Minimal lenght elements of Thompson's groups F(p)

We describe a method for determining the minimal length of elements in the generalized Thompson's groups F(p). We compute the length of an element by constructing a tree pair diagram for the element, classifying the nodes of the tree and summing associated weights from the pairs of node classifications. We use this method to effectively find minimal length representatives of an element.

The Discrimination of Colored Acrylic, Cotton, and Wool Textile Fibers Using Micro-Raman Spectroscopy. Part 1 : In Situ Detection and Characterization of Dyes

Raman spectroscopy has been applied to characterize fiber dyes and determine the discriminating ability of the method. Black, blue, and red acrylic, cotton, and wool samples were analyzed. Four excitation sources were used to obtain complementary responses in the case of fluorescent samples. Fibers that did not provide informative spectra using a given laser were usually detected using another wavelength. For any colored acrylic, the 633-nm laser did not provide Raman information. The 514-nm laser provided the highest discrimination for blue and black cotton, but half of the blue cottons produced noninformative spectra. The 830-nm laser exhibited the highest discrimination for red cotton. Both visible lasers provided the highest discrimination for black and blue wool, and NIR lasers produced remarkable separation for red and black wool. This study shows that the discriminating ability of Raman spectroscopy depends on the fiber type, color, and the laser wavelength.

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

I have faith in my thing, you know what I mean? Mixed method elements on individual investments on religious markets.

In contemporary society, religious signification and secular systems mix and influence each other. Holistic conceptions of a world in which man is integrated harmoniously with nature meet representations of a world run by an immanent God. On the market of the various systems, the individual goes from one system to another, following his immediate needs and expectations without necessarily leaving any marks in a meaningful long term system. This article presents the first results of an ongoing research in Switzerland on contemporary religion focusing on (new) paths of socialization of modern that individuals and the various (non-) belief systems that they simultaneously develop

The Importance of Graduates for the Scottish Economy: A “Micro-to-Macro” Approach

There have been numerous attempts to assess the overall impact of Higher Education Institutions on regional economies in the UK and elsewhere. There are two disparate approaches focussing on: demand-side effects of HEIs, exerted through universities’ expenditures within the local economy; HEIs’ contribution to the “knowledge economy”. However, neither approach seeks to measure the impact on regional economies that HEIs exert through the enhanced productivity of their graduates. We address this lacuna and explore the system-wide impact of the graduates on the regional economy. An extensive and sophisticated literature suggests that graduates enjoy a significant wage premium, often interpreted as reflecting their greater productivity relative to non-graduates. If this is so there is a clear and direct supply-side impact of HEI activities on regional economies through the employment of their graduates. However, there is some dispute over the extent to which the graduate wage premium reflects innate abilities rather than the impact of higher education per se. We use an HEI-disaggregated computable general equilibrium model of Scotland to estimate the impact of the growing proportion of graduates in the Scottish labour force that is implied by the current participation rate and demographic change, taking the graduate wage premium in Scotland as an indicator of productivity enhancement. We conduct a range of sensitivity analyses to assess the robustness of our results. While the detailed results do, of course, vary with alternative assumptions about future graduate retention rates and the size of the graduate wage premium, for example, they do suggest that the long-term supply-side impacts of HEIs provide a significant boost to regional GDP. Furthermore, the results suggest that the supply-side impacts of HEIs are likely to be more important than the expenditure impacts that are the focus of most “impact” studies.