine provides drinking water for over 300,000 people throughout Waterloo Region, and approximately 75% of its potable water. The Waterloo Moraine is currently not protected by provincial legislation although there is an active movement from citizens to see that this takes place.

Louisette Lanteigne and David Wellhauser of Waterloo have used the Environmental Bill of Rights to submit a Request for Review for a Waterloo Moraine Protection Act. This resulted in a 16-month review of source water and groundwater protection for the Waterloo Moraine. The findings were to be published in September 2008.

Function
In the vicinity where the three ice lobes began to retreat, sits the recharge areas that allow surface water to enter back into the ground source. The speed of absorption depends on the density of aquifers and aquitards. Aquifers are made up of sand, gravel and silt where the water filters down relatively quickly. The shallow aquifers feed area bodies of water such as creeks and streams while the deeper aquifers feed down to replenish the ground water. The aquitards are the protective layers of clay that slowly filters the water and act to protect the main source from contamination. Left on its own, it is a naturally renewable way to gather fresh drinking water.

Ground water recharge
The moraine covers much of the City of Waterloo, Kitchener, Wellesley, Wilmot and North Dumfries, covering 400 sqkm of land. Almost half of the ground water recharge takes place on only 15% of the Grand River watershed and 80% occurs on only 30% of the land mass most of which is located at the west end of Waterloo Region in the townships of Wilmot and Wellesley.

Threats
The ground water travels down from west to east feeding area wells throughout the region. Subdivision developments in the west end would create more impervious surfaces in the vicinity of the recharge area. Instead of allowing the water to refill the source, the run off will be diverted to sewage systems instead. This will mean a permanent decrease in the volume of water entering area wells. The reduction of water in the wells will significantly increase the parts per billion of contaminants in the system jeopardizing the quality of water in the aquifer and increasing the costs of filtration.

If an increase in traffic follows the development in the vicinity of the aquifer, there will be an increased risk of contamination by road salt which is, according to Environment Canada, a known toxic substance. Road salt is a form of chloride that kills fish and pollutes area creeks and streams.

title: Waterloo Moraine


text:
Gribov ambiguity

In gauge theory, especially in non-abelian gauge theories, global problems at gauge fixing are often encountered. Gauge fixing means choosing a representative from each gauge orbit, that is, choosing a section of a fiber bundle. The space of representatives is a submanifold (of the bundle as a whole) and represents the gauge fixing condition. Ideally, every gauge orbit will intersect this submanifold once and only once. Unfortunately, this is often impossible globally for non-abelian gauge theories because of topological obstructions and the best that can be done is make this condition true locally. A gauge fixing submanifold may not intersect a gauge orbit at all or it may intersect it more than once. The difficulty arises because the gauge fixing condition is usually specified as a differential equation of some sort, e.g. that a divergence vanish (as in the Landau or Lorenz gauge). The solutions to this equation may end up specifying multiple sections, or perhaps none at all. This is called a Gribov ambiguity (named after Vladimir Gribov).

Gribov ambiguities lead to a nonperturbative failure of the BRST symmetry, among other things.

A way to resolve the problem of Gribov ambiguity is to restrict the relevant functional integrals to a single Gribov region whose boundary is called a Gribov horizon. Still one can show that this problem is not resolved even when reducing the region to the first Gribov region. The only region for which this ambiguity is resolved is the fundamental modular region (FMR).

Background
When doing computations in gauge theories, one usually needs to choose a gauge. Gauge degrees of freedom do not have any direct physical meaning, but they are an artifact of the mathematical description we use to handle the theory in question. In order to obtain physical results, these redundant degrees of freedom need to be discarded in a suitable way

In Abelian gauge theory (i.e. in QED) it suffices to simply choose a gauge. A popular one is the Lorenz gauge $$\partial^\mu A_\mu = 0$$, which has the advantage of being Lorentz invariant. In non-Abelian gauge theories (such as QCD) the situation is more complicated due to the more complex structure of the non-Abelian gauge group.

The Faddeev–Popov formalism, developed by Ludvig Faddeev and Victor Popov, provides a way to deal with the gauge choice in non-Abelian theories. This formalism introduces the Faddeev–Popov operator, which is essentially the Jacobian determinant of the transformation necessary to bring the gauge field into the desired gauge. In the so-called Landau gauge $$\partial_\mu A_\mu^a = 0$$, this operator has the form
 * $$\partial_\mu \mathcal D_\mu^{ab} \;,$$

where $$\mathcal D_\mu^{ab}$$ is the covariant derivative in the adjoint representation. The determinant of this Faddeev–Popov operator is then introduced into the path integral using ghost fields.

This formalism, however, assumes that the gauge choice (like $$\partial_\mu A_\mu^a = 0$$) is unique — i.e. for each physical configuration there exists exactly one $$A_\mu^a$$ that corresponds to it and that obeys the gauge condition. In non-Abelian gauge theories of Yang–Mills type, this is not the case for a large class of gauges, though, as was first pointed out by Gribov.

Gribov's construction
Gribov considered the question of, given a certain physical configuration, how many different gauge copies of this configuration obey the Landau gauge condition $$\partial_\mu A_\mu^a = 0$$. No configurations without any representatives are known. It is perfectly possible, though, for there to be more than one.

Consider two gauge fields $$A_\mu^a$$ and $${A_\mu^a}'$$, and assume they both obey the Landau gauge condition. If $${A_\mu^a}'$$ is a gauge copy of $$A_\mu^a$$, we would have (assuming they are infinitesimally close to each other):
 * $${A_\mu^a}' = A_\mu^a + \mathcal D_\mu^{ab} \omega^b$$

for some function $$\omega^b$$. If both fields obey the Landau gauge condition, we must have that
 * $$\partial_\mu \mathcal D_\mu^{ab} \omega^b = 0 \;,$$

and thus that the Faddeev–Popov operator has at least one zero mode. If the gauge field is infinitesimally small, this operator will not have zero modes. The set of gauge fields where the Faddeev–Popov operator has its first zero mode (when starting from the origin) is called the "Gribov horizon". The set of all gauge fields where the Faddeev–Popov operator has no zero modes (meaning this operator is positive definite) is called the "first Gribov region" $$\Omega$$.

If gauge fields have gauge copies, these fields will be overcounted in the path integral. In order to counter that overcounting, Gribov argued we should limit the path integral to the first Gribov region. In order to do so, he considered the ghost propagator, which is the vacuum expectation value of the inverse of the Faddeev–Popov operator. If this operator is always positive definite, the ghost propagator cannot have poles — which is called the "no-pole condition". In usual perturbation theory (using the usual Faddeev–Popov formalism), the propagator does have a pole, which means we left the first Gribov region and overcounted some configurations.

Deriving a perturbative expression for the ghost propagator, Gribov finds that this no-pole condition leads to a condition of the form
 * $$\langle\sigma[A]\rangle = \left\langle \frac{Ng^2}{Vd(N^2-1)} \int \frac{d^dq}{(2\pi)^d} A_\mu^a(-q) \frac1{q^2} A_\mu^a(q) \right\rangle < 1 \;,$$

with N the number of colors (which is 3 in QCD), g the gauge coupling strength, V the volume of space-time (which goes to infinity in most applications), and d the number of space-time dimensions (which is 4 in the real world). The functional $$\sigma[A]$$ is a shorthand for the expression between the angular brackets. In order to impose this condition, Gribov proposed to introduce a Heaviside step function containing the above into the path integral. The Fourier representation of the Heaviside function is:
 * $$H(1-\sigma[A]) = \int_{-i\infty+\epsilon}^{+i\infty+\epsilon} \frac{d\beta}{2\pi i\beta} e^{\beta(1-\sigma[A])} \;.$$

In this expression, the parameter $$\beta$$ is called the "Gribov parameter". The integration over this Gribov parameter is then performed using the method of steepest descent. This method gives an equation for the Gribov parameter, which is called the gap equation. Plugging the solution to this equation back into the path integral yields a modified gauge theory.

With the modification stemming from the Gribov parameter, it turns out that the gluon propagator is modified to
 * $$D^{ab}_{\mu\nu} (k) = \delta^{ab} \left(\delta_{\mu\nu} - \frac{k_\mu k_\nu}{k^2}\right) \frac1{k^2 + \frac{2N g^2}{Vd(N^2-1)} \frac{\beta_0}{k^2}} \;,$$

where $$\beta_0$$ is that value of $$\beta$$ that solves the gap equation. The ghost propagator is also modified and, at one-loop order, displays a behavior $$\propto 1/k^4$$.

The Gribov–Zwanziger action
Several years later, Daniel Zwanziger also considered the Gribov problem. He used a different approach. Instead of considering the ghost propagator, he computed the lowest eigenvalue of the Faddeev–Popov operator as a perturbative series in the gluon field. This yielded a certain function, which he called the "horizon function", and the vacuum expectation value of this horizon function must be limited to at most one in order to stay within the first Gribov region. This condition can be expressed by introducing the horizon function into the path integral (in a way analogous to how Gribov did the same) and imposing a certain gap equation on the vacuum energy of the resulting theory. This yielded a new path integral with a modified action, which is, however, nonlocal. At leading order, the results are identical to the ones previously found by Gribov.

In order to more easily deal with the action he found, Zwanziger introduced localizing fields. Once the action had become local, it was possible to prove that the resulting theory is renormalizable — i.e. all infinities generated by loop diagrams can be absorbed by multiplicatively modifying the content (coupling constant, field normalization, Gribov parameter) already present in the theory without needing extra additions.

Zwanziger furthermore noted that the resulting gluon propagator does not admit a Källén–Lehmann spectral representation, which signals that the gluon cannot be a physical particle any longer. This is often interpreted as signaling color confinement.

Properties of the first Gribov region
As the first Gribov region plays a pivotal role in the resolution of the Gribov ambiguity, it has attracted additional attention over the years since Gribov's first paper. The Landau gauge can be defined as being the gauge that extremizes the functional
 * $$||A||^2 = \int d^dx A_\mu^a(x) A_\mu^a(x) \;.$$

A simple extremum (maximum or minimum) of this functional is the usual Landau gauge. Demanding a minimum (which is equivalent with demanding that the Faddeev–Popov operator be positive) lands one in the first Gribov region.

This condition still includes relative minima, though. It has been shown that there are still Gribov copies within the first Gribov region that are related to each other by a topologically trivial gauge transformation. The space of gauge functions that absolutely minimize the functional $$||A||^2$$ defined above is called the "fundamental modular region". It is unknown how to restrict the path integral to this region, though.

The first Gribov region has been shown to be bounded in all directions, such that no arbitrarily large field configurations are taken into account when restricting the path integral to this region. Furthermore, the first Gribov region is convex, and all physical configurations have at least one representative inside it.

Later developments
In 2013 it was proven that the two formalisms — Gribov's and Zwanziger's — are equivalent to all orders in perturbation theory.

One challenge for the Gribov–Zwanziger formalism is that the BRST symmetry is broken. This breaking can be interpreted as dynamical symmetry breaking. The breaking is "soft" (i.e. proportional to a parameter with positive mass dimension, in this case the Gribov parameter), such that renormalizability can still be proven. Unitarity is still problematic, however. More recently, however, a claim for a BRST-preserved Gribov–Zwanziger action has been made in the literature.

For a long time, lattice simulations seemed to indicate that the modified gluon and ghost propagators proposed by Gribov and Zwanziger were correct. In 2007, however, computers had become sufficiently strong to probe the region of low momenta, where the propagators are most modified, and it turned out that the Gribov–Zwanziger picture is not correct. Instead, the gluon propagator goes to a constant value when the momentum is taken to zero, and the ghost propagator still goes like 1/k2 at low momenta. This is the case for both 3 and 4 space-time dimensions. A solution to this discrepancy has been proposed, adding condensates to the Gribov–Zwanziger action.

title: Gribov ambiguity


text: User talk:80.45.148.153

title: User talk:80.45.148.153


text:
Best evidence rule

The best evidence rule is a legal principle that holds an original of a document as superior evidence. The rule specifies that secondary evidence, such as a copy or facsimile, will be not admissible if an original document exists and can be obtained. The rule has its roots in 18th-century British law, at a time when copies would be rewritten by hand and hence more vulnerable to inaccuracies.

History and description
The best evidence rule has its origins in the 18th century case Omychund v Barker (1780) 1 Atk, 21, 49; 26 ER 15, 33. Wherein Lord Harwicke stated that no evidence was admissible unless it was "the best that the nature of the case will allow."

According to Blackstone's Criminal Practice, the best evidence rule in England and Wales, as used in earlier centuries, "is now all but defunct." Lord Denning MR said that "nowadays we do not confine ourselves to the best evidence. We admit all relevant evidence. The goodness or badness of it goes only to weight and not to admissibility."

In the United States, the best evidence rule is part of Article X of the Federal Rules of Evidence (Rules 1001-1008). The rule specifies the guidelines under which a party may request that it be allowed to submit into evidence a copy of the contents of a document, recording or photograph at a trial when the "original document is not available." If the party is able to provide an acceptable reason for the absence of the original, then "secondary evidence" or copies of the original document can be admitted as evidence. The best evidence rule is only applied in situations where a party attempts to substantiate a non-original document submitted as evidence during a trial. Admissibility of documents before state court systems may vary.

In Australia, the rule was effectively abolished with the 1995 enactment of the Uniform Evidence Law. Section 51 provides: "The principles and rules of the common law that relate to the means of proving the contents of documents are abolished."

title: Best evidence rule


text:
Lacus Doloris

Lacus Doloris (Latin dolōris, "Lake of Sorrow") is a small lunar mare located in the Terra Nivium region at 16.8° N, 8.6° E. It is 103 km in diameter.

title: Lacus Doloris


text:
Talk:Boy's surface

Old comments on parameterization
I'd like to propose moving the section on the Structure of Boy's Surface in front of the section on parameterization. Wikipedia is addressed to a general audiance, who are more likely to relate to the pictures than the equations. --agr 15:47, 6 Jun 2005 (UTC)
 * There being no objection, I went ahead and made the change. --agr 18:01, 21 October 2005 (UTC)

I think the images could use more transparency and smoothness. Drawing them opaque and polygonized like this makes it harder to see what's happening. There's a sketchy idea of what I mean on my page but maybe a raytrace would look better. I'd also like to see a more prominent treatment of the locus of self-intersection points (a single triple point connecting three loops of double points). —David Eppstein 21:56, 13 September 2006 (UTC)

 * I put together: this afternoon.  If you think that looks right feel free to insert it as you see fit (I assume you have done most of the organizing of this article.)  Let me know if you would like a smaller verision too, it does seem rather big now.  — A13ean (talk)

 * Pretty! And a lot more understandable than what's there now. I'll work on getting it in and making the other images a little less space-consuming. —David Eppstein 05:03, 4 November 2006 (UTC)

 * Seems like Boys surface is used as a halfway stage in a Sphere eversion http://torus.math.uiuc.edu/jms/Papers/isama/color/opt2.htm, something to this effect should be included. --Salix alba (talk) 22:45, 13 September 2006 (UTC)

 * Doing some google digging finds [Imaging maths - Unfolding polyhedra] which talks about a discreet Boy's surface, with a reference
 * U. Brehm, How to build minimal polyhedral models of the Boy surface. Math. Intelligencer 12(4):51-56 (1990).
 * other interesting links are
 * A New Polyhedral Surface
 * discussed the imposibility of tight imersions of the real projective plane.
 * http://www.jp-petit.com/science/maths_f/maths_f.htm
 * seems to have some interesting stuff, but its in french? --Salix alba (talk) 18:30, 14 September 2006 (UTC)

 * As long as you're finding things in Google, there's also Another discrete Boy's surface. A little more explanation: if you have a collection of cuboids in Euclidean space, meeting face-to-face, you can form a collection of 2-manifolds by drawing three equatorial quadrilaterals in each cuboid and connecting pairs of quadrilaterals from cuboids that share faces. Sometimes (in the meshing literature) this collection of surfaces is called the "spatial twist continuum". This paper finds a collection of cuboids from which this construction forms a Boy's surface. It can also be interpreted as a similar construction on the surface of a four-polytope with cuboid faces. —David Eppstein 20:16, 14 September 2006 (UTC)
 * That wouldn't be you in the references would it ;-)? I think I get the idea. After a bit of smoothing it does make for a nice model [[Image:Nice boys.gif|200px|right]]. The tight immersions stuff seems quite interesting space for a new article? --Salix alba  22:06, 14 September 2006 (UTC)

Bryant / Kusner
It should be noted that the article by Hermann Karcher and Ulrich Pinkall which can be found here attributes the parametrization formula to Rob Kusner instead of Robert Bryant. Instead it credits Bryant with a general result about rational immersions of some kind of minimal surfaces, of which this parametrization is a special case apparently. regards, High on a tree 21:05, 6 December 2006 (UTC)

 * It looks like the parameterization used for the statue is from Kusner, which is (as far as I can tell) different from the parameterization currently given in the article which is attributed to Bryant. That parameterization with the credit to Bryant also appears in Apery's book.  If there are no objections, we can change the mention in the "statue" section.  Thanks, High on a tree!  Sorry this is rather late.    A13ean 02:35, 26 June 2007 (UTC)

 * Upon even more in depth digging it turns out that this class of parameterizations is due to a collaboration between Bryant and Kusner, and they are commonly refered to as "Bryant-Kusner parameterizations". So a compromise it is, and unless no one objects I'll make the change.  A13ean 02:38, 20 September 2007 (UTC)

Javaview model
The Boy Surface

Here's a model of Boy's that one can move around, for those of us who like to play with things. If anyone else thinks that it's worth it feel free to link it, but I'll refrain since I made it. — A13ean (talk)

 * I like it! It's much more helpful IMHO to have something one can rotate freely instead of seeing it animated.  So I'll add it.  --C S (Talk) 23:36, 13 May 2007 (UTC)

Left and right handed boys
Something should be said about left and right-handed Boy's surfaces, which are not regularly homotopic. --C S (Talk) 11:17, 8 April 2007 (UTC)

False claim
The page says that the Boy surface is homeomorphic to RP^2, but that is just impossible, as there are a compact non orientable surface cannot be embedded in R^3... —Preceding unsigned comment added by 201.252.9.131 (talk • contribs)

 * It's not embedded, it's immersed. —David Eppstein 00:03, 19 July 2007 (UTC)

 * That's irrelevant. The problem is with the word homeomorphic, which is evidently wrong.

In fact, the argument presented in the "Relating the Boy's surface..." section is bogus: what's said there does not imply that the parametrization is injective in the interior of the disk. Mariano (talk) 02:47, 3 December 2008 (UTC)

Hilbert
I changed 'Hilbert' in the article to 'David Hilbert', hoping that it would help those who (like myself) weren't aware of who 'Hilbert' referred to. I am not, however, certain that it is indeed in reference to David Hilbert, but his biographical information (lifetime, profession, nationality, etc.) strongly suggests that this is true. Please correct my edit if I am mistaken. Thank you. Spinnick597 00:38, 28 September 2007 (UTC)
 * That's the right one. A13ean 11:05, 28 September 2007 (UTC)

Parametrization and implicit equation
The given parametrization of Boy's surface is either inconsistent or some essential information is lacking: the coordinates of a point are expressed rationally in terms of $$g_1,g_2, g_3,$$ which are themselves irrational functions of the real and imaginary parts of a complex number, named by the same letter as the third coordinate of the points of the surface. The problem is that, the expression of $$x,y,z$$ in terms of $$g_1,g_2, g_3$$ implies immediately that $$x^2+y^2+z^2=1.$$ Thus this complicate parametrization is simply a strange parametrization of the unit sphere.

 * No, because the denominator is $$g_1^2+g_2^2+g_3^2$$ not $$\sqrt{g_1^2+g_2^2+g_3^2}$$. —Tamfang (talk) 07:38, 8 June 2014 (UTC)

By the way, beside a lacking correct parametrization, other fundamental properties are lacking: I believe that Boy's surface is algebraic. Therefore, an implicit equation must be provided, or, at least, its degree must be given (from the picture, I guess 6). Also, it must been said if Boy's surface admits a rational parametrization. I guess that it is true, because, otherwise, Boy's surface would not be isomorphic (that is birationally equivalent) to the projective plane. D.Lazard (talk) 15:35, 4 April 2014 (UTC)

 * I'm also bothered that the Bryant parametrization has a boundary. Could someone explain how that is? —Tamfang (talk) 07:38, 8 June 2014 (UTC)
 * This is explained in section "Property of Bryant-Kusner parametrization": this is a two fold parameterization, and the condition that the magnitude of z is not greater than 1 is here only for having a bijective parameterization (outside the unit sphere). D.Lazard (talk) 09:44, 8 June 2014 (UTC)

I have added an external link to a page that answers to my preceding questions. It remains to edit the article to include these answers. D.Lazard (talk) 09:44, 8 June 2014 (UTC)

two-period parametrization
I wish I had the skill to derive a parametrization based on trig functions and the stitching illustrated here. Has no one done so? Would it be a double or a quadruple cover? —Tamfang (talk) 05:14, 29 June 2014 (UTC)
 * Given the three-fold symmetry of the usual embeddings, wouldn't it make more sense to start with a hexagon with opposite edges glued, instead of a square? —David Eppstein (talk) 05:17, 29 June 2014 (UTC)
 * The first external link of the article contains various parameterizations and references to the articles where they are defined. It explains also (in French) why Boy's surface differs from other realizations of projective plane (all singular points are simple crossing points — no cusps). I guess that the answer to your question is in this link and its references. By the way, it would be useful to expand the article, using this link. D.Lazard (talk) 09:27, 29 June 2014 (UTC)
 * IMHO the easiest way to derive a parametrization is to start with the unit circle, and write x(theta, phi), y(theta, phi), z(theta, phi) making sure that each coordinate function is periodic in phi -> pi - phi. This last part is pretty easy, you can chose a subset of the spherical harmonics that satisfy it.  This is how John Hughes found his parametrization of Boy's surface -- he projected a 7-vertex polygon model on the spherical harmonics to solve for the three functions, also taking use of the three-fold symmetry.  This is also how the parametrization for the other immersion of the real projective plane was found, although in that case there's not any three-fold symmetry.  a13ean (talk) 17:32, 1 July 2014 (UTC)

Eliminating confusion caused by a poor choice of variable names
Given that x, y and z are conventionally used as the three spatial coordinates in Cartesian 3-space, it would be wise to choose some letter other than z to represent the complex variable of the definition. Doing so would avoid confusing the non-mathematicians in our audience (and also promote clarity and rigour among the mathematicians!) I suggest using the letter w for the complex variable, as is often done. This would obviously require a thorough edit of the article, at least the Parametrization section, to replace all instances of z (except for those that refer to the third spatial coordinate) with w.

yoyo (talk) 13:22, 29 October 2015 (UTC)
 * I agree. Moreover, it is written z(z) in the article. I'll do that. D.Lazard (talk) 14:47, 29 October 2015 (UTC)

Construction
I find the "Construction" section pretty obscure. Some diagrams seem pretty necessary. Does anyone know where that's from? --Dylan Thurston (talk) 15:20, 4 October 2016 (UTC)

Connection to Borromean rings
I realised that there is a way to use Borromean rings to help visualise the immersion:-

- First, set up or imagine the rings as symmetrical ovals, e.g. ellipses, each placed symmetrically in a plane orthogonal to the others.

- Then look at them along the body diagonal of a cube symmetrically containing them, to see the threefold rotational symmetry.

- Then bisect them at a plane orthogonal to that diagonal and discard one part.

- From the set of three ovals, each enclosing the next, that gives you three roughly J shaped sloping and slanting arches, with their feet forming a regular hexagon, each arch going over the next and linking opposite vertices of the hexagon.

- Looking at the arches two at a time lets you see that each strip bridging opposite edges of the hexagon can be set up to fit with the others, though the creasing still needs a straightforward rounding off.

Is this merely a visual aid that at least helped me, or is there a deeper association? And is it worth it/acceptable to put any of this in the article? PMLawrence (talk) 04:15, 19 July 2020 (UTC)

New Video
I created a new video, which shows the construction from a Mobius strip, various slices of u and v. Not sure if it is worth it to add a link to the main page, or upload the video. I'd need some advice. Coolwanglu (talk) 20:20, 3 November 2023 (UTC)

title: Talk:Boy's surface


text:
Wikipedia:Articles for deletion/Ishak

Delete and quickly. This is nonsense. Just making sure it doesn't fall through the cracks because of multiple editors. Antares33712 15:47, 6 Jun 2005 (UTC)

title: Wikipedia:Articles for deletion/Ishak


text:
Talk:The Golden Cockerel

Page moved
--DrG 09:52, 2005 Jun 8 (UTC)

title: Talk:The Golden Cockerel


text:
Ergoldsbach

Ergoldsbach is a municipality in Bavaria, about 20 km north of Landshut and 80 km northeast of Munich in Germany.

Geography
Ergoldsbach is surrounded by many thick forests, in the hill country of the Landshut region, in Lower Bavaria. A protruding point is the Kapellenberg ("chapel hill") nearly 500 m (1600 ft.) above sea level. On the top of the wooded hill lies an old chapel. In Ergoldsbach, there is a small brook called Goldbach (from there: Ergoldsbach). Altogether the municipality covers an area of over 57 km² and maintains a road network of 98 km in total length.

The municipality of Ergoldsbach consists of the additional localities and townships of:
 * Dürrenhettenbach
 * Iffelkofen
 * Jellenkofen
 * Kläham
 * Langenhettenbach
 * Leonhardshaun
 * Martinshaun
 * Oberdörnbach
 * Osterhaun
 * Paindlkofen
 * Prinkofen
 * Siegensdorf
 * Unterdörnbach
 * Wölflkofen

As well as the settlements of Frauenwies, Haselwies, Kienoden, Reicherstetten, Stocka.

History
The first mention of Ergoldsbach in writing dates back to 822. The land belonged to the Landshut Rentamt and the District Court of Teisbach in the electorate of Bavaria. At this time, Ergoldsbach had its own market court with a magistrate. Resulting from its location along the Landshut–Regensburg road, it developed through trade with the farming population. In the year 1403 it became a Municipality with Market town rights. Later on, some fires changed the town forever. In 1860 the Erlus brickworks were established, along with the opening of a railway line from Landshut to Geiselhöring, which resulted in an economic boom for the town. After a fire, the Erlus factory relocated its head office to Neufahrn nearby. All that remained in Ergoldsbach was the chimney. In 1913 a hospital was built in Ergoldsbach, which operated until 1977. After this it was used by the Red Cross, until conversion into a nursing home for seniors in 2004.

Incorporation
The Market town/municipality Ergoldsbach was founded between 1972-1978 by incorporating Prinkofen, Langenhettenbach, Paindlkofen, Kläham and Martinshaun.

Events leading to the rescue of KZ prisoners 1945
In April 1945, policeman Max Maurer of the SS was delivered with 13 Jewish KZ prisoners, allegedly with the order to shoot them. Maurer took the prisoners to the property of Anna Gnadl, where a day later they were recovered by the American advancement. According to John Weiner, one of the 13, Maurer saved the prisoners' lives. This was recognised in 1997, when Yad Vashem of Israel presented the Righteous among the Nations award.

Infrastructure
Ergoldsbach is on the Munich–Regensburg railway line and is served by Agilis and Deutsche Bahn. The Bundesstraße 15, an important federal highway, also runs through the town. In the near future a new road with four lanes is planned to reduce the traffic load on the marketplace in the town's center. The town belongs to the water authority of Rottenburg.

Development
In 2007, the area owned by the Stiegler and Ziegler families was developed into a new centre. With the demolition of Fassadenbaus, space was created for a supermarket and car park. In Jellenkofen there is a business park with a total area of 39.000 m². Furthermore, residential building areas are available on the Kapellenberg. A secondary school in the nearby Ergolding, established in 2013, gives the municipality of Ergoldsbach a boost.

Education and Youth

 * Ergoldsbach Kindergarten with branches in Ergoldsbach and Kläham.
 * Ergoldsbach Verbandsschule with a Grundschule (primary school) and a Hauptschule (secondary school), which has recently been completely refurbished.
 * Ergoldsbach Jugendtreff (youth club) next to the Werk II Plaza.

Entertainment

 * The Goldbach Hall, a sports and multipurpose hall with the capacity to seat 1000 spectators.

Sports and Leisure

 * The new Ergoldsbach sports centre was opened on 16 July 2004.
 * Ergoldsbach has two beach volleyball courts (in Kläham and Jellenkofen) and a number of football ovals.
 * Ergoldsbach also has an outdoor public swimming pool.
 * A skate park is being planned.
 * There is also a tennis club located in Ergoldsbach, called the TCE. It has its own club house with 6 tennis courts (sand).

Fire Brigade
In and around the municipality of Ergoldsbach there are several Freiwillige Feuerwehren (volunteer fire departments):

FF Ergoldsbach; FF Kläham; FF Langenhettenbach; FF Martinshaun; FF Paindlkofen; FF Prinkofen.

Religion

 * About 75% of the Ergoldsbach population are Catholic. The parish church St. Peter and Paul (Ergoldsbach) is located near the town centre.  The smaller church or chapel of the region is also located in Ergoldsbach (Agatha Chapel).
 * About 7% of the Ergoldsbach population are Lutheran. The circa 1970 church is located at the recreation area on Badstraße ('bath road').   The service alternates between the aforementioned Ergoldsbach church and the Friedenskirche ('peace church') in Neufahrn.
 * An increasing proportion of the Ergoldsbach population now belongs to Islam.

Economy
First and foremost, Ergoldsbach is a commuter community. A large proportion of the population travel every day to Landshut, Munich, Dingolfing and Regensburg. In Ergoldsbach itself, is the Erlus corporation among other companies. There a variety of supermarkets, two bakeries with outlets in Neufahrn, Essenbach, Landshut, etc. and other small businesses.

Clubs
In Ergoldsbach and its surroundings, there are about 60 fairly large clubs.

Twin Towns and Sister Cities

 * In the year 2004 a partnership was established with the Italian city Montefiascone.
 * Ergoldsbach is a partner of the municipality Ergolding.

Books about Ergoldsbach

 * Roger DEVAUX : Treize Qu'ils Etaient - Life of the French prisoners of war at the peasants of low Bavaria (1939–1945) - Treize Qu'ils Etaient - Mémoires et Cultures - 2007 - ISBN 2-916062-51-3

title: Ergoldsbach


text:
User talk:Grim...

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title: User talk:Grim...


text:
Talk:Mamoru Oshii

Untitled
Where does it say that Stanley Kubrick considered Oshii a genius? I'm just curious if it's actually true or not. —The preceding unsigned comment was added by 164.107.121.141 (talk • contribs).

Upcoming works
[03/25/2005] 	Production Complete on "Mezame No Hakobune" Chief Direction by Mamoru Oshii

Theater hall completely modeled around film's theme to be featured at EXPO 2005 AICHI JAPAN

to be continued ... or modified see relevant page —The preceding unsigned comment was added by 82.126.139.161 (talk • contribs).

Quotes
There are quite a few quotes... perhaps they should be moved to Wikiquote. --Maru (talk) 20:44, 2 October 2005 (UTC)

Kubrick thing is obviously made up, got rid of it —The preceding unsigned comment was added by 222.152.197.26 (talk • contribs).

'Obsessions' doesn't sound very encyclopedic to me... 135.196.137.154 15:51, 27 October 2006 (UTC)

stubby
This is so irrelevent that for a moment I thought it was a joke/vandalism... a pun on the idea of the section being a "stub": So i removed it. If there's some reference in the text to Oshii having mentioned this dog in his work or interviews then it would be fine to go back in I guess but for now it seems totally confusing.

I dunno where to begin with convivial seriocomic so i've left that for now. :)135.196.137.154 15:59, 27 October 2006 (UTC)

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BetacommandBot (talk) 14:43, 2 January 2008 (UTC)

YouTube Link?
I listed the Washowski brothers as being influenced by Oshii. I added a link from YouTube that supported the claim, yet it was removed by an automated bot. What should I do? —Preceding unsigned comment added by Stepusual (talk • contribs) 00:41, 12 September 2008 (UTC)

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Anon edits
So seems to be pretty active on this article. Lately he's apparently removed everything from the 'Selective works' section which he didn't either direct or write; what do other contributors make of this?

Quote
'[Anno] Oshii (Mamoru)-san says "Now that the pioneers of anime have died, it will die with them." He says the history of anime ended long ago.' http://web.archive.org/web/20071018065110/www.cjas.org/~leng/anno-ikuhara.txt --Gwern (contribs) 21:37 14 December 2009 (GMT)

Interview
From Protoculture Addicts: "Anecdotes from Mr. Mamoru Oshii". --Gwern (contribs) 13:28 25 March 2010 (GMT)

External links modified
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title: Talk:Mamoru Oshii


text:
Stekšys

Stekšys (or Steksė) (other spellings include Stakys, Stejkint, Stekintas, Stegikintas, Stegutas) was a duke of Lithuania, killed in 1214 near Lielvārde during an attack against Livonia. He is one of the earliest mentioned Lithuanian dukes. He succeeded duke Daugirutis, who killed himself while in Livonian captivity in 1213. After these two deaths, Lithuanian raids to the Livonian lands decreased in frequency and historians assume a period of decline in the unification process of the Baltic tribes.

Tomas Baranauskas suggests that Daujotas and Vilikaila, dukes mentioned in a 1219 treaty with Halych-Volhynia, were Stekšys' sons.

title: Stekšys


text:
User:Mosmi

Sports a chino-textured soul and the aura of an Anglican vicar.

Mosmi.com

Last update: Mosmi 21:42, 31 October 2010 (UTC)

title: User:Mosmi


text:
Talk:Research report

Is this really the only use?
 * No. Research reports are also used by governments (notoriously!), universities, and non-profit organizations. This article is far too limited to the business research report. Kaijan 12:25, 25 January 2006 (UTC)

Listing analysts? Why are the names of research analysts being included beside the companies they work for? These people are not themselves notable beyond being employees of the company and do not merit inclusion on this page (those linking to active pages are other people with the same name, in one cse long deceased!). These companies often employ 100's of people in this role, there does not appear to be any reason to include these names over their peers, or at all. Lastemperor —Preceding comment was added at 10:41, 14 February 2008 (UTC)

Spam linkage
2/3's of this article seems to be external links to firms—these do not seem informative per WP:EL, just advertising. I am considering deleting these sections en masse, but pause here to ask if anyone can suggest a better approach. / edg ☺ ☭ 15:06, 22 July 2009 (UTC)

Bajo rendimiento de los estudiantes
Que hace que los estudiantes tenga un bajo rendimiento 181.37.87.79 (talk) 19:20, 7 July 2022 (UTC)

title: Talk:Research report


text:
Julius Leopold Theodor Friedrich Zincken

Julius Leopold Theodor Friedrich Zincken or Zinken also Sommer (15 April 1770 in Braunschweig – 8 February 1856 in Braunschweig) was a German entomologist. He also appears in literature cited as Zinken-Sommers and Zinken gennant Sommers.

He was co-editor, with Ernst Friedrich Germar of Magazin der Entomologie Hendel & Son. Halle. also known as Germar's Magazine in which he wrote many articles and described new species and genera especially in the Tineidae.

Zincken's collection was sold on his death. Its subsequent history is unknown.

Works
Partial list

 * Zincken, J. L. T. F. 1817. Die Linneischen Tineen, in ihre natürlichen Gattungen aufgelöst und beschrieben. Magazin der Entomologie, Halle 2: 24–113.
 * Zincken, J. L. T. F. 1818. Die Lineeischen Tineen, in ihre natürlichen Gattungen aufgelöst und beschrieben. Magazin der Entomologie, Halle 3: 114–116.
 * Zincken, J. L. T. F. 1821. Die Linnéeischen Tineen, in ihre natürlichen Gattungen aufgelöst und beschrieben. Magazin der Entomologie, Halle 4: 231–245.
 * Zincken, J. L. T. F. 1821. Nachtrag zur Monographie der Gattung Chilo. Magazin der Entomologie, Halle 4: 246–258.
 * Zincken genannt Sommer, J. L. T. F. 1829. Anweisung zum Seidenbau überhaupt und insbesondere in Bezuge auf das nördliche Deutschland, nach den neuesten Verbesserungen desselben und nach eigenen Erfahrungen und über die Naturgeschichte des Seidenspinners selbst angestellten Versuchen abgefasst, Braunschweig, Meyer
 * Zincken genannt Sommer, J. L. T. F. 1831. Beitrag zur Insecten-Fauna von Java. Erste Abtheilung. Nova Acta Leopoldina 15: 1.
 * Zincken genannt Sommer, J. L. T. F. 1832. Anweisung für Gartenbesitzer und Landleute, wie dieselben in jedem Monate des Jahres zu verfahren haben, um in ihren Gärten Obst und Gartenfrüchte vor den Zerstörungen durch schädliche Insekten an leichtesten zu schützen, Braunschweig, Meyer


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Franklin Garrett

Franklin Miller Garrett (September 25, 1906 – March 5, 2000) was an American historian, the only official historian of Atlanta, Georgia. His massive Atlanta and Environs: A Chronicle of its People and Events is a book about the city's history.

Biography
A native of Milwaukee, he moved to Atlanta in 1914. He graduated from Technological High School in Atlanta, Georgia. He joined the Atlanta Historical Society in 1927 (a year after it was founded) which is today known as the Atlanta History Center. He served as historian for the Coca-Cola Company for 28 years. After retirement he devoted his full-time efforts to the Atlanta History Center.

Garrett was married to Frances Steele Garrett, who died in September 2005.

Awards

 * Named "official historian" of the city by Atlanta City Council, 1974
 * Honorary doctorate from Oglethorpe University
 * Honorary doctorate from Georgia State University on June 20, 1998
 * Shining Light award for community service
 * The Georgia Railroad Named EMD GP 38-2 locomotive number 6051, as The Franklin M. Garrett in 1980. This locomotive ran on the Georgia R.R. until 1983, when the Georgia was Merged into Seaboard System. Seaboard System kept the name on the locomotive. The 6051 pulled the Last Georgia Mixed Train out of Atlanta in 1983. This locomotive today is CSXT 2702, retaining the name, and was to assigned to Atlanta's Tilford Yard. However Tilford was torn out completely in 2018 and the 2702 is currently assigned to Hamlet, North Carolina, the former Seaboard Air Line hump yard and is used on Hamlet-Raleigh, North Carolina and Hamlet-Columbia, South Carolina local trains.

Books

 * (First published in 1954, later expanded to 3 volumes by Garrett and a fourth by another author)

title: Franklin Garrett


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Tukang Besi language

Tukang Besi is an Austronesian language spoken in the Tukangbesi Islands in southeast Sulawesi in Indonesia by a quarter million speakers. A Tukang Besi pidgin is used in the area.

Phonology
The northern dialect of Tukang Besi has 25 consonant phonemes and a basic 5-vowel system. It features stress which is usually on the second-to-last syllable. The language has two implosive consonants, which are uncommon in the world's languages. The coronal plosives and have prenasalized counterparts which act as separate phonemes.

Notes:
 * only appears in loanwords, but it contrasts with
 * and are not phonemic and appear only as allophones of, which appears only in loanwords.

Vowels

 * a –
 * e –
 * i –
 * o –
 * u –

Consonants

 * b –
 * b̠ –
 * c –
 * d –
 * d̠ –
 * g –
 * h –
 * j –
 * k –
 * l –
 * m –
 * mb –
 * mp –
 * n –
 * nd –
 * ns –
 * nt –
 * ng –
 * ngg –
 * ngk –
 * nj –
 * p –
 * r –
 * s –
 * t –
 * w –

Nouns
Tukang Besi does not have grammatical gender or number. It is an ergative–absolutive language.

Verbs
Tukang Besi has an inflectional future tense, which is indicated with a prefix, but no past tense.

Word order
Tukang Besi uses verb–object–subject word order, which is also used by Fijian. Like many Austronesian languages, it has prepositions, but places adjectives, genitives, and determiners after nouns. Yes–no questions are indicated by a particle at the end of the sentence.

title: Tukang Besi language


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1930–31 in Swedish football

The 1930-31 season in Swedish football, starting August 1930 and ending July 1931:

Division 2 Norra 1930–31

Norra

Södra

National team results
🇸🇪 Sweden: Olle Bengtsson - Herbert Lundgren, Gunnar Zacharoff - Rune Carlsson, Wilhelm Petersén, Helge Liljebjörn - Rune Wenzel, Harry Dahl, Per Kaufeldt, Carl-Erik Holmberg, Evert Hansson.

🇸🇪 Sweden: Sigfrid Lindberg - Axel Alfredsson, Arne Johansson - Folke Fredenlund, Nils Rosén, Erik Granath - Charles Brommesson, Gunnar Olsson, Harry Lundahl, Albin Dahl, Knut Kroon.

🇸🇪 Sweden: Eivar Widlund - Erik Linder, Helge Zachrisson - John Kristiansson, Torsten Lindskog, Gösta Nordström - Gösta Dunker, Åke Andersson, Bertil Karlsson, John "Tjodde" Nilsson, Axel Johansson.

🇸🇪 Sweden: Sigfrid Lindberg - Axel Alfredsson, Arne Johansson - Folke Fredenlund, Nils Rosén, Einar Snitt - John "Jompa" Nilsson, Erik Persson, Per Kaufeldt, Ernst Wahlberg, Wilhelm Engdahl.

🇸🇪 Sweden: Anders Rydberg - Herbert Samuelsson, Arne Johansson - Helge Liljebjörn, Nils Rosén, Ernst Andersson - John "Jompa" Nilsson, Erik Persson, Per Kaufeldt, Albin Dahl, Knut Kroon.

🇸🇪 Sweden: Anders Rydberg - Herbert Samuelsson, Arne Johansson - Helge Liljebjörn, Nils Rosén, Ernst Andersson - John "Jompa" Nilsson, Rolf Gardtman, Sune Zetterberg, Sven Rydell, Evert Hansson.

🇸🇪 Sweden: Anders Rydberg - Herbert Samuelsson, Arne Johansson - Helge Liljebjörn, Nils Rosén, Ernst Andersson - John "Jompa" Nilsson, Rolf Gardtman, Sune Zetterberg, Sven Rydell, Evert Hansson.

🇸🇪 Sweden: Eivar Widlund - Axel Alfredsson, Sven Andersson - Walfrid Persson, Thure Svensson, Einar Snitt - Gösta Dunker, Ragnar Jacobsson, Sune Zetterberg, John Sundberg, Rune Eriksson.

🇸🇪 Sweden: Martin Larsson - Gusten Berg, Nils Berggren - Rune Carlsson, Thure Svensson, Einar Snitt - Georg Johansson, Sven Rydell, John Sundberg, Hans Garpe, Sigurd Roos.

title: 1930–31 in Swedish football


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Lacus Lenitatis

Lacus Lenitatis (Latin lēnitātis, for "Lake of Softness") is a small lunar mare in the Terra Nivium region on the Moon. It is located at 14.3° N, 12.1° E and is 78 km in diameter.

title: Lacus Lenitatis


text: User talk:205.174.22.26

title: User talk:205.174.22.26


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Meriwether Smith

Meriwether Smith (1730 – January 25, 1790) was an American planter from Essex County, Virginia.

Smith was first elected to the Virginia House of Burgesses in 1770. He was a vocal opponent of the 1765 Stamp Act, and a representative in the revolutionary conventions that replaced the burgesses in 1775 and 1776. He was elected as a delegate to the Continental Congress in 1778, 1779, and 1780, although he did not serve the 1779 term. He was a member of the Virginia House of Delegates from 1776 to 1778 and again in 1781. In 1788 he was a member of the Virginia convention that ratified the U.S. Constitution; an Anti-Federalist, he voted against ratification.

Smith was married twice, first to Alice Lee in 1760 and after her death to Elizabeth Daingerfield in 1769. His son by Alice was George William Smith who was Governor of Virginia from part of 1811. Meriwether died in Essex County in January 1790 , and was buried in a family plot on his plantation, "Bathurst."

title: Meriwether Smith


text:
Talk:The Master Trust Bank of Japan

Untitled
rolledback copyvio from JCR, at

Please sign your comments on this page. I found the article unreadable and edited it substantially. Naerhu 01:36, 28 December 2006 (UTC)

title: Talk:The Master Trust Bank of Japan