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	<updated>2026-08-09T10:39:59Z</updated>
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	<entry>
		<id>https://en.formulasearchengine.com/w/index.php?title=Linear-fractional_programming&amp;diff=24216</id>
		<title>Linear-fractional programming</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/w/index.php?title=Linear-fractional_programming&amp;diff=24216"/>
		<updated>2013-10-30T12:36:55Z</updated>

		<summary type="html">&lt;p&gt;134.169.202.216: /* Transformation to a linear program */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;&#039;&#039;&#039;Charge transfer coefficient&#039;&#039;&#039;, and &#039;&#039;&#039;symmetry factor&#039;&#039;&#039; (symbols &#039;&#039;α&#039;&#039; and &#039;&#039;β&#039;&#039;, respectively) are two related parameters used in description of the [[chemical kinetics|kinetics]] of [[Electrochemistry|electrochemical]] [[electrochemical reaction|reaction]]s. They appear in the [[Butler-Volmer equation]] and related expressions.&lt;br /&gt;
&lt;br /&gt;
The symmetry factor and the charge transfer coefficient are dimensionless.&amp;lt;ref&amp;gt;IUPAC. &amp;quot;Quantities, Units and Symbols in Physical Chemistry&amp;quot; (&amp;quot;The Green Book&amp;quot;), 2nd edition, Blackwell Science, 1993. [http://www.scribd.com/doc/44380146/Iupac-The-Green-Book-Quantities-Units-and-Symbols-in-Physical-Chemistry (on line)]&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
According to an [[IUPAC]] definition,&amp;lt;ref&amp;gt;IUPAC. Compendium of Chemical Terminology, 2nd ed. (the &amp;quot;Gold Book&amp;quot;). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. {{doi|10.1351/goldbook}}. [http://goldbook.iupac.org/C00906.html Entry: &amp;quot;Cathodic transfer coefficient&amp;quot;.]&amp;lt;/ref&amp;gt; for a reaction with a single rate-determining step, the charge transfer coefficient for a cathodic reaction (&#039;&#039;&#039;the cathodic transfer coefficient&#039;&#039;&#039;, &#039;&#039;α&amp;lt;sub&amp;gt;c&amp;lt;/sub&amp;gt;&#039;&#039;) is defined as:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac {\alpha_c} {\nu} = - \left(\frac {RT} {nF} \right)  \left( \frac {\partial ln(|I_{red}|)} {\partial E}\right)_{T,p,c_{i,interface}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The &#039;&#039;&#039;anodic transfer coefficient&#039;&#039;&#039; (&#039;&#039;α&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;&#039;&#039;) is defined by analogy:&amp;lt;ref&amp;gt;http://goldbook.iupac.org/A00371.html&amp;lt;/ref&amp;gt;&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac {\alpha_a} {\nu} =  \left( \frac {RT} {nF} \right)  \left( \frac {\partial ln(|I_{ox }|)} {\partial E}\right)_{T,p,c_{i,interface}}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where:&lt;br /&gt;
*&amp;lt;math&amp;gt;\nu&amp;lt;/math&amp;gt;: [[Stoichiometry#Stoichiometric coefficient|stoichometric number]], i.e., the number of activated complexes formed and destroyed in the overall reaction (with n electrons)&lt;br /&gt;
* &amp;lt;math&amp;gt;R&amp;lt;/math&amp;gt;: [[universal gas constant]]&lt;br /&gt;
* &amp;lt;math&amp;gt;T&amp;lt;/math&amp;gt;: [[absolute temperature]]&lt;br /&gt;
* &amp;lt;math&amp;gt;n&amp;lt;/math&amp;gt;: number of electrons involved in the electrode reaction&lt;br /&gt;
* &amp;lt;math&amp;gt;F&amp;lt;/math&amp;gt;: [[Faraday constant]]&lt;br /&gt;
* &amp;lt;math&amp;gt;E&amp;lt;/math&amp;gt;: [[electrode potential]]&lt;br /&gt;
* &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt;: [[partial current|partial cathodic (anodic) current]]&amp;lt;ref&amp;gt;http://goldbook.iupac.org/P04407.html&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;IUPAC. &#039;&#039;ELECTRODE REACTION ORDERS, TRANSFER COEFFICIENTS AND RATE CONSTANTS. APPLICATION OF DEFINITIONS AND RECOMMENDATIONS FOR PUBLICATION OF PARAMETERS.&#039;&#039; Pure &amp;amp; Appi. Chern., Vol. 52, pp.233—240, 1979. [http://www.iupac.org/publications/pac/1980/pdf/5201x0233.pdf (pdf)]&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Interpretation==&lt;br /&gt;
&lt;br /&gt;
The charge transfer coefficient signifies the fraction of the interfacial potential at an [[electrode]]-[[electrolyte]] interface that helps in lowering the free [[energy barrier]] for the electrochemical reaction. The electroactive [[ion]] present in the interfacial region experiences the interfacial potential and electrostatic work is done on the ion by &#039;&#039;a part&#039;&#039; of the interfacial electric field. It is charge transfer coefficient that signifies &#039;&#039;this part&#039;&#039; that is utilized in activating the ion to the top of the free energy barrier.&lt;br /&gt;
&lt;br /&gt;
==Batteries and fuel cells==&lt;br /&gt;
&lt;br /&gt;
In operating [[Battery (electricity)|batteries]] and [[fuel cell]]s, charge transfer coefficient is the parameter that signifies the fraction of [[overpotential]] that affects the [[current density]]. This parameter has had a mysterious significance in electrochemical kinetics for over three quarters of the previous century. It can also be said that charge transfer coefficient is the heart of electrode kinetics.&lt;br /&gt;
&lt;br /&gt;
==Symmetry factor==&lt;br /&gt;
&lt;br /&gt;
The symmetry factor (or barrier symmetry factor) is a coefficient similar to the transfer coefficient, but applicable only to single-step reactions.&lt;br /&gt;
&lt;br /&gt;
The sum of anodic symmetry factor and cathodic symmetry factor is equal to one:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\beta_c + \beta_a = 1&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
===Interpretation===&lt;br /&gt;
{{Empty section|date=October 2011}}&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
{{Reflist}}&lt;br /&gt;
&lt;br /&gt;
[[Category:Dimensionless numbers of chemistry]]&lt;br /&gt;
[[Category:Electrochemistry]]&lt;/div&gt;</summary>
		<author><name>134.169.202.216</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/w/index.php?title=Haloacetate_dehalogenase&amp;diff=19602</id>
		<title>Haloacetate dehalogenase</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/w/index.php?title=Haloacetate_dehalogenase&amp;diff=19602"/>
		<updated>2012-12-04T14:13:43Z</updated>

		<summary type="html">&lt;p&gt;134.169.106.141: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{enzyme&lt;br /&gt;
| Name = phosphonoacetate hydrolase&lt;br /&gt;
| EC_number = 3.11.1.2&lt;br /&gt;
| CAS_number = 153570-68-4&lt;br /&gt;
| IUBMB_EC_number = 3/11/1/2&lt;br /&gt;
| GO_code = 0047400&lt;br /&gt;
| image = File:1ei6.png&lt;br /&gt;
| width = &lt;br /&gt;
| caption = Structure of phosphonoacetate hydrolase. PDB entry {{PDBe|1e16}}. Zinc ions and phosphonoformate are shown in the active site.&lt;br /&gt;
}}&lt;br /&gt;
In [[enzymology]], a &#039;&#039;&#039;phosphonoacetate hydrolase&#039;&#039;&#039; ({{EC number|3.11.1.2}}) is an [[enzyme]] that [[catalysis|catalyzes]] the [[chemical reaction]]&lt;br /&gt;
&lt;br /&gt;
:phosphonoacetate + H&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;O &amp;lt;math&amp;gt;\rightleftharpoons&amp;lt;/math&amp;gt; acetate + phosphate&lt;br /&gt;
&lt;br /&gt;
Thus, the two [[substrate (biochemistry)|substrates]] of this enzyme are [[phosphonoacetate]] and [[water|H&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;O]], whereas its two [[product (chemistry)|products]] are [[acetate]] and [[phosphate]].&lt;br /&gt;
&lt;br /&gt;
This enzyme belongs to the family of [[hydrolase]]s, specifically those acting on carbon-phosphorus bonds.  The systematic name of this enzyme class is &#039;&#039;&#039;phosphonoacetate phosphonohydrolase&#039;&#039;&#039;. This enzyme participates in [[aminophosphonate metabolism]].  It employs one [[cofactor (biochemistry)|cofactor]], [[zinc]].  &lt;br /&gt;
&lt;br /&gt;
==Structural studies==&lt;br /&gt;
&lt;br /&gt;
The [[tertiary structure|structure]] of this enzyme, with the [[Protein Data Bank|PDB]] accession code {{PDB link|1EI6}}, shows it adopts the [[alkaline phosphatase]] fold.&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
{{reflist|1}}&lt;br /&gt;
* {{cite journal | author = McGrath JW, Wisdom GB, McMullan G, Larkin MJ, Quinn JP | date = 1995 | title = The purification and properties of phosphonoacetate hydrolase, a novel carbon-phosphorus bond-cleavage enzyme from Pseudomonas fluorescens 23F | journal = Eur. J. Biochem.  | volume = 234 | pages = 225&amp;amp;ndash;30  | pmid = 8529644 | doi = 10.1111/j.1432-1033.1995.225_c.x | issue = 1 }}&lt;br /&gt;
&lt;br /&gt;
{{hydrolase-stub}}&lt;br /&gt;
&lt;br /&gt;
[[Category:EC 3.11.1]]&lt;br /&gt;
[[Category:Zinc enzymes]]&lt;br /&gt;
[[Category:Enzymes of known structure]]&lt;/div&gt;</summary>
		<author><name>134.169.106.141</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/w/index.php?title=User:Fropuff/Draft_2&amp;diff=297815</id>
		<title>User:Fropuff/Draft 2</title>
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		<updated>2006-03-13T08:55:29Z</updated>

		<summary type="html">&lt;p&gt;134.169.128.68: /* Definition */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;33 year old Sail Maker Hyslop from Vernon, has lots of hobbies and interests which include butterflies, [http://brooksstrain.tripod.co.uk/aussie-property.html buying a property in singapore] developers in singapore and music-drums. Constantly loves touring places like  Tino and Tinetto).&lt;/div&gt;</summary>
		<author><name>134.169.128.68</name></author>
	</entry>
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