In 1964 Salat presented a notion of asymptotic density single dimensional subseries. Using this he series theorems similar to the following. If dn be decreasing sequence such that lim infn ndn > 0 and let subseries (x) = ?? k=1 ?k(x)dk dk convergent, then p(x) limn p(n,x)/n=0. Following Salat?s patten, we present double natural variation theorem.

For simplicity, we adopt the following convention: X is a complex unitary space, x, y, w, g, g1, g2 are points of X, z is a Complex, q, r, M are real numbers, s1, s2, s3, s4 are sequences of X, k, n, m are natural numbers, and N1 is an increasing sequence of naturals. Let us consider X, s1. We say that s1 is convergent if and only if: (Def. 1) There exists g such that for every r such that r > ...

The papers [23], [24], [4], [5], [2], [20], [21], [9], [1], [22], [13], [15], [16], [12], [10], [11], [17], [14], [25], [3], [7], [6], [19], and [8] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: X denotes a complex Banach algebra, w, z, z1, z2 denote elements of X, k, l, m, n denote natural numbers, s1, s2, s3, s, s ′ denote sequences of...

OBJECTIVE In Brazil, not many studies have investigated the validation of cognitive tests in the ageing population and none of them has analyzed the psychometric properties of Tuokko's Clock Test. The objective of the study was to translate and adapt the test to the Brazilian context, and to assess its construct validation. METHODS This is a cross-sectional population-based study, involving 3...

We analyze Euler-Galerkin approximations (conforming finite elements in space and implicit Euler in time) to coupled PDE systems in which one dependent variable, say u, is governed by an elliptic equation and the other, say p, by a parabolic-like equation. The underlying application is the poroelasticity system within the quasi-static assumption. Different polynomial orders are used for the uan...

Objective: To validate the Spanish version of the questionnaire Gambrill and Richey Assertiveness for people with schizophrenia. Method: he sample comprised a total of 125 people with schizophrenia on treatment in one of the psychosocial rehabilitation centers participating in the study. The instruments used to assess convergent and discriminant validity are the Communication Skills Questionnai...

Previous neurophysiological and neurobiological research has revealed different areas of multisensory integration in the CNS. Behavioral consequences of multimodal convergent stimuli arrays (visual/auditory/ somatosensory) have been observed on different kinds of higher mammals (cats, monkeys). Multisensory convergence neurons output directly affects motor behavior: Depending on convergent or d...

Convergent evolution occurs when the same trait arises independently in multiple lineages. In most cases of phenotypic convergence such transitions are adaptive, so finding the underlying molecular causes of convergence can provide insight into the process of adaptation. Convergent evolution at the genomic level also lends itself to study by comparative methods, although molecular convergence c...