Goodstein's argument is, essentially, that the hereditary representation, , of any given natural number in the natural number base , can be mirrored in Cantor Arithmetic, and used to well-define a finite, decreasing, sequence of transfinite ordinals, each of which is not smaller than the ordinal...

Some alternative Bayes Factors: Intrinsic, Posterior and Fractional have been proposed to overcome the difficulties presented when prior information is weak and improper prior are used. Additional difficulties also appear when the models are separated or nonnested. This paper presents some...

In this paper, by the use of Potential Theory, some representation results for multivariate functions from the Sobolev spaces (Ω), in terms of the double layer potential and the fundamental solution of Laplace's equation are pointed out. Applications for multivariate inequalities of Ostrowski...

Let ∈ ℂ be a nontrivial involution; i.e., = ≠ ±. We say that ∈ ℂ is -symmetric (-skew symmetric) if = ( = − ). Let be one of the following subsets of ℂ: (i) -symmetric matrices; (ii) Hermitian -symmetric matrices; (iii) -skew symmetric matrices; (iv) Hermitian -skew symmetric...

We prove that multifractal functions, characterized by their wavelet representation can be estimated in the white noise model by a Bayesian estimation method. We give rates of convergence for two different models. Further, we study empirical methods for estimating the hyperparameters of the...