The AKS primality test (also known as Agrawal–Kayal–Saxena primality test and cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal‚ Neeraj Kayal‚ and Nitin Saxena‚ computer scientists at the Indian Institute of Technology Kanpur‚ on August 6‚ 2002‚ in a paper titled "PRIMES is in P".[1] The authors received many accolades‚ including the 2006 Gödel Prize and the 2006 Fulkerson Prize‚ for this work. The algorithm determines whether a number
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Pythagorean Theorem: Some False Proofs Even smart people make mistakes. Some mistakes are getting published and thus live for posterity to learn from. I ’ll list below some fallacious proofs of the Pythagorean theorem that I came across. Some times the errors are subtle and involve circular reasoning or fact misinterpretation. On occasion‚ a glaring error is committed in logic and leaves one wondering how it could have avoided being noticed by the authors and editors. Proof 1 One such error appears
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The mission of the United States government is to provide liberty and justice‚ which in turn leads to tranquility‚ prosperity‚ and happiness. The founders of the United States wrote up the Constitution to try to fulfill this task and build a better nation. Ever since the creation of the government‚ laws‚ amendments‚ and bills have been passed and rejected. All created by the federal‚ state‚ and local governments to aid in the creation of a better tomorrow for the country. As the law is laid down
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Timothy Kennedy American Political Parties Professor Lindberg “Voter Apathy” Voter Apathy is referenced as a term to describe the phenomena of steady decline in political participation over the past 30 years. Apathy can be defined as the lack of interest‚ enthusiasm‚ emotion or concern towards a specific topic. Statistically‚ “voter apathy” may be displayed at the polls‚ but public activism is still a major part of society. For example‚ the “Occupy” movement is in every city with large amounts of
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punishing crimes. This provision prohibits the government from punishing any person for any felony with any penalty which has not been prescribed by the law. Article 21 - Is not a penal provision. It neither defines a crime nor provides a punishment for one. It has simply announced the policy of the government with reference to punishment of alleged criminal acts. It is a guaranty to the citizen of this country that no act of his‚ will be considered criminal until the government has made it so by law
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Chebyshev’s Theorem and The Empirical Rule Suppose we ask 1000 people what their age is. If this is a representative sample then there will be very few people of 1-2 years old just as there will not be many 95 year olds. Most will have an age somewhere in their 30’s or 40’s. A list of the number of people of a certain age may look like this: |Age |Number of people | |0 |1 | |1 |2 | |2 |3
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Gauss Markov Theorem In the mode [pic]is such that the following two conditions on the random vector [pic]are met: 1. [pic] 2. [pic] the best (minimum variance) linear (linear functions of the [pic]) unbiased estimator of [pic]is given by least squares estimator; that is‚ [pic]is the best linear unbiased estimator (BLUE) of [pic]. Proof: Let [pic]be any [pic]constant matrix and let [pic]; [pic] is a general linear function of [pic]‚ which we shall take as an estimator of [pic]. We must specify
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PUBLIC SERVICE BROADCASTING1 Mark Armstrong University College London March 2005: final version July 2005 Abstract This essay discusses the merits of public intervention in the provision of television broadcasting services. I argue that intervention was justified in the past‚ when there were just a few channels and when advertising was the sole source of commercial funds
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individuals with new means of expressions. On the other hand‚ the free flow of information has raised the call for content regulation‚ not least to restrict minors’ access to potentially harmful information. This schism has led to legal attempts to regulate content and to new selfregulatory schemes implemented by private parties. The attempts to regulate content raise the question of how to define Internet in terms of “public sphere” and accordingly protect online rights of expression. The dissertation
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PRUDENTIAL REGULATIONS FOR CORPORATE / COMMERCIAL BANKING (Updated on January 31‚ 2011) BANKING POLICY & REGULATIONS DEPARTMENT STATE BANK OF PAKISTAN Disclaimer: State Bank of Pakistan compiles a booklet of Prudential Regulations from time to time for convenience of users. Updated version of such a booklet containing amendments in the regulations made through circulars/Circular letters to date is being issued. Due care has been taken while incorporating amendments‚ however‚ errors and
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