formulasearchengine - User contributions [en]

Radiocarbon dating

2015-01-07T03:24:05Z

162.129.251.87: /* Physical and Chemical details */

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Partial regression plot

2014-02-03T01:01:23Z

162.129.251.86: Fixed small typo

'''Polynomial conjoint measurement''' is an extension of the [[theory of conjoint measurement]] to three or more attributes. It was initially developed by the mathematical psychologists David Krantz (1968) and [[Amos Tversky]] (1967). The theory was given a comprehensive mathematical exposition in the first volume of ''Foundations of Measurement'' (Krantz, Luce, Suppes & Tversky, 1971), which Krantz and Tversky wrote in collaboration with the mathematical psychologist [[R. Duncan Luce]] and philosopher [[Patrick Suppes]]. Krantz & Tversky (1971) also published a non-technical paper on polynomial conjoint measurement for behavioural scientists in the journal ''Psychological Review''.

As with the theory of conjoint measurement, the significance of polynomial conjoint measurement lies in the quantification of natural attributes in the absence of concatenation operations. Polynomial conjoint measurement differs from the two attribute case discovered by Luce & Tukey (1964) in that more complex composition rules are involved.

==Polynomial conjoint measurement==
===Krantz's (1968) schema===

Most scientific theories involve more than just two attributes; and thus the two variable case of conjoint measurement has rather limited scope. Moreover, contrary to the theory of ''n'' - component conjoint measurement, many attributes are non-additive compositions of other attributes (Krantz, et al., 1971). Krantz (1968) proposed a general schema to ascertain the sufficient set of cancellation axioms for a class of polynomial combination rules he called ''simple polynomials''. The formal definition of this schema given by Krantz, et al., (1971, p.328) is as follows.

Let <math>Y =\big\{y_1, y_2, \ldots, y_n \big\}</math>. The set <math>S\left(Y\right)</math> is the smallest set of simple polynomials such that:
* <math>y_i \in S\left(Y\right), i = 1,\ldots, n</math>;
* <math>Y_1, Y_2 \subset Y </math> such that <math>Y_1 \cap Y_2 = \varnothing, G_1 \in S\left(Y_1\right)</math> and <math>G_2 \in S\left(Y_2\right)</math>, then <math>G_1 + G_2\, </math> and <math>G_1 G_2\, </math> are in <math>S\left(Y\right)</math>.

Informally, the schema argues:
a) single attributes are simple polynomials;
b) if ''G''1 and ''G''2 are simple polynomials that are disjoint (i.e. have no attributes in common), then ''G''1 + ''G''2 and ''G''1 <math>\times</math> ''G''2 are simple polynomials; and
c) no polynomials are simple except as given by a) and b).

Let ''A'', ''P'' and ''U'' be single disjoint attributes. From Krantz’s (1968) schema it follows that four classes of simple polynomials in three variables exist which contain a total of eight simple polynomials:
* ''Additive'': <math>A + P + U\, </math>;
* ''Distributive'': <math>\left(A + P\right)U\, </math>; plus 2 others obtained by interchanging ''A'', ''P'' and ''U'';
* ''Dual distributive'': <math>A P + U\, </math> plus 2 others as per above;
* ''Multiplicative'': <math>A P U\, </math>.

Krantz’s (1968) schema can be used to construct simple polynomials of greater numbers of attributes. For example, if D is a single variable disjoint to A, B, and C then three classes of simple polynomials in four variables are A + B + C + D, D + (B + AC) and D + ABC. This procedure can be employed for any finite number of variables. A simple test is that a simple polynomial can be ‘split’ into either a product or sum of two smaller, disjoint simple polynomials. These polynomials can be further ‘split’ until single variables are obtained. An expression not amenable to ‘splitting’ in this manner is not a simple polynomial (e.g. AB + BC + AC (Krantz & Tversky, 1971)).

===Axioms===

Let <math>A = \big\{a, b, c, \ldots \big\}</math>, <math>P = \big\{p, q, r, \ldots \big\}</math> and <math>U = \big\{u, v, w, \ldots \big\}</math> be non-empty and disjoint sets. Let " <math>\succsim</math> " be a simple order. Krantz et al. (1971) argued the quadruple <math>Z = \langle A, P, U, \succsim \rangle</math> is a ''polynomial conjoint system'' if and only if the following axioms hold.

* ''WEAK ORDER''.

* ''SINGLE CANCELLATION''. The relation " <math>\succsim</math> " satisfies single cancellation upon ''A'' whenever <math>\left(a, p, u\right)\succsim \left(b, p, u\right)</math> if and only if <math>\left(a, q, v\right)\succsim \left(b, q, v\right)</math> holds for all <math>a, b \in A; p, q \in P</math> and <math>u, v \in U</math>. Single cancellation upon ''P'' and ''U'' is similarly defined.

* ''DOUBLE CANCELLATION''. The relation " <math>\succsim</math> " upon <math>A \times P </math> satisfies double cancellation if and only if for all <math>a, b, c \in A</math> and <math>p, q, r \in P</math>, <math>\left(a, q, u\right)\succsim \left(b, p, u\right)</math> and <math>\left(b, r, u\right)\succsim \left(c, q, u\right)</math> therefore <math>\left(a, r, u\right)\succsim \left(c, p, u\right)</math> is true for all <math>u \in U</math>. The condition holds similarly upon <math>A \times U</math> and <math>U \times P</math>.

* ''JOINT SINGLE CANCELLATION''. The relation " <math>\succsim</math> " upon <math>A \times P</math> satisfies joint single cancellation such that <math>\left(a, p, u\right)\succsim \left(b, q, u\right)</math> if and only if <math>\left(a, p, v\right)\succsim \left(b, q, v\right)</math> is true for all <math>a, b \in A; p, q \in P</math> and <math>u, v \in U</math>. Joint independence is similarly defined for <math>A \times U</math> and <math>U \times P</math>.

* ''DISTRIBUTIVE CANCELLATION''. Distributive cancellation holds upon <math>A \times P \times U</math> if and only if <math>\left(a, p, u\right)\succsim \left(c, r, v\right)</math>, <math>\left(b, q, u\right)\succsim \left(d, s, v\right)</math> and <math>\left(d, r, v\right)\succsim \left(b, p, u\right)</math> implies <math>\left(a, q, u\right)\succsim \left(c, s, v\right)</math> is true for all <math>a, b, c, d\in A; p, q, r, s \in P</math> and <math>u, v\in U</math>.

* ''DUAL DISTRIBUTIVE CANCELLATION''. Dual distributive cancellation holds upon <math>A \times P \times U</math> if and only if
<math>\left(a, r, w\right)\succsim \left(c, s, v\right)</math>, <math>\left(d, p, u\right)\succsim \left(b, t, x\right)</math>, <math>\left(d, r, x\right)\succsim \left(e, s, u\right)</math> and <math>\left(c, t, y\right)\succsim \left(d, q, y\right)</math> implies <math>\left(a, p, v\right)\succsim \left(b, q, w\right)</math> is true for all <math>a, b, c, d, e\in A; p, q, r, s, t \in P</math> and <math>u, v, w, x, y\in U</math>.

*''SOLVABILITY''. The relation " <math>\succsim</math> " upon <math>A \times P \times U</math> is solvable if and only if for all <math>a, b\in A; p, q \in P</math> and <math>u, v \in U</math>, there exists <math>c \in A; r \in P</math> and <math>w \in U</math> such that <math>a \sim \left(b, q, w\right) \sim \left(b, r, v\right) \sim \left(c, q, v\right)</math>.

* ''ARCHIMEDEAN CONDITION''.

===Representation theorems===

The quadruple <math>Z = \langle A, P, U, \succsim \rangle</math> falls into one class of three variable simple polynomials by virtue of the joint single cancellation axiom.

==References==
* Krantz, D.H. (1968). A survey of measurement theory. In G.B. Danzig & A.F. Veinott (Eds.), ''Mathematics of the Decision Sciences'', part 2 (pp.314-350). Providence, RI: American Mathematical Society.
* Krantz, D.H.; Luce, R.D; Suppes, P. & Tversky, A. (1971). ''Foundations of Measurement, Vol. I: Additive and polynomial representations''. New York: Academic Press.
* Krantz, D.H. & Tversky, A. (1971). Conjoint measurement analysis of composition rules in psychology. ''Psychological Review'', ''78'', 151-169.
* Luce, R.D. & Tukey, J.W. (1964). Simultaneous conjoint measurement: a new scale type of fundamental measurement. ''Journal of Mathematical Psychology'', ''1'', 1-27.
* Tversky, A. (1967). A general theory of polynomial conjoint measurement. ''Journal of Mathematical Psychology'', ''4'', 1-20.

[[Category:Psychometrics]]
[[Category:Decision theory]]
[[Category:Measurement]]

Rhodopsin kinase

2014-01-14T20:51:05Z

162.129.251.86: added Oguchi disease sentence

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*http://www.xist.org/cntry/turkey.aspx?levels=Marmara
*:''Triggered by <code>\bxist\.org\b</code> on the global blacklist''|bot=Cyberbot II}}
{{Other uses|Yenice (disambiguation)}}
{{Use dmy dates|date=February 2012}}
{{Infobox settlement 
|settlement_type = District
|coordinates_region = TR
|subdivision_type = Country
|subdivision_name = {{TUR}}
|timezone=[[Eastern European Time|EET]]
|utc_offset=+2
|map_caption = Location of Yenice within Turkey.
|timezone_DST=[[Eastern European Summer Time|EEST]]
|utc_offset_DST=+3
|official_name = Yenice
|image_skyline =
|image_caption =
|image_blank_emblem =
|blank_emblem_type =
|image_map = Çanakkale districts.png
|subdivision_type1=[[Regions of Turkey|Region]]
|subdivision_name1 = Marmara
|subdivision_type2=[[Provinces of Turkey|Province]]
|subdivision_name2 = Çanakkale
| area_footnotes = {{Turkey district areas|SOURCE}}
| area_blank1_title = District
| area_blank1_km2 = {{Turkey district areas|Çanakkale|Yenice}}
| population_footnotes = {{Turkey district populations|SOURCE|Çanakkale}}
| population_urban = {{Turkey district populations|Çanakkale|Yenice|şehir}}
| population_as_of = {{Turkey district populations|YEAR}}
| population_blank1_title = District
| population_blank1 = {{Turkey district populations|Çanakkale|Yenice|toplam}}
| population_density_blank1_km2 = auto
|elevation_m = 255
|pushpin_map = Turkey
|pushpin_label_position = 
|pushpin_map_caption = Location of Yenice
|pushpin_mapsize =
|latd = 39
|latm = 56
|latNS = N
|longd = 27
|longm = 15
|longEW = E
|postal_code_type = [[Postal code]]
|postal_code = 17xxx
|blank_info = 17
|blank_name= [[Turkish car number plates|Licence plate]]
|area_code = 286
|leader_title = Mayor
|leader_name = Veysel Acar ([[Justice and Development Party (Turkey)|AKP]])
|website = [http://www.yenicebelediyesi.bel.tr/ www.yenicebelediyesi.bel.tr]
|leader_name1 =
|gwebsite = [http://www.canakkaleyenice.gov.tr/ www.canakkaleyenice.gov.tr]
}}
'''Yenice''' is a town and district of [[Çanakkale Province]] in the [[Marmara Region|Marmara]] region of [[Turkey]]. According to the 2000 census, population of the district is 35,796 of which 6,903 live in the town of Yenice.<ref>[http://report.tuik.gov.tr/reports/rwservlet?adnksdb2=&ENVID=adnksdb2Env&report=idari_yapi_09sonrasi.RDF&p_il1=17&p_yil=2010&p_dil=2&desformat=html Statistical Institute]</ref><ref>{{cite web|url=http://www.xist.org/cntry/turkey.aspx?levels=Marmara|title=Statistical information on Turkey's administrative units|accessdate=19 April 2009|author=GeoHive}}</ref> The district covers an area of {{convert|1417|km2|sqmi|0|abbr=on}},<ref>{{cite web|url=http://www.statoids.com/ytr.html|title=Statistical information on districts of Turkey|accessdate=19 April 2009|author=Statoids}}</ref> and the town lies at an elevation of {{convert|255|m|ft|0|abbr=on}}.

==History==
On 18 March 1953 Yenice was subject to a [[1953 Western Turkey earthquake|devastating 7.4 <math>M_\mathrm{w}</math> earthquake]] which left 998 dead and thousands of buildings damaged.<ref name=USGS>{{cite web|url=http://earthquake.usgs.gov/learning/today/his_03_18.php|title=Today In Earthquake History:March 18|publisher=[[United States Geological Survey]]|date=16 July 2008|accessdate=7 July 2009}} {{Dead link|date=October 2010|bot=H3llBot}}</ref> a previous devastating earthquake had occurred here in 1440 AD.<ref>Kürçer, Akın (2008) "The Yenice–Gönen active fault (NW Turkey): Active tectonics and palaeoseismology" ''Tectonophysics'' 453: pp. 263–275</ref>

==Economy==
People's basic occupation is agricultural work. Cereals, beans, tomatoes and tobacco are grown. There is a tomato paste processing plant in Yenice. Important towns in the district include: Kalkım, Hamdibey and Pazarköy.

Tourism is a relatively new component of Yenice's economy; however, wild boar hunting is becoming popular as a tourist attraction.<ref>[http://www.basmakci.com/eski/Yazdir.asp?yaz=forum&id=3907 "Başmakçı Kültür (Bashmakchi Culture)"], in Turkish</ref>

==Notable people from Yenice==
İbrahim Bodur(entrepreneur)
Nuri Bilge Ceylan (director)
http://tr.wikipedia.org/wiki/Nuri_Bilge_Ceylan

==Notes==
{{Reflist}}

==External links==
* [http://www.canakkaleyenice.gov.tr/ District governor's official website] {{tr icon}}
* {{cite web|url=http://www.fallingrain.com/world/TU/17/Yenice2.html|title=Geographical information on Yenice, Turkey|accessdate=19 April 2009|author=Falling Rain Genomics, Inc}}
* [http://www.canakkaleabc.com/yenice/yceharita.jpg Road map of Yenice and environs]
* [http://wowturkey.com/forum/viewtopic.php?t=42390 Various images of Yenice, Çanakkale]
* [http://www.panoramio.com/photo/113250 Photo of Yenice, Çanakkale], Pamoramio
{{-}}

{{Districts of Turkey|provname=Çanakkale|image=Canakkale}}

{{coord|39|55|51|N|27|15|29|E|display=title|region:TR_type:city}}

{{DEFAULTSORT:Yenice, Canakkale}}
[[Category:Populated places in Çanakkale Province]]
[[Category:Districts of Çanakkale Province]]

{{Çanakkale-geo-stub}}

Dihydropteroate synthase

2012-06-26T02:07:50Z

162.129.251.68:

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