We introduce a family of norms on the $n \times n$ complex matrices. These norms arise from a probabilistic framework, and their construction and validation involve probability theory, partition combinatorics, and trace polynomials in noncommuting variables. As a consequence, we obtain a generalization of Hunter’s positivity theorem for the complete homogeneous symmetric polynomials.

We extend our study of variability regions, Ali et al. [‘An application of Schur algorithm to variability regions of certain analytic functions–I’, Comput. Methods Funct. Theory, to appear] from convex domains to starlike domains. Let $\mathcal {CV}(\Omega )$ be the class of analytic functions f in ${\mathbb D}$ with $f(0)=f'(0)-1=0$ satisfying $1+zf''(z)/f'(z) \in {\Omega }$ . As an application of the main result, we determine the variability region of $\log f'(z_0)$ when f ranges over $\mathcal {CV}(\Omega )$ . By choosing a particular $\Omega $ , we obtain the precise variability regions of $\log f'(z_0)$ for some well-known subclasses of analytic and univalent functions.

Many agree that one cannot consciously form a belief just because one wants to. And many also agree this is a puzzling component of our conscious belief-forming processes. I will look at three views on how to make sense of this puzzle and show that they all fail in some way. I then offer a simpler explanation that avoids all the pitfalls of those views, which is based instead on an analysis of our conscious reasoning combined with a commonly accepted account of the concept of belief. I conclude that no epistemic norm or aim is actually needed to explain why we cannot deliberatively believe whatever we want.

For several years now, Michael Rea has been working to foster a fruitful discussion between theologians and analytic philosophers, and his article review nicely exemplifies those efforts. Rea recognises that he and I agree on several key points, the most important of which is that ‘cataphatic theology can be done without idolatry or violence’. He wonders, though, whether Theology without Metaphysics succeeds in providing a model for such theology, since he thinks it is liable to several objections. By addressing them, I hope to demonstrate that my model is indeed viable, though I would be surprised if this were sufficient to persuade Professor Rea to adopt it. As I see it, more than one model, including Professor Rea’s, may do justice to the relevant phenomena; here I want to argue, against Rea's criticisms, that mine does too.

Contrary to what is often assumed, norm-internalisation does not always lead to compliance. Normative judgements may be simultaneously internalised and outwardly rejected. Non-compliance is at times a result of hyper-awareness of the particular origin of norms, rather than an unwillingness of the would-be-recipients to do ‘good’ deeds, or their inability to understand what is ‘good’. Such is often the case for non-Western states, as I demonstrate in this article by utilising the sociological concepts of stigma and stigmatisation. In its inability to acknowledge this dynamic, which has its roots in the colonial past of the international order, the constructivist model of norm-diffusion commits two errors. On the one hand, it falls short as a causal explanation, conflating internalisation with socialisation, and socialisation with compliance. On the other hand, it reproduces existing hierarchies in the international system, treating only non-compliance as endogenously driven, but compliance as a result of external stimuli. As there is a great deal of correlation between non-compliance and political geography, such a depiction, coupled with the fact that most norms under scrutiny are ‘good’ norms, once again casts non-Western states as having agency only when they commit ‘bad’ deeds.

Transfer factors of 226Ra, 210Pb and 210Po from soil contaminated with naturally occurring radioactive materials (NORM) in oilfields to some grazing plants were determined using pot experiments. Contaminated soil was collected from a dry surface evaporation pit from a Syrian oilfield in the Der Ezzor area. Five types of plants (Atriplex halimus L., Atriplex canescens, Atriplex Leucoclada Bioss, Alfalfa and Bermuda grass) were grown and harvested three times over two years. The results show that the mean transfer factors of 226Ra from the contaminated soil to the studied plant species were 1.6 × 10-3 for Atriplex halimus L., 2.1 × 10-3 for Atriplex canescens, 2.5 × 10-3 for Atriplex Leucoclada Bioss, 8.2 × 10-3 for Bermuda grass, and the highest value was 1.7 × 10-2 for Alfalfa. Transfer factors of 210Pb and 210Po were higher than 226Ra TFs by one order of magnitude and reached 7 × 10-3, 1.1 × 10-2, 1.2 × 10-2, 3.2 × 10-2 and 2.5 × 10-2 for Atriplex halimus, Atriplex canescens, Atriplex Leucoclada Bioss, Bermuda grass and Alfalfa, respectively. The results can be considered as base values for transfer factors of 226Ra, 210Pb and 210Po in semiarid regions.

We give precise conditions under which the composition of a norm with a convex function yields a uniformly convex function on a Banach space. Various applications are given to functions of power type. The results are dualized to study uniform smoothness and several examples are provided.