text:
User:Gsandi

en:user:Gsandi

= About myself =

I am a multilingual member of the Wikipedia community. I love anything connected with multilingual applications - I have even created my own (Romance) conlang (artificial language), and translated three chapters of Le Petit Prince into it! (Yes, it's on my web site: )

My special interests are:

 * Linguistics, particularly of the comparative-historical kind (Indo-European, Uralic, Japanese)
 * Con-langing and con-worlding (the creation of imaginary languages, worlds, countries) - as such I am an active participant in the zompist bboard message board
 * Transportation systems, with a special love for streetcars/trams/trolley cars/LRT systems
 * Beautiful carnivores, in particular tigers and cats
 * Geography and history, in particular those of countries I have lived or worked in (in fact, there are six of these: Hungary, Ghana, Canada, France, Switzerland, India) or whose languages I have studied (Japan, Brazil, Spain ...)
 * Mathematics, with special interest in probability and number theory
 * Space sciences, in particular space colonization and the search for extraterrestrial intelligence (I wouldn't mind finding evidence for terrestrial intelligence either)
 * Intellectual games such as bridge, chess and (recently) sudoku
 * Science fiction (Robert Heinlein and Poul Anderson being among my favourite authors)
 * Website creation and maintenance (my site is at: )

By background, I am Hungarian by birth and Canadian by adoption. I started my life in Budapest and have now moved to Vancouver, B.C., the top city in the world for quality of life according to some surveys. This is not the first time I have lived here, as I did my graduate studies at UBC. I am now retired, after working for decades for a UN organization in Geneva, Switzerland.

I am more likely to do much of my work in the English wiki, because I feel more comfortable writing in formal (scholarly or journalistic) style in English than in my native Hungarian. I am, however, an editor by trade (among other things), and a notorious "pedant" - I dislike inaccuracies, spelling and grammatical mistakes, all of which I am likely to correct in any language version of the wikipedia, my competence in the given language permitting. The possibility of correcting an Encyclopedia is one of the pleasures of the wikipedia, after all.

I am enough of a patriot to think that creating/expanding on articles of Hungarian interest in the English wikipedia will be of benefit to my native country's reputation in the world. And, as I have just discovered, I can do the same for articles of Canadian interest in the Hungarian wiki!

= List of countries I have been to =

(brief visits to airports or railway stations do not count):

Africa
Benin Central African Republic Ghana Sierra Leone

The Americas
Argentina Brazil Canada Colombia Mexico Peru United States

Asia
China (including Hong Kong and Macau) India Japan Philippines Singapore South Korea Thailand

Australia and the Pacific
Australia New Zealand

Europe
Andorra Austria Belgium Czech Republic Denmark Finland France Germany Hungary Ireland Italy Netherlands Liechtenstein Luxembourg Monaco Norway Portugal Romania Slovakia Slovenia Spain Sweden Switzerland United Kingdom (including Jersey, not strictly speaking part of the UK) Vatican City

hu:user:Gsandi

title: User:Gsandi


text:
John Pasta

John Robert Pasta (October 22, 1918 – June 5, 1981) was an American computational physicist and computer scientist who is remembered today for the Fermi–Pasta–Ulam–Tsingou experiment, the result of which was much discussed among physicists and researchers in the fields of dynamical systems and chaos theory, and as the head of the department of Computer Science at the University of Illinois at Urbana-Champaign from 1964 to 1970.

Early life
Pasta was born in New York City in 1918, the eldest of four children, and grew up in Queens. He attended the New York public schools and became interested in physics at an early age when an uncle gave him some of his old college books. After graduating from Townsend Harris High School, he entered City College of New York in 1935 and completed three years. The Depression forced him to drop out and to take a job as a real estate title examiner. In August 1941, he became a patrolman for the New York City Police Department. In 1942, he was drafted into the US Army, became an officer in the Signal Corps, and took courses on electronics and radar at Harvard and MIT. He married Betty Ann Bentzen at the Little Church Around the Corner in New York City in May 1943.

During World War II, Pasta served in Europe, mostly as cryptographical security officer and radar officer, for which he was awarded the Bronze Star and the Belgian Fourragère. After being discharged in 1946, he took advantage of the GI Bill to finish his undergraduate work at City College that same year and enter graduate school at New York University to study mathematics and physics. As a graduate student he became a research fellow in the department of physics at Brookhaven National Laboratory, and completed his thesis on "Limiting Procedures in Quantum Electrodynamics" in 1951 under the guidance of Hartland Snyder. He became a staff member of the Los Alamos Laboratory in August 1951.

1951–1963
At Los Alamos National Laboratory Pasta would begin his work on his most famous projects.

In 1952, working under Nicholas Metropolis on the MANIAC I, John Pasta aided in the construction of an early computer that specialized in calculations around weapons design.

After working on the MANIAC I, Pasta continued on to work in the project he is most known for, the Fermi–Pasta–Ulam–Tsingou problem.

After working alongside Enrico Fermi, Stanislaw Ulam, and Mary Tsingou, Pasta went on to work for the Atomic Energy Commission as the only computer expert, eventually developing the branch of mathematics and computers to an entire division.

1964–1981
In 1964, Pasta became a research professor of physics at the Department of Computer Science at the University of Illinois, and later became the head of the department. He died in 1981, in Washington, DC.

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

title: John Pasta


text: Category talk:1954 Atlantic hurricane season


text: Category talk:1953 Atlantic hurricane season


text: Category talk:1952 Atlantic hurricane season


text: Category talk:1950 Atlantic hurricane season


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List of schools in Sandefjord

Schools in Sandefjord, Norway include:

Higher education

 * Norwegian school of management (BI Vestfold)

Secondary/high schools
All external links are in Norwegian.
 * Sandefjord videregående skole
 * Skagerak International School
 * Skiringssal folkehøyskole

Middle schools
All external links are in Norwegian.
 * Skagerak Middle School,
 * Breidablikk
 * Ranvik
 * Varden
 * Bugården

Primary schools
All external links are in Norwegian.
 * Skagerak Primary School, IB World School delivering Primary Years Programme (PYP)
 * Haukerød, north of the city
 * Krokemoa, approximately 4 km west of the city
 * Byskolen, the oldest school in Sandefjord
 * Unneberg, the smallest in the municipality
 * Gokstad, by the north end of Østerøya
 * Virik
 * Sande, close to the city
 * Framnes
 * Fevang
 * Helgerød
 * Mosserød
 * Store Bergan
 * Ormestad

title: List of schools in Sandefjord


text: Category talk:1951 Atlantic hurricane season


text: Category talk:1940s Atlantic hurricane seasons


text:
USS Murzim

USS Murzim (AK-95) was a Crater-class cargo ship commissioned by the US Navy for service in World War II. She was named after Murzim, the star in constellation Canis Major. Murzim was manned by United States Coast Guard personnel and was responsible for delivering troops, goods and equipment to locations in the Asiatic-Pacific Theater.

In light of the Mount Hood tragedy, which involved the complete explosion of another ammunition ship, USS Mount Hood (AE-11), it became clear that those on Murzim and other ammo ships were running the risk of nearly instantaneous death by catastrophic explosion at every moment of their stint in the Pacific Theater. Nevertheless, the crew worked even under the threat of air attack warnings, transferring their cargo to other fighting ships.

Construction
Murzim was laid down 10 July 1942, under a United States Maritime Commission (MARCOM) contract, MC hull 633, as Liberty ship SS Brigham Young by California Shipbuilding Corporation, Terminal Island, Los Angeles, California; and launched 17 August 1942; sponsored by Mrs. Albert E. Bowen; renamed Murzim 17 March 1943; acquired by the Navy under bareboat charter from the MARCOM on 8 April 1943; converted for use as a naval cargo ship by the Los Angeles Shipbuilding & Drydock Company, Los Angeles, California; and commissioned 14 May 1943.

Service history
For almost two months Murzim operated along the west coast of the United States under the 11th Naval District; thence, after loading general cargo, she departed from San Francisco on 8 July 1943, and arrived at New Caledonia on 5 August. She then began cargo shuttle runs among American bases in the South Pacific and during the next year, she delivered supplies from ports in Australia, New Zealand, and New Caledonia to the New Hebrides, the Fiji Islands, and the Solomon Islands. She carried out several voyages between Nouméa and Guadalcanal, and in the spring of 1944 she extended her runs northward along the Solomon chain to Bougainville, New Georgia, Green Island, and the Russells. In mid-June she sailed from the Solomons via New Guinea to the Admiralties where she discharged cargo at Manus. After steaming to Australia for a cargo of ammunition, she returned to New Guinea 24 August.

For almost two months, Murzim supplied antiaircraft ammunition to ships at Hollandia preparing for the invasion of the Philippines. After filling her holds with ammunition from Brisbane and Sydney Australia, she sailed without escort for the Philippines on 24 October. Arriving in Leyte Gulf on 29 October, she began duty as an ammo station ship. During the next three months she supplied ships from cruisers to LSTs with a variety of ammunition which ranged from 6 in to 20 mm. Despite numerous air alerts, her crew carried out the dangerous business of transferring ammunition to ships alongside. During an enemy air attack on 27 November, her 20 mm guns splashed a Japanese plane attacking the cargo ship from starboard.

Between 27 January and 4 February 1945, Murzim steamed in convoy to Manus where she replenished her holds with ammunition. Thence, after joining a convoy at Hollandia, she returned to Leyte on 22 March, and resumed ammo station duty in Leyte Gulf. During the closing weeks of the war against Japan, she delivered cargo to Manus and cruised to the Philippines with additional supplies of ammunition.

End-of-war decommission
Following the Japanese surrender, Murzim was authorized for use in atomic tests in the Marshalls, and was ordered to transfer to joint Task Force 1, 25 February 1946. However, she was assigned to the 14th Naval District for inactivation 11 March, and she decommissioned at Pearl Harbor 7 June. She remained at Pearl Harbor until March 1947, when she was towed to San Francisco. Her name was struck from the Navy Directory 23 June. Murzim was transferred to MARCOM 5 August 1947, and entered the National Defense Reserve Fleet, Suisun Bay.

On 19 March 1973, she was sold to Nicolai Joffe Corporation, for $168,113, to be scrapped. She was withdrawn from the fleet 27 July 1973.

Awards
Murzim received one battle star for World War II service.

title: USS Murzim


text:
Jiří Bicek

Jiří Bicek (born December 3, 1978) is a Slovak former professional ice hockey winger. He played in the National Hockey League with the New Jersey Devils between 2000 and 2004, winning the Stanley Cup with them in 2003. The rest of his career, which lasted from 1995 to 2018, was mainly spent in Europe. Internationally Bicek played for the Slovak national team at several tournaments, including the 1997 and 2009 World Championships.

Playing career
Bicek was drafted 131st overall by the New Jersey Devils in the 1997 NHL Entry Draft. He then proceeded to play 7 pro seasons in North America, mostly playing for the Albany River Rats of the AHL. In 423 games in Albany, Bicek scored 75 goals and 167 assists for 242 points. In those last four seasons, he was called up to the Devils sporadically. During the 2004–05 NHL lockout, Bicek returned to Slovakia to play for HC Košice. He played 54 games there and scored 18 goals and 41 points. In 62 career NHL games, Bicek has scored 6 goals and 7 assists for 13 points. He won a Stanley Cup in 2003 with the Devils.

During the 2006–2007 season he played for Swedish team Brynäs IF and Finnish KalPa before moved 2008 to JYP in the SM-Liiga, he joined to end of the year 2008 to EHC Biel.

Awards

 * 2003 — NHL Stanley Cup

title: Jiří Bicek


text:
User talk:Evenprime

Welcome!

Hello,, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers: I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~~); this will automatically produce your name and the date. If you need help, check out Where to ask a question, ask me on my talk page, or place  on your talk page and someone will show up shortly to answer your questions. Again, welcome! CambridgeBayWeather 21:12, 8 October 2005 (UTC)
 * The five pillars of Wikipedia
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 * Help pages
 * Tutorial
 * How to write a great article
 * Manual of Style

Geo Storm article
Hello, I noticed you left me a message on my talk page about the Geo Storm article, so I'll go ahead and speak. Anyway, the reason why I tagged it was because it doesn't seem to be organized quite well. A table like the ones I have been adding to stubs recently would help. You can try copy-pasting the table from the Dodge Spirit article to the Storm article and add any necessary information. For example, I think the "Dimensions" section would work better if the actual dimensions were posted on a table instead of a separate section. Also, treat the article as if it were going to be entered in a printed encyclopedia. After all, Wikipedia IS an encyclopedia, right? Hope this helps! --ApolloBoy 00:26, 15 October 2005 (UTC)

 * OK, I just looked over it, and I think you fixed it up enough, so I removed the cleanup tag. By the way, I didn't create the Dodge Spirit article. --ApolloBoy 06:50, 15 October 2005 (UTC)

Autocross + FF
I was just making observations based on national results, the winners in most stock classes (except A stock) are dominated by FF type cars, like the Integra, Celica, and Mini Cooper S. I'll re-word it so it doesn't say preferred.. Something like 'perform well'? Morwan 11:54, 8 December 2005 (UTC)

 * I liked the "fairly popular" that you went with. Some classes (e.g. H-stock) are almost entirely FF, so naturally the winners are FF.  That doesn't mean FF is the best way to go, just that it is a common, inexpensive layout. Evenprime 15:51, 8 December 2005 (UTC)

Geo Storm
That article looks great, one of the best rookie efforts I've seen. With a little more work it could be a Featured Article. One problem is that it is very vague on geography. The article never says where the car was sold, and statements like "they are still fairly common in the used car market" need to be specified, as they probably don't apply to the entire world. I would also consider dumping Image:1993geostorm.jpg, the article has a number of good free use pictures, so there is no reason to keep a somewhat dubious fair use one. - SimonP 15:46, 14 February 2006 (UTC)

thanks for the input. I'll try to get some geography info, and I will loose the commercial picture as soon as I get an equivalent one for that model year.

Image copyright problem with Image:Asept05-33.jpg
Thanks for uploading Image:Asept05-33.jpg. However, the image may soon be deleted unless we can determine the copyright holder and copyright status. The Wikimedia Foundation is very careful about the images included in Wikipedia because of copyright law (see Wikipedia's Copyright policy).

The copyright holder is usually the creator, the creator's employer, or the last person who was transferred ownership rights. Copyright information on images is signified using copyright templates. The three basic license types on Wikipedia are open content, public domain, and fair use. Find the appropriate template in Image copyright tags and place it on the image page like this:.

Please signify the copyright information on any other images you have uploaded or will upload. Remember that images without this important information can be deleted by an administrator. If you have any questions, feel free to contact me. Thank you. Zsinj Talk 00:35, 25 February 2006 (UTC)

GeoStorm table
For the images, pick the ones that best illustrate what is being said in the text (ie. whatever the modifications were on). As for the table, consider something like this. That table is just a result of copy&pasting from another article. It may work out good or it may not. It is just an idea to consider. --maclean 25 20:34, 5 March 2006 (UTC)

Geo Storm Images
did you take those pictures in the Geo Storm article? Their copyright status is the only thing holding it back from becoming featured. --Karrmann

 * All the images except one are ones I took. My dad took the one of me driving with the wheel off the ground.  (I had another autocross picture in the article - one I took of my dad autocrossing the same car - but removed it because apolloboy said there was too much motorsports emphasis.)  Tell me how to set the copywrite on these pictures so it is no longer a problem.... Evenprime 03:30, 8 March 2006 (UTC)

 * Thanks for clearing up those issues, Evenprime. It's too bad that it seemed to happen too late for the FA to happen -- I would have been happy to change my vote once that problem was solved.--Bcrowell 01:59, 13 March 2006 (UTC)

 * Are you sure it is too late? The page is still a candidate? Evenprime 17:23, 14 March 2006 (UTC)

Congrats
Put this on your Userpage! --Karrmann

Thank you! I will continue trying to improve it. I've added a table to the year to year changes section, and will be taking more photos to finish it out.

Geo Storm FAC
I noticed you got the Geo Storm up as a FAC again, so here is a step by step process of what to do.

1. Add the tag to the talk page you've already done that 2. now here. I already blanked that page. Add to it the reason why you think it should be featured. 3. add this ((Wikipedia:Featured article candidates/Geo Storm)) to the top of the list on this article and you will be good to go!

If you need further assistance, fell free to PM me! --Karrmann

Andrews University referencing
Please note that the ref/note format for referencing has been discontinued in favour of the more advanced and tags. Cheers, Ans  e  ll  Review my progress! 23:17, 27 May 2006 (UTC)

RfA Notification
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Gerardo Bonilla
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File:1992StormFront.jpg listed for deletion
A file that you uploaded or altered, File:1992StormFront.jpg, has been listed at Files for deletion. Please see the to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. Cloudbound (talk) 20:57, 3 May 2012 (UTC)

Need input on Article
I need your help on this article for Amazing Discoveries....https://en.wikipedia.org/wiki/Amazing_Discoveries as it needs work to keep it from being deleted from Wikipedia. Any help would be appreciated. Thanks. Simbagraphix (talk)
 * Also if could get your input on this related article for Walter Veith....https://en.wikipedia.org/wiki/Walter_Veith
 * ....Thanks.Simbagraphix (talk) 17:47, 25 March 2014 (UTC)

Proposed deletion of Sport Compact Car

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Proposed deletion of British autocross

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Nomination of British autocross for deletion
A discussion is taking place as to whether the article British autocross is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted.

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Proposed deletion of Autocross (disambiguation)

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title: User talk:Evenprime


text:
Fermi–Pasta–Ulam–Tsingou problem

In physics, the Fermi–Pasta–Ulam–Tsingou (FPUT) problem or formerly the Fermi–Pasta–Ulam problem was the apparent paradox in chaos theory that many complicated enough physical systems exhibited almost exactly periodic behavior – called Fermi–Pasta–Ulam–Tsingou recurrence (or Fermi–Pasta–Ulam recurrence) – instead of the expected ergodic behavior. This came as a surprise, as Enrico Fermi, certainly, expected the system to thermalize in a fairly short time. That is, it was expected for all vibrational modes to eventually appear with equal strength, as per the equipartition theorem, or, more generally, the ergodic hypothesis. Yet here was a system that appeared to evade the ergodic hypothesis. Although the recurrence is easily observed, it eventually became apparent that over much, much longer time periods, the system does eventually thermalize. Multiple competing theories have been proposed to explain the behavior of the system, and it remains a topic of active research.

The original intent was to find a physics problem worthy of numerical simulation on the then-new MANIAC computer. Fermi felt that thermalization would pose such a challenge. As such, it represents one of the earliest uses of digital computers in mathematical research; simultaneously, the unexpected results launched the study of nonlinear systems.

The FPUT experiment

In the summer of 1953 Enrico Fermi, John Pasta, Stanislaw Ulam, and Mary Tsingou conducted computer simulations of a vibrating string that included a non-linear term (quadratic in one test, cubic in another, and a piecewise linear approximation to a cubic in a third). They found that the behavior of the system was quite different from what intuition would have led them to expect. Enrico Fermi thought that after many iterations, the system would exhibit thermalization, an ergodic behavior in which the influence of the initial modes of vibration fade and the system becomes more or less random with all modes excited more or less equally. Instead, the system exhibited a very complicated quasi-periodic behavior. They published their results in a Los Alamos technical report in 1955. Enrico Fermi died in 1954, and so this technical report was published after Fermi's death.

In 2020, National Security Science magazine featured an article on Tsingou that included her commentary and historical reflections on the FPUT problem. In the article, Tsingou states "I remember sitting there one day with Pasta and Ulam," as they brainstormed "some problems we could do on the computer, some really mathematical problems." They tried several things, but, eventually, "they came up with this vibrating string."

The FPUT experiment was important both in showing the complexity of nonlinear system behavior and the value of computer simulation in analyzing systems.

Name change
The original paper names Fermi, Pasta, and Ulam as authors (although Fermi died before the report was written) with an acknowledgement to Tsingou for her work in programming the MANIAC simulations. Mary Tsingou's contributions to the FPUT problem were largely ignored by the community until published additional information regarding the development and called for the problem to be renamed to grant her attribution as well.

The FPUT lattice system
Fermi, Pasta, Ulam, and Tsingou simulated the vibrating string by solving the following discrete system of nearest-neighbor coupled oscillators. We follow the explanation as given in Richard Palais's article. Let there be N oscillators representing a string of length $$\ell$$ with equilibrium positions $$p_j = jh,\ j = 0, \dots, N - 1$$, where $$h = \ell/(N - 1)$$ is the lattice spacing. Then the position of the j-th oscillator as a function of time is $$X_j(t) = p_j + x_j(t)$$, so that $$x_j(t)$$ gives the displacement from equilibrium. FPUT used the following equations of motion:

 * $$m\ddot{x}_j = k(x_{j+1} + x_{j-1} - 2x_j)[1 + \alpha(x_{j+1} - x_{j-1})].$$

This is just Newton's second law for the j-th particle. The first factor $$k(x_{j+1} + x_{j-1} - 2x_j)$$ is just the usual Hooke's law form for the force. The factor with $$\alpha$$ is the nonlinear force. We can rewrite this in terms of continuum quantities by defining $$c = \sqrt{\kappa/\rho}$$ to be the wave speed, where $$\kappa = k/h$$ is the Young's modulus for the string, and $$\rho = m/h^3$$ is the density:

 * $$\ddot{x}_j = \frac{c^2}{h^2} (x_{j+1} + x_{j-1} - 2x_j)[1 + \alpha(x_{j+1} - x_{j-1})].$$

Connection to the KdV equation
The continuum limit of the governing equations for the string (with the quadratic force term) is the Korteweg–de Vries equation (KdV equation.) The discovery of this relationship and of the soliton solutions of the KdV equation by Martin David Kruskal and Norman Zabusky in 1965 was an important step forward in nonlinear system research. We reproduce below a derivation of this limit, which is rather tricky, as found in Palais's article. Beginning from the "continuum form" of the lattice equations above, we first define u(x, t) to be the displacement of the string at position x and time t. We'll then want a correspondence so that $$u(p_j, t)$$ is $$x_j(t)$$.

 * $$\ddot{x}_j = \frac{c^2}{h^2} (x_{j+1} + x_{j-1} - 2x_j)[1 + \alpha(x_{j+1} - x_{j-1})].$$

We can use Taylor's theorem to rewrite the second factor for small $$h$$ (subscripts of u denote partial derivatives):

 * $$\begin{align}

\left(\frac{x_{j+1} + x_{j-1}-2x_j}{h^2}\right) &= \frac{u(x + h, t) + u(x - h, t) - 2u(x, t)}{h^2} \\ &= u_{xx}(x, t) + \left(\frac{h^2}{12}\right)u_{xxxx}(x, t) + O(h^4). \end{align}$$

Similarly, the second term in the third factor is

 * $$\alpha(x_{j+1} - x_{j-1}) = 2\alpha hu_x(x, t) + \left(\frac{\alpha h^3}3\right) u_{xxx}(x, t) + O(h^5).$$

Thus, the FPUT system is

 * $$\frac{1}{c^2} u_{tt} - u_{xx} = (2\alpha h) u_x u_{xx} + \left(\frac{h^2}{12}\right) u_{xxxx} + O(\alpha h^2, h^4).$$

If one were to keep terms up to O(h) only and assume that $$2\alpha h$$ approaches a limit, the resulting equation is one which develops shocks, which is not observed. Thus one keeps the O(h2) term as well:

 * $$\frac{1}{c^2} u_{tt} - u_{xx} = (2\alpha h) u_x u_{xx} + \left(\frac{h^2}{12}\right) u_{xxxx}.$$

We now make the following substitutions, motivated by the decomposition of traveling-wave solutions (of the ordinary wave equation, to which this reduces when $$\alpha, h$$ vanish) into left- and right-moving waves, so that we only consider a right-moving wave. Let $$\xi = x - ct,\ \tau = (\alpha h)ct,\ y(\xi, \tau) = u(x, t)$$. Under this change of coordinates, the equation becomes

 * $$y_{\xi\tau} - \left(\frac{\alpha h}{2}\right) y_{\tau\tau} = -y_\xi y_{\xi\xi} - \left(\frac{h}{24\alpha}\right) y_{\xi\xi\xi\xi}.$$

To take the continuum limit, assume that $$\alpha/h$$ tends to a constant, and $$\alpha, h$$ tend to zero. If we take $$\delta = \lim_{h \to 0} \sqrt{h/(24\alpha)}$$, then

 * $$y_{\xi\tau} = -y_\xi y_{\xi\xi} - \delta^2 y_{\xi\xi\xi\xi}.$$

Taking $$v = y_\xi$$ results in the KdV equation:

 * $$v_\tau + v v_\xi + \delta^2 v_{\xi\xi\xi} = 0.$$

Zabusky and Kruskal argued that it was the fact that soliton solutions of the KdV equation can pass through one another without affecting the asymptotic shapes that explained the quasi-periodicity of the waves in the FPUT experiment. In short, thermalization could not occur because of a certain "soliton symmetry" in the system, which broke ergodicity.

A similar set of manipulations (and approximations) lead to the Toda lattice, which is also famous for being a completely integrable system. It, too, has soliton solutions, the Lax pairs, and so also can be used to argue for the lack of ergodicity in the FPUT model.

Routes to thermalization
In 1966, Félix Izrailev and Boris Chirikov proposed that the system will thermalize, if a sufficient amount of initial energy is provided. The idea here is that the non-linearity changes the dispersion relation, allowing resonant interactions to take place that will bleed energy from one mode to another. A review of such models can be found in Roberto Livi et al. Yet, in 1970, Joseph Ford and Gary H. Lunsford insist that mixing can be observed even with arbitrarily small initial energies. There is a long and complex history of approaches to the problem, see Thierry Dauxois (2008) for a (partial) survey.

Recent work by Miguel Onorato et al. demonstrates a very interesting route to thermalization. Rewriting the FPUT model in terms of normal modes, the non-linear term expresses itself as a three-mode interaction (using the language of statistical mechanics, this could be called a "three-phonon interaction".) It is, however, not a resonant interaction, and is thus not able to spread energy from one mode to another; it can only generate the FPUT recurrence. The three-phonon interaction cannot thermalize the system.

A key insight, however, is that these modes are combinations of "free" and "bound" modes. That is, higher harmonics are "bound" to the fundamental, much in the same way that the higher harmonics in solutions to the KdV equation are bound to the fundamental. They do not have any dynamics of their own, and are instead phase-locked to the fundamental. Thermalization, if present, can only be among the free modes.

To obtain the free modes, a canonical transformation can be applied that removes all modes that are not free (that do not engage in resonant interactions). Doing so for the FPUT system results in oscillator modes that have a four-wave interaction (the three-wave interaction has been removed). These quartets do interact resonantly, i.e. do mix together four modes at a time. Oddly, though, when the FPUT chain has only 16, 32 or 64 nodes in it, these quartets are isolated from one-another. Any given mode belongs to only one quartet, and energy cannot bleed from one quartet to another. Continuing on to higher orders of interaction, there is a six-wave interaction that is resonant; furthermore, every mode participates in at least two different six-wave interactions. In other words, all of the modes become interconnected, and energy will transfer between all of the different modes.

The three-wave interaction is of strength $$1/\alpha$$ (the same $$\alpha$$ as in prior sections, above). The four-wave interaction is of strength $$1/\alpha^2$$ and the six-wave interaction is of strength $$1/\alpha^4$$. Based on general principles from correlation of interactions (stemming from the BBGKY hierarchy) one expects the thermalization time to run as the square of the interaction. Thus, the original FPUT lattice (of size 16, 32 or 64) will eventually thermalize, on a time scale of order $$1/\alpha^8$$: clearly, this becomes a very long time for weak interactions $$\alpha \ll 1$$; meanwhile, the FPUT recurrence will appear to run unabated. This particular result holds for these particular lattice sizes; the resonant four-wave or six-wave interactions for different lattice sizes may or may not mix together modes (because the Brillouin zones are of a different size, and so the combinatorics of which wave-vectors can sum to zero is altered.) Generic procedures for obtaining canonical transformations that linearize away the bound modes remain a topic of active research.

However, a recent study found that there are divergences in the canonical transformation used to remove the three-wave interactions due to the presence of small denominators. These small denominators become more prominent when the lower modes are excited, and are more significant as the system size is increased. These results also show an indication that there could be a stochasticity threshold in the $$\alpha$$-Fermi–Pasta–Ulam–Tsingou system.

title: Fermi–Pasta–Ulam–Tsingou problem


text:
Talk:Graham Coxon

Hometown
Graham is from Fordham, in the borough of Colchester. Shouldn't this article be updated to show that. I know it's the same borough, but it's still a village in its own right and pretty boring with that - Fordham needs help.

work with Paul Weller, Mani and Zak Starkey?
I just saw them all performing live on BBC1, on Friday Night with Jonathon Ross, I hadn't heard anything about this, something needs to be added to the article! This is a pretty amazing super group! Does anybody have any better photographs than the one used? — Preceding unsigned comment added by Iheartsausages (talk • contribs) 14:09, 21 May 2012 (UTC)

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Graham Coxon Deletion Log
Regarding the deletion log made by admin SlimVirgin on BLP Graham Coxon, user Suzi Grossman should provide further clarification on claim that 'the section about him having a daughter born in 2016 is factually incorrect our client sees this as abusive and is causing upset to him and his family'. Several other sources cite the birth of a child on 2016. User should clarify whether (a) the year of birth is inaccurate or (b) reports about the birth were fictitious and fall under vandalism guidelines. In case of the latter, record should be made that such reports reports are in fact false so that other publications can make similar revisions. Furthermore, the information on remainder of the session ('personal life') are citable and verifiable so removal of the whole paragraph was arguably not necessary unless user has provided further reasoning. — Preceding unsigned comment added by 68.197.251.249 (talk) 17:24, 2 September 2018 (UTC)

Picture?
Should there be a new picture? This one seems kind of outdated. Rowdythere (talk) 15:01, 3 September 2021 (UTC)

title: Talk:Graham Coxon


text:
User talk:Baisevous

Welcome!

Hello,, and welcome to Wikipedia! Thank you for your contributions. I hope you like the place and decide to stay. Here are a few good links for newcomers: I hope you enjoy editing here and being a Wikipedian! Please sign your name on talk pages using four tildes (~~); this will automatically produce your name and the date. If you need help, check out Where to ask a question, ask me on my talk page, or place  on your talk page and someone will show up shortly to answer your questions. Again, welcome! CambridgeBayWeather 21:12, 8 October 2005 (UTC)
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title: User talk:Baisevous


text: File:Cocorosie-noahsark.jpg

title: File:Cocorosie-noahsark.jpg


text:
Talk:Polans

Move
I suggest moving this to Polans (disambiguation) and having Polans as a redirect to Polans (eastern) with "otheruses" on top of course. Eastern tribe seem a more likely aim of the search but please object if I am wrong.

Since the entry is empty the move does not require a vote. I just don't want to make life more difficult if this move seems controversial. So, I would like to hear if there are objections. --Irpen 21:13, 8 October 2005 (UTC)

 * Neither meaning is primary outside its geographical context, so it's not a case of primary topic disambiguation. · Naive cynic · 21:49, 27 October 2005 (UTC)

 * Also, the descendants of the western Polans might have a different view on that. Halibutt 19:24, 5 November 2005 (UTC)

They might. I just asked. --Irpen 19:54, 5 November 2005 (UTC)

 * Nyah, you suggested, which is a different thing ;) Halibutt 04:53, 6 November 2005 (UTC)

Khazars
By the 9th century, the Polans were ruled by the Khazars paid tribute to them

What?

Urpunkt (talk) 01:28, 20 January 2010 (UTC)

title: Talk:Polans


text:
Arab conquest of Egypt

The Arab conquest of Egypt, led by the army of 'Amr ibn al-'As, took place between 639 and 642 AD and was overseen by the Rashidun Caliphate. It ended the seven-century-long Roman period in Egypt that had begun in 30 BC, and widely speaking Greco-Roman period that had lasted about a millennium.

Shortly before the conquest, Byzantine (Eastern Roman) rule in the country had been shaken, as Egypt had been conquered and occupied for a decade by the Sasanian Empire in 618–629, before being recovered by the Byzantine emperor Heraclius. The Caliphate took advantage of Byzantines' exhaustion to invade Egypt.

During the mid-630s, the Romans had already lost the Levant and its Ghassanid allies in Arabia to the Caliphate. The loss of the prosperous province of Egypt and the defeat of the Byzantine armies severely weakened the empire, resulting in further territorial losses in the centuries to come.

Background
In 640, Heraclius was the Byzantine emperor, Cyrus of Alexandria was both the governor of Egypt (praefectus Aegypti) and the government-appointed Patriarch of Alexandria, and Theodore was the commander-in-chief of the Byzantine army in the province.

Following the death of Muhammad in 632 AD, the Arab armies of the Rashidun Caliphate began expanding toward both Sasanian Persia and the Byzantine Empire. Neither of the two former powers was prepared for the aggressive expansion of the Arabs, as both largely underestimated Islam and its growing support; this is best depicted by the ambivalent views held by the Byzantines and the painstakingly slow reaction of the Sasanians.

After defeating the Byzantines at Yarmuk (636) and the Persians at Qadisiyah (637), the gaze of the Arab generals turned towards the riches of Byzantine Africa. After the Siege of Jerusalem, it was Amr ibn al-As who suggested an invasion of Egypt to the Caliph, being familiar with the country's prosperity both from visiting it as a merchant and from leading the expedition to Gaza in 637. Appealing to the Caliph, he said "the conquest of Egypt will give great power to the Muslims and will be a great aid to them, for it is the wealthiest land and the weakest in fighting and war power."

After being convinced by Amr to proceed with the invasion, the caliph Umar is said to have had "an eleventh-hour change of heart", but too late to stop it. This element of the story, which conveys the caliph's wariness at allowing a general to seize such an asset, may have been a later embellishment in light of Amr's subsequent reputation as a stubbornly independent governor.

Crossing the Egyptian border
According to Arab sources, In December 639, 'Amr ibn al-'As left for Egypt with a force of 4,000 troops. Most of the soldiers belonged to the Arab tribe of 'Ak, but Al-Kindi mentioned that one third of the soldiers belonged to the Arab tribe of Ghafik. The Arab soldiers were also joined by some Roman and Persian converts to Islam. However, 'Umar, the Muslim caliph, reconsidered his orders to Amr and considered it unwise to expect to conquer such a large country as Egypt with a mere 4,000 soldiers. Accordingly, he wrote a letter to 'Amr ordering him to "return with all haste to the court of the Caliph, so that his soldiers might join additional campaigns being planned elsewhere", however there was a provision in the letter stating that 'Amr's first duty was the protection of his troops, and if he found himself on Egyptian soil by the time he received the letter, the Caliph would leave overall strategic command of movement to him, so as to not unduly burden troops already in the field.

The messenger, 'Uqbah ibn 'Amr, caught up with Amr at Rafah, a little short of the Egyptian frontier. Guessing what might be in the letter, 'Amr ordered the army to quicken its pace. Turning to 'Uqbah, 'Amr said that he would receive the caliph's letter from him when the army had halted after the day's journey. 'Uqbah, unaware of the contents of the letter, agreed and marched along with the army. The army halted for the night at Shajratein, a little valley near the city of El Arish, which 'Amr knew to be beyond the Egyptian border. 'Amr then received and read 'Umar's letter and went on to consult his companions as to the course of action to be adopted. The unanimous view was that as they had received the letter on Egyptian soil, they had permission to proceed.

When 'Umar received the reply, he decided to watch further developments and to start concentrating fresh forces at Madinah that could be dispatched to Egypt as reinforcements. On Eid al-Adha, the Muslim army marched from Shajratein to El Arish, a small town lacking a garrison. The town put up no resistance, and the citizens offered allegiance on the usual terms.

Conquest of Pelusium and Belbeis
According to tradition, Cyrus of Alexandria had a beautiful daughter named Armenousa, who he desired to marry to Heraclius Constantine. Constantine accepted the marriage proposal, so in late 639 Armenousa left Babylon in a grand marriage procession which included two thousand horsemen, along with slaves and a long caravan laden with treasures that served both as dowry and tribute. On her way to Constantine, who was in Caesarea, she heard of the Arab army approaching Egypt and dispatched a regiment of her guards to defend Pelusium, a garrison city considered to be the eastern gateway to Egypt at the time, while she herself remained in Belbeis with more of her guards and sent warnings to her father Cyrus. However, Alfred J. Butler dismisses Armenousa's story as a myth.

In of December 639 or early January 640, the Muslim army reached Pelusium. The siege of the town dragged on for two months. In February 640, an assault group, led by the prominent Huzaifah ibn Wala, successfully captured the fort and city.

The losses incurred by the Muslim army were ameliorated by the number of Sinai Bedouins, who, taking the initiative, had joined them in conquering Egypt. The Bedouins belonged to the tribes of Rashidah and Lakhm.

The ease with which Pelusium fell to the Muslims and the lack of Roman reinforcements during the month-long siege is often attributed to the treachery of Cyrus, who was also the Greek Patriarch of Alexandria (not the one recognised by most of the population, who was Pope Benjamin I).

After the fall of Pelusium, the Muslims marched to Belbeis, 65 km (40 mi) from Memphis via desert roads, and besieged it. Belbeis was the first place in Egypt that the Byzantines showed some measure of resistance towards the Arabs. Two Christian monks, accompanied by Cyrus of Alexandria and the famous Roman general Aretion, came out to negotiate with 'Amr ibn al-'As. Aretion had been the Byzantine governor of Jerusalem and had fled to Egypt when the city fell to the Muslims. 'Amr gave them three options: convert to Islam, pay the jizya, or fight. They requested three days to reflect and then, according to Al-Tabari, requested two extra days.

At the end of the five days, the two monks and the general decided to reject Islam and the jizya and fight the Muslims, thus disobeying Cyrus, who wanted to surrender and pay jizya. Cyrus left for the Babylon Fortress. The battle resulted in a Muslim victory during which Aretion was killed and Armenousa was captured, but sent back to Cyrus. 'Amr ibn al-'As subsequently attempted to convince the native Egyptians to aid the Arabs and surrender the city, based on the kinship between Egyptians and Arabs via Hajar. When the Egyptians refused, the siege resumed until the city fell around the end of March 640.

Siege of Babylon Fortress
Amr had assumed that Egypt would be a pushover but was quickly proven wrong. Even at the outposts of Pelusium and Belbeis, the Muslims had met stiff resistance, with sieges of two and one months, respectively. As Babylon, near what is now Cairo, was a larger and more important city, resistance on a larger scale was expected. The Muslims arrived at Babylon some time in May 640.

Babylon was a fortified city, and Theodore had indeed prepared it for a siege. Outside the city, a ditch had been dug, and a large force was positioned in the area between the ditch and the city walls. The Muslims besieged the fort, a massive structure 18 m high with walls more than 2 m thick and studded with numerous towers and bastions and a force of some 4,000 men. Early Muslim sources place the strength of the Byzantine force in Babylon at about six times the strength of the Muslim force. For the next two months, fighting remained inconclusive, with the Byzantines repulsing every Muslim assault.

Realising that Babylon was too strong to take, 'Amr sent a detachment to raid the city of Faiyum. The Byzantines had anticipated that and so had strongly guarded the roads that led to the city and had fortified their garrison in the nearby town of Lahun. At this time, the governor of Faiyum was Domentianus, while Anastasius was the prefect of its province, Arcadia Aegypti, and Theodosius was the prefect of Alexandria. The defence of Arcadia Aegypti was entrusted to a certain John, who Hermann Zotenberg identifies with the John, Duke of Barca or Barcaina mentioned by Nicephorus. He had brought the Ecthesis and a portion of the True Cross from Patriarch Sergius to Cyrus, and was likely on a direct commission from Emperor Heraclius.

When the Muslims realised that Faiyum was also too strong for them to take, they headed towards the Western Desert, where they looted as many cattle and animals as they could. They subsequently headed to a town in the Faiyum district named Bahnasa (not to be confused with Oxyrhynchus 50 miles further south), which was defeated and the city was captured. According to John of Nikiû, "they compelled the city to open its gates, and they put to the sword all that surrendered, and they spared none, whether old men, babe, or woman." The Arabs then noticed that John, with a small group of 50 men, had been following them. John and his men ran retreated to their base at Abûît, but their hiding place was betrayed by a Bedouin chief and they were all killed.

When news of John's death reached Theodore, who was commanding the garrison at Babylon, 'his lamentations were more grievous than the lamentations of David over Saul when he said: "How are the mighty fallen, and the weapons of war perished!"' as John of Nikiu puts it. Theodore hurried his troops up the Nile while Anastasius and Theodosius rushed from Nikiû to Babylon to strengthen it, while a further force was sent from Babylon to Abûît to strengthen it under Leontius, who was "obese in person, quite without energy and unacquainted with warlike affairs". When he arrived, he found Theodore and his troops there already making sorties every day against the Arab base at Bahnasa. Judging that Amr would soon be defeated, Leontius left only half of his men there, going back to Babylon with the other half.

The Arabs eventually gave up on attempting to take Faiyum and returned northwards. Theodore gave orders for the body of John, which had been thrown in the Nile, to be found. It was retrieved with a net, embalmed with honour and sent back to Heraclius. As Theodore was commander-in-chief, Heraclius blamed him for John's death. Feeling that he was blamed due to negative reports from Theodosius and Anastasius, Theodore formed an enmity with them.

Reinforcements from Madinah
In July, 'Amr wrote to 'Umar requesting reinforcements, but before the letter reached him, the caliph had already dispatched 4,000 men, mostly veterans of the Syrian campaigns, to bolster Amr's strength. Even with the reinforcements, 'Amr was unsuccessful and so, by August, 'Umar had assembled another 4,000-strong force, consisting of four columns, each of 1,000 elite men. Zubayr ibn al-Awwam, a renowned warrior and commander, veteran of the Battle of Yarmouk and once a part of Khalid ibn al-Walid's elite mobile guard, was appointed the supreme commander of the army.

'Umar had also offered Zubayr the chief command and governorship of Egypt, but Zubayr had declined. The column commanders included Miqdad ibn al-Aswad, 'Ubaidah ibn as-Samit and Kharijah ibn Hudhaifah. The reinforcements arrived at Babylon sometime in September 640, bringing the total strength of the Muslim force to 12,000 (and likely far less, given losses incurred), still quite modest.

It is said that a Coptic soldier, seeing the size of the Muslim force, expressed amazement that such a small force could stand against the Emperor's army, whereto another soldier replied that Arabs could not yield, and had to either emerge victorious or die to the last man. In another anecdote, some Roman soldiers refused to fight, saying 'We have small chance against the men who have conquered Chosroes and Caesar in Syria.'

Battle of Heliopolis
When Zubayr arrived, he pointed out to ‘Amr that the Roman-garrisoned city of Heliopolis was a short distance away, and that troops from there could relieve the Siege of Babylon. To remove this threat, ‘Amr went with about half of his men there.

The Muslim army reached Heliopolis, 15 km (10 mi) from Babylon, in July 640. The city boasted the Sun Temple of the Pharaohs and grandiose monuments and learning institutions. There was the danger that forces from Heliopolis could attack the Muslims from the flank while they were engaged with the Roman army at Babylon.

There was a cavalry clash near the current neighbourhood of Abbaseya. The engagement was not decisive, but it resulted in the occupation of the fortress located between the current neighborhoods of Abdyn and Azbakeya. The defeated Byzantine soldiers retreated to either the Babylon Fortress or the fortress of Nikiû. Zubayr and some of his handpicked soldiers scaled the Heliopolis city wall at an unguarded point and, after overpowering the guards, opened the gates for the army to enter the city. After the capture of Heliopolis, 'Amr returned to Babylon.

Conquering of Fayoum and Babylon
When news of the Muslims' victory at Heliopolis reached Fayoum, its governor, Domentianus, and his troops fled without informing the people of Fayoum and Abuit that they were abandoning their cities to the enemy. When news reached 'Amr, he sent troops across the Nile to invade Fayoum and Abuit, capturing the entire province of Fayoum with practically no resistance. Fayoum's population was enslaved, and the city was looted (the traditional fate of cities that had resisted).

Emissaries were exchanged between Theodore and 'Amr, leading to 'Amr meeting Theodore in person. Then, with negotiations stalled, during the night of 20 December, a company of handpicked warriors, led by Zubayr, managed to scale the wall, kill the guards, and open the gates for the Muslim army to enter. The city was captured by the Muslims the following morning with tactics similar to those that had been used by Khalid ibn Walid at Damascus. However, Theodore and his army managed to slip away to the island of Rauda during the night, whence they continued to fight the Muslims.

During this time, Theodore assembled an army in the Nile Delta and put two generals in charge of defending Samannud. Hearing of this, 'Amr went north to destroy this army. The two generals in Samannud refused to fight the Muslims, but Theodore fought 'Amr there and defeated him, inflicting many casualties on the Muslims. Unable to damage any cities in the Nile Delta, they retreated back to Babylon. However, Theodore was unable to follow up this victory by recapturing Babylon.

The final assault of the Muslims was on Good Friday, April 6 641, and by Easter Monday the Roman troops had evacuated and began marching to Nikiû. The Romans were given a few days to evacuate so they might celebrate Easter. Many Copts who were imprisoned in Babylon, either for refusing to accept Chalcedon or on suspicion of treachery, were released from prison by the Romans, but Eudocianus, the brother of Domentianus, had them scourged and their hands cut off. The Siege of Babylon had lasted seven months.

Surrender of Thebaid (Southeastern Egypt)
On 22 December, Cyrus of Alexandria entered a treaty with the Muslims, recognizing Muslim sovereignty over the whole of Egypt and effectively over Thebaid, and agreeing to pay Jizya at the rate of 2 diners per male adult. The treaty was subject to the approval of the emperor Heraclius, but Cyrus stipulated that even if the emperor repudiated the treaty, he and the Egyptians, would honour its terms. Cyrus asked Heraclius to ratify the treaty and offered an argument in support. 'Amr submitted a detailed report to Umar recommending ratification. He desired that as soon as the reactions of Heraclius were known, he should be informed so that further necessary instructions could be issued promptly. Upon hearing about this, Heraclius was furious and sent Cyrus a letter full of insults, calling him an abject coward and a heathen and asking whether 100,000 Romans were a match for 12,000 barbarians.

March to Alexandria
The Byzantine commanders, knowing full well that the Muslims' next target was Alexandria, set out to repel the Muslims through continued sallies from the fort or, at least, to exhaust them and erode their morale in a campaign of attrition. In February 641, 'Amr set off for Alexandria from Babylon with his army, encountering defending regiments all along the route. On the third day of their march the Muslims' advance guard encountered a Byzantine detachment at Tarnut on the west bank of the Nile. The Byzantines failed to inflict heavy losses but were able to delay the advance by a full day. The Muslim commanders decided to halt the main army at Tarnut and send an advance guard of cavalry forward to clear the path.

The Muslims came to Kebrias of Abadja, where Domentianus and his soldiers were. He cravenly fled the city in a small boat, leaving his soldiers to their fate. They attempted to follow him, but in the panic the boatmen fled to their home provinces, leaving many of the soldiers stranded. When the Arabs arrived, the soldiers threw their weapons into the water before their enemies, hoping to be spared, but instead they were all massacred. According to John of Nikiu, the only man who lived to tell the tale was a “gallant warrior” named Zacharias. The Muslims then passed by Sais and, finding the family of Theodorus there, killed all of them.

Now 30 km from Tarnut, the Byzantine detachment that had withdrawn from Tarnut the day before joined another that was already at Shareek, and both attacked and routed the Muslim cavalry. The next day, before the Byzantines could annihilate the Muslim advance guard completely, the main Muslim army arrived, prompting the Byzantines to withdraw. The following day, the whole army marched forward without an advance guard. The Muslims reached Sulteis, where they encountered another Byzantine detachment. Hard fighting followed, but the Byzantine resistance soon broke down and they withdrew to Alexandria.

The Muslims halted at Sulteis for a day, still two days' march from Alexandria. After another day's march, the Muslim forces arrived at Kirayun, 20 km from Alexandria. There, the Muslim advance to Alexandria was blocked by a Byzantine force about 20,000 strong. The resulting action remained indecisive for ten days. However, on the tenth day, the Muslims launched a vigorous assault, forcing the defeated Byzantines to retreat to Alexandria. With the way to Alexandria clear, the Muslims reached the capital's outskirts in March.

Theodore and Cyrus in Constantinople
Heraclius died in February 641, two months before the fall of the Babylon Fortress, and was succeeded by his two sons Constantine III and Heraclonas as co-emperors. Heraclonas' mother, Martina, ruled through Heraclonas because of his young age and consistently opposed Constantine. Constantine, following his father's wishes, summoned Cyrus and Theodore to Constantinople to discuss the invasion. Cyrus was in favour of surrendering to the Muslims, whereas Theodore wanted to continue fighting them and hoped the Emperor would send reinforcements to Egypt. Constantine had been preparing a fleet to send to Egypt, but died on May 25 after a reign of just 100 days. With Heraclonas as sole emperor, Martina gained complete control over the government. She had Heraclonas give Cyrus express permission to make peace at any price with the Arabs, but also gave him reinforcements and a new general named Constantine to replace John. After Theodore and Cyrus' left for Egypt with reinforcements, Martina was deposed by Valentine, who sent envoys to Rhodes with a message to Cyrus' troops, telling them to return to Constantinople and not to side with Cyrus. He also sent a letter to Alexandria telling the defenders not to obey Martina, and to keep fighting. Theodore was pleased to hear this, and without telling Cyrus or anyone but the captain, he secretly attempted to sail from Rhodes to Pentapolis. However, the captain of the ship claimed the wind was contrary to him, and Theodore was stuck with Cyrus. They returned to Alexandria on September 14, 641, the Feast of the Cross.

Meanwhile in Egypt, Anastius had been appointed temporary prefect of Egypt, and during his time the Muslims captured both Babylon and Nikiu. Domentianus and his soldiers were guarding Nikiu. When he saw the enemy approaching cravenly fled the city in a small boat, leaving his soldiers to their fate. They attempted to follow him, but in the panic the boatmen fled to their home provinces, leaving many of the soldiers stranded. When the Arabs arrived, the soldiers threw their weapons into the water before their enemies, hoping to be spared, but instead they were all massacred. According to John of Nikiu, the only man who lived to tell the tale was a "gallant warrior" named Zacharias. The Muslims then passed by Sais and, finding relatives of Theodore there, killed them. John of Nikiu also says that "Egypt also had become enslaved to Satan. A great strife had broken out between the inhabitants of Lower Egypt, and these were divided into two parties. Of these, one sided with Theodore, but the other wished to join the Moslem." The Muslims had also begun their Siege of Alexandria.

Conquest of Alexandria
When Theodore returned to Alexandria, he dismissed Domentianus as the military commander of the garrison and exiled him from the city, replacing him with Menas, who was a non-Chalcedonian Copt and popular with the army. Menas held a grudge against Domentianus' brother Eudocianus for Eudocianus' torture of the Coptic prisoners in Babylon. Theodore was angry with Domentianus for his cowardly flight from Nikiu and took Menas' side in their quarrel. Despite being brothers-in-law, Domentianus also disrespected Cyrus and showed him unreasonable hatred. He enlisted the Blues in Alexandria to his side, to which Menas responded by enlisting the Greens. There also came to Alexandria Philiades, prefect of the province of Faiyum and brother of Patriarch George I of Alexandria. Philiades was Menas' friend, but unlike Menas he was corrupt and unpopular, so much so that he was nearly lynched.

Since Theodore and Cyrus' arrival in Egypt was on September 14, 641, the Feast of the Cross, a great procession was organised from their landing place to the Caesareum Church. Their entire path was covered in carpets, hymns were sung, and a piece of the True Cross which was earlier brought to Egypt by John, Duke of Barcaina, and stored by the monks of Tabenna, was carried with Cyrus and Theodore to the Caesareum. The Psalm reading of the day was, but the deacon said another psalm hoping to praise Cyrus and congratulate him on his return. This was said to be a bad omen. Cyrus then gave a sermon about the discovery of the True Cross, perhaps encouraging them to resist the siege in the name of the Cross, despite having already decided in himself to forsake the Cross and surrender to the Muslims.

Cyrus then went to Babylon to negotiate with 'Amr, and agreed the following treaty: He then returned to Alexandria and reported the terms of this humiliating treaty to Theodore and Constantine, convincing them that it was necessary and telling them to report it to the Emperor Heraclonas, who ratified it in what may had been his last act as Emperor, as he died in November. The local populace was not informed of it until an Arab army approached Alexandria to receive the tribute, and the Byzantine generals told the people not to resist. Realising what had happened, a furious mob attempted to stone Cyrus, but he said to them "I have made this treaty in order to save you and your children" and wept before them, which calmed the riot down. The first installment of tribute was paid on 10 December 641, sealing the surrender of Alexandria.
 * 1) Payment of a fixed tribute by all who came under the treaty.
 * 2) An armistice of about eleven months, to expire the first day of the Coptic month Paophi, i.e. September 28, 642.
 * 3) During the armistice the Arab forces to maintain their positions, but to keep apart and undertake no military operations against Alexandria; the Roman forces to cease all acts of hostility.
 * 4) The garrison of Alexandria and all troops there to embark and depart by sea, carrying all their possessions and treasure with them: but any Roman soldiers quitting Egypt by land to be subject to a monthly tribute on their journey.
 * 5) No Roman army to return or attempt the recovery of Egypt.
 * 6) The Muslims to desist from all seizure of churches, and not to interfere in any way with the Christians.
 * 7) The Jews to be suffered to remain at Alexandria.
 * 8) Hostages to be given by the Romans, viz. 150 military and 50 civilian, for the due execution of the treaty.

After the siege was over, Cyrus negotiated with 'Amr to allow the Egyptians who had taken refuge in Alexandria during the war to return to their lands, but he apparently did not allow them to do so. Towns along the northern coast of the Nile Delta remained outside Muslim control for some more years; 'Amr evidently did not consider them a priority. He began building his new capital, Fustat, just outside Babylon, and the Byzantine prefects and governors of Egypt either converted to Islam to retain their positions, or were replaced by Muslims. 'Amr and these Muslim governors forced the Christians to work for them, and made them dig a canal from the Nile to the Red Sea. According to John of Nikiu, 'Amr broke the terms of the treaty he had made with Cyrus. Cyrus fell into depression and died on Holy Thursday, March 21, 642. Theodore was appointed governor of Egypt after Cyrus' death, and arranged the withdrawal of Byzantine forces from Alexandria. On September 17, 642, Theodore left Egypt and set sail for Cyprus with the last Roman troops. Then on September 29, the 11 months of armistice ended, and 'Amr marched at the head of his Arab army into Alexandria, and thus ended Roman Egypt.

Invasion of Nubia
In the summer of 642, 'Amr ibn al-'As sent an expedition to the Christian kingdom of Nubia, which bordered Egypt to the south, under the command of his cousin 'Uqbah ibn Nafi as a pre-emptive raid to announce the arrival of new rulers in Egypt. 'Uqbah ibn Nafi, who later made a great name for himself as the conqueror of Africa and led his horse to the Atlantic, had an unhappy experience in Nubia. No pitched battle was fought, but there were only skirmishes and haphazard engagements, the type of warfare in which the Nubians excelled. They were skilful archers and subjected the Muslims to a merciless barrage of arrows, resulting in 250 Muslims losing their eyes in the engagement.

The Nubian cavalry displayed remarkable speed, even more so than the Muslim cavalry. The Nubians would strike hard and then vanish before the Muslims could recover and counterattack. The hit-and-run raids took their toll on the Muslim expedition. 'Uqbah reported that to 'Amr, who ordered 'Uqbah to withdraw from Nubia, terminating the expedition. A treaty was finally concluded with the Nubians in 651–2, securing the southern frontier of Muslim rule in Egypt.

Byzantine counterattack
In 645, the newly installed Eastern Roman Emperor Constans II was determined to retake the land, and ordered a large fleet to carry troops to Alexandria. These troops, under Manuel, took the city by surprise from its small Arab garrison towards the end of 645 in an amphibious attack - thus temporarily winning Alexandria back.

Amr at the time might have been in Mecca, and was quickly recalled to take command of the Arab forces in Egypt. On returning to Egypt, he engaged the Byzantines at the small fortified town of Nikiou (ⲡϣⲁϯ Pashati), about two-thirds of the way from Alexandria to Fustat, with the Arab forces numbering around 15,000, against a smaller Byzantine force. The Arabs prevailed, and the Byzantine forces retreated in disarray, back to Alexandria.

Although the Byzantines closed the gates against the pursuing Arabs, the city of Alexandria eventually fell to the Arabs, who stormed the city sometime in the summer of that year. The defeat of Manuel's forces marked the last attempt by the Byzantine Empire to recapture Egypt for some 500 years, before Emperor Manuel I Komnenos sent a failed expedition there in the 12th century.

Egypt under Muslim rule
In The Great Arab Conquests, Hugh Kennedy writes that Cyrus, the Roman governor, had exiled the Coptic patriarch, Benjamin. When 'Amr occupied Alexandria, a Coptic nobleman (duqs) called Sanutius persuaded him to send out a proclamation of safe conduct for Benjamin and an invitation to return to Alexandria. When Benjamin arrived, he was then instructed by the governor to resume control over the Coptic Church. He arranged for the restoration of the monasteries in the Wadi Natrun, which had been ruined by the Chalcedonean Christians; four of them still survive as functioning monasteries.

On Benjamin's return, the Egyptian population also worked with him. Kennedy wrote, "The pious biographer of Coptic patriarch Benjamin presents us with the striking image of the patriarch prayed for the success of the Muslim commander Amr against the Christians of the Cyrenaica. Benjamin survived for almost twenty years after the fall of Egypt to the Muslims, dying of full years and honour in 661. His body was laid to rest in the monastery of St Macarius, where he is still venerated as a saint. There can be no doubt that he played a major role in the survival of the Coptic Church". Benjamin also prayed for 'Amr when he attempted to take Libya.

Kennedy also wrote, "Even more striking is the verdict of John of Nikiu. John was no admirer of Muslim government and was fierce in his denunciation, but he says of Amr: 'He extracted the taxes which had been determined upon but he took none of the property of the churches, and he committed no act of spoliation or plunder, and he preserved them throughout all his days.... Of all the early Muslim conquests, that of Egypt was the swiftest and most complete. Within a space of two years the country had come entirely under Arab rule. Even more remarkably, it has remained under Muslim rule ever since. Seldom in history can so massive a political change have happened so swiftly and been so long lasting."

The Coptic Chronicler Severus ibn al-Muqaffa claims that “The Arabs in the land of Egypt had ruined the country.… They burnt the fortresses and pillaged the provinces, and killed a multitude of the saintly monks who were in them and they violated a multitude of the virgin nuns and killed some of them with the sword.” "Egypt had become enslaved to Satan" concludes John of Nikiu.

Uqba ibn Nafi then used Egypt as a launch pad to move across North Africa, all the way to the Atlantic Ocean. Kennedy wrote that when Uqba reached the Atlantic, he is said to have ridden his horse into the sea until the water was below his chest, and then shouted, 'O Lord, if the sea did not stop me, I would go through lands like Alexander the Great, defending your faith'. Kennedy writes further that the image of a warrior whose conquest in the name of God was stopped only by the ocean remains important in the history of the conquests.

Fustat, the new capital
During the Egyptian campaign, Alexandria was the capital of Egypt. When Alexandria was captured by the Muslims, the houses vacated by the Byzantines were occupied by the Muslims, who were impressed and attracted by Alexandria, "the queen of cities". 'Amr wanted Alexandria to remain the capital of Muslim Egypt. He wrote to 'Umar to propose that but 'Umar refused on the basis that Alexandria was a maritime city, and there would always be a danger that the Byzantine Navy would attack. He suggested instead for the capital would be established at a central location further inland, where no mass of water separated it from Arabia.

As 'Amr's tent was to be the focal point of the city, the city was called Fustat, meaning in Arabic "the tent". The first structure to be built was the mosque that later became famous as Mosque of 'Amr ibn al-'As. In the course of time, Fustat extended to include the old town of Babylon to the west, becoming the bustling commercial centre of Egypt.

Umar's reforms
To consolidate his rule in Egypt, Umar imposed the jizya on Egyptians. During later Umayyad rule, higher taxes would be levied. With Umar's permission, Amr decided to build a canal to join the Nile with the Red Sea to open new markets for Egyptian merchants and an easy route to Arabia and Iraq. The project was presented to Umar, who approved it. A canal was dug and, within a few months, was opened for merchants. It was named "Nahar Amir ul-Mu'mineen" (the canal of the Commander of the Faithful), after Umar's title.

title: Arab conquest of Egypt


text:
Andrea Luchesi

Andrea Luca Luchesi (also spelled Lucchesi; 23 May 1741 – 21 March 1801) was an Italian composer. He knew Mozart and Beethoven.

Biography
Andrea Luchesi was born at Motta di Livenza, near Treviso the eleventh child of Pietro Luchese and Caterina Gottardi. The rather wealthy family descended from groups of noble families who had moved from Lucca to Venice in the 14th century (hence the name Luchese; from 1764/65 Andrea began to use the name Luchesi, which we can find written by his contemporaries also as Lucchesi, Lughesi, Luckesi, Lucchezzy, etc.). He grew up in his native town, receiving musical and general education from his elder brother Matteo, a priest, public tutor and organist.

By 1757 he moved to Venice. The protection of the nobleman Jseppo Morosini enabled him to study with eminent musicians: Gioacchino Cocchi, Padre Paolucci, Giuseppe Saratelli, Domenico Gallo, Ferdinando Bertoni and (the best-known of them) Baldassare Galuppi. His career in Venice developed quickly: examiner of the organists commission in 1761, then organist at San Salvatore (1764), composer of works for "organ or cembalo", instrumental, sacred and theatre music. He composed for official celebrations, the last (1771) being the solemn funeral of the Duke of Montealegre, Spanish ambassador to Venice. As a famous virtuoso he was invited to play organ in and outside Venice, e.g. was in charge of inaugurating the new organ of the basilica of Saint Anthony in Padua.

In the spring of 1765 his opera L'isola della fortuna was performed at the Hoftheater in Vienna.

While on tour in Italy in 1771, Leopold and Wolfgang Mozart met Andrea Luchesi and received one of his concertos for cembalo (Wolfgang was still playing the concerto in 1777, while Leopold and Nannerl often used the concerto for teaching and practising purposes). At the end of 1771, Luchesi traveled to Bonn on a three-year contract, invited by the Prince Elector Archbishop of Cologne Maximilian Friedrich von Königsegg-Rothenfels, who wished to raise the quality level of his court orchestra. After the death of the previous Kapellmeister (Ludwig van Beethoven senior, i.e. the grandfather of Beethoven), Andrea Luchesi was nominated official court Kapellmeister in 1774.

He acquired the principality's citizenship and in 1775 married Anthonetta Josepha d'Anthoin, daughter of Maximilian Friederich's senior counselor. With the exception of a visit to Venice in 1783-84, he lived in Bonn until his death in 1801, although his role as Kapellmeister ended in 1794, when the French invasion troops suppressed the court.

The young Beethoven was at the court chapel from 1781 to 1792 as assistant organist, cembalo and viola player. Although Beethoven's musical and compositional training was probably influenced by Luchesi's presence, we have no evidence of any formal pupil/teacher relationship between the two. When the court organist Christian Gottlob Neefe temporarily replaced the Kapellmeister as conductor and teacher during his 1783-84 absence, Luchesi assigned the organ service to the very young Beethoven. There is also no evidence of Luchesi's having taught other young Bonn musicians who went on to international renown: Antonin Reicha, Bernhard and Andreas Romberg, and Ferdinand Ries.

He had one daughter, who lived in Bonn till her death, and four sons. According to Neefe the first two sons (Maximilian Friederich, born 11 December 1775, and M. Jakob Ferdinand, born 18 December 1777) were gifted musicians. Luchesi died on 21 March 1801 at the age of 59 in Bonn.

Works

 * L’isola della fortuna, opera buffa with libretto by Giovanni Bertati, performed at the Hoftheater, Vienna, in 1765; also in Venice (1765) and at the Royal Theater in Lisbon (1767).
 * Ademira, opera seria, for the Ascension Day in Venice (1784), to honour the visit of king Gustavus III of Sweden
 * Other operas: Il marito geloso (1766), Le donne sempre donne (1767), Il giocatore amoroso (1769), Il matrimonio per astuzia (1771), Il Natal di Giove, L’inganno scoperto ovvero il conte Caramella (1773, with libretto from Carlo Goldoni), L’amore e la misericordia guadagnano il gioco (1794).
 * Oratorio Sacer trialogus (1768)
 * Stabat Mater (about 1770)
 * Requiem (1771) in F, for the state funeral of the duke of Montealegre in San Geremia's.
 * Various masses and sacred works, including: Mass for San Lorenzo in Venice, Mass for the "Festa della concezione di Maria" in Verona, Te Deum for the Incurabili conservatory in Venice
 * Passione di N.S. Gesù Cristo (1776), on a text from Metastasio (recorded cd by Tactus)
 * Many organ works, including:
 * 12 sonatas known as Donelli Collection (completed by 1764), now at the Naples Conservatory
 * 6 sonatine and 8 divertimenti, now at the Library of Congress, Washington, D.C.
 * 2 sonates pour l’orgue in the 'Menus plaisirs du Roi', Paris
 * Celebration music for the feast of San Rocco in Venice (1769)
 * Serenata for the duke of Brunswick (1764)
 * Cantata for the duke of Württemberg (1767)
 * 2 Symphonies (by 1768)
 * 6 Sonatas 'per il cembalo con l’accompagnamento di un violino' Op.1 (Bonn, 1772)
 * Sonata in fa ‘per il cimbalo’ (1771-73?), now at the University of Münster
 * 3 Symphonies op. 2 (Bonn,1773) - lost
 * Concerto for harpsichord (Bonn,1773) – four more concertos/trios are lost
 * Cantata for the election to Bishop of Archiduke Max Franz (1785 – attributed to Luchesi in the Bonn Stadtarchiv)
 * Sonate facile for cembalo and violin (Leipzig, 1796)

title: Andrea Luchesi


text:
Talk:U.S. Route 50

Lengths in Ohio
From the SLDs
 * Hamilton 36.08
 * Clermont 18.43
 * Brown 8.41-0.01
 * Highland 28.59
 * Ross 37.68
 * Vinton 30.16
 * Athens 39.04
 * Washington 10.61

Lengths in California
From the bridge log
 * Yolo 3.16
 * Sacramento 21.74+2.48
 * El Dorado 80.44+3.93-4.22+32.16-32.49

Lengths in Illinois
From the GIS data
 * Monroe 3.55
 * St. Clair 12.80-4.71+16.17+4.44+4.2-3.58+5.64
 * Clinton 32.02
 * Marion 1.45+14.68-14.42-1.45+24.23
 * Clay 23.73
 * Richland 20.97
 * Lawrence 21.59

title: Talk:U.S. Route 50


text: User talk:86.131.71.7

title: User talk:86.131.71.7


text:
Snub square tiling

In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. Its Schläfli symbol is s{4,4}.

Conway calls it a snub quadrille, constructed by a snub operation applied to a square tiling (quadrille).

There are 3 regular and 8 semiregular tilings in the plane.

Uniform colorings
There are two distinct uniform colorings of a snub square tiling. (Naming the colors by indices around a vertex (3.3.4.3.4): 11212, 11213.)

Circle packing
The snub square tiling can be used as a circle packing, placing equal diameter circles at the center of every point. Every circle is in contact with 5 other circles in the packing (kissing number).
 * 1-uniform-9-circlepack.svg

Wythoff construction
The snub square tiling can be constructed as a snub operation from the square tiling, or as an alternate truncation from the truncated square tiling.

An alternate truncation deletes every other vertex, creating a new triangular faces at the removed vertices, and reduces the original faces to half as many sides. In this case starting with a truncated square tiling with 2 octagons and 1 square per vertex, the octagon faces into squares, and the square faces degenerate into edges and 2 new triangles appear at the truncated vertices around the original square.

If the original tiling is made of regular faces the new triangles will be isosceles. Starting with octagons which alternate long and short edge lengths, derived from a regular dodecagon, will produce a snub tiling with perfect equilateral triangle faces.

Example:

Related k-uniform tilings
This tiling is related to the elongated triangular tiling which also has 3 triangles and two squares on a vertex, but in a different order, 3.3.3.4.4. The two vertex figures can be mixed in many k-uniform tilings.

Related topological series of polyhedra and tiling
The snub square tiling is third in a series of snub polyhedra and tilings with vertex figure 3.3.4.3.n.

The snub square tiling is third in a series of snub polyhedra and tilings with vertex figure 3.3.n.3.n.

title: Snub square tiling


text:
Benedict Iroha

Benedict "Ben" Iroha (born 29 November 1969) is a Nigerian former professional association football player who played as a left-back or left midfielder.

Career
Iroha started his career in Nigeria, scoring the first ever goal in the newly professional Nigerian league in 1990 for Iwuanyanwu Nationale, who went on to win the league that year.

Iroha was originally a midfielder before national coach Clemens Westerhof converted him to play left back. His club career in Europe was largely unsuccessful, and Iroha was allocated to San Jose Clash in 1996. Iroha ended up playing in the inaugural MLS match against D.C. United, and is credited with the league's first-ever assist. The next season, he was traded to D.C. United, where he won the league title but was dropped to comply with salary restrictions. He entered negotiations with the team to re-sign his contract, but they were halted after Iroha was called up to the World Cup squad for Nigeria. After a move to Spanish side Elche CF in 1997, he moved to Watford in December 1998, playing ten games for the Hertfordshire side. A problem with bunions forced him to the sidelines, and he retired in March 2000.

International career
Playing for the Nigerian national team, he has featured in the 1994 FIFA World Cup and the 1998 FIFA World Cup as well as when they won the 1994 African Nations Cup.

Coaching career
After retiring, he returned to the US to coach in the youth department of FC Dallas. Most recently, he was an assistant with the Nigerian U-17 team that won the 2007 FIFA U-17 World Cup and head coach of Nigeria's Dolphins FC. Iroha is on the staff of Heartland of Owerri.

title: Benedict Iroha


text:
Talk:Forever Free (novel)

Untitled
Bold text Haldeman butchered the ending. silsor 21:20, 8 October 2005 (UTC)
 * Quite. —Cryptic (talk) 09:23, 9 October 2005 (UTC)
 * This book is proof that any science fiction novel with God as a character sucks. -- llywrch (talk) 00:46, 24 June 2008 (UTC)

I can't believe he actually put a Westworld reference in. One worthy of noting in the synopsis, even. Jesus. Bieeanda (talk) 02:36, 7 June 2010 (UTC)

sentence needs reworked
"Forever Free is much shorter than the preceding book and its ending involves an archtypical Deus Ex Machina." Reads a bit too much like a sentence found in a book review. Drop the size of book comparison and instead just stating "archtypical Deus Ex Machina", describe the circumstances, this is in the spoils section. Jon 16:39, 20 June 2006 (UTC)
 * There's not much more to say about it, it really is that bad. After a series of increasingly bizarre events, God Himself jumps out of the pantry and says "LOL, I DID IT!"  The End.  Now aren't you glad you didn't buy the book? silsor 22:27, 20 June 2006 (UTC)

 * When I read it, back in the day - I remember it was a great mystery to see what was causing all these things. I remember thinking the whole 'God did it' explination was the BIGGEST cop-out I had ever seen. I'm still pissed about it. Raul654 05:17, 28 August 2006 (UTC)

Disimbaguation needed?
Should there be a Disimbaguation for this title? There is another book called Forever Free by Joy Adamson and is the third book in the Born Free series. Lighthope 05:43, 15 August 2007 (UTC)

there are somthings wrong with the synopsis. some of it is assumptions, if you look at the last few chapters of the book. for example the namless never states if there are more than one. yet the synpsis says gods —Preceding unsigned comment added by 86.136.106.153 (talk) 16:04, 6 April 2010 (UTC)

This Art Is A Mess
badly written, poor grammar, run-on sentences, etc.. ive started to try to clean it up, but without complete paragraph restructuring its a Badly Written Article.Moss Ryder (talk) (bad punctuation and sp in my post, but i double and treble check it for articles.

title: Talk:Forever Free (novel)


text:
Wikipedia:Articles for deletion/Captain Stabbin

 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or on a Votes for Undeletion nomination).  No further edits should be made to this page.

The result of the debate was Result: Delete under CSD A7 -- (drini's page| ☎ ) 01:34, 19 October 2005 (UTC)

Captain Stabbin
I know it has a bunch of Google hits, but is this website really notable? --Hottentot
 * keep (and expand). Alexa rank of 4,194! — brighterorange  (talk) 23:18, 8 October 2005 (UTC)
 * keep unfortunately. Notable within the field of nautical pornography. Pburka 01:46, 9 October 2005 (UTC)
 * Comment: can something be done about the link (no wiki, or that thing where it isn't followed)? -- Kjkolb 04:06, 9 October 2005 (UTC)
 * Delete nn Porncruft --JAranda | yeah 04:23, 9 October 2005 (UTC)
 * Keep and expand. Popular web site and performer; the article is pretty useless but can be expanded. MCB 19:03, 10 October 2005 (UTC)

Keep and expand
 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in an undeletion request). No further edits should be made to this page.


text: Category talk:1930s Atlantic hurricane seasons


text:
Bryan Smolinski

Bryan Anthony Smolinski (born December 27, 1971) is an American former professional ice hockey center. The Boston Bruins drafted him 21st overall in 1990. He played in the National Hockey League (NHL) for the Pittsburgh Penguins, New York Islanders, Los Angeles Kings, Ottawa Senators, Chicago Blackhawks, Vancouver Canucks and Montreal Canadiens. He had also previously played with the Port Huron Icehawks of the International Hockey League (IHL).

Drafted
Smolinski grew up in Genoa, Ohio and graduated from Cardinal Stritch High School in Oregon, Ohio. He played junior hockey for the Stratford Cullitons and played college hockey for the Michigan State Spartans. After his freshman year, the Boston Bruins drafted him in the first round (21st overall) in the 1990 NHL Entry Draft. Smolinski completed a four-year tenure with the Spartans before joining the Bruins for the end of the 1992–93 season.

National Hockey League
In his rookie campaign of 1993–94 Smolinski tallied 31 goals and 51 points. After a 31-point season in the shortened 1994–95 campaign, Smolinski was traded in the summer of 1995 alongside Glen Murray to the Pittsburgh Penguins for Kevin Stevens and Shawn McEachern. In his only season with the Penguins in 1995–96, he scored a career-high 40 assists and 64 points. However, Smolinski and the Penguins could not agree on a new contract in the off-season and he sat out the start of the next season, playing for the Detroit Vipers of the IHL. In November 1996, general manager Mike Milbury of the New York Islanders traded defenseman Darius Kasparaitis and rookie Andreas Johansson for the rights to negotiate a contract with Smolinski.

Smolinski played three seasons for the Islanders before being traded in June 1999 as part of an eight-player deal that saw him, Žigmund Pálffy, goaltender Marcel Cousineau, and fourth-round selection previously acquired from the New Jersey Devils (Daniel Johansson) traded to the Los Angeles Kings for Olli Jokinen, Josh Green, Mathieu Biron, and a first-round selection (Taylor Pyatt). Smolinski played four seasons for the Kings, before being traded to the Ottawa Senators at the trade deadline for defense prospect Tim Gleason on March 11, 2003.

During the 2004–05 NHL lockout, Smolinski was an assistant hockey coach at Cranbrook Kingswood before briefly playing for the Motor City Mechanics of the United Hockey League (UHL). Returning to the Senators for the 2005–06 season, he was traded in the subsequent off-season on July 9, 2006, to the Chicago Blackhawks in a three-way deal with the Senators and San Jose Sharks. Smolinski started the 2006–07 season with the Blackhawks but was later traded prior to the trade deadline to the Vancouver Canucks on February 26, 2007, for a conditional second round draft pick.

Becoming a free agent in the 2007 off-season, Smolinski signed a one-year contract with the Montreal Canadiens on July 2, 2007. On October 22, Smolinski played in his 1,000th career game, against the Bruins.

After the NHL
After his stint with the Montreal Canadiens, Smolinski began an assistant coaching job for a Michigan high school team, Birmingham Unified. With Smolinski's help, the team became District Champions for the first time in four years.

Without an NHL job, on February 24, 2009, Smolinski signed a deal with the Port Huron Icehawks of the IHL. On April 30, 2009, Smolinski signed a deal with the Milwaukee Admirals of the AHL. He is currently working with the National Hockey League as a regional director in their Learn To Play (LTP) program. In 2015, he was inducted into the National Polish-American Sports Hall of Fame.

Smolinski also referees high school hockey in Michigan.

Championships
2016 Michigan Amateur Hockey Association 30+ Recreational Division State Champions

title: Bryan Smolinski


text: Category talk:1920s Atlantic hurricane seasons


text:
Schrödinger functional

In mathematical physics, some approaches to quantum field theory are more popular than others. For historical reasons, the Schrödinger representation is less favored than Fock space methods. In the early days of quantum field theory, maintaining symmetries such as Lorentz invariance, displaying them manifestly, and proving renormalisation were of paramount importance. The Schrödinger representation is not manifestly Lorentz invariant and its renormalisability was only shown as recently as the 1980s by Kurt Symanzik (1981).

The Schrödinger functional is, in its most basic form, the time translation generator of state wavefunctionals. In layman's terms, it defines how a system of quantum particles evolves through time and what the subsequent systems look like.

Background
Quantum mechanics is defined over the spatial coordinates $$\mathbf{x}$$ upon which the Galilean group acts, and the corresponding operators act on its state as $$\hat{\mathbf x}\psi(\mathbf{x})= \mathbf{x}\psi(\mathbf{x})$$. The state is characterized by a wave function $$\psi(\mathbf{x})=\langle\mathbf{x}|\psi\rangle$$ obtained by projecting it onto the coordinate eigenstates defined by $$\hat{\mathbf x}\left|\mathbf{x}\right\rangle = \mathbf{x}\left|\mathbf{x}\right\rangle$$. These eigenstates are not stationary. Time evolution is generated by the Hamiltonian, yielding the Schrödinger equation $$i\partial_0\left|\psi(t)\right\rangle = \hat{H}\left|\psi(t)\right\rangle$$.

However, in quantum field theory, the coordinate is the field operator $$\hat{\phi}_\mathbf{x}=\hat{\phi}(\mathbf{x})$$, which acts on the state's wave functional as
 * $$\hat{\phi}(\mathbf{x}) \Psi\left[\phi(\cdot)\right] = \operatorname\phi\left(\mathbf{x}\right) \Psi\left[\phi(\cdot)\right] ,$$

where "$⋅$" indicates an unbound spatial argument. This wave functional
 * $$\Psi\left[\phi(\cdot)\right] = \left\langle\phi(\cdot)|\Psi\right\rangle$$

is obtained by means of the field eigenstates
 * $$\hat{\phi}(\mathbf{x}) \left|\Phi(\cdot)\right\rangle = \Phi(\mathbf{x}) \left|\Phi(\cdot)\right\rangle ,$$

which are indexed by unapplied "classical field" configurations $$\Phi(\cdot)$$. These eigenstates, like the position eigenstates above, are not stationary. Time evolution is generated by the Hamiltonian, yielding the Schrödinger equation,
 * $$i\partial_0\left|\Psi(t)\right\rangle = \hat{H}\left|\Psi(t)\right\rangle .$$

Thus the state in quantum field theory is conceptually a functional superposition of field configurations.

Example: scalar field
In the quantum field theory of (as example) a quantum scalar field $$\hat{\phi}(x)$$, in complete analogy with the one-particle quantum harmonic oscillator, the eigenstate of this quantum field with the "classical field" $$\phi(x)$$ (c-number) as its eigenvalue,
 * $$\hat{\phi}(x)\left|\phi\right\rangle =\phi\left(x\right)\left|\phi\right\rangle $$

is (Schwartz, 2013)
 * $$\left|\phi\right\rangle \propto e^{-\int dx\frac{1}{2}~(\phi(x)-\hat{\Phi}_{+}(x))^{2}}\left|0\right\rangle $$

where $$\hat{\Phi}_{+}\left(x\right)$$ is the part of $$\hat{\phi}\left( x\right)$$ that only includes creation operators $$a^\dagger_k$$. For the oscillator, this corresponds to the representation change/map to the |x⟩ state from Fock states.

For a time-independent Hamiltonian $H$, the Schrödinger functional is defined as
 * $$\mathcal{S}[\phi_2,t_2;\phi_1,t_1]=\langle\,\phi_2\,|e^{-iH(t_2-t_1)/\hbar}|\,\phi_1\,\rangle.$$

In the Schrödinger representation, this functional generates time translations of state wave functionals, through
 * $$\Psi[\phi_2,t_2] = \int\!\mathcal{D}\phi_1\,\,\mathcal{S}[\phi_2,t_2;\phi_1,t_1]\Psi[\phi_1,t_1] .$$

States
The normalized, vacuum state, free field wave-functional is the Gaussian

 * $$\Psi_0[\phi] = \det{}^{\frac{1}{4}} \left(\frac{K}{\pi}\right)\; e^{-\frac{1}{2}\int d\vec{x} \int d\vec{y}\, \phi(\vec{x}) K(\vec{x},\vec{y}) \phi(\vec{y}) } = \det{}^{\frac{1}{4}}\left(\frac{K}{\pi}\right)\; e^{-\frac{1}{2}\phi\cdot K \cdot\phi},$$

where the covariance K is

 * $$K(\vec{x},\vec{y}) = \int \frac{d^3 k}{(2\pi)^3} \omega_{\vec k}\,e^{i \vec{k}\cdot(\vec{x}-\vec{y})}.$$

This is analogous to (the Fourier transform of) the product of each k-mode's ground state in the continuum limit, roughly (Hatfield 1992)

 * $$\Psi_0[\tilde\phi] = \lim_{\Delta k\to 0}\;\prod_{\vec k} \left(\frac{\omega_{\vec k}}{\pi}\right)^{\frac 1 4} e^{-\frac{1}{2}\omega_{\vec k}\tilde\phi(\vec k)^2 \frac{\Delta k^3}{(2\pi)^3}} \to \left(\prod_{\vec k} \left(\frac{\omega_{\vec k}}{\pi}\right)^{\frac 1 4}\right) e^{-\frac{1}{2}\int\frac{d^3k}{(2\pi)^3} \omega_{\vec k}\tilde\phi(|\vec k|)^2}.$$

Each k-mode enters as an independent quantum harmonic oscillator. One-particle states are obtained by exciting a single mode, and have the form,

 * $$\Psi[\phi] \propto \int d\vec{x} \int d\vec{y}\, \phi(\vec{x}) K(\vec{x},\vec{y}) f(\vec{y}) \Psi_0[\phi] = \phi\cdot K\cdot f\, e^{-\frac{1}{2}\phi\cdot K\cdot\phi} .$$

For example, putting an excitation in $$\vec{k}_1$$ yields (Hatfield 1992)

 * $$\Psi_1[\tilde\phi] = \left(\frac{2 \omega_{k_1}}{(2\pi)^3}\right)^{\frac 1 2} \tilde\phi(\vec{k}_1) \Psi_0[\tilde\phi]$$
 * $$\Psi_1[\phi] = \left(\frac{2 \omega_{k_1}}{(2\pi)^3}\right)^{\frac 1 2} \int d^3 y\,e^{-i \vec{k}_1 \cdot \vec y}\phi(\vec y)\Psi_0[\phi] .$$

(The factor of $$(2\pi)^{-3/2}$$ stems from Hatfield's setting $$\Delta k = 1$$.)

Example: fermion field
For clarity, we consider a massless Weyl–Majorana field $$\hat\psi(x)$$ in 2D space in SO+(1, 1), but this solution generalizes to any massive Dirac bispinor in SO+(1, 3). The configuration space consists of functionals $$\Psi[u]$$ of anti-commuting Grassmann-valued fields $u(x)$. The effect of $$\hat\psi(x)$$ is

 * $$\hat\psi(x)|\Psi\rangle = \frac{1}{\sqrt 2}\left(u(x) + \frac{\delta}{\delta u(x)}\right) |\Psi\rangle .$$

title: Schrödinger functional


text: Category talk:1910s Atlantic hurricane seasons