Glutamate dehydrogenase: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older editNewer edit →
No edit summary
en>Frze
m Undid revision 593887165 by 77.77.56.235 (talk)
Line 1: Line 1:
In [[number theory]], the '''Bateman–Horn conjecture''' is a statement concerning the frequency of [[prime number]]s among the values of a system of [[polynomial]]s, named after mathematicians [[Paul T. Bateman]] and Roger A Horn, of [[The University of Utah]], who proposed it in 1962. It provides a vast generalization of such conjectures as the [[First Hardy–Littlewood conjecture|Hardy and Littlewood conjecture]] on the density of [[twin prime]]s or their conjecture on primes of the form ''n''<sup>2</sup>&nbsp;+&nbsp;1; it is also a strengthening of [[Schinzel's hypothesis H|Schinzel's&nbsp;hypothesis&nbsp;H]]. It remains unsolved as of January 2014.
== Nike Free 5.0 Uk Companies Must Engage Facebook Visitors ==


==Definition==
Companies Must Engage Facebook Visitors<br><br>New information helps companies discover how to move beyond superficial usage of social websites to more active consumer commitment. So, experts advise hearing aid technology activity of "Millennials" using a company's Facebook page.<br><br>"We wanted to uncover what the younger generation, those 18  to 29 year olds are accomplishing on services. Those are the Facebook generation," McCorkindale said.<br><br>McCorkindale and colleagues surveyed 414 individuals between ages 18 and 29 regarding their interaction with organizations Facebook pages.<br><br>"With numerous companies making an effort and your money on social media marketing, we must understand not just social websites tools although the tricks of understanding it," McCorkindale said.<br><br>They found while 75 % said on the list of "liked" a nice gain or relief organization on Facebook, 69 percent stated that once they "liked" the firm, they rarely or never returned for the page.<br><br>Only 15 % on the respondents said they visited organizations' fan pages weekly. Most respondents (44 %) spent less than Thirty minutes a day on Facebook.<br><br>While in the research, investigators found Millennials forget to frequently visit an organization's Facebook for the reason that site won't reward or entice men and women to give back. "In public relations, among the list of basics of the we perform is build relationships to hopefully get people to do getting some sort of behavior," she said.<br><br>"It's clear that the 18 to 29 year olds usually are not as committed to a company as the organization may think they can be once they select the 'like' button or click 'follow.' It's fairly consistent from the research that Millennials like organizations that offer something time for them."<br><br>Common incentives employed to entice an individual revisit a Facebook page include discounts, coupons, sample products or information a thief might not exactly receive elsewhere.<br><br>However, researchers found that too [http://nikefree50uk.mycylex.co.uk/ Nike Free 5.0 Uk] much are able to turn the Millennial generation away for the site.<br><br>"There is actually a threshold where Millennials [http://nikeairmax1uk.mycylex.co.uk/ Cheap Nike Air Max 1 Uk] will disconnect from a business or group whenever they become too annoyed together with the amount of emails or updates they may be [http://hermesbeltuk.mycylex.co.uk/ Hermes Belt Replica] receiving," McCorkindale added.<br><br>45 percent of the people surveyed said they made a Facebook page in the event it became to annoying.<br><br>Researchers saw that the Millennials age bracket discovered fan pages through friends or by stumbling for the page. Only 28 percent said that they actively hunted for an organization's page.<br><br>Millennials surveyed tended to "like" nonprofit organizations they'd caused or with [http://cheaptimberlandbootsuk.mycylex.co.uk/ Timberland Boots Uk] whom friends stood a relationship. They typically "liked" fan pages of sororities or fraternities, sports teams, college organizations and bands.<br><br>Researchers discovered successful usage of social websites goes beyond being "liked" considering that the demographics may be not like an organization's strategy. Additionally, merely being 'liked' may overestimate a persons true interest in the internet site.<br><br>"It's not about the number of people they like your page, because they may not be the correct people, they usually would possibly not really enjoy you, they may do it due to pressure from friends," McCorkindale said.<br><br>"Instead of organizations looking to superficially push these relationships and superficially push 'likes,' what is required be aware of the audience, build their bond and have interaction the audience.<br><br>"If you will definitely be in existence in the social networking sphere, you've got to be listening, you have to answer the questions people ask of you through social websites. If issues or questions go unanswered, that breaks the connection," she said. "If they won't manage the space, they can shouldn't be making use of the space."<ul>
The Bateman–Horn conjecture provides a conjectured density for the positive integers at which a given set of polynomials all have prime values. For a set of ''m'' distinct [[irreducible polynomial]]s ''ƒ''<sub>1</sub>,&nbsp;...,&nbsp;''ƒ''<sub>''m''</sub> with integer coefficients, an obvious necessary condition for the polynomials to simultaneously generate prime values infinitely often is that they satisfy [[Bunyakovsky's property]], that there does not exist a prime number ''p'' that divides their product  ''f''(''n'') for every positive integer ''n''. For, if not, then one of the values of the polynomials must be equal to ''p'', which can only happen for finitely many values of ''n''.
 
 
  <li>[http://www.mistachasezodiacs.com/index.php?option=com_kunena&func=view&catid=4&id=202846&Itemid=53#202846 http://www.mistachasezodiacs.com/index.php?option=com_kunena&func=view&catid=4&id=202846&Itemid=53#202846]</li>
An integer ''n'' is prime-generating for the given system of polynomials if every polynomial ''ƒ<sub>i</sub>''(''n'') produces a prime number when given ''n'' as its argument. If ''P(x)'' is the fraction of prime-generating integers among the positive integers less than ''x'', then the Bateman–Horn conjecture states that
 
 
  <li>[http://swapsomething.net/forum.php?mod=viewthread&tid=196278 http://swapsomething.net/forum.php?mod=viewthread&tid=196278]</li>
:<math>P(x) \sim \frac{C}{D} \int_2^x \frac{dt}{(\log t)^m},\,</math>
 
 
  <li>[http://mcpos.net/news/html/?165572.html http://mcpos.net/news/html/?165572.html]</li>
where ''D'' is the product of the degrees of the polynomials and where ''C'' is the product over primes ''p''
 
 
  <li>[http://enseignement-lsf.com/spip.php?article65#forum18435088 http://enseignement-lsf.com/spip.php?article65#forum18435088]</li>
:<math>C = \prod_p \frac{1-N(p)/p}{(1-1/p)^m}\ </math>
 
 
  <li>[http://www.histoirepassion.eu/spip.php?article7/ http://www.histoirepassion.eu/spip.php?article7/]</li>
with <math>N(p)</math> the number of solutions to
 
 
</ul>
:<math>f(n) \equiv 0 \pmod p.\ </math>
 
Bunyakovsky's property implies  <math>N(p) < p</math> for all primes ''p'',
so each factor in the infinite product ''C'' is positive.
Intuitively one then naturally expects that the constant ''C'' is itself positive, and with some work this can be proved.
(Work is needed since some infinite products of positive numbers equal zero.)
 
==Negative numbers==
As stated above, the conjecture is not true: the single polynomial ''ƒ''<sub>1</sub>(''x'')&nbsp;=&nbsp;&minus;''x'' produces only negative numbers when given a positive argument, so the fraction of prime numbers among its values is always zero. There are two equally valid ways of refining the conjecture to avoid this difficulty:
*One may require all the polynomials to have positive leading coefficients, so that only a constant number of their values can be negative.
*Alternatively, one may allow negative leading coefficients but count a negative number as being prime when its absolute value is prime.
It is reasonable to allow negative numbers to count as primes as a step towards formulating more general conjectures that apply to other systems of numbers than the integers, but at the same time it is easy
to just negate the polynomials if necessary to reduce to the case where the leading coefficients are positive.
 
==Examples==
If the system of polynomials consists of the single polynomial ''ƒ''<sub>1</sub>(''x'')&nbsp;=&nbsp;''x'', then the values ''n'' for which ''ƒ''<sub>1</sub>(''n'') is prime are themselves the prime numbers, and the conjecture becomes a restatement of the [[prime number theorem]].
 
If the system of polynomials consists of the two polynomials ''ƒ''<sub>1</sub>(''x'')&nbsp;=&nbsp;''x'' and ''ƒ''<sub>2</sub>(''x'')&nbsp;=&nbsp;''x''&nbsp;+&nbsp;2, then the values of ''n'' for which both ''ƒ''<sub>1</sub>(''n'') and ''ƒ''<sub>2</sub>(''n'') are prime are just the smaller of the two primes in every pair of [[twin prime]]s. In this case, the Bateman–Horn conjecture reduces to the [[Twin prime#First Hardy–Littlewood conjecture|Hardy–Littlewood conjecture]] on the density of twin primes, according to which the number of twin prime pairs less than ''x'' is
:<math>\pi_2(x) \sim 2  \prod_{p\ge 3} \frac{p(p-2)}{(p-1)^2}\frac{x}{(\log x)^2 } \approx 1.32 \frac {x}{(\log x)^2}.</math>
 
==Analogue for polynomials over a finite field==
 
When the integers are replaced by the polynomial ring ''F''[''u''] for a finite field ''F'', one can ask how often a finite set of polynomials ''f''<sub>''i''</sub>(''x'') in ''F''[''u''][''x''] simultaneously takes  irreducible values in ''F''[''u''] when we substitute for ''x'' elements of ''F''[''u'']. Well-known analogies between integers and ''F''[''u''] suggest an analogue of the Bateman–Horn conjecture over ''F''[''u''], but the analogue is wrong. For example, data suggest that the polynomial
 
::<math>x^3 + u\,</math>
 
in ''F''<sub>3</sub>[''u''][''x''] takes (asymptotically) the expected number of irreducible values when ''x'' runs over polynomials in ''F''<sub>3</sub>[''u''] of odd degree, but it appears to take (asymptotically) twice as many irreducible values as expected when ''x'' runs over polynomials of degree that is 2 mod 4, while it (provably) takes ''no'' irreducible values at all when ''x'' runs over nonconstant polynomials with degree that is a multiple of 4. An analogue of the Bateman–Horn conjecture over ''F''[''u''] which fits numerical data uses an additional factor in the asymptotics which depends on the value of ''d'' mod 4, where ''d'' is the degree of the polynomials in ''F''[''u''] over which ''x'' is sampled.
 
==References==
*{{citation|last1=Bateman|first1=Paul T.|last2=Horn|first2=Roger A.|title=A heuristic asymptotic formula concerning the distribution of prime numbers|journal=Mathematics of Computation|volume=16|year=1962|pages=363–367|mr=148632|doi=10.2307/2004056|zbl=0105.03302 }}
* {{citation |last=Guy | first=Richard K. | authorlink=Richard K. Guy | title=Unsolved problems in number theory | publisher=[[Springer-Verlag]] |edition=3rd | year=2004 |isbn=978-0-387-20860-2 | zbl=1058.11001 }}
* {{citation|last1=Friedlander|first1=John|last2=Granville|first2=Andrew|title=Limitations to the equi-distribution of primes. IV.|journal=Proceedings: Mathematical and Physical Sciences|volume=435|number=1893|year=1991|pages=197–204}}.
 
{{DEFAULTSORT:Bateman-Horn conjecture}}
[[Category:Conjectures about prime numbers]]
[[Category:Analytic number theory]]

Revision as of 03:57, 12 February 2014

Nike Free 5.0 Uk Companies Must Engage Facebook Visitors

Companies Must Engage Facebook Visitors

New information helps companies discover how to move beyond superficial usage of social websites to more active consumer commitment. So, experts advise hearing aid technology activity of "Millennials" using a company's Facebook page.

"We wanted to uncover what the younger generation, those 18 to 29 year olds are accomplishing on services. Those are the Facebook generation," McCorkindale said.

McCorkindale and colleagues surveyed 414 individuals between ages 18 and 29 regarding their interaction with organizations Facebook pages.

"With numerous companies making an effort and your money on social media marketing, we must understand not just social websites tools although the tricks of understanding it," McCorkindale said.

They found while 75 % said on the list of "liked" a nice gain or relief organization on Facebook, 69 percent stated that once they "liked" the firm, they rarely or never returned for the page.

Only 15 % on the respondents said they visited organizations' fan pages weekly. Most respondents (44 %) spent less than Thirty minutes a day on Facebook.

While in the research, investigators found Millennials forget to frequently visit an organization's Facebook for the reason that site won't reward or entice men and women to give back. "In public relations, among the list of basics of the we perform is build relationships to hopefully get people to do getting some sort of behavior," she said.

"It's clear that the 18 to 29 year olds usually are not as committed to a company as the organization may think they can be once they select the 'like' button or click 'follow.' It's fairly consistent from the research that Millennials like organizations that offer something time for them."

Common incentives employed to entice an individual revisit a Facebook page include discounts, coupons, sample products or information a thief might not exactly receive elsewhere.

However, researchers found that too Nike Free 5.0 Uk much are able to turn the Millennial generation away for the site.

"There is actually a threshold where Millennials Cheap Nike Air Max 1 Uk will disconnect from a business or group whenever they become too annoyed together with the amount of emails or updates they may be Hermes Belt Replica receiving," McCorkindale added.

45 percent of the people surveyed said they made a Facebook page in the event it became to annoying.

Researchers saw that the Millennials age bracket discovered fan pages through friends or by stumbling for the page. Only 28 percent said that they actively hunted for an organization's page.

Millennials surveyed tended to "like" nonprofit organizations they'd caused or with Timberland Boots Uk whom friends stood a relationship. They typically "liked" fan pages of sororities or fraternities, sports teams, college organizations and bands.

Researchers discovered successful usage of social websites goes beyond being "liked" considering that the demographics may be not like an organization's strategy. Additionally, merely being 'liked' may overestimate a persons true interest in the internet site.

"It's not about the number of people they like your page, because they may not be the correct people, they usually would possibly not really enjoy you, they may do it due to pressure from friends," McCorkindale said.

"Instead of organizations looking to superficially push these relationships and superficially push 'likes,' what is required be aware of the audience, build their bond and have interaction the audience.

"If you will definitely be in existence in the social networking sphere, you've got to be listening, you have to answer the questions people ask of you through social websites. If issues or questions go unanswered, that breaks the connection," she said. "If they won't manage the space, they can shouldn't be making use of the space."

Retrieved from "https://en.formulasearchengine.com/index.php?title=Glutamate_dehydrogenase&oldid=236239"