Displaying similar documents to “Strictly associated models, prime basis factorials: an application”

Pocklington's Theorem and Bertrand's Postulate

Marco Riccardi (2006)

Formalized Mathematics

Similarity:

The first four sections of this article include some auxiliary theorems related to number and finite sequence of numbers, in particular a primality test, the Pocklington's theorem (see [19]). The last section presents the formalization of Bertrand's postulate closely following the book [1], pp. 7-9.

On the Properties of the Möbius Function

Magdalena Jastrzebska, Adam Grabowski (2006)

Formalized Mathematics

Similarity:

We formalized some basic properties of the Möbius function which is defined classically as [...] as e.g., its multiplicativity. To enable smooth reasoning about the sum of this number-theoretic function, we introduced an underlying many-sorted set indexed by the set of natural numbers. Its elements are just values of the Möbius function.The second part of the paper is devoted to the notion of the radical of number, i.e. the product of its all prime factors.The formalization (which is...

Inference for random effects in prime basis factorials using commutative Jordan algebras

Vera M. Jesus, Paulo Canas Rodrigues, João Tiago Mexia (2007)

Discussiones Mathematicae Probability and Statistics

Similarity:

Commutative Jordan algebras are used to drive an highly tractable framework for balanced factorial designs with a prime number p of levels for their factors. Both fixed effects and random effects models are treated. Sufficient complete statistics are obtained and used to derive UMVUE for the relevant parameters. Confidence regions are obtained and it is shown how to use duality for hypothesis testing.