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Talk:Plant hormone

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Commercial Uses of Plant Hormones

 * Abeles, F. B., Holm, R. E., & Gahagan, H. E. Abscission: the role of aging. Plant Physiology 42, 1351-56, 1967.
 * Adedipe, N. O., Hunt, L. A., & Fletcher, R. A. Effects of Benzyladenine on Photosynthesis growth and senescence of the bean plant. Phys. Plant. 25, 151-53, 1979.
 * Addicott, F. T., Carns, H. R., Lyon, J. L., Smith, O. E., & McMeans, J. L. On the physiology of Abscisins. Recrulateurs Naturels de la Croissance Vegetale, pp. 687-703. Paris: C.N.R.S., 1964.
 * Barrington, E. J. W. Hormones. The New Encyclopaedia Britannica. Macropaedia v. 8, pp. 1074-88. Chicago: Encyclopaedia Britannica, Inc., 1975.
 * Beevers, L., Loveys, B., Pearson, J. A., & Wareing, P. F. Phytochrome and hormonal expansion and greening of etiolated wheat leaves. Planta 90, 286-94, 1970.
 * Black, M. Abscisic Acid in seed germination and dormancy. Abscisic Acid, ed. F. T. Addicott, pp. 331-364. New York: Praeger, 1983.
 * Booth ? Nature London 194-204
 * Brown, A. W., Reeve, D. R., & Crozier, A. The effect of light on the Gibberellin metabolism and growth of Phaseolus coccineus seedlings. Planta 126, 83-91, 1975.
 * Burg, S. P., & Burg, E. A. The interaction between Auxin and Ethylene and its role in plant growth. PKAS 55, 262-69, 1966.
 * Davis & Wareing ? Planta 65 p. 139
 * Engelke, A. L., Hamzi, H. Q., & Skoog. F. Cytokinin-Gibberellin regulation of shoot development and leaf form in tobacco plantlets. Amer. J. of Botany 60, 491-95, 1973.
 * Esashi, Y., & Leopold, A. C. Plant Physiology 44, 1470, 1970.
 * Goeschl, J. D., Pratt, H. K., & Bonner, B. An effect of light on the production of Ethylene and the growth of the plumula portion of the etiolated pea seedling. Plant Physiology 42, 1077-80, 1967.
 * Goldthwaite, J. J. Further studies of hormone regulated senescence in Rumex leaf tissue. Plant Growth Substances, 1970, ed. D. J. Carr, pp. 581-88. Berlin: Springer, 1972.
 * Hayes, P. M., & Patrick J. W. Photosynthate transport in stems of Phaseolus vulgaris treated with Gibberellic Acid, Indole 3-Acetic Acid or Kinetin. Effects at the14site of hormone application. Planta 166: 371-79, 1985.
 * Hewett, E. W., & Wareing, P. F. Cytokinins in Populus x robusta Schneid: Light effects on endogenous levels. Planta 114, 119-129, 1973.
 * Houck, D. H., & Lamotte, C. E. Primary phloem regeneration without concomitant xylem regeneration--its hormone control in Coleus. Amer. J. Botany 64, 799-809, 1977.
 * Imaseki, H. Hormonal control of wound-induced responses. Encyclopedia of Plant Physiology. v. 11, ed. R. P. Pharis & D. M. Reid, p. 504, Heidelberg: Springer Verlag, 1985.
 * Jacobs, W. P. Comparison of the movement and vascular differentiation effects of the endogenous Auxin and of phenoxyacetic weed killers in stems and petioles of Coleus and Phaesolus. Ann. N.Y. Acad. Sci. 144, 102-117, 1967.
 * Jahardhan, K. V., Vasudeva, N., & Gopel, N. H. Diurnal variation of endogenous Auxin in arabica coffee leaves. J. Plant Crops 1 (Suppl), 93-95, 1973.
 * Kawase, M. Effects of flooding on Ethylene concentration in horticultural plants. J. Am. Soc. Hortic. Sci. 97, 584-88, 1972.
 * Lecoq, C., Koukkari, W. L., & Brenner, M. L. Rhythmic changes in Abscisic Acid (Abscisic Acid) content of soybean leaves. Plant Physiology 72 (suppl.), 52, 1983.
 * Manos, P.J., & Goldthwaite, J. A kinetic analysis of the effects of Gibberellic acid, Zeatin, and Abscisic Acid on leaf tissue senescence in Rumex. Plant Physiology 55, 192-98, 1975.
 * Marre, E. Effects of fusiccocin and hormones on plant cell membrane activities, observations and hypothesis. Regulation of Cell Membrane Activities in Plants. eds. Marre, E. & Caffer, O. Amsterdam: Elsevier/North Holland Biomedical Press, pp. 175-202, 1977.
 * McMichael, B. L., & Hanny, B. W. Endogenous levels of Abscisic Acid in Water stressed cotton leaves. Agron. J. 69, 979-82, 1982.
 * Mitsuhashi-Kato, M., Mishibaoka, H., & Shimokoriyama, M. Anatomical and physiological aspects of developmental processes of adventitious root formation. Plant and Cell Physiology 19, 393-400, 1978.
 * Nooden, L. D. Senescence in the whole plant. Senescence in Plants, ed. K. V. Thimann, Boca Raton, FL: CRC Press, 1980.
 * Palmer, J. H., & Phillips, I. D. J. The effect of the terminal bud indole acetic acid and nitrogen supply on the growth and orientation of the petiole of the Helianthus. Annus. Physiol. Plant 16, 572-84, 1963.
 * Pooviah, B. W., and Leopold, A. C. Deferral of leaf senescence with calcium. Plant Physiology 52, 236-39, 1973.
 * ??, Phys. Plant v. 51 375-79
 * Reid, D. M., and Wample, R. L. Water relations and plant hormones. Chapter 14 in Volume 11, Hormonal Regulation of Development III, eds. A. Pirson and M. H. Zimmerman. Heidelberg: Springer Verlag, 1985.
 * Reinhold, L. Phytohormones and the orientation of growth. Phytohormones and Related Compounds a Comprehensive Treatise, v. II, ed. by D. S. Letham, P. B. Goodwin, and T.J. V. Higgins. Amsterdam: Elsevier/North Holland Biomedical Press, 1978.
 * Ross, E. L. Growth regulators and conifers: their physiology and potential uses in forestry. Plant Growth Regulating Chemicals, v. II, ed. by L. G. Nickell. Boca Raton, FL: CRC.
 * Sachs, T., and Thimann, K. V. The Role of Auxin and Cytokinin in the Release of Buds from Dominance. Amer. J. Bot. 54, 136-44, 1967.
 * Sembdner, G., Gross, D., Liebisch, H. W., and Schneidner, G. Bio-synthesis and metabolism of plant hormones. Hormonal Regulation of Development 1, ed. J. MacMillen, Heidelberg: Springer Verlag, 1980.
 * Skoog, F., and Miller, W. Chemical regulation of growth and organ formation in plant tissues cultured in vitro. Symp. Soc. Exp. Biol. 11, 118, 1957.
 * Snow, R. Plagiotropism and correlative inhibition. New Phytologist 44, 110-117, 1945.
 * Sutcliffe, J. F. Regulation in the whole plant. In Transport in Plants v. 2. Part B: Tissues and Organs. Encyclopedia of Plant Physiology, ed. U. Luttge and M. G. Pitman. Heidelberg: Springer Verlag, 1976.
 * Thimann, K. V. Cell Enlargement and Growth. Hormone Action in the Whole Life of the Plant Amherst: Univ. of Mass. Press, 1977.
 * Thompson, M. J., Meudt, W. J., Mardava, N. B., Dutky, S. R.1Lusby, W. R., and Spaulding, D. W. Synthesis of Brassinosteroid and relationship of structure to plant growth promoting effect. Steroid 39 #1, 89-105, 1982.
 * Torrey, J. G. Auxin control of vascular pattern formation in regenerating pea root meristems grown in vitro. Amer. J. Bot. 44, 859-870, 1957.
 * Van Staden, J., and Smith, A. R. The synthesis of Cytokinin in excised roots of maize and tomato under aseptic conditions. Annals Bot. 42, 751-753, 1978.
 * Varner, J. E. GA-controlled synthesis of alpha-amylase in barley endosperm. Plant Physiology 39, 413-415, 1964.
 * Wain, R. L. Some development in research on plant growth inhibitors. Proc. Roy, Soc. B. 191, 335-352, 1975.
 * Wareing, P. F., and Phillips, I. D. J. Growth and Differentiation in Plants. Great Britain: Pergamon Press, 1981.
 * Webb, D. P., Van Staden, J., and Wareing, T. F. Seed dormancy in Acer. In J. Exp. Bot. 24, 105-106, 1973.
 * Wright, S. T. C. The effect of plant growth regulator treatments on the levels of ethylene emanating from excised turgid and wilted wheat leaves. Planta 148, 381-88, 1980.
 * ZeevABArt, J. A. D. Giberellin and flowering. The Biochemistry and Physiology of Giberellin, v. 2, ed. A. Crozier, New York: Praeger, 1983.
 * Zimmerman, P. W., and Hitchcock, A. E. Initiation and stimulation of adventitious roots caused by unsaturated hydrocarbon Gases. Contributions to the Boyce Thompson Institute 5, 351-369, 1933.

Comments by Socrtwo
I removed this attribution from the article body:

 * My name is Paul Pruitt. I received a BA from Swarthmore College in 1984, where I studied under Dr. Mark Jacobs. My bachelor's thesis was an examination of all aspects of plant senescence, including the role of hormones. I also received an MA from the University of Pennsylvania in 1986, where I studied plants under Scott Poethig among others. I have been studying the plant physiological hormone literature and thinking about plant hormones for 20 years. I'm currently an unemployed but experienced IT support analyst who has his own small file recovery and virtual Helpdesk business. The Website can be seen here. If you have any questions or comments, send them to s.socrtwo@verizon.com. --Socrtwo 02:05, 27 Apr 2004 (UTC)

-

This is socrtwo again. You know we could use some scientist editing of the entries.

-

Hi folks, here's a confession, I'm an arch speculator. The information I wrote in the article, (which I mostly wrote) is speculation albeit simple speculation based on experimental evidence.

I wrote most of the bullets for the different plant hormones too although they are clear experimental findings. I did not make up the information except where specified. I will try to find the specific references for each of the findings and reference it for each plant hormone.

According to the rules of this Wiki, speculation does not belong here. Please correct the article, and I will relegate my thoughts to a more appropriate forum. Let's just say it's a placeholder for now.--socrtwo 01:06, Mar 11, 2005 (UTC)

Why plural
Shouldn't this page at Plant hormone? ✑whkoh | ✖ 01:07, Oct 23, 2004 (UTC)

Yes. apparently somebody connected the two, because they lead to the same place.--socrtwo 00:51, Mar 11, 2005 (UTC)

Why I Removed the Hormone Theory Section
This article should properly contain a history of plant hormones and currently accepted scientific theory not my speculations even if I think they are right. An encyclopedia is a place for knowledge not speculation.--socrtwo 03:41, August 11, 2005 (UTC)

Phytochrome
Is phytochrome legitimately considered a plant hormone, and if not, why not?

Jeeb 21:57, 30 October 2005 (UTC)
 * Phytochrome is just an enzyme,... it is not transported through the body of the plant and so there is can't be any signal function related to that movement, so it's function is not related with coordination of different parts of the plant body, so it is not hormone. It is working locally in chloroplast membrane.  R eo  ON   |   + + +  18:03, 25 April 2006 (UTC)

In fact, phytochrome is actually a pigment. It can be in an active (Pfr) stage or an inactive (Pr) stage. It activates via red light and is not produced in response to any situation.

Move to Plant growth regulators
Why? It is more correct, cus phytohormones are just chemical substances naturally occuring in plants. On the other hand PGRs are both phytohormones and other chemical (synthetical) substances used in labs.--Juan de Vojníkov 10:17, 13 January 2007 (UTC)

Expansion
Finally the article was rescued of its stubness. Nice work. I think that this kind of article could benefit from a summarising table, as was done at the end of the Hebrew article. Aside from the chemical structures it lists the biosynthetic progenitors of each hormone (tryptophan and methionine for auxin and ethylene, for example) and the positive and negative effect in summary. Images in such a long article would also be nice. I'd love to to all this myself if the expansion is done. Pixie 22:58, 7 September 2007 (UTC)
 * I have a lot more to add, but would rather build around what you have suggested (I am not competent enough to do this my self though)- so if you want to take over for now that would be great. I can add here and there. My back ground in this field is limited to PGRs used in tissue culture 20 years ago and many of those are synthetic, so will work on a section for PGRs used in tissue culture after the main parts are done. I would also be greatfull for a through editing and general clean-up (another area I am not competent in)Hardyplants 23:09, 7 September 2007 (UTC)

Needs edited for:
... grammar, spelling, run-on sentences, etc.

I don't have the time to do it right. Native English speaker, please, with scientific background? Thanks! —Preceding unsigned comment added by 66.18.161.69 (talk) 22:47, 12 September 2007 (UTC)

I need to learn Wikipedia editing practices better before I could volunteer to take that on but I did remove a pro-Nazi bit of grafitti that has no place in an article on plant hormones anyway. Spidra (talk) 01:49, 25 April 2013 (UTC)

The speculator is back
The speculator is back. If this article represents the current state of the field, I think the state of the field lacks enough speculative encompassing explanatory theory. For instance, for the most basic question: "What are the Functions of Plant Hormones?," here are my educated speculations...

 * Auxin is a growth signal that the plant cells make when they have more than enough Oxygen (and Carbon Dioxide?) then they need just to survive. So in this case the plant signals that at least in the gases department, all signals are go for growth.
 * Similarly Cytokinin is the same kind of signal for minerals nutrition.
 * Salicylic Acid is the same kind of signal for water nutrition.
 * Jasmonate is the same kind of signal for light or sugar resources.
 * Conversely Ethylene is a signal of gas shortages. When a cell doesn't have enough Oxygen or Carbon Dioxide to grow, let alone remain the same size, they release Ethylene which eases such shortages but also causes the plant to prune back itself (but still maximizing Oxygen - mostly - and Carbon Dioxide which is probably only needed for growth, not survival).
 * Abscisic Acid is the same sort of signal for water.
 * Gibberellin is the shortage signal for sugar.
 * Strigolactones are the signal for mineral shortages.

Of course this simplification may not be true. However may be some of the other chemicals looked at recently like NO and Brassinosteroids (I know they were discovered a while ago) may fit the roles.

Maybe we should just start with the roles and assign the hormones later. There may be one dominant increase in hormone in each case of gas (or maybe just Oxygen as Carbon Dioxide abundance can be covered with the sugar abundance), water, sugar and mineral abundances and shortages.

The most controversial of my assertion would be that Auxin is mainly an Oxygen abundance signal and that Gibberellin is not a growth signal but a shortages one.

You can see where the logic of all these idea go at my longer version: http://planthormones.info/.socrtwo (talk) 04:06, 30 May 2013 (UTC)
 * New edits are welcome, but since this is a mature and large area, I would recommend sticking to WP:SECONDARY sources: reviews in major review journals, monographs, and textbooks. The general advice is to reserve any speculation for your blog. --Smokefoot (talk) 04:17, 30 May 2013 (UTC)

The section on the '5' major classes of plant hormone is based on a reference from 1979. I would argue that this list has been substantially expanded since then. As entire fields of research work on these more recently discovered hormones, I believe they should be included in the main list, rather than relegated to 'other hormones'. Personally I would say that the main list should comprise: auxin, ABA, cytokinin, GA and ethylene, plus: brassinosteroid, JA, SA and strigolactones. The definition of hormone in plant science is difficult because the term was originally defined for animals, making it difficult for the same definition to apply for plants. The consensus in the field is that the above mentioned compounds act as 'hormones' Scotanist (talk) 09:50, 28 April 2018 (UTC)

Plants hormones
Under agriculture ss3 102.89.47.214 (talk) 17:53, 4 April 2024 (UTC)

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title: Talk:Plant hormone


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Talk:Isthmian League

Name
but why is it called "Isthmian"??????????? Cutler 00:20, 16 May 2004 (UTC)

I've added a note referring to the ancient Isthmian Games, so called because they were celebrated near the isthmus of Corinth. --rossb 23:14, 26 December 2005 (UTC)

Correct explanation added Martyn Smith 08:48, 23 June 2006 (UTC)

The current explanation of the name seems extremely unconvincing. I've never heard of South-East England being referred to as and ishthmus. Can you substantiate this? --rossb 15:48, 15 December 2006 (UTC)

The name is derived from the fact that the geographical location of most of the clubs participating describe an isthmus of land around London and South-East England. - this is surely a joke and has therefore been removed. League most likely named after the Isthmian games http://en.wikipedia.org/wiki/Isthmian_Games - but I haven't added it because I can't find proof.

It was most obviously named in the spirit of the Greeks - other contemporary leagues were called Athenian (1912), Hellenic and Spartan (1907). Since at least the 19th century, it has been common across many sporting disciplines to associate teams, clubs, leagues etc. with legendary Greek athleticism. — Preceding unsigned comment added by AtomBoy (talk • contribs) 19:49, 26 January 2011 (UTC)
 * That explanation (thankfully now banished from the article) was clearly a total load of rubbish. Apart from the fact that an isthmus is simply the term for a thin strip of land that joins two other landmasses and therefore has no defined shape, the founding clubs were all from London itself, and there's no way London can be described as "shaped like an isthmus" (whatever the hell such a shape might be)..... -- ChrisTheDude (talk) 17:38, 13 February 2011 (UTC)

Promotion and relegation
I spent some time trying to find out how many teams each year are promoted, relegated and play-off in each league at each level up as far as the National Conference. Can anyone clarify this in this article or related articles on the English football league structure? In the box at the foot of the page, it looks like the blue bar entitled "Women's" is a heading for the detail below. Blue bars higher up contain headings. FA Cup and Women's FA Cup should be on separate lines. JMcC 14:27, 23 May 2006 (UTC)

 * Re promotion/relegation - try English football league system and ask there or check some of the external links.
 * I've tried to do change the template but for some reason its not coming up on the page anymore. I'll keep working on it. --Robdurbar 15:01, 23 May 2006 (UTC)

 * Fixed it, there was a noinclude tag in the table that I hadn't noticed. --Robdurbar 15:08, 23 May 2006 (UTC)

Servowarm Isthmian League
I also remember the League being known as the Servowarm Isthmian League. A quick "google" confirms this. But I am not sure that I have added this detail in the correct chronological order. Honuswagner 03:48, 25 September 2006 (UTC)

upeh tags
derry 2A00:23C7:BB10:8B00:1965:6909:F504:5F1B (talk) 15:58, 22 November 2021 (UTC)

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User:Mldl

Marc Liddell
webpage.

2004/05 Modules

 * Field (mathematics)
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User:Newby~enwiki

does anyone have more info on feijoas, eg. how to prepare them and how to eat them?

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Venetic language

Venetic is an extinct Indo-European language, usually classified into the Italic subgroup, that was spoken by the Veneti people in ancient times in northeast Italy (Veneto and Friuli)  and part of modern Slovenia, between the Po Delta and the southern fringe of the Alps, associated with the Este culture.

The language is attested by over 300 short inscriptions dating from the 6th to the 1st century BCE. Its speakers are identified with the ancient people called Veneti by the Romans and Enetoi by the Greeks. It became extinct around the 1st century when the local inhabitants assimilated into the Roman sphere. Inscriptions dedicating offerings to Reitia are one of the chief sources of knowledge of the Venetic language.

Linguistic classification
Venetic is a centum language. The inscriptions use a variety of the Northern Italic alphabet, similar to the Etruscan alphabet.

The exact relationship of Venetic to other Indo-European languages is still being investigated, but the majority of scholars agree that Venetic, aside from Liburnian, shared some similarities with the Italic languages and so is sometimes classified as Italic. However, since it also shared similarities with other Western Indo-European branches (particularly Celtic languages and Germanic languages), some linguists prefer to consider it an independent Indo-European language. Venetic may also have been related to the Illyrian languages once spoken in the western Balkans, though the theory that Illyrian and Venetic were closely related is debated by current scholarship.

While some scholars consider Venetic plainly an Italic language, more closely related to the Osco-Umbrian languages than to Latin, many authorities suggest, in view of the divergent verbal system, that Venetic was not part of Italic proper, but split off from the core of Italic early.

A 2012 study has suggested that Venetic was a relatively conservative language significantly similar to Celtic, on the basis of morphology, while it occupied an intermediate position between Celtic and Italic, on the basis of phonology. However these phonological similarities may have arisen as an areal phenomenon. Phonological similarities to Rhaetian have also been pointed out.

In 2016, Celtologist Peter Schrijver argued that Venetic and Italic together form one sub-branch of an Italo-Celtic branch of Indo-European, the other sub-branch being Celtic.

Fate
During the period of Latin-Venetic bilingual inscriptions in the Roman script, i.e. 150–50 BCE, Venetic became flooded with Latin loanwords. The shift from Venetic to Latin resulting in language death is thought by scholarship to have already been well under way by that time.

Features
Venetic had about six, possibly seven, noun cases and four conjugations (similar to Latin). About 60 words are known, but some were borrowed from Latin (liber.tos. < libertus) or Etruscan. Many of them show a clear Indo-European origin, such as vhraterei < PIE *bʰréh₂trey = to the brother.

Phonology
In Venetic, PIE stops *bʰ, *dʰ and *gʰ developed to, and , respectively, in word-initial position (as in Latin and Osco-Umbrian), but to ,  and , respectively, in word-internal intervocalic position (as in Latin). For Venetic, at least the developments of *bʰ and *dʰ are clearly attested. Faliscan and Osco-Umbrian have, and  internally as well.

There are also indications of the developments of PIE *kʷ > kv, *gʷ- > w- and PIE *gʷʰ- > f- in Venetic, the latter two being parallel to Latin; as well as the regressive assimilation of the PIE sequence *p...kʷ... > *kʷ...kʷ..., a feature also found in Italic and Celtic.

Language sample
A sample inscription in Venetic, found on a bronze nail at Este (Es 45):

Another inscription, found on a situla (vessel such as an urn or bucket) at Cadore (Ca 4 Valle):

Scholarship
The most prominent scholars who have deciphered Venetic inscriptions or otherwise contributed to the knowledge of the Venetic language are Pauli, Krahe, Pellegrini, Prosdocimi, and Lejeune. Recent contributors include Capuis and Bianchi.

title: Venetic language


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User:Empyrix

Yo.

Free-style rapper.

When I'm 23, gonna be famous.

When I'm 25, the world stops.

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User:Adamsmithusa~enwiki

I have just discovered Wikipedia and I must say, I am fascinated. I look forward to exploring its resources and making contributions in the future. May 15, 2004 adamsmithusa

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Marcus Aemilius Lepidus (consul 187 BC)

Marcus Aemilius Lepidus (c. 230 – 152 BC) was a Roman consul, Pontifex Maximus, Censor and Princeps Senatus. A scion of the ancient Patrician gens Aemilia, he was most likely the son of Marcus Aemilius Lepidus, with his brothers being Lucius and Quintus.

According to Polybius, Lepidus was "the handsomest man of his time," as well as, in the words of Diodorus, being "gifted with superior intelligence". Combining these qualities with an impeccable aristocratic birth, political skill and a reputation for bravery, Lepidus soon rose to become one of the leading Romans of his generation.

Lepidus was the great-grandfather of Marcus Aemilius Lepidus the Triumvir.

Early life
Although he was only 15 at the time of the Battle of Cannae in the 2nd Punic War, it was then that Lepidus first distinguished himself. If not at Cannae itself, then in one of the battles closely following it, Lepidus saved the life of one of his countrymen by killing his assailant. For this act of gallantry, the Senate ordered an equestrian statue of the young man erected on the Capitoline to commemorate the deed. It was a remarkable honour for one so young and one that marked Lepidus out for the future greatness he would achieve.

Later that year, 216 BC, Lepidus' father, Marcus Aemilius Lepidus, who had been an augur and twice consul, died and Marcus and his two brothers staged funeral games for three days in his honour.

Eastern missions
In 201, Lepidus and two colleagues were sent as ambassadors by the Senate to king Ptolemy V of Egypt, both to announce Rome's victory over Carthage and ensure that Rome's alliance with Egypt would continue through the coming war with Philip V of Macedon, which the Romans were preparing for. Ptolemy was still only a young boy at this time and there is a tradition that Lepidus for a time acted himself during his stay in Egypt as the king's guardian and for a time governed the country. This appeal to Rome for the Senate to send a regent to them was, according to Justin, made by the Egyptians themselves.

At this time also, while in Alexandria, Lepidus sailed to meet personally with Philip while the king was besieging Abydus, in an attempt to persuade him to lift the siege and abandon his attacks on Pergamum and the Rhodians, who had appealed to Rome. Lepidus delivered a message from the Senate that Philip of Macedon must cease from making war on any other Greeks and agree to pay compensation to Attalus I of Pergamum and Rhodes for any damage caused. If Philip would not agree to these terms then he and Macedon would soon find themselves at war with Rome. Rejecting the demands and saying that he was ready for war, Philip took the city and Lepidus departed. The result of the king's refusal of these terms was the outbreak of the Second Macedonian War.

Attempts at the Consulship
In 193 Lepidus served as curule aedile along with his kinsman Lucius Aemilius Paullus, during which time the two Aemilii constructed two new porticoes, or arcades, in Rome, one of them being the Porticus Aemilia.

Elected as Praetor in 192, Lepidus served his term from 191 and into 190 as the governor of Sicily. Due to the ongoing war between Rome and Antiochus in the East, Lepidus was charged with the defence of the island from attack as well as ensuring that one-fifth of all the corn produced was sent to support the armies campaigning in Greece.

In 190 Lepidus left Sicily early before his term as governor had expired without first asking the permission of the Senate to do so and hastened back to Rome in order to stand in the consular elections. This, however, counted against him and made him unpopular with the people as he was accused of abandoning his province and responsibilities in order to satisfy personal ambition. Following the vote, only one candidate, Marcus Fulvius Nobilior, a rival of Lepidus, had achieved the required majority, but that still meant that the other consulship was vacant. However, the following day, Nobilior co-opted the candidate who had come second, Gnaeus Manlius Vulso, as his colleague and the two assumed the Consulship for 189. Lepidus had polled third out of the four candidates, behind Manlius but ahead of Marcus Valerius Messalla. This humiliating defeat for the aristocratic patrician Lepidus, who likely saw the consulship as his birthright, further embittered a hatred that had already existed between him and Nobilior.

The following election, held later in 189, Lepidus again stood as a candidate for the consulship. Nobilior, however, returned to Rome to conduct and oversee the elections and he used his position to prevent any votes being cast for Lepidus, his personal enemy. As a result, although this time unfairly, Lepidus once more suffered the humiliation of defeat in the elections and could justly blame Nobilior. Instead, Marcus Valerius Messalla, who the previous year had polled behind Lepidus, and Gaius Livius Salinator were elected consul.

For the third successive time, Lepidus stood as a consular candidate in 188, and this time he was successful and was elected consul with Gaius Flaminius as his colleague.

Consulship
In 187 Lepidus was at last consul, and, as he and Flaminius assumed office, word reached the Senate that the Ligurians were preparing to make war on Rome. The threat of attack so close to Rome made the Senate take the matter seriously and it quickly decreed that both Consuls should have Liguria assigned as their joint-province and command. Lepidus opposed this, protesting that Nobilior and Manlius were still acting like kings in the East even though their terms had expired and yet the Senate still intended to confine both consuls to Liguria without recalling or replacing either of the two Eastern commanders. Either Nobilior and Manlius should be replaced, or their armies should be disbanded and they return to Rome. The Senate agreed to recall Nobilior and Manlius from the East, but reiterated its decision that both Lepidus and Flaminius were to take command in Liguria.

First man in Rome
From 180 onwards, he was elected pontifex maximus and from 179, he was princeps senatus. That same year he was also elected censor along with his great rival Marcus Fulvius Nobilior. In 175, he was elected consul for the second time. He oversaw construction of the Via Aemilia in 187, a Roman road from the town of Placentia to Ariminum, still in use and one of the most important roads in Northern Italy. He established the Roman colonies of Parma and Mutina and gave his name to the Roman castrum of Regium Lepidi (today Reggio Emilia).

title: Marcus Aemilius Lepidus (consul 187 BC)


text:
Talk:Virgin River

Date question
The first American party to see it, led by Jedediah Smith did arrive 1826, but if Thomas Virgin was badly wounded in an attack by Mohave people, that mean that he came in the second trip to California, and that was 1827. So Thomas Virgin was not in the first party to see the river. אביהו (talk) 18:57, 25 May 2016 (UTC)

Naming
The National Park Service says: "It is believed that the Virgin River was named 'La Virgen' by Spanish Catholic Missionaries in honor of the Virgin Mary."75.169.147.21 (talk) 22:14, 23 January 2021 (UTC)

title: Talk:Virgin River


text:
Burdur Province

Burdur Province is a province of Turkey, located in the southwest and bordering Muğla and Antalya to the south, Denizli to the west, Afyon to the north, and Isparta to the east. Its area is 7,175 km2, and its population is 273,799 (2022). The provincial capital is Burdur city.

Burdur is located in the Lakes Region of Turkey and has many lakes of various sizes, the largest of which, Burdur Lake, is named after the province. Salda Lake is the second largest lake in the province and is considered to be one of the cleanest lakes in the world.

Districts
Burdur province is divided into 11 districts (capital district in bold):
 * Ağlasun
 * Altınyayla
 * Bucak
 * Burdur
 * Çavdır
 * Çeltikçi
 * Gölhisar
 * Karamanlı
 * Kemer
 * Tefenni
 * Yeşilova

title: Burdur Province


text:
Dong Yuan

Dong Yuan (, Gan: dung3 ngion4; c. 934 – c. 962) was a Chinese painter.

He was born in Zhongling (钟陵; present-day Jinxian County, Jiangxi Province). Dong Yuan was active in the Southern Tang Kingdom of the Five Dynasties and Ten Kingdoms period. He was from Nanjing, which was a center for culture and the arts.

He was known for both figure and landscape paintings, and exemplified the elegant style which would become the standard for brush painting in China for the next nine centuries. He and his pupil Juran (巨然) were the founders of the Southern style of landscape painting, known as the Jiangnan Landscape style. Together with Jing Hao and Guan Tong of the Northern style they constituted the four seminal painters of that time.

As with many artists in China, his profession was as an official, here he studied the existing styles of Li Sixun and Wang Wei. However, he added to these masters' techniques; he included more sophisticated perspective.

Works
The Xiao and Xiang Rivers or Scenes along the Xiao and Xiang Rivers, a painting on silk (49.80 cm by 141.30 cm), is one of his best-known masterpieces. It demonstrates his exquisite techniques, and his sense of composition. The clouds break the background mountains into a central pyramid composition and a secondary pyramid, by softening the mountain line, he makes the immobile effect more pronounced.

The inlet by breaking the landscape into groups makes the serenity of the foreground more pronounced, instead of simply being a border to the composition, it is a space of its own, into which the boat on the far right intrudes, even though it is tiny compared to the mountains. Left of center, he uses his unusual brush stroke techniques, later copied in countless paintings, to give a strong sense of foliage to the trees, which contrasts with the rounded waves of stone that make up the mountains themselves. This gives the painting a more distinct middle ground, and makes the mountains have an aura and distance which gives them greater grandeur and personality. He also used "face like" patterns in the mountain on the right. A painting attributed to Dong Yuan, The Riverbank, is housed in the Metropolitan Museum of Art, and was a gift from New York financier Oscar Tang, though some scholars believe it may be a modern forgery by Zhang Daqian.

title: Dong Yuan


text:
Theresa LePore

Theresa LePore is a former Supervisor of Elections for Palm Beach County, Florida. She designed the infamous "butterfly ballot" used in the 2000 presidential election. This would lead the press to nickname her "Madame Butterfly". Following the controversial results of the 2000 election, she lost her re-election bid in September 2004 and left office in January 2005.

Career
LePore grew up in Palm Beach County, attending Cardinal Newman High School in West Palm Beach, Palm Beach State College in Lake Worth and Florida Atlantic University in Boca Raton.

She started her career in the Supervisor of Elections Office in 1971 as a file clerk. She quickly rose through the ranks and achieved the position of Chief Deputy Supervisor in the late 1970s. During the 1980s she also moonlighted as a ramp clerk at Palm Beach International Airport.

In 1996 LePore changed her political party registration to Democratic after deciding to run for the position of Supervisor of Elections. She was elected as the Palm Beach County Supervisor of Elections in November, 1996 and re-elected without opposition in November, 2000. In 2004 she lost re-election as Election Supervisor. Prior to the election she had changed her political party designation to independent. After leaving the Supervisor of Elections Office in January, 2005, she was employed by the Palm Beach County State Attorney's Office for a short period, enabling her to receive her full pension from Palm Beach County.

She then worked at her alma mater, Cardinal Newman High School in West Palm Beach, Florida as director of development until January 2009.

LePore is (or was) a member of the following organizations:
 * American Society of Public Administration
 * The Election Center
 * Kiwanis of Flagler Sunrise
 * League of Women Voters
 * International Association of Clerks, Recorders, Election Officials and Treasurers
 * Women's Chamber of Commerce of the Palm Beaches
 * Florida State Association of Supervisors of Election. Theresa served terms as Secretary, Vice-President, and President of FSASE.
 * Executive Women of the Palm Beaches
 * The Hispanic Chamber of Commerce of PBC
 * Hispanic Human Resources Council
 * Girl Scouts of Southeast Florida

She is writing a book about the 2000 election and the butterfly ballot she designed.

Election controversy
In 2000, to accommodate the large number of presidential candidates eligible in Florida, LePore designed a staggered two-page format with candidate names on alternating sides of a central punch button column. Conservatives falsely commented that the same ballot was successfully used in the 1996 election; in fact, it had never been used in a Palm Beach County election among rival candidates for office. In 2000, the confusing design led to an increased number of miscast votes in the presidential election (votes that would otherwise have been a decisive reversal) and consequently achieved notoriety.

A study by The Palm Beach Post speculated that voters confused by Palm Beach County's butterfly ballot cost Al Gore the presidency.

Popular culture
In Jay Roach's Recount, LePore is played by Jayne Atkinson.

title: Theresa LePore


text:
Kalakukko

Kalakukko is a traditional Finnish dish from the region of Savonia made from fish (e.g., perch, vendace, loach, smelt, or salmon) baked inside a loaf of bread. Kalakukko is especially popular in Kuopio, capital city of the Northern Savonia region. Kuopio is home to many kalakukko bakeries. The city also hosts an annual kalakukko baking contest.

Flour
Traditionally, kalakukko is prepared with rye flour (like ruisleipä), although wheat is often added to make the dough more pliable. The filling consists of fish, pork and bacon, and is seasoned with salt (unless the pork is already salted). After being baked for several hours, traditionally in a masonry oven, kalakukko looks much like a large loaf of rye bread. If prepared correctly, bones of the fish soften and the meat and fish juices cook thoroughly inside the bread. This results in a moist filling.

Fish
Traditionally, the fish used in kalakukko is either vendace (muikku), or European perch (ahven). Sometimes salmon is used. In southern Savonia the vendace is advocated as the only fish for the true kalakukko whereas in the northern parts of the province the same is said about the perch. Instead of fish, combinations of potato and pork or rutabaga and pork are also used. The appropriate drink to accompany kalakukko is buttermilk or piimä.

Kalakukko will keep for a long time when unopened. It used to be a practical lunch for workers away from home.

Serving
Kalakukko can be reheated in an oven. It takes about one hour in 130 °C if the size of the kalakukko is about 1 kg. It can also be eaten cold. The usual way to eat kalakukko is to open the top with a sharp knife, eat the top with butter, and then slice some of the bread making the hole on the top larger and eat it with the filling.

Etymology
Some Finnish speakers today find the name kalakukko somewhat amusing, as kala is Finnish for "fish" and kukko is "rooster", leading to the often used but non-morphological translation, "fish cock". Previous theories suggested that the archaic form of kukko is derived from the same root as kukkaro (purse). Kukko also might come from a Finnish word of kukkula, hill, because the dish is elevated. However, in 2008 new research demonstrated that kukko is a loan from Low German and shares the same origin as modern German küchen (to cook) and English cake.

Kalakukko obtained Traditional Speciality Guaranteed (TSG) status in Europe in 2002.

Hanna Partanen's kalakukko bakery
Hanna Partanen's (1891–1969) kalakukko bakery in Kuopio, Northern Savonia was Finland's most famous kalakukko bakery at its time. Famous guests have included American presidents and Soviet leaders along with President of Finland Urho Kekkonen. The bakery still bakes kalakukko by hand from Finnish materials in the same central location at Kasarmikatu 15 in Kuopio. The bakery is currently run by Hanna's grandson Lauri Partanen and employs 10 to 20 people depending on the season.

title: Kalakukko


text:
Talk:Linen

Linum Oleum
Mention of linum oleum content and effects, washing etc could be added. Linen is claimed to help people suffering from dry skin as well as being less attractive to various micro-organisms. — Preceding unsigned comment added by Blades (talk • contribs) 00:51, 16 May 2004 (UTC)

Hoplite cuirass
"Contrary to popular belief, linen was probably never used as material for the Hoplite cuirass because of its price. Hoplite cuirass was made of leather"

This is contrary to information on the de Wikipedia and major belief. I have not yet seen any reference/document sustaining any of these two positions. Cost is a good argument against linen, but bronze was also more expensive than leather. -- Zwiebeltuete 84.148.73.66 13:57, 14 June 2006 (UTC)

 * This has been added in the revision as of 13:46, 18 September 2005 by 212.182.194.29. So there is probably not much change to get more information -- Zwiebeltuete 84.148.69.42 12:47, 22 June 2006 (UTC)

 * Also, leather would be expensive too since before industrialization people didn't eat beef in the enormous quantities they do today. Unless the statement is sourced soon I'd suggest deleting it. --63.167.237.65 15:20, 26 September 2006 (UTC)
 * Oops, the above was me. --Wilhelm Ritter 15:23, 26 September 2006 (UTC)

Changes made
We made several changes to this article according to things we learned in our textile class, from textbooks and research. We feel that we added some important information while deleting several items that were repetitive. We could not varify some of the things mentioned in the article, so it would be good if more references would be added. — Preceding unsigned comment added by TextileStudentsVJ (talk • contribs) 23:12, 17 June 2006 (UTC)

Revision
We made a change to the revision on "Producers of Linen" to accuratly reflect our referenced source. Saying that Beligum and Ireland produce the "best" linen may be right, but it is somewhat subjective and not what is stated in the reference. — Preceding unsigned comment added by TextileStudentsVJ (talk • contribs) 02:37, 21 June 2006 (UTC)

Removing link
Removing the 123linen link since it is a non-informational link to a store that cares very little about the linen material. — Preceding unsigned comment added by 24.61.41.24 (talk) 00:02, 29 September 2006 (UTC)

Artistic use
added that linen is used as underground for paintings. Many famous painters used (and still use) linen (e.g. Van Gogh, Rembrandt, Picasso, etc etc) Arnoutf 21:52, 9 November 2006 (UTC)

Manchester
Why is linen called "manchester" in Australia? I assume there is a connection with Manchester, the English city, but I haven't been able to find much information online about it. 217.155.20.163 23:39, 8 April 2007 (UTC)

 * It seems this is a referral to bedding in general. In Australian bedding is called Manchester or linen. It's not necessarily 'linen' and can be cotton sheets etc. More than likely most cotton goods in Australia originated from Manchester in the early history of colonisation and has stuck. Ozdaren (talk) 06:41, 16 January 2011 (UTC)

 * As explained at Manchester, soft furnishings are known as Manchester in Australia, New Zealand, and South Africa because it was the world's major producer of such fabrics during the industrial revolution. Grutness...wha?  23:51, 24 August 2013 (UTC)

Linen's History needs work
The bits under "Linen's History" are inappropriate for the style. I would add the template to that effect, but I can't remember where it's at. - (talk) 09:46, 29 April 2007 (UTC)

 * I could not understand the meaning of "During the late war..." Could someone please modify this text? 98.218.53.99 (talk) 03:33, 6 May 2013 (UTC)

History in the New World
I am reading a book (The Discovery of Chocolate, by James Runcie) in which mention is made of cotton and linen cloths in Mexico at the time when Cortes first reached the city. There is a clear implication that linen had been discovered independently by civilisations on both sides of the Atlantic. Is this correct? --King Hildebrand 14:06, 15 July 2007 (UTC)

Phoenicians in Ireland
The statement that the Phoenecians "besides developing the tin mines of Cornwall, introduced flax growing and the making of linen into Ireland" is unsourced and not accepted among academic historians. See the WP article on Phoenicia: "It is often mentioned that Phoenicians ventured north into the Atlantic ocean as far as Great Britain, where the tin mines in what is now Cornwall provided them with important materials, although no archaeological evidence supports this belief and reliable academic authors see this belief as hollow (see Malcolm Todd - 1987, reference below)." — Preceding unsigned comment added by 75.46.33.114 (talk) 01:05, 17 July 2007 (UTC)

Religion
The Bible also uses fine linen as a symbol for the righteous acts of the saints (Revelation 19:8). 209.50.178.50 (talk) 14:03, 19 June 2008 (UTC)

 * Why use Proverbs 31:22 over 31:13? Hebrew has a few words for linen, but Pishtan is the more common one, and that is the word used in 31:13. 31:22 refers to shesh. It is also possible that shesh refers to hemp. — Preceding unsigned comment added by 69.124.116.101 (talk) 05:35, 6 September 2019 (UTC)

Reassessment
I am reclassing this a the new C-class, as there are just too many gaps in the coverage (especailly history) to qualify as B-class under the new guidelines. - PKM (talk) 18:24, 5 July 2008 (UTC)

Clarifications, please
Would a qualified editor please explain:

 * What a "node" in this context is
 * How "lea" is pronounced

Also, am I parsing the following correctly when I interpret this sentence:

"The use of linen for priestly vestments was not confined to the Israelites, but from Plutarch, who lived and wrote one hundred years after the birth of Christ, we know that also the priests of Isis wore linen because of its purity."

as meaning "... to the Israelites; from Plutarch, writing one hundred years after the birth of Christ ..."

Joshua McGee (talk) 03:31, 17 October 2008 (UTC)

Grist
This is a specific length, or indirect grist system

Whatever is an "indirect grist system"? --jpgordon:==( o ) 17:58, 11 July 2009 (UTC)

History
The history section has been identified as inaccurate, grossly incomplete, and written in an archaic style since 2007. I've tagged it for cleanup. - PKM (talk) 06:06, 6 August 2009 (UTC)

 * The statement that linen dates back to 8000 B.C. cannot be proven and therefore shouldn't be in the text.76.6.94.233 (talk) 07:45, 11 March 2010 (UTC)

 * You miss the point in the difference between written historical records and a scientifically dated object, but I agree the reference should contain a footnote. — Preceding unsigned comment added by 64.252.7.200 (talk) 06:29, 6 April 2013 (UTC)

 * Huge amount of British wealth was created on the back of linen workers and later linen mills. Technology to extract, spin, weave, etc linen was vastly improved by Victorian entrepreneurs like Marshall who turned a cottage industry into full-scale production. This should be included in the History section. —Preceding unsigned comment added by 213.122.142.21 (talk) 14:33, 21 January 2011 (UTC)

Currency
It seems unlikley that the paper currency in the US and other countries is 25% linen and 75% cotton. This leaves 0% anything else, including wood..? If correct, I should emphasize or link this to currency page? I can't find this info elsewhere e.g. banknotes Roggg (talk) 16:38, 24 August 2009 (UTC)

Photo is not flax being harvested but wheat straw?
The photo with the red machine is odd. I cannot see any flax on the left waiting to be harvested, as the photo says. Is it just loose wheat left by a combine harvester being gathered up and turned into 'swiss rolls'? 92.15.13.152 (talk) 11:23, 20 December 2010 (UTC)

section: antiquity
its basically three examples of "and they opened the grave and LO BEHOLD the thousand year old linen was intact. cry out miracle." notwithstanding the flags for citation needed (yes its needed, but hell i dont give a heed for them - i am fully ready to take the statements as verifiable even without the citations being in place) but what i want to ask while reading this: so what - how do i get to know more about linen as an object of encyclopedical curiosity - by being told these repetitive, somewhat looking to be picked and beyond being put in front of my reader's eyes to behold and fall in awe not commented, or elaborated further - pieces of data? i am not going as far as to suggest the removal of the whole "antiquity" section but at least if you edited this article before and you keep an eye on it pls contemplate for a moment on what ever does it want to tell the reader about linen. if it is really like "and at favorable environmental conditions some linens did not decompose for several thousand years" then cut the examples (put them in the citations, sources, etc part at the bottom) and instead go for the straight statement. but then it would be more encyclopedical to put it in a broader scope so say instead that plant based material can stay intact for thousands of years well preserved.89.134.199.32 (talk) 22:59, 16 December 2019 (UTC).

section: religion
Theres one really valuable piece of information here: https://www.mechon-mamre.org/p/pt/pt0319.htm#19

Because by reading the translated source it cometh upon the reder as obvious that it is not about linen but a figure of speech to forbid mixing religious practices. well done. 89.134.199.32 (talk) 23:13, 16 December 2019 (UTC).

Rise of cotton
I believe that cotton began to replace linen around the 19th century causing the linen/flax industries to decline, certainly in Ireland & England. This should probably be mentioned in the Modern History section but I don't have a current source to hand.Djm-leighpark (talk) 17:32, 31 October 2021 (UTC)

A Commons file used on this page or its Wikidata item has been nominated for deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion: Participate in the deletion discussion at the nomination page. —Community Tech bot (talk) 12:22, 4 July 2022 (UTC)
 * KT 28.jpg

title: Talk:Linen


text:
Robby Benson

Robby Benson (born Robin David Segal; January 21, 1956 ) is an American actor, director, and musician. He rose to prominence as a teen idol in the late 1970s, appearing in the sports films One on One (1977) and Ice Castles (1978). He subsequently garnered more fame for voicing the Beast in the Disney animated film Beauty and the Beast (1991) and its numerous sequels and spin-offs. He has also worked as a television director, including six episodes of the sitcom Friends.

In addition to acting and directing, Benson is an activist in the field of heart research, having undergone four open-heart surgeries since age 28 to correct congenital aortic valve defects and related damage. In 2012, he published a memoir recounting his medical journey and numerous surgeries.

Early life
Benson was born in Dallas, Texas, the son of Freda Ann (née Benson), a singer, actor, and business promotions manager, and Jerry Segal, a writer. His family is Jewish. When Benson was five years old, his family relocated to New York City, where he was raised. He subsequently took his mother's name as his stage name when he was 10. Benson attended the Lincoln Square Academy in Manhattan, where he graduated at age fourteen as the class valedictorian.

Career
Benson made his film debut with an uncredited role in Wait Until Dark (1967) as the Boy Tossing Ball and his Broadway debut in The Rothschilds (1970). Benson had an early role on the daytime soap Search for Tomorrow (1971–1972). As a film actor, Benson was well known for teenage roles in coming of age films, such as 1972's Jory, 1973's Jeremy, and as Billy Joe McAllister in 1976's Ode to Billy Joe. He had an appearance in a 1973 commercial for Reese's Peanut Butter Cups alongside Donny Most who would later co-star in Happy Days.

In 1975, Benson appeared in Death Be Not Proud and Lucky Lady. That year, he also screen tested for the role of Luke Skywalker in Star Wars, a role which eventually went to Mark Hamill. In 1977, Benson starred in One on One (which he co-wrote with his father and needed no double for the authentic looking college basketball scenes due to his prowess at the game) and the TV movie The Death of Richie. In 1978, he co-starred in The End and Ice Castles. Benson, who had never ice skated before, learned to skate in order to film the movie, which had numerous skating scenes, including ice hockey. In 1980, Benson starred in Die Laughing and Tribute.

In 1981, he costarred in The Chosen, based on the book of the same name by Chaim Potok. The New York Times gave the film a mixed review, but noted that Benson's character was "full of a gentle inquisitiveness that cannot help but win the audience's sympathy." Benson played Olympic 10,000-meter gold medalist Billy Mills in the 1983 film Running Brave. From the filming of this movie Benson implemented his training for the 1983 New York City Marathon, completing the race in 3:05:15. In 1991, he starred as the voice of Beast in the animated Disney film Beauty and the Beast, directed by Gary Trousdale and Kirk Wise, and starring alongside Paige O'Hara as Belle. Later in the 1990s he voiced lead character J.T. Marsh on the sci-fi cartoon series Exosquad.

His 2007 novel Who Stole the Funny?: A Novel of Hollywood landed Benson on the Los Angeles Times Bestseller list. Benson's medical memoir I'm Not Dead ... Yet! was released in June 2012. Outside of acting, Benson is also a musician and composer. He has composed songs in several films and has also won a RIAA Gold Records award for the song "We Are Not Alone" in the John Hughes film The Breakfast Club.

Benson has been a professor at New York University's Tisch School of the Arts, the University of Utah and the University of South Carolina. It was announced he would serve as a professor of Practice in the fall of 2013 at Indiana University. Benson left the university after the Spring 2016 semester when his three-year contract expired.

Personal life
Benson has been married to singer and actress Karla DeVito since July 11, 1982. The pair met while starring together in The Pirates of Penzance. Together they have two children, daughter Lyric (b. 1983) and son Zephyr (b. 1992). He practices Transcendental Meditation.

Health problems and activism
While a teenager, Benson was diagnosed with a heart murmur caused by a bicuspid aortic valve defect. He began experiencing symptoms such as dizziness and losing consciousness in his late twenties, and subsequently underwent open-heart surgery in October 1984 to repair the valve defect. He received a bovine valve transplant, which lasted fifteen years. After the bovine valve failed, Benson had a second surgery in 2000, during which he underwent the Ross procedure. For six years after his second surgery, Benson had consistent struggles breathing. He subsequently underwent a third open-heart surgery, during which it was discovered that his breathing problems were caused by the previous procedure causing his aortic valve to buckle and close. In 2010, Benson received a delicate fourth surgery known as the "reverse Ross procedure" to correct damage to his heart.

Benson is an activist and fundraiser for heart research, which, in 2004, led him to write the book, lyrics and music for an original Off-Broadway play called Open Heart, in which he also starred. Benson also has spoken about his dealing with post-surgical cardiac depression, commenting after his fourth surgery: "They still saw your chest right down the middle, but they've done it [to me] enough that you no longer think about it as life-threatening. It's just a very tough surgery to go through. Doctors have also gotten better at helping you through the healing process. How we heal and how we deal with cardiac depression and how we can jump start our lives and get back on track. Doctors used to never talk about things like that and now they do."

Director

 * White Hot (1989)
 * Modern Love (1990)
 * Family Album (TV Series) - 4 episodes
 * 1.3 "Guardian Angel" (1993)
 * 1.4 "Winter, Spring, Summer or Fall All You Gotta Do Is Call..." (1993)
 * 1.5 "Salon, Farewell, Auf Wiedersehn, Goodbye" (1993)
 * 1.6 "Will You Still Feed Me?" (1993)
 * Evening Shade (TV Series) - 8 episodes
 * 3.14 "Private School" (1993)
 * 3.22 "Teaching Is a Good Thing" (1993)
 * 3.24 "The Graduation" (1993)
 * 4.8 "Wood and Evan's Excellent Adventure" (1993)
 * 4.11 "Chain of Fools" (1993)
 * 4.12 "Sleepless in Arkansas" (1993)
 * 4.14 "The People's Choice" (1994)
 * Monty (TV Series) - 2 episodes
 * 1.3 "The Son Also Rises" (1994)
 * 1.6 "Baby Talk" (1994)
 * Muddling Through (TV Series) - 2 episodes
 * 1.2 "Let It Be Normal" (1994)
 * 1.5 "Second Time's the Charm" (1994)
 * Good Advice (TV Series) - 2 episodes
 * 2.3 "Divorce, Egyptian Style" (1994)
 * 2.12 "Lights, Camera, Friction!" (1994)
 * The George Wendt Show (TV Show) - 1 episode
 * 1.2 "A Need for See" (1995)
 * Bringing Up Jack (TV Series) - 1 episode
 * Thunder Alley (TV Series) - 21 episodes
 * 1.2 "The Love Triangle" (1994)
 * 1.4 "Girls' Night Out" (1994)
 * 1.5 "Bloodsuckers" (1994)
 * 1.6 "Happy Endings" (1994)
 * 2.1 "Never Say Die" (1994)
 * 2.2 "Speak No Evil" (1994)
 * 2.3 "Easy Money" (1994)
 * 2.4 "Get a Job" (1994)
 * 2.5 "First Date" (1994)
 * 2.6 "Give 'Em Hell, Bobbi" (1994)
 * 2.7 "Sex, Lies & Popcorn" (1994)
 * 2.8 "The Garage Sale" (1994)
 * 2.9 "Accidentally at First Sight" (1995)
 * 2.10 "Are We There Yet?" (1995)
 * 2.12 "The Trouble with Harry" (1995)
 * 2.13 "Workin' Man's Blues" (1995)
 * 2.14 "A Little Me Time" (1995)
 * 2.15 "I Am Spartacus" (1995)
 * 2.17 "Just a Vacation" (1995)
 * 2.18 "Buzz Off, Buzzard Boy" (1995)
 * 2.19 "No Swing Set" (1995)
 * Dream On (TV Series) - 1 episodes
 * 6.1 "Try Not to Remember" (1995)
 * Ellen (TV Series) - 25 episodes
 * 3.1 "Shake, Rattle and Rumble" (1995)
 * 3.2 "These Successful Friends of Mine" (1995)
 * 3.3 "The Shower Scene" (1995)
 * 3.4 "The Bridges of L.A. County" (1995)
 * 3.5 "Hello, I Must Be Going" (1995)
 * 3.6 "Trick or Treat - Who Cares?" (1995)
 * 3.7 "She Ain't Friendly, She's My Mother" (1995)
 * 3.8 "Salad Days" (1995)
 * 3.9 "The Movie Show" (1995)
 * 3.10 "What's Up, Ex-Doc?" (1995)
 * 3.11 "Ellen's Choice" (1995)
 * 3.12 "Do You Fear What I Fear?" (1995)
 * 3.13 "Horschak's Law" (1996)
 * 3.14 "Morgan, P.I." (1996)
 * 3.15 "Oh, Sweet Rapture" (1996)
 * 3.16 "Witness" (1996)
 * 3.17 "Ellen: With Child" (1996)
 * 3.18 "Lobster Diary" (1996)
 * 3.19 "Two Ring Circus" (1996)
 * 3.20 "A Penney Saved..." (1996)
 * 3.21 "Too Hip for the Room" (1996)
 * 3.22 "Two Mammograms and a Wedding" (1996)
 * 3.23 "Go Girlz" (1996)
 * 3.24 "When the Vow Breaks: Part 1" (1996)
 * 3.26 "When the Vow Breaks: Part 2" (1996)
 * Life with Roger (TV Series) - 1 episode
 * Pearl (TV Series) - 1 episodes
 * 1.2 "Teacher's Pet" (1996)
 * Common Law (TV Series) - 1 episodes
 * 1.1 "Pilot" (1996)
 * Sabrina, the Teenage Witch (TV Series) - 3 episodes
 * 1.1 "Pilot" (1996)
 * 1.10 "Sweet & Sour Victory (1996)
 * 1.17 "First Kiss" (1997)
 * Friends (TV Series) - 6 episodes
 * 1.22 "The One with the Ick Factor" (1995)
 * 3.12 "The One with All the Jealousy" (1997)
 * 3.13 "The One Where Monica and Richard Are Just Friends" (1997)
 * 3.14 "The One with Phoebe's Ex-Partner" (1997)
 * 3.18 "The One with the Hypnosis Tape" (1997)
 * 3.24 "The One with the Ultimate Fighting Champion" (1997)
 * House Rules (TV Series) - 1 episodes
 * 1.7 "Who Knew?" (1998)
 * The Naked Truth (TV Series) - 14 episodes
 * 2.8 "The Scoop" (1997)
 * 2.9 "The Birds" (1997)
 * 3.1 "Things Change" (1997)
 * 3.2 "Her Girl Friday" (1997)
 * 3.3 "Bully for Dave" (1997)
 * 3.4 "Liesl Weapon" (1997)
 * 3.5 "Bridesface Revisited" (1997)
 * 3.7 "Look at Me! Look at Me!" (1997)
 * 3.12 "Women on the Verge of a Rhytidectomy" (1998)
 * 3.13 "8 1/2" (1998)
 * 3.14 "The Neighbor of Bath" (1998)
 * 3.15 "Day of the Locos" (1998)
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 * 3.16 "Muddy for Nothing" (1998)
 * Reunited (TV Series) - 1 episodes
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Producer

 * Die Laughing (1980)
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Writer

 * One on One (1977)
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Composer

 * Walk Proud (1979)
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Singles

 * "Blue Balloon (The Hourglass Song)" (1973)
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 * "All I Want Is Love" (1980)

title: Robby Benson


text:
User:David Newton/Sandbox

SI Progress
So far SIs up to SI 1987/827 have been gone through.

Maths Experiments
$$(M-P)\frac{I}{P}$$

$$\frac{I}{100 - I}$$

2024

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American casualties in Operation Iraqi Freedom have contributed by far the largest proportion of those killed and wounded in the invasion and subsequent occupation of Iraq. In the time since the start of the invasion nearly 1,800 service personnel have been killed in action. Some 14,000 troops have been wounded in action during the same time period.

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title: User:David Newton/Sandbox


text:
Benjamin Salisbury

Benjamin David Salisbury (born October 19, 1980) is an American actor and dancer best known for playing the role of Brighton Sheffield on the CBS television sitcom The Nanny from 1993 to 1999.

Early life and education
Born in Minneapolis, Minnesota, on October 19, 1980, to parents David Arthur Salisbury and Mindy Jo (née Schneidewind) Salisbury. In 1998, he graduated from Wayzata High School in Plymouth, Minnesota, and enrolled in American University in Washington, D.C., that fall.

Career
An accomplished dancer, Salisbury would often treat The Nanny studio audiences to improvisational routines when the cameras were not rolling.

Salisbury also played Martin Short's son in the 1992 film Captain Ron, and appeared in D3: The Mighty Ducks (1996) as the sports announcer.

Benjamin played the voice of Tin Boy on The Oz Kids in 1996.

Salisbury was a contestant on Jeopardy!, where he competed in an episode of Teen Celebrity Jeopardy! against Kirsten Dunst and Joseph Gordon-Levitt. Salisbury won with $1 but received $15,000 for his charity, while Dunst and Levitt each received $10,000 for theirs.

He appeared in the 2004 reunion of the sitcom The Nanny titled The Nanny Reunion: A Nosh to Remember with Fran Drescher, Renée Taylor, Rachel Chagall and others from The Nanny cast.

In 2005, he had a minor role as a train expert on the episode "Sabotage" of the series Numb3rs. In August 2006, Salisbury was featured in Domino's Pizza commercials featuring Fudge-ums, Domino's then-new mini-brownies.

As of February 2017, Salisbury is working at Universal Studios Hollywood as the director of operations for the park.

Personal life
Salisbury married his wife Kelly Murkey in 2006. He has three children. It was announced in 2013 they had divorced.

title: Benjamin Salisbury


text:
Amenable group

In mathematics, an amenable group is a locally compact topological group G carrying a kind of averaging operation on bounded functions that is invariant under translation by group elements. The original definition, in terms of a finitely additive measure (or mean) on subsets of G, was introduced by John von Neumann in 1929 under the German name "messbar" ("measurable" in English) in response to the Banach–Tarski paradox. In 1949 Mahlon M. Day introduced the English translation "amenable", apparently as a pun on "mean".

The critical step in the Banach–Tarski paradox construction is to find inside the rotation group SO(3) a free subgroup on two generators. Amenable groups cannot contain such groups, and do not allow this kind of paradoxical construction.

Amenability has many equivalent definitions. In the field of analysis, the definition is in terms of linear functionals. An intuitive way to understand this version is that the support of the regular representation is the whole space of irreducible representations.

In discrete group theory, where G has the discrete topology, a simpler definition is used. In this setting, a group is amenable if one can say what proportion of G any given subset takes up. For example, any subgroup of the group of integers $$(\Z, +)$$ is generated by some integer $$p \geq 0$$. If $$p = 0$$ then the subgroup takes up 0 proportion. Otherwise, it takes up $$1/p$$ of the whole group. Even though both the group and the subgroup has infinitely many elements, there is a well-defined sense of proportion.

If a group has a Følner sequence then it is automatically amenable.

Definition for locally compact groups
Let G be a locally compact Hausdorff group. Then it is well known that it possesses a unique, up-to-scale left- (or right-) translation invariant nontrivial ring measure, the Haar measure. (This is a Borel regular measure when G is second-countable; there are both left and right measures when G is compact.) Consider the Banach space L∞(G) of essentially bounded measurable functions within this measure space (which is clearly independent of the scale of the Haar measure).

Definition 1. A linear functional Λ in Hom(L∞(G), R) is said to be a mean if Λ has norm 1 and is non-negative, i.e. f ≥ 0 a.e. implies Λ(f) ≥ 0.

Definition 2. A mean Λ in Hom(L∞(G), R) is said to be left-invariant (respectively right-invariant) if Λ(g·f) = Λ(f) for all g in G, and f in L∞(G) with respect to the left (respectively right) shift action of g·f(x) = f(g−1x) (respectively f·g(x) = f(xg−1)).

Definition 3. A locally compact Hausdorff group is called amenable if it admits a left- (or right-)invariant mean.

Example
As an example for compact groups, consider the circle group. The graph of a typical function f ≥ 0 looks like a jagged curve above a circle, which can be made by tearing off the end of a paper tube. The linear functional would then average the curve by snipping off some paper from one place and gluing it to another place, creating a flat top again. This is the invariant mean, i.e. the average value $$\Lambda(f)=\int_{\mathbb{R}/\mathbb{Z}} f \ d\lambda$$ where $$\lambda$$ is Lebesgue measure.

Left-invariance would mean that rotating the tube does not change the height of the flat top at the end. That is, only the shape of the tube matters. Combined with linearity, positivity, and norm-1, this is sufficient to prove that the invariant mean we have constructed is unique.

As an example for locally compact groups, consider the group of integers. A bounded function f is simply a bounded function of type $$f: \Z \to \R$$, and its mean is the running average $$\lim_n \frac{1}{2n+1} \sum_{k=-n}^n f(k)$$.

Equivalent conditions for amenability
contains a comprehensive account of the conditions on a second countable locally compact group G that are equivalent to amenability:

 * Existence of a left (or right) invariant mean on L∞(G). The original definition, which depends on the axiom of choice.
 * Existence of left-invariant states. There is a left-invariant state on any separable left-invariant unital C*-subalgebra of the bounded continuous functions on G.
 * Fixed-point property. Any action of the group by continuous affine transformations on a compact convex subset of a (separable) locally convex topological vector space has a fixed point. For locally compact abelian groups, this property is satisfied as a result of the Markov–Kakutani fixed-point theorem.
 * Irreducible dual. All irreducible representations are weakly contained in the left regular representation λ on L2(G).
 * Trivial representation. The trivial representation of G is weakly contained in the left regular representation.
 * Godement condition. Every bounded positive-definite measure μ on G satisfies μ(1) ≥ 0. Valette improved this criterion by showing that it is sufficient to ask that, for every continuous positive-definite compactly supported function f on G, the function Δ–$1/2$f has non-negative integral with respect to Haar measure, where Δ denotes the modular function.
 * Day's asymptotic invariance condition. There is a sequence of integrable non-negative functions φn with integral 1 on G such that λ(g)φn − φn tends to 0 in the weak topology on L1(G).
 * Reiter's condition. For every finite (or compact) subset F of G there is an integrable non-negative function φ with integral 1 such that λ(g)φ − φ is arbitrarily small in L1(G) for g in F.
 * Dixmier's condition. For every finite (or compact) subset F of G there is unit vector f in L2(G) such that λ(g)f − f is arbitrarily small in L2(G) for g in F.
 * Glicksberg−Reiter condition. For any f in L1(G), the distance between 0 and the closed convex hull in L1(G) of the left translates λ(g)f equals |∫f|.
 * Følner condition. For every finite (or compact) subset F of G there is a measurable subset U of G with finite positive Haar measure such that m(U Δ gU)/m(U) is arbitrarily small for g in F.
 * Leptin's condition. For every finite (or compact) subset F of G there is a measurable subset U of G with finite positive Haar measure such that m(FU Δ U)/m(U) is arbitrarily small.
 * Kesten's condition. Left convolution on L2(G) by a symmetric probability measure on G gives an operator of operator norm 1.
 * Johnson's cohomological condition. The Banach algebra A = L1(G) is amenable as a Banach algebra, i.e. any bounded derivation of A into the dual of a Banach A-bimodule is inner.

Case of discrete groups
The definition of amenability is simpler in the case of a discrete group, i.e. a group equipped with the discrete topology.

Definition. A discrete group G is amenable if there is a finitely additive measure (also called a mean)—a function that assigns to each subset of G a number from 0 to 1—such that

 * 1) The measure is a probability measure: the measure of the whole group G is 1.
 * 2) The measure is finitely additive: given finitely many disjoint subsets of G, the measure of the union of the sets is the sum of the measures.
 * 3) The measure is left-invariant: given a subset A and an element g of G, the measure of A equals the measure of gA.  (gA denotes the set of elements ga for each element a in A.  That is, each element of A is translated on the left by g.)

This definition can be summarized thus: G is amenable if it has a finitely-additive left-invariant probability measure. Given a subset A of G, the measure can be thought of as answering the question: what is the probability that a random element of G is in A?

It is a fact that this definition is equivalent to the definition in terms of L∞(G).

Having a measure μ on G allows us to define integration of bounded functions on G. Given a bounded function f: G → R, the integral

 * $$\int_G f\,d\mu$$

is defined as in Lebesgue integration. (Note that some of the properties of the Lebesgue integral fail here, since our measure is only finitely additive.)

If a group has a left-invariant measure, it automatically has a bi-invariant one. Given a left-invariant measure μ, the function μ−(A) = μ(A−1) is a right-invariant measure. Combining these two gives a bi-invariant measure:

 * $$\nu(A) = \int_{g\in G}\mu \left (Ag^{-1} \right ) \, d\mu^-.$$

The equivalent conditions for amenability also become simpler in the case of a countable discrete group Γ. For such a group the following conditions are equivalent:

 * Γ is amenable.
 * If Γ acts by isometries on a (separable) Banach space E, leaving a weakly closed convex subset C of the closed unit ball of E* invariant, then Γ has a fixed point in C.
 * There is a left invariant norm-continuous functional μ on ℓ∞(Γ) with μ(1) = 1 (this requires the axiom of choice).
 * There is a left invariant state μ on any left invariant separable unital C*-subalgebra of ℓ∞(Γ).
 * There is a set of probability measures μn on Γ such that ||g · μn − μn||1 tends to 0 for each g in Γ (M.M. Day).
 * There are unit vectors xn in ℓ2(Γ) such that ||g · xn − xn||2 tends to 0 for each g in Γ (J. Dixmier).
 * There are finite subsets Sn of Γ such that |g · Sn Δ Sn| / |Sn| tends to 0 for each g in Γ (Følner).
 * If μ is a symmetric probability measure on Γ with support generating Γ, then convolution by μ defines an operator of norm 1 on ℓ2(Γ) (Kesten).
 * If Γ acts by isometries on a (separable) Banach space E and f in ℓ∞(Γ, E*) is a bounded 1-cocycle, i.e. f(gh) = f(g) + g·f(h), then f is a 1-coboundary, i.e. f(g) = g·φ − φ for some φ in E* (B.E. Johnson).
 * The reduced group C*-algebra (see the reduced group C*-algebra Cr*(G)) is nuclear.
 * The reduced group C*-algebra is quasidiagonal (J. Rosenberg, A. Tikuisis, S. White, W. Winter).
 * The von Neumann group algebra (see von Neumann algebras associated to groups) of Γ is hyperfinite (A. Connes).

Note that A. Connes also proved that the von Neumann group algebra of any connected locally compact group is hyperfinite, so the last condition no longer applies in the case of connected groups.

Amenability is related to spectral theory of certain operators. For instance, the fundamental group of a closed Riemannian manifold is amenable if and only if the bottom of the spectrum of the Laplacian on the L2-space of the universal cover of the manifold is 0.

Properties

 * Every (closed) subgroup of an amenable group is amenable.
 * Every quotient of an amenable group is amenable.
 * A group extension of an amenable group by an amenable group is again amenable. In particular, finite direct product of amenable groups are amenable, although infinite products need not be.
 * Direct limits of amenable groups are amenable. In particular, if a group can be written as a directed union of amenable subgroups, then it is amenable.
 * Amenable groups are unitarizable; the converse is an open problem.
 * Countable discrete amenable groups obey the Ornstein isomorphism theorem.

Examples

 * Finite groups are amenable. Use the counting measure with the discrete definition. More generally, compact groups are amenable. The Haar measure is an invariant mean (unique taking total measure 1).
 * The group of integers is amenable (a sequence of intervals of length tending to infinity is a Følner sequence). The existence of a shift-invariant, finitely additive probability measure on the group Z also follows easily from the Hahn–Banach theorem this way. Let S be the shift operator on the sequence space ℓ∞(Z), which is defined by (Sx)i = xi+1 for all x ∈ ℓ∞(Z), and let u ∈ ℓ∞(Z) be the constant sequence ui = 1 for all i ∈ Z. Any element y ∈ Y:=range(S − I) has a distance larger than or equal to 1 from u (otherwise yi = xi+1 - xi would be positive and bounded away from zero, whence xi could not be bounded). This implies that there is a well-defined norm-one linear form on the subspace Ru + Y taking tu + y to t. By the Hahn–Banach theorem the latter admits a norm-one linear extension on ℓ∞(Z), which is by construction a shift-invariant finitely additive probability measure on Z.
 * If every conjugacy class in a locally compact group has compact closure, then the group is amenable. Examples of groups with this property include compact groups, locally compact abelian groups, and discrete groups with finite conjugacy classes.
 * By the direct limit property above, a group is amenable if all its finitely generated subgroups are. That is, locally amenable groups are amenable.
 * By the fundamental theorem of finitely generated abelian groups, it follows that abelian groups are amenable.
 * It follows from the extension property above that a group is amenable if it has a finite index amenable subgroup. That is, virtually amenable groups are amenable.
 * Furthermore, it follows that all solvable groups are amenable.

All examples above are elementary amenable. The first class of examples below can be used to exhibit non-elementary amenable examples thanks to the existence of groups of intermediate growth.

 * Finitely generated groups of subexponential growth are amenable. A suitable subsequence of balls will provide a Følner sequence.
 * Finitely generated infinite simple groups cannot be obtained by bootstrap constructions as used to construct elementary amenable groups. Since there exist such simple groups that are amenable, due to Juschenko and Monod, this provides again non-elementary amenable examples.

Nonexamples
If a countable discrete group contains a (non-abelian) free subgroup on two generators, then it is not amenable. The converse to this statement is the so-called von Neumann conjecture, which was disproved by Olshanskii in 1980 using his Tarski monsters. Adyan subsequently showed that free Burnside groups are non-amenable: since they are periodic, they cannot contain the free group on two generators. These groups are finitely generated, but not finitely presented. However, in 2002 Sapir and Olshanskii found finitely presented counterexamples: non-amenable finitely presented groups that have a periodic normal subgroup with quotient the integers.

For finitely generated linear groups, however, the von Neumann conjecture is true by the Tits alternative: every subgroup of GL(n,k) with k a field either has a normal solvable subgroup of finite index (and therefore is amenable) or contains the free group on two generators. Although Tits' proof used algebraic geometry, Guivarc'h later found an analytic proof based on V. Oseledets' multiplicative ergodic theorem. Analogues of the Tits alternative have been proved for many other classes of groups, such as fundamental groups of 2-dimensional simplicial complexes of non-positive curvature.

title: Amenable group


text:
Yorketown

Yorketown may refer to:
 * Yorketown, New Jersey
 * Yorketown, South Australia

title: Yorketown


text:
Talk:Amenable group

From PlanetMath
I simply took it from PlanetMath, let me know if it is not ok by some reason, they seem to hve GLP as well, but maybe a bit different flavor... Tosha 01:03, 16 May 2004 (UTC)

PlanetMath should be OK - as far as I know. Just add a link to the original article. Charles Matthews 08:34, 16 May 2004 (UTC)

Suggestions
It needs rewriting anyway..

 * Amenability makes sense for any toplogical group, and the notion is used in that generality

 * Missing is Folner's condition.

CSTAR 00:07, 17 May 2004 (UTC)

 * I agree, but I think it is already something to start from. Tosha 10:51, 19 May 2004 (UTC)

Soviet superiority
There are 12 or more conditions equivalent to amenability listed in an encyclopedia (the Soviet one) ... we should get writing ...

Charles Matthews 10:53, 19 May 2004 (UTC)

Simplified definition
I've added the simplified definition for discrete groups. There's a whole branch of math, geometric group theory, where groups are always discrete. We (geometric group theorists) totally ignore the possibility of topological groups; $$L^\infty$$ scares us.

''I'd like to see the article reorganized to emphasize that both definitions are equally legitimate in different contexts. Right now, the organization makes it look like the $$L^\infty$$ definition is the main one. (Although I agree it is more general than the discrete version.)'' Done.

Finally, my apologies if there's a mistake in the definition I added. I'll check it against a reference soon.

Dbenbenn 15:22, 4 Nov 2004 (UTC)

 * Apparently "soon" means "three months later". I found and corrected a small error.  Unfortunately, my reference is not currently citable.  I'll add the citation eventually.  dbenbenn | talk 00:43, 13 Feb 2005 (UTC)

 * It might be a good idea to refer to the "measure" in the second definition as a "finitely-additive measure" since most of the time, "measure" means countably-additive. It's confusing, since interesting amenable groups generally *do not* have countably-additive left-invariant probability measures.--Mattday 02:42, 26 September 2005 (UTC)

See also amenable algebra?
Should this be "amenable Banach algebra"? Also a red link, but a thing which is definitely defined AND very well connected to amenable groups. (A group is amenable [iff] the group Banach algebra $$L^1$$ is). A Geek Tragedy 15:53, 6 May 2007 (UTC) I made that article A Geek Tragedy 18:19, 25 May 2007 (UTC)

Pun?
I do not see the pun in the translation of M.M. Day. Admittedly, I am not a native English speaker, but so are many of the readers of Wikipedia. I think it should be explained. In either case, one should cite a source claiming that the translation is due to M.M. Day, and preferably expanding "M.M." part into full first and middle names. Boris Bukh (talk) 02:53, 17 April 2008 (UTC)
 * Fixed. Mahlon Marsh Day. Amenable group is one where you are *able* to find a *mean*, as in definition 1. See  for instance. JackSchmidt (talk) 03:07, 17 April 2008 (UTC)
 * Um. Was that the real reason, or an after-the-fact joke? The latter sounds a bit more plausible to me. By the way the pun doesn't work in American English (the middle syllable sounds like "men" rather than "mean"). --Trovatore (talk) 03:16, 17 April 2008 (UTC)

Firstly while editors may quibble over the use of the word "pun", let me remind them that the original paper of von Neumann was not cited in this article or the lead before I added it. Secondly, the myth of the "pun" is on mathematical record in many secondary sources. I have not been able to check the book of Greenleaf on Invariant Means, but for example

The term "amenable" was coined by M. Day about 1949 apparently as a pun ...
 * Bruce Blackadar writes in his article in Contemporary Mathematics Vol 365 (2004):

The term amenable was introduced by M.M. Day (as a pun).
 * In Paterson's book on amenability we read on Page 1

The first to use the adjective "amenable" was MM Day in [Day], apparently with a pun in mind. This is the abstract for an AMS meeting where the term was first introduced: [http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.bams/1183514222 Means on semigroups and groups, Bull. A.M.S. 55 (1949) 1054-1055]. Were any WP editors at this meeting? Mathsci (talk) 07:14, 17 April 2008 (UTC)
 * The same is said in Volker Runde's "Lectures on Amenability":

 * I will add link to this question on Mathematics StackExchange: Why is “Amenable Group” a pun? --Kompik (talk) 14:44, 15 March 2017 (UTC)

This is the worst pun in the history of the world. — Preceding unsigned comment added by 217.33.144.171 (talk) 15:22, 12 February 2018 (UTC)

Right-invariant
There seems to be a difference in the definitions of right-invariant and left-invariant (specifically, in the right-/left-actions).

$$L_g$$ is defined to be $$(L_gf)(h) = f(g^{-1}h)$$ while $$R_g$$ is defined to be $$(R_gf)(h) = f(hg)$$. Should it perhaps not be $$(R_gf)(h) = f(hg^{-1})$$? I'm not at work so I don't have any books in from of me to check but, well, that doesn't seem consistent...

Farpov (talk) 15:06, 30 May 2010 (UTC)

Tagging
expressed the view on my user talk page and at WP:SPI that the references, cited inline now, do not accord with what is in the article. I did not write this article. I have added to it significantly, keeping to the format of the original editors (I only have limited amounts of time for wikipedia). The views of Dricherby should have been expressed here, not on my user talk page. Perhaps he could please explain here which particular portions of the content are not in the references? Are there some problems of separability that concern him? (That is one point where I have been careful about what I have added.) He tagged the article after three edits by what appeared to be trolling by sockpuppets of the banned editor. The named account that edited this article was blocked indefinitely as a sockpuppet of Echigo mole, the troll sock community banned editor that apparently edited this article before him. Please could Dricherby try not to enable banned editors on wikipedia, particularly in specialist areas areas where he has no expertise at all? Thanks. Mathsci (talk) 13:12, 24 August 2012 (UTC)

Discrete group
A discrete group is equipped with the discrete topology, not with none at all. The references used to support this assertion in the article, namely, , , are not very useful without page references, so it is hard to say whether or not they support the assertion as made, but in any case it is incompatible with the Wikipedia article on the subject. Reak spoughly (talk) 14:39, 13 September 2012 (UTC)

Open problem since 1950
It is not clear what is means to say that the converse is "an open problem since 1950". Presumably it has always been open, and 1950 was the date on which it was first explicitly posed? Whatever it means, a reference would be helpful here. Reak spoughly (talk) 14:57, 13 September 2012 (UTC)
 * Sorry for the decade-long necromancy here, but I thought this was a very interesting point. In some Platonic sense, the question existed before 1950; it was just that no human mathematician had publicly posed it.  But in that same sense, it very likely had an answer, which simply was not known to human mathematicians, so perhaps it was not really "open".  In any case the "since 1950" text no longer appears in the article, so I suppose there's nothing for us to decide here. --Trovatore (talk) 19:44, 26 November 2022 (UTC)

Extension
An extension of amenable goups is amenable. Does this mean an extension of an amenable group by an amenable group? Is there a reference? Santander sorrow (talk) 08:27, 5 October 2012 (UTC)
 * I presume this is what is meant: it is certainly the case that an extension of an amenable group by an amenable group is again amenable. See for exmple Terry Tao's blog for 23 Jan 2010  or 14 Apr 2009 .  Do these count as Reliable sources?  Lichfielder (talk) 08:58, 5 October 2012 (UTC)

Axiom of choice nonsense
"The original definition, which depends on the axiom of choice." This makes no sense; a definition does not depend on an axiom.

 * Agreed. It should be removed or rephrased.  2001:171C:2E6F:B411:500F:5331:A8AF:90B9 (talk) 09:13, 2 July 2020 (UTC)

as a pun on... what?
To a non-native English speaker the pun is not obvious: a pun on what?

I'm supposing it is a pun on Mahlon Day's middlename initial ("M."): a"emm"nable. But that can't be right. Can boring translations of foreign (German) terms be technically classified as puns? To a NNES pun usually refers to a funny (joyful) wordplay, but messbar->amenable fails this criterion. Mdob (talk) 20:19, 17 November 2018 (UTC)
 * The idea is that you can put a mean on the group (a probability measure gives you the mean value of a function, by integrating), so it's a-mean-able. It doesn't really work in American English. --Trovatore (talk) 20:24, 17 November 2018 (UTC)

 * Thank you! I'll add that to the article. Mdob (talk) 16:33, 18 November 2018 (UTC)

Probable errors
"Note that A. Connes also proved that the von Neumann group algebra of any connected locally compact group is hyperfinite, so the last condition no longer applies in the case of connected groups."

Probably the stated condition is not equivalent, but a consequence of the other conditions. Otherwise, the Connes result would prove too much.

"Amenability is related to the spectral problem of Laplacians. For instance, the fundamental group of a closed Riemannian manifold is amenable if and only if the bottom of the spectrum of the Laplacian is 0 (R. Brooks, T. Sunada)."

Spectrum of the Laplacian on the universal cover?

2001:171C:2E6F:B411:500F:5331:A8AF:90B9 (talk) 09:13, 2 July 2020 (UTC)

 * I precised the statement of Brooks' theorem. (I don't know what Sunada proved on this topic.) Regarding your first point I don't understand what you are saying: that hyperfiniteness of the von Neumann algebra is not sufficient to guarantee amenability for discrete groups? jraimbau (talk) 12:12, 2 July 2020 (UTC)

"Amenability" listed at Redirects for discussion
An editor has identified a potential problem with the redirect Amenability and has thus listed it for discussion. This discussion will occur at Redirects for discussion/Log/2022 November 26 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 1234qwer1234qwer4 10:46, 26 November 2022 (UTC)

title: Talk:Amenable group