Strong Grobner bases for polynomials over a principal ideal ring

Grobner bases have been generalised to polynomials over a commutative ring A in several ways. Here we focus on strong Grobner bases, also known as D-bases. Several authors have shown that strong Grobner bases can be effectively constructed over a principal ideal domain. We show that this extends to any principal ideal ring. We characterise Grobner bases and strong Grobner bases when A is a principal ideal ring. We also give algorithms for computing Grobner bases and strong Grobner bases which generalise known algorithms to principal ideal rings. In particular, we give an algorithm for computing a strong Grobner basis over a finite-chain ring, for example a Galois ring.

Individual and societal bases of national identity - A comparative multi-level analysis

In a previous study (Jones and Smith, 1999) we established that much the same core pattern of national identity characterizes many developed countries. Using the national identity module from the 1995 International Social Survey Programme, we identified two dimensions of national identity: an ascriptive dimension resembling the concept of ethnic identity described in the historical and theoretical literature, and a voluntarist dimension closer to the notion of civic identity. Some writers view these dimensions in terms of a historical sequence but we find that both constructs coexist in the minds of individual respondents in the nations we examine (we exclude Bulgaria and the Philippines from the present but not the earlier analysis). The dataset used for the multilevel analyses reported here consists of 28 589 respondents in the remaining 21 countries included in the national identity database for the 1995 round of surveys. The macrosociological literature on national identity does not offer well-defined predictions about what precise patterns of national identification we might expect to find among the masses of the developed countries. There are, however, recurring themes from which one can construct plausible hypotheses about how countries might differ according to their level of development, broadly conceived. Thus, we hypothesize that forces such as post-industrialism and globalization tend to favour the more open voluntaristic form of national identity over the more restrictive ascribed form. We develop different multi-level models in order to evaluate specific hypotheses pertaining to such issues, by simultaneously relating individual and societal characteristics to the relative strength of individual commitment to these different types of national identity.

Ring flexibility within tricyclic antidepressant drugs

The internal flexibility of the central seven-membered ring of a series of tricyclic antidepressant drugs (TCAs), imipramine {l}, amitriptyline {2}, doxepin {3}, and dothiepin {4}, has been investigated by H-1 and C-13 nuclear magnetic (NMR) techniques. Two dynamic processes were examined: ring inversion and bridge flexing. H-1 NMR lineshape analysis was used to obtain ring inversion barriers for 2-4. These studies yielded energy barriers of 14.3, 16.7, and 15.7 +/- 0.6 kcal/mol for the hydrochloride salts of doxepin, dothiepin, and amitriptyline, respectively. The barriers for the corresponding free bases were lower by 0.6 kcal/mol on average. (CT1)-C-13 relaxation measurements were used to determine the degree of bridge flexing associated with the central seven-membered ring for all four compounds. By fitting the T-1 data to a two-state jump model, lifetimes and amplitudes of rapid bridge flexing motions were determined. The results show that imipramine has the fastest rate of bridge flexing, followed by amitriptyline, doxepin, and dothiepin. The pharmacological profiles of the TCAs are complex and they interact with many receptor sites, resulting in numerous side effects and a general lack of understanding of their precise mode of action in different anxiety-related disorders. They all have similar three-dimensional structures, which makes it difficult to rationalize their differing relative potency in different assays/clinical settings. However, the clear finding here that there are significantly different degrees of internal mobility suggests that molecular dynamics should be an additional factor considered when trying to understand the mode of action of this clinically important family of molecules. (C) 2001 Wiley-Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 90:713-721, 2001.

China and Southeast Asia

In the new millennium, no issue in international relations will be more important than how to accommodate the rising power of China. Many analysts, especially in the United States, see China as a significant threat to American interests in Asia. Washington has treaty commitments in both Northeast and Southeast Asia and retains a substantial military presence in the region. Beijing claims it does not seek to replace the United States reigning global hegemony, but seeks to promote a multi-polar world in which six states (the US, China, the EU, Russia, Japan, and India) would have pre-eminent status.