But this truth is distorted by its extreme application: the assumption of the separate existence of tradition.

Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.

Upon receipt of an application which the Export-Import Bank is prepared to consider, the Export-Import Bank will inform the Department of Economic Affairs of the identity of the applicant, the nature of the proposed business, the amount of the proposed loan, and the general purposes for which the loan proceeds would be expended.

When the Export-Import Bank is prepared to act favorably upon an application, it will so notify the Department of Economic Affairs and will indicate the interest rate and the repayment period which would be used under the proposed loan.

Within sixty days after the receipt of notice that the Export-Import Bank is prepared to act favorably upon an application the Department of Economic Affairs will indicate to the Export-Import Bank whether or not the Department of Economic Affairs has any objection to the proposed loan.

In this article we will concentrate on the advances in the application of electronics in bio-medical research laboratories because this is where tomorrow's commonplace equipment originates.

The best known field of application for builders is in heavy-duty, spray-dried detergent formulations for household use.

Hard-surface cleaning in household application is represented by two classes of alkaline products: ( 1 ) the formulations made expressly for machine dishwashers, and ( 2 ) the general-purpose cleaners used for walls and woodwork.

In a typical application -- the making of rigid urethane foam sandwich panels -- an amount of foam mixture calculated to expand 10 to 20% more than the volume of the panel is poured into the panel void and the top of the panel is locked in place by a jig.

Senator McClellan is proposing the application of anti-trust measures to unions in transportation.

In 2009, the American Anthropological Association's Commission on the Engagement of Anthropology with the US Security and Intelligence Communities released its final report concluding, in part, that, " When ethnographic investigation is determined by military missions, not subject to external review, where data collection occurs in the context of war, integrated into the goals of counterinsurgency, and in a potentially coercive environment – all characteristic factors of the HTS concept and its application – it can no longer be considered a legitimate professional exercise of anthropology.

In the typical application of ANOVA, the null hypothesis is that all

application of the method is best determined by problem pattern recognition

* One-way ANOVA is used to test for differences among two or more independent groups ( means ), e. g. different levels of urea application in a crop.

This is usually done on the basis that the lower court judge erred in the application of law, but it may also be possible to appeal on the basis of court misconduct, or that a finding of fact was entirely unreasonable to make on the evidence.

A common application of the compounds of sodium is the sodium-vapour lamp, which emits very efficient light.

* To obtain a declaration on a legal document, such as an application for voter registration, that the information provided by the applicant is truthful to the best of the applicant's knowledge.

An emerging application is the use of antimony in microelectronics.

The most stable of these is < sup > 124 </ sup > Sb with a half-life of 60. 20 days, which has an application in some neutron sources.

The second longest-lived isotope of astatine, astatine-211, is the only one currently having any commercial application, being employed in medicine to diagnose and treat some diseases via its emission of alpha particles ( helium-4 nuclei ).

In computing, an applet is any small application that performs one specific task that runs within the scope of a larger program, often as a plug-in.

Provided that an applet is hosted by an operating system, it can function as any other normal software application but is and performs only a small set of tasks.

The Department of Justice has published " ADA 2010 Revised Requirements: Accessible Pools-Means of Entry and Exit ", which is designed to assist pool owners and operators with understanding the new accessibility requirements, the application of the requirements and the longstanding obligations of pool owners and operators in connection with the new requirements.

The term Bayesian refers to Thomas Bayes ( 1702 – 1761 ), who proved a special case of what is now called Bayes ' theorem in a paper titled " An Essay towards solving a Problem in the Doctrine of Chances ".

For example, naive Bayes and linear discriminant analysis are joint probability models, whereas logistic regression is a conditional probability model.

Thomas Bayes attempted to provide a logic that could handle varying degrees of confidence ; as such, Bayesian probability is an attempt to recast the representation of probabilistic statements as an expression of the degree of confidence by which the beliefs they express are held.

Using the probability calculus of Bayes Theorem, Salmon concludes that it is very improbable that the universe was created by the type of intelligent being theists argue for.

* November 24 – Bayes ' theorem is first announced.

* Sir Isaac Newton's Method of Fluxions ( 1671 ), describing his method of differential calculus, is first published ( posthumously ) and Thomas Bayes publishes a defense of its logical foundations ( anonymously ).

The weight of evidence is the logarithm of the Bayes factor, which in this case is simply the factor by which the odds of the hypothesis changes when the observation is made.

In probability theory and statistics, Bayes ' theorem ( alternatively Bayes ' law or Bayes ' rule ) is a theorem with two distinct interpretations.

In the Bayesian interpretation, Bayes ' theorem is fundamental to Bayesian statistics, and has applications in fields including science, engineering, economics ( particularly microeconomics ), game theory, medicine and law.

The application of Bayes ' theorem to update beliefs is called Bayesian inference.

Bayes ' theorem is named for Thomas Bayes (; 1701 – 1761 ), who first suggested using the theorem to update beliefs.

Bayes ' theorem can be used to calculate the probability that the person is a woman.

Bayes ' theorem under this interpretation is most easily visualized using tree diagrams, as shown to the right.

is: Formúla Bayes

In statistics, Bayesian inference is a method of inference in which Bayes ' rule is used to update the probability estimate for a hypothesis as additional evidence is learned.

The critical point about Bayesian inference, then, is that it provides a principled way of combining new evidence with prior beliefs, through the application of Bayes ' rule.

The theorem which we prove is more general than what we have described, since it works with the primary decomposition of the minimal polynomial, whether or not the primes which enter are all of first degree.

In the primary decomposition theorem, it is not necessary that the vector space V be finite dimensional, nor is it necessary for parts ( A ) and ( B ) that P be the minimal polynomial for T.

This theorem is similar to the theorem of Kakutani that there exists a circumscribing cube around any closed, bounded convex set in Af.

According to Cauchy's functional equation theorem, the logarithm is the only continuous transformation that transforms real multiplication to addition.

One motivation for this use is that a number of generally accepted mathematical results, such as Tychonoff's theorem, require the axiom of choice for their proofs.

However, that particular case is a theorem of Zermelo – Fraenkel set theory without the axiom of choice ( ZF ); it is easily proved by mathematical induction.

The debate is interesting enough, however, that it is considered of note when a theorem in ZFC ( ZF plus AC ) is logically equivalent ( with just the ZF axioms ) to the axiom of choice, and mathematicians look for results that require the axiom of choice to be false, though this type of deduction is less common than the type which requires the axiom of choice to be true.

In Martin-Löf type theory and higher-order Heyting arithmetic, the appropriate statement of the axiom of choice is ( depending on approach ) included as an axiom or provable as a theorem.

Assuming ZF is consistent, Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model ( the constructible universe ) which satisfies ZFC and thus showing that ZFC is consistent.

Assuming ZF is consistent, Paul Cohen employed the technique of forcing, developed for this purpose, to show that the axiom of choice itself is not a theorem of ZF by constructing a much more complex model which satisfies ZF ¬ C ( ZF with the negation of AC added as axiom ) and thus showing that ZF ¬ C is consistent.

It is possible, however, that there is a shorter proof of a theorem from ZFC than from ZF.

** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.

** König's theorem: Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals.

** Tychonoff's theorem stating that every product of compact topological spaces is compact.