In recent decades, by exploiting the algebraic properties of the Frobenius in positive characteristic, many so-called homological conjectures and intersection conjectures have been established, culminating into the powerful theory of tight closure and big Cohen–Macaulay algebras. In the present article, I give a survey of how these methods also can be applied directly in characteristic zero by ...

Internet search has become the most common way that people deal with issues and problems in everyday life. The wide use of Internet search has largely changed the way people search for and store information. There is a growing interest in the impact of Internet search on users' affect, cognition, and behavior. Thus, it is essential to develop a tool to measure the changes in psychological chara...

To date, fMRI research has been concerned primarily with evincing generic principles of brain function through averaging data from multiple subjects. Given rapid developments in both hardware and analysis tools, the field is now poised to study fMRI-derived measures in individual subjects, and to relate these to psychological traits or genetic variations. We discuss issues of validity, reliabil...

a tiling of a surface is a decomposition of the surface into pieces, i.e. tiles, which cover it without gaps or overlaps. in this paper some special polygonal tiling of sphere, ellipsoid, cylinder, and torus as the most abundant shapes of fullerenes are investigated.

In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...

With great interest we read the article by Kelly et al. on the measurement of physical activity (PA) and sedentary behavior (SB) (Kelly P et al. Int J Behav Nutr Phys Act 13:(1) 32, 2016). We appreciate the invitation of the authors to provide feedback on their ideas and we take this opportunity to contribute to the discussion. Our main proposition is that this field can learn much from the fie...

INTRODUCTION Despite the widespread use of deprivation indices in public health, they are rarely explicitly or extensively validated, owing to the complex nature of the exercise. METHODS Based on the proposals of British researchers, we sought to validate Quebec's material and social deprivation index using criteria of validity (content, criterion and construct validity), reliability and resp...

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