This paper deals with nonlinear least-squares problems involving the tting to data of parameterized analytic functions. For generic regression data, a general result establishes the countability, and under stronger assumptions niteness, of the set of functions giving rise to critical points of the quadratic loss function. In the special case of what are usually called \single-hidden layer neura...

Let H be a countable subgroup of the metrizable compact abelian group G and f : H → T = R/Z a (not necessarily continuous) character of H . Then there exists a sequence (χn) ∞ n=1 of (continuous) characters of G such that limn→∞ χn(α) = f(α) for all α ∈ H and (χn(α)) ∞ n=1 does not converge whenever α ∈ G \ H . If one drops the countability and metrizability requirement one can obtain similar r...

Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable...

This paper proposes a method for detecting determiner errors, which are highly frequent in learner English. To augment conventional methods, the proposed method exploits a strong tendency displayed by learners in determiner usage, i.e., mistakenly omitting determiners most of the time. Its basic idea is simple and applicable to almost any conventional method. This paper also proposes combining ...

The purpose of this paper is to contribute the theory profinite semigroups by considering special class consisting those all whose finitely generated closed subsemigroups are countable, which said be locally countable. We also call countable a pseudovariety V (of finite semigroups) for pro-V investigate operations preserving local countability pseudovarieties and show that, in contrast with fin...