Certain Unramified Metabelian Extensions Using Lemmermeyer Factorizations

We study solutions to the Brauer embedding problem with restricted ramification. Suppose $G$ and $A$ are a abelian groups, $E$ is a central extension of $G$ by $A$, and $f:\text{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})\rightarrow G$ a continuous homomorphism. We determine conditions on the discriminant of $f$ that are equivalent to the existence of an unramified lift $\widetilde{f}:\text{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})\rightarrow E$ of $f$. As a consequence of this result, we use conditions on the discriminant of $K$ for $K/\mathbf{Q}$ abelian to classify and count unramified nonabelian extensions $L/K$ normal over $\mathbf{Q}$ where the (nontrivial) commutator subgroup of $\text{Gal}(L/\mathbf{Q})$ is contained in its center. This generalizes a result due to Lemmermeyer, which states that a quadratic field $\mathbf{Q}(\sqrt{d})$ has an unramified extension normal over $\mathbf{Q}$ with Galois group $H_8$ the quaternion group if and only if the discriminant factors $d=d_1 d_2 d_3$ as a product of three coprime discriminants, at most one of which is negative, satisfying the following condition on Legendre symbols: $$\left(\frac{d_i d_j}{p_k}\right)=1$$ for $\{i,j,k\}=\{1,2,3\}$ and $p_i$ any prime dividing $d_i$

No limits : exploring the psychology of unsolicited credit card limit increase offers

The issue of credit card debt has become an increasing concern in recent years. In Australia, for example, there is currently $42.5 billion worth of outstanding debt on credit cards, with$30 billion (over 70 per cent) bearing interest. Further, in 2001, Visa reported that 32 per cent of consumers had not paid their card off in the previous 12 months, which suggests that interest-bearing debt in Australia is held by approximately only 113 of credit card borrowers. An important element of credit card marketing is the use of psychological manipulations to encourage consumers to take-up credit. In this article, we examine the use of language and imagery in unsolicited credit card limit increase offers, and how these might influence consumers\u27 decisions to increase their credit card limit. The analysis found that the use of terms that focused on the benefits of credit card use, such as &quot;choice&quot;, &quot;freedom&quot;, and &quot;peace of mind&quot; were used consistently to convince consumers to increase their credit card limit, whereas the use the of terms that could be considered more pragmatic and with direct reference to the nature of the product, such as &quot;debt&quot;, &quot;repayment&quot; and &quot;loan&quot;, were rarely used. Similarly, the use of colour, text changes, and images, were used which may have an influence over a consumer\u27s ability to rationally consider whether the increase is appropriate for them. The paper concludes by recommending that government and representative bodies need to take into account the psychological manipulations used by credit card providers when developing consumer policy and codes of ethics.<br /

Additional file 1: of A functional genomic model for predicting prognosis in idiopathic pulmonary fibrosis

Additional Methods and Tables. (DOCX 103 kb

Additional file 4: Figure S3. of A functional genomic model for predicting prognosis in idiopathic pulmonary fibrosis

Concordance of IPF prognostic predictor genes between training and each validation cohort. The fold change of each gene between predicted low-risk and high-risk prognosis patients was plotted between training (X-axis) and validation cohort (Y-axis). (PPTX 51 kb