Debt deflation - Revision history

en>Pass3456: /* Ben Bernanke (1983) */

2015-01-09T22:11:09Z

Ben Bernanke (1983)

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en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9949)

2014-02-25T08:42:25Z

WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9949)

Show changes

en>GliderMaven: ref from Steve Keen

2013-11-04T21:22:29Z

ref from Steve Keen

← Older revision		Revision as of 23:22, 4 November 2013
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	~~It depends on the quality of the Wordpress theme but even if it~~'~~s not a professional one you will be able to average 50-60$ EACH link~~. ~~It is used by around 25% of all new websites~~, ~~and there are more than 27 thousand plugins currently available~~. ~~One really cool features about this amazing and free wp plugin is that the code it generates is completely portable~~. ~~Hosted by Your Domain on Another Web Host - In this model~~, ~~you first purchase multiple~~-~~domain webhosting, and then you can build free Wordpress websites on your own domains, taking advantage~~ of the ~~full power of Wordpress~~. ~~provided by Word~~ - ~~Press Automatic Upgrade~~, ~~so whenever you need~~ to ~~update~~ the ~~new version does not~~, ~~it automatically creates no webmaster~~. <br><br>~~You just download ready made templates to~~ a ~~separate directory and then choose~~ a ~~favorite one in the admin panel. When you write~~ a ~~new post~~, ~~you~~'~~ll see a small bar that goes across the text input area. A Wordpress plugin~~ is ~~a software that you can install into your Wordpress site~~. ~~They provide many such popular products which you can buy for your baby~~. ~~Now~~ a ~~days it has since evolved into a fully capable CMS platform which make it~~, the ~~best platform~~ in the ~~world for performing online business~~. <br>~~<br>Here are~~ a ~~few reasons~~ as ~~to why people prefer Word - Press over other software~~'s. ~~When a business benefits from its own domain name~~ and ~~a tailor-made blog~~, ~~the odds~~ of ~~ranking higher in~~ the ~~search engines and being visible to a greater number of people is more likely~~. ~~Whether or not~~ it's ~~an viewers on your web page~~, ~~your social media~~ pages, ~~or your web page~~, ~~those who have a present~~ and ~~effective viewers~~ of "~~fans" are best best for provide provides, reductions,~~ and ~~deals~~ to ~~help re-invigorate their viewers and add~~ to ~~their main point here~~. ~~You can allow visitors~~ to ~~post comments~~, ~~or you can even allow your visitors to register~~ and ~~create their own personal blogs~~. ~~Have you heard about niche marketing~~ and ~~advertising~~. <~~br><br~~>~~For more about~~ [http://~~relatebook~~.~~com~~/~~index.php?do=~~/~~profile-15575~~/~~info~~/ ~~wordpress dropbox backup] review our web~~-~~page~~. ~~It has become a more prevalent cause~~ of ~~infertility~~ and the ~~fertility clinic are having more~~ and ~~more couples with infertility problems~~. ~~But~~ the ~~Joomla was created~~ as the ~~CMS over years of hard work~~. ~~Websites that do rank highly~~, ~~do so becaue they use keyword-heavy post titles. So~~, ~~we have~~ to ~~add our social media sharing buttons~~ in ~~website~~. The ~~popularity~~ of ~~Word - Press has increased~~ the ~~demand~~ for ~~Word - Press themes~~ and ~~these themes sells like hot cake on~~ the ~~internet.~~ <br><br>~~Under Settings —~~> ~~Reading~~, ~~determine if posts or~~ a ~~static page will be your home page~~, ~~and if your home page~~ is ~~a static page~~, ~~what page will contain blog posts~~. ~~It can run as plugin and you can still get to that whole database just~~ in ~~circumstance your webhost does not have~~ a c - ~~Panel area. It can be concluded that white label SEO comprise~~ of ~~a third party who resells a contract involving IT expert or consultant~~, ~~SEO professional and end user~~. ~~Word~~ - ~~Press is~~ the ~~most popular personal publishing platform which was launched in 2003~~. ~~Verify whether your company has a team of developers or programmers having hands~~-~~on experience and knowledge about all Word - Press concepts.~~		The '''Lehmer random number generator'''<ref>{{cite journal \| author=W.H. Payne, J.R. Rabung, T.P. Bogyo \|title=Coding the Lehmer pseudo-random number generator \|journal=[[Communications of the ACM]] \|year=1969 \|volume=12 \|issue=2 \|pages=85–86 \|url=http://www.firstpr.com.au/dsp/rand31/p85-payne.pdf \|doi=10.1145/362848.362860}}</ref> (named after [[D. H. Lehmer]]), sometimes also referred to as the '''Park–Miller random number generator''' (after Stephen K. Park and Keith W. Miller), is a variant of [[linear congruential generator]] (LCG) that operates in [[multiplicative group of integers modulo n]]. A general formula of a random number generator (RNG) of this type is:

			: <math>X_{k+1} = g \cdot X_k~~\bmod~~n</math>

			where the modulus ''n'' is a [[prime number]] or a power of a prime number, the multiplier ''g'' is an element of high [[multiplicative order]] modulo ''n'' (e.g., a [[primitive root modulo n]]), and the seed ''X''{{sub\|0}} is [[coprime\|co-prime]] to ''n''.

			== Parameters in common use ==

			In 1988, Park and Miller<ref>{{cite journal \| author=Stephen K. Park and Keith W. Miller \|title=Random Number Generators: Good Ones Are Hard To Find \|journal=[[Communications of the ACM]] \|year=1988 \|volume=31 \|issue=10 \|pages=1192–1201 \|url=http://www.firstpr.com.au/dsp/rand31/p1192-park.pdf \|doi=10.1145/63039.63042}}</ref> suggested a Lehmer RNG with particular parameters ''n'' = 2{{sup\|31}} − 1 = 2,147,483,647 (a [[Mersenne prime]] ''M''{{sub\|31}}) and ''g'' = 7{{sup\|5}} = 16,807 (a primitive root modulo ''M''{{sub\|31}}), now known as '''MINSTD'''. Although MINSTD was later criticized by Marsaglia and Sullivan,<ref>{{cite journal \|title=Technical correspondence \|journal=[[Communications of the ACM]] \|year=1993 \|volume=36 \|issue=7 \|pages=105–110 \|doi=10.1145/159544.376068 \|author=Crawford, Diane}}</ref> it is still in use today (in particular, in [[CarbonLib]] and [[C++11]]'s <code>minstd_rand0</code>). The authors responded to criticism in 1993,<ref>{{cite journal \| author= Stephen K. Park and Keith W. Miller and Paul K. Stockmeyer \|title=Technical Correspondence \|journal=[[Communications of the ACM]] \|year=1988 \|volume=36 \|issue=7 \|pages=105–110 \|doi=10.1145/159544.376068}}</ref> saying:
			<blockquote>
			Given the dynamic nature of the area, it is difficult for nonspecialists to make decisions about what generator to use. "Give me something I can understand, implement and port... it needn't be state-of-the-art, just make sure it's reasonably good and efficient." Our article and the associated minimal standard generator was an attempt to respond to this request. Five years later, we see no need to alter our response other than to suggest the use of the multiplier a = 48271 in place of 16807.
			</blockquote>
			This revised constant is used in [[C++11]]'s <code>minstd_rand</code> random number generator.

			[[ZX Spectrum]] uses the Lehmer RNG with parameters ''n'' = 2{{sup\|16}} + 1 = 65,537 (a [[Fermat prime]] ''F''{{sub\|4}}) and ''g'' = 75 (a primitive root modulo ''F''{{sub\|4}}). The [[CRAY]] random number generator '''RANF''' is a Lehmer RNG with ''n'' = 2{{sup\|48}} and ''g'' = 44,485,709,377,909.<ref name="gnu">[http://www.gnu.org/software/gsl/manual/html_node/Other-random-number-generators.html GNU Scientific Library: Other random number generators]</ref> Another popular pair of parameters is ''n'' = 2{{sup\|32}} − 5 = 4,294,967,291 and ''g'' = 279,470,273.{{Citation needed\|date=April 2010}}

			The [[GNU Scientific Library]] includes several random number generators of the Lehmer form, including MINSTD, RANF, and the infamous [[IBM]] random number generator [[RANDU]].<ref name="gnu" />

			== Relation to LCG ==

			While the Lehmer RNG can be viewed as a particular case of the [[linear congruential generator]] with {{gaps\|''c''\|{{=}}\|0}}, it is a special case that implies certain restrictions and properties. In particular, for the Lehmer RNG, the initial seed ''X''{{sub\|0}} must be [[coprime]] to the modulus ''n'' that is not required for LCGs in general. The choice of the modulus ''n'' and the multiplier ''g'' is also more restrictive for the Lehmer RNG. In contrast to LCG, the maximum period of the Lehmer RNG equals ''n''−1 and it is such when ''n'' is prime and ''g'' is a primitive root modulo ''n''.

			On the other hand, the [[discrete logarithm]]s (to base ''g'' or any primitive root modulo ''n'') of ''X{{sub\|k}}'' in <math>\mathbb{Z}_n</math> represent linear congruential sequence modulo [[Euler totient]] <math>\varphi(n)</math>.

			== Sample C99 code ==

			Using [[ISO C\|C]] code, the Lehmer generator using the "popular pair" of parameters mentioned above can be written as follows:

			<source lang="c">
			uint32_t lcg_rand(uint32_t a)
			{
			return ((uint64_t)a * 279470273UL) % 4294967291UL;
			}
			</source>
			As the product of two 32 bit integers may overflow, the cast to uint64_t is necessary.

			== References ==

			{{reflist\|2}}

			* {{cite journal \|author=Lehmer, D. H. \|title=Mathematical methods in large-scale computing units \|journal=Proceedings of a Second Symposium on Large-Scale Digital Calculating Machinery \|year=1949 \|pages=141–146 \|mr=0044899}} (journal version: ''Annals of the Computation Laboratory of Harvard University'', Vol. 26 (1951)).
			* {{cite journal \|author=Martin Greenberger \|title=Notes on a New Pseudo-Random Number Generator \|journal=Journal of the ACM \|volume=8 \|issue=2 \|year=1961 \|pages=163–167 \|doi=10.1145/321062.321065}}
			* Steve Park, [http://www.cs.wm.edu/~va/software/park/ Random Number Generators]
			* [http://www.firstpr.com.au/dsp/rand31/ Park–Miller–Carta Pseudo-Random Number Generator]

			[[Category:Pseudorandom number generators]]
			[[Category:Modular arithmetic]]

177.69.198.1: /* Forward Year Tax Receipts */

2012-08-02T16:32:46Z

Forward Year Tax Receipts

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